================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:22 SCORE: 11.00 ================================================================================ 4 A Complete Guide to the Futures mArket The essence of a futures market is in its name: Trading involves a commodity or financial instrument for a future delivery date, as opposed to the present time. Thus, if a cotton farmer wished to make a current sale, he would sell his crop in the local cash market. However, if the same farmer wanted to lock in a price for an anticipated future sale (e.g., the marketing of a still unharvested crop), he would have two options: He could locate an interested buyer and negotiate a contract specifying the price and other details (quantity, quality, delivery time, location, etc.). alternatively, he could sell futures. some of the major advantages of the latter approach are the following: 1. The futures contract is standardized; hence, the farmer does not have to find a specific buyer. 2. The transaction can be executed virtually instantaneously online. 3. The cost of the trade (commissions) is minimal compared with the cost of an individualized forward contract. 4. The farmer can offset his sale at any time between the original transaction date and the final trading day of the contract. The reasons this may be desirable are discussed later in this chapter. 5. The futures contract is guaranteed by the exchange. Until the early 1970s, futures markets were restricted to commodities (e.g., wheat, sugar, copper, cattle). since that time, the futures area has expanded to incorporate additional market sec- tors, most significantly stock indexes, interest rates, and currencies (foreign exchange). The same basic principles apply to these financial futures markets. Trading quotes represent prices for a future expiration date rather than current market prices. For example, the quote for December 10-year T -note futures implies a specific price for a $100,000, 10-year U. s. Treasury note to be delivered in December. Financial markets have experienced spectacular growth since their introduction, and today trading volume in these contracts dwarfs that in commodities. nevertheless, futures markets are still commonly, albeit erroneously, referred to as commodity markets, and these terms are synonymous. ■ Delivery shorts who maintain their positions in deliverable futures contracts after the last trading day are obligated to deliver the given commodity or financial instrument against the contract. similarly, longs who maintain their positions after the last trading day must accept delivery. in the com- modity markets, the number of open long contracts is always equal to the number of open short contracts (see section V olume and Open interest). Most traders have no intention of making or accepting delivery, and hence will offset their positions before the last trading day. (The long offsets his position by entering a sell order, the short by entering a buy order.) it has been estimated that fewer than 3 percent of open contracts actually result in delivery. some futures contracts (e.g., stock indexes, eurodollar) use a cash settlement process whereby outstanding long and short positions are offset at the prevailing price level at expiration instead of being physically delivered. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:23 SCORE: 19.00 ================================================================================ 5FOr Beginners Only ■ Contract Specifications Futures contracts are traded for a wide variety of markets on a number of exchanges both in the United states and abroad. The specifications for these contracts, especially details such as daily price limits, trading hours, and ticker symbols, can change over time; exchange web sites should be con- sulted for up-to-date information. Table 1.1 provides the following representative trading details for six futures markets ( e-mini s&P 500, 10-year T -note, euro, Brent crude oil, corn, and gold):  1. exchange. note that some markets are traded on more than one exchange. in some cases, different contracts for the same commodity (or financial instrument) may even be traded on the same exchange. 2. ticker symbol. The quote symbol is the letter code that identifies each market (e.g., es for the e-mini s&P 500, C for corn, eC for the euro), combined with an alphanumeric suffix to represent the month and year. 3. Contract size. The specification of a uniform quantity per contract is one of the key ways in which a futures contract is standardized. By multiplying the contract size by the price, the trader can determine the dollar value of a contract. For example, if corn is trading at $4.00/bushel (bu), the contract value equals $20,000 ($4 × 5,000 bu per contract). if Brent crude oil is trading at $48.30, the contract value is $48,300 ($48.30 × 1,000 barrels). although there are many impor- tant exceptions, very roughly speaking, higher per-contract dollar values will imply a greater potential/risk level. (The concept of contract value has no meaning for interest rate contracts.) 4. Price quoted in. This row indicates the relevant unit of measure for the given market. 5. Minimum price fluctuation (“tick”) size and value. This row indicates the minimum increment in which prices can trade, and the dollar value of that move. For example, the mini- mum fluctuation for the e-mini s&P 500 contract is 0.25 index points. Thus, you can enter an order to buy December e-mini s&P futures at 1,870.25 or 1,870.50, but not 1,870.30. The minimum fluctuation for corn is 1 4 ¢/bu, which means you can enter an order to buy December corn at $4.01 1 2 or $4.01 3 4 , but not $4.01 5 8 per bushel. The tick value is obtained by multiply- ing the minimum fluctuation by the contract size. For example, for Brent crude oil, one cent ($0.01) per barrel × 1,000 barrels = $10. For corn, 1 4 50 00 12 50¢/bu ×=,$ .. 6. Contract months. each market is traded for specific months. For example, the e-mini s&P 500 futures contract is traded for March, June, september, and December. Corn is traded for March, May, July, september, and December. Table 1.2 shows the letter designations for each month of the year, which are added (along with the contract year) to a market’s base ticker symbol to create a contract-specific ticker symbol. For example, December 2017 e-mini s&P 500 futures have a ticker symbol of esZ17, while the symbol for the March 2018 contract is esH18. The symbol for May 2017 corn is CK17. The last trading day for a contract typically occurs on a specified date in the contract month, although in some markets (such as crude oil), the last trading day falls in the month preceding the contract month. For most markets, futures are listed for contract months at least one year forward from the current date. However, trading activity is normally heavily concentrated in the nearest two contracts. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:25 SCORE: 15.00 ================================================================================ 7FOr Beginners Only Daily Price limit 7%, 13%, and 20% limits are applied to the futures fixing price, effective 8:30 a.m. to 3 p.m. CT , Mon–Fri. 7%, 13%, and 20% limits are applied to the futures fixing price, effective 8:30 a.m. to 3 p.m. CT , Mon–Fri. ( see exchange for specifics.) n/a n/a $0.25 n/a Settlement type Cash settlement Deliverable Deliverable Physical delivery based on eFP delivery, with an option to cash settle against the iCe Brent index price for the last trading day of the futures contract. Deliverable Deliverable First Notice Day n/a Final business day of the month preceding the contract month. n/a n/a last business day of month preceding contract month. The last business day of the month preceding the delivery month. last Notice Day n/a Final business day of the contract month. n/a n/a The business day after the last contract’s last trading day. The second-to-last business day of the delivery month. last trading Day Until 8:30 a.m. on the 3rd Friday of the contract month. 12:01 p.m. on the 7th business day preceding the last business day of the delivery month. 9:16 a.m. CT on the second business day immediately preceding the third W ed of the contract month. The last business day of the second month preceding the relevant contract month. Business day prior to the 15th calendar day of the contract month. The third-to-last business day of the delivery month. Deliverable Grade n/a U.s. T -notes with a remaining term to maturity of 6.5 to 10 years from the first day of the delivery month. n/a n/a #2 yellow at contract price, #1 yellow at a 1.5 cent/bushel premium, #3 yellow at a 1.5 cent/bushel discount. gold delivered under this contract shall assay to a minimum of 995 fineness. 7 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:27 SCORE: 28.00 ================================================================================ 9FOr Beginners Only approaching expiration (frequently first notice day—see item 10). Daily price limits can change frequently, so traders should consult the exchange on which their products trade to ensure they are aware of current thresholds. 9. Settlement type. Markets are designated either as physically deliverable or cash settled. in Table 1.1, the e-mini s&P 500 futures are cash settled, while all the other markets can be physi- cally delivered. 10. First notice day. This is the first day on which a long can receive a delivery notice. First notice day presents no problem for shorts, since they are not obligated to issue a notice until after the last trading day. Furthermore, in some markets, first notice day occurs after last trading day, presenting no problem to the long either, since all remaining longs at that point presumably wish to take delivery. However, in markets in which first notice day precedes last trading day, longs who do not wish to take delivery should be sure to offset their positions in time to avoid receiving a delivery notice. (Brokerage firms routinely supply their clients with a list of these important dates.) although longs can pass on an undesired delivery notice by liquidating their position, this transaction will incur extra transaction costs and should be avoided. Last notice day is the final day a long can receive a delivery notice. 11. last trading day. This is the last day on which positions can be offset before delivery becomes obligatory for shorts and the acceptance of delivery obligatory for longs. as indicated previously, the vast majority of traders will liquidate their positions before this day. 12. Deliverable grade. This is the specific quality and type of the underlying commodity or finan- cial instrument that is acceptable for delivery. ■ Volume and Open Interest V olume is the total number of contracts traded on a given day. V olume figures are available for each traded month in a market, but most traders focus on the total volume of all traded months. Open interest is the total number of outstanding long contracts, or equivalently, the total number of outstanding short contracts—in futures, the two are always the same. When a new contract begins trading (typically about 12 to 18 months before its expiration date), its open interest is equal to zero. if a buy order and sell order are matched, then the open interest increases to 1. Basically, open interest increases when a new buyer purchases from a new seller and decreases when an existing long sells to an existing short. The open interest will remain unchanged if a new buyer purchases from an existing long or a new seller sells to an existing short. V olume and open interest are very useful as indicators of a market’s liquidity. not all listed futures mar- kets are actively traded. some are virtually dormant, while others are borderline cases in terms of trading activity. illiquid markets should be avoided, because the lack of an adequate order flow will mean that the trader will often have to accept very poor trade execution prices if he wants to get in or out of a position. generally speaking, markets with open interest levels below 5,000 contracts, or average daily volume levels below 1,000 contracts, should be avoided, or at least approached very cautiously. new markets will usually exhibit volume and open interest figures below these levels during their ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:28 SCORE: 17.00 ================================================================================ 10a COMPleTe gUiDe TO THe FUTUres MarKeT initial months (and sometimes even years) of trading. By monitoring the volume and open interest fi gures, a trader can determine when the market’s level of liquidity is suffi cient to warrant participa- tion. Figure 1.1 shows February 2016 gold (top) and april 2016 gold (bottom) prices, along with their respective daily volume fi gures. February gold’s volume is negligible until november 2015, at which point it increases rapidly into December and maintains a high level through January (the February contract expires in late February). Meanwhile, april gold’s volume is minimal until Janu- ary, at which point it increases steadily and becomes the more actively traded contract in the last two days of January—even though the February gold contract is still a month from expiration at that point. The breakdown of volume and open interest fi gures by contract month can be very useful in determining whether a specifi c month is suffi ciently liquid. For example, a trader who prefers to initiate a long position in a nine-month forward futures contract rather than in more nearby con- tracts because of an assessment that it is relatively underpriced may be concerned whether its level of trading activity is suffi cient to avoid liquidity problems. in this case, the breakdown of volume and open interest fi gures by contract month can help the trader decide whether it is reasonable to enter the position in the more forward contract or whether it is better to restrict trading to the nearby contracts. Traders with short-term time horizons (e.g., intraday to a few days) should limit trading to the most liquid contract, which is usually the nearby contract month. FIGURE  1.1 V olume shift in gold Futures Chart created using Tradestation. ©Tradestation T echnologies, inc. all rights reserved. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:33 SCORE: 10.00 ================================================================================ 15FOr Beginners Only this wide discount, the hedge is still very profitable because the price differential is ultimately far outweighed by the intervening price decline. Thus, the relevant question is not whether the futures-implied cash price is attractive relative to the current cash price, but rather whether it is attractive relative to the expected future cash price. 6. The hedger does not precisely lock in a transaction price. His effective price will depend on the basis. For example, if the cotton producer sells futures at 85¢/lb, assuming a −3¢ basis, his effective sales price will be 80¢/lb, rather than the anticipated 82¢/lb, if the actual basis at the time of offset is −5¢. However, it should be emphasized that this basis-price uncertainty is far smaller than the outright price uncertainty in an unhedged position. Furthermore, by using reasonably conservative basis assumptions the hedger can increase the likelihood of achieving, or bettering, the assumed locked-in price. 7. a lthough a hedger plans to buy or sell the actual commodity, it will usually be far more efficient to offset the futures position and use the local cash market for the actual transaction. Futures should be viewed as a pricing tool, not as a vehicle for making or taking delivery. 8. Most standard discussions of hedging make no mention whatsoever of price forecasting. This omission seems to imply that hedgers need not be concerned about the direction of prices. although this conclusion may be valid for some hedgers (e.g., a middleman seek- ing to lock in a profit margin between the purchase and sales price), it is erroneous for most hedgers. There is little sense in following an automatic hedging program. rather, the hedger should evaluate the relative attractiveness of the price protection offered by futures. Price forecasting would be a key element in making such an evaluation. in this respect, it can easily be argued that price forecasting is as important to many hedgers as it is to speculators. ■ Trading The trader seeks to profit by anticipating price changes. For example, if the price of December gold is $1,150/oz, a trader who expects the price to rise above $1,250/oz will go long. The trader has no intention of actually taking delivery of the gold in December. right or wrong, the trader will offset the position sometime before expiration. For example, if the price rises to $1,275 and the trader decides to take profits, the gain on the trade will be $12,500 per contract (100 oz × $125/ oz). if, on the other hand, the trader’s forecast is wrong and prices decline to $1,075/oz, with the expiration date drawing near, the trader has little choice but to liquidate. in this situation, the loss would be equal to $7,500 per contract. note that the trader would not take delivery even given a desire to maintain the long gold position. in this case, the trader would liquidate the December contract and simultaneously go long in a more forward contract. (This type of transaction is called a rollover and would be implemented with a spread order—defined in the next section.) Traders should avoid taking delivery, since it can often result in substantial extra costs without any com- pensating benefits. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:37 SCORE: 31.00 ================================================================================ 19FOr Beginners Only Spread a spread involves the simultaneous purchase of one futures contract against the sale of another futures contract, either in the same market or in a related market. in essence, a spread trader is primarily concerned with the difference between prices rather than the direction of price. an example of a spread trade would be: Buy 1 July cotton/sell 1 December cotton, July 200 points premium December. This order would be executed if July could be bought at a price 200 points or less above the level at which December is sold. such an order would be placed if the trader expected July cotton to widen its premium relative to December cotton. not all brokerages will accept all the order types in this section (and may offer others not listed here). Traders should consult with their brokerage to determine which types of orders are available to them. ■ Commissions and Margins in futures trading, commissions are typically charged on a per-contract basis. in most cases, large traders will be able to negotiate a reduced commission rate. although commodity commissions are relatively moderate, commission costs can prove substantial for the active trader—an important rea- son why position trading is preferable unless one has developed a very effective short-term trading method. Futures margins are basically good-faith deposits and represent only a small percentage of the con- tract value (roughly 5 percent with some significant variability around this level). Futures exchanges will set minimum margin requirements for each of their contracts, but many brokerage houses will frequently require higher margin deposits. since the initial margin represents only a small portion of the contract value, traders will be required to provide additional margin funds if the market moves against their positions. These additional margin payments are referred to as maintenance. Many traders tend to be overly concerned with the minimum margin rate charged by a broker- age house. if a trader is adhering to prudent money management principles, the actual margin level should be all but irrelevant. as a general rule, the trader should allocate at least three to five times the minimum margin requirement to each trade. Trading an account anywhere near the full margin allowance greatly increases the chances of experiencing a severe loss. Traders who do not maintain at least several multiples of margin requirements in their accounts are clearly overtrading. ■ Tax Considerations Tax laws change over time, but for the average speculator in the United states, the essential elements of the futures contract tax regulations can be summarized in three basic points: 1. There is no holding period for futures trades (i.e., all trades are treated equally, regardless of the length of time a position is held, or whether a position is long or short). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:57 SCORE: 10.00 ================================================================================ 39TYPES OF CHARTS FIGURE  4.6 W eekly Bar Chart Perspective: Coff ee Nearest Futures Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. ■ Linked Contract Series: Nearest Futures versus Continuous Futures The time period covered by the typical weekly or monthly bar chart requires the use of a series of contracts. Normally, these contracts are combined using the nearest futures approach: a contract is plotted until its expiration and then the subsequent contract is plotted until its expiration, and so on. Traders should be aware that a nearest futures chart may refl ect signifi cant distortions due to the price gaps between the expiring month and the subsequent contract. Figure 4.7 provides two clear examples of this type of distortion. The top chart is a live cattle weekly nearest futures chart; the bottom chart is a live cattle weekly continuous futures chart, which will be defi ned momentarily. The nearest futures chart implies a large 7.175-cent (6 percent) one- week gain in the price of cattle from the August 31 close to the September 7, 2012 close. However, this price jump never really took place because the price gap represented nothing more than the expi- ration of the lower-priced August 2012 cattle contract and the switch to the higher-priced October 2012 cattle contract. In contrast, the continuous futures chart, which, as will be explained shortly, refl ects actual price movements, showed that price had rallied only 0.45 cents from August 31 to September 7, 2012. Almost exactly a year later the same relationship between the prices in diff erent contract months produced an even more noteworthy discrepancy: While the nearest futures chart showed a 3.15-cent gain from August 30 to September 6, 2013, the continuous futures chart shows cattle prices actually declined 1.125 cents between these dates. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:63 SCORE: 10.00 ================================================================================ 45 Chapter 5 ■ The Necessity of Linked-Contract Charts Many of the chart analysis patterns and techniques detailed in Chapters 6 through 9 require long- term charts—often charts of multiyear duration. This is particularly true for the identification of top and bottom formations, as well as the determination of support and resistance levels. A major problem facing the chart analyst in the futures markets is that most futures contracts have relatively limited life spans and even shorter periods in which these contracts have significant trading activity. For many futures contracts (e.g., currencies, stock indexes) trading activity is almost totally concentrated in the nearest one or two contract months. For example, in Figure 5.1, there were only about two months of liquid data available for the March 2016 Russell 2000 Index Mini futures contract when it became the most liquid contract in this market as the December 2015 con - tract expiration approached. This market is not particularly unusual in this respect. In many futures markets, almost all trading is concentrated in the nearest contract, which will have only a few months (or weeks) of liquid trading history when the prior contract approaches expiration. Linking Contracts for Long- T erm Chart Analysis: Nearest versus Continuous Futures ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:64 SCORE: 11.00 ================================================================================ 46A COMPLETE GUIDE TO THE FUTURES MARKET The limited price data available for many futures contracts—even those that are the most actively traded contracts in their respective markets—makes it virtually impossible to apply most chart analy- sis techniques to individual contract charts. Even in those markets in which the individual contracts have a year or more of liquid data, part of a thorough chart study would still encompass analyzing multiyear weekly and monthly charts. Thus, the application of chart analysis unavoidably requires linking successive futures contracts into a single chart. In markets with very limited individual con- tract data, such linked charts will be a necessity in order to perform any meaningful chart analysis. In other markets, linked charts will still be required for analyzing multiyear chart patterns. ■ Methods of Creating Linked-Contract Charts Nearest Futures The most common approach for creating linked-contract charts is typically termed nearest futures. This type of price series is constructed by taking each individual contract series until its expiration and then continuing with the next contract until its expiration, and so on. Although, at surface glance, this approach appears to be a reasonable method for constructing linked-contract charts, the problem with a nearest futures chart is that there are price gaps between expiring and new contracts—and quite frequently, these gaps can be very substantial. For exam- ple, assume the September coff ee contract expires at 132.50 cents/lb and the next nearest con- tract (December) closes at 138.50 cents/lb on the same day. Further assume that on the next day FIGURE  5.1 March 2016 Russell 2000 Mini Futures Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:65 SCORE: 25.00 ================================================================================ 47 Linking ContraCts for Long-term Chart anaLysis December coffee falls 5 cents/lb to 133.50—a 3.6 percent drop. A nearest futures price series will show the following closing levels on these two successive days: 132.50 cents, 133.50 cents. In other words, the nearest futures contract would show a one-cent (0.75 percent) gain on a day on which longs would actually have experienced a huge loss. This example is by no means artificial. Such distortions— and indeed more extreme ones—are quite common at contract rollovers in nearest futures charts. The vulnerability of nearest futures charts to distortions at contract rollover points makes it desir- able to derive alternative methods of constructing linked-contract price charts. One such approach is detailed in the next section. Continuous (Spread-adjusted) price Series The spread-adjusted price series known as “continuous futures” is constructed by adding the cumulative dif- ference between the old and new contracts at rollover points to the new contract series. 1 An example should help clarify this method. Assume we are constructing a spread-adjusted continuous price series for gold using the June and December contracts. 2 If the price series begins at the start of the calendar year, initially the values in the series will be identical to the prices of the June contract expiring in that year. Assume that on the rollover date (which need not necessarily be the last trading day) June gold closes at $1,200 and December gold closes at $1,205. In this case, all subsequent prices based on the December contract would be adjusted downward by $5—the difference between the December and June contracts on the rollover date. Assume that at the next rollover date December gold is trading at $1,350 and the subsequent June contract is trading at $1,354. The December contract price of $1,350 implies that the spread-adjusted continuous price is $1,345. Thus, on this second rollover date, the June contract is trading $9 above the adjusted series. Consequently, all subsequent prices based on the second June contract would be adjusted downward by $9. This procedure would continue, with the adjustment for each contract dependent on the cumulative total of the present and prior transition point price differences. The resulting price series would be free of the distortions due to spread differences that exist at the rollover points between contracts. The construction of a continuous futures series can be thought of as the mathematical equivalent of taking a nearest futures chart, cutting out each individual contract series contained in the chart, and pasting the ends together (assuming a continuous series employing all contracts and using the same rollover dates as the nearest futures chart). Typically, as a last step, it is convenient to shift the scale of the entire series by the cumulative adjustment factor, a step that will set the current price of the series equal to the price of the current contract without changing the shape of the series. The construction of a continuous futures chart is discussed in greater detail in Chapter 18. 1 T o avoid confusion, readers should note that some data services use the term continuous futures to refer to linking together contracts of the same month (e.g., linking from March 2015 corn when it expires to March 2016 corn, and so on). Such charts are really only a variation of nearest futures charts—one in which only a single contract month is used—and will be as prone to wide price gaps at rollovers as nearest futures charts, if not more so. These types of charts have absolutely nothing in common with the spread-adjusted continuous futures series described in this section—that is, nothing but the name. It is unfortunate that some data services have decided to use this same term to describe an entirely different price series than the original meaning described here. 2 The choice of a combination of contracts is arbitrary. One can use any combination of actively traded months in the given market. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:298 SCORE: 21.00 ================================================================================ 280 A Complete Guide to the Futures mArket series. For example, a 15­year test run for a typical market would require using approximately 60 to 90 individual contract price series. Moreover, using the individual contract series requires an algo­ rithm for determining what action to take at the rollover points. As an example of the type of problem that may be encountered, it is entirely possible for a given system to be long in the old contract and short in the new contract or vice versa. These problems are hardly insurmountable, but they make the use of individual contract series a somewhat unwieldy approach. The awkwardness involved in using a multitude of individual contracts is not, however, the main problem. The primary drawback in using individual contract series is that the period of meaningful liquidity in most contracts is very short—much shorter than the already limited contract life spans. T o see the scope of this problem, examine a cross section of futures price charts depicting the price action in the one ­year period prior to expiration. In many markets, contracts don’t achieve meaning­ ful liquidity until the final five or six months of trading, and sometimes even less. This problem was illustrated in Chapter 5. The limited time span of liquid trading in individual contracts means that any technical system or method that requires looking back at more than about six months of data—as would be true for a whole spectrum of longer ­term approaches—cannot be applied to individual contract series. Thus, with the exception of short­term system traders, the use of individual contract series is not a viable alternative. It’s not merely a matter of the approach being difficult but, rather, its being impossible because the necessary data simply do not exist. ■ Nearest Futures The problems in using individual contract series as just described has led to the construction of vari­ ous linked price series. The most common approach is almost universally known as nearest futures. This price series is constructed by taking each individual contract series until its expiration and then continuing with the next contract until its expiration, and so on. This approach may be useful for constructing long ­term price charts for purposes of chart analysis, but it is worthless for providing a series that can be used in the computer testing of trading systems. The problem in using a nearest futures series is that there are price gaps between expiring and new contracts—and quite frequently these gaps can be very substantial. For example, assume the July corn contract expires at $4 and that the next nearest contract (September) closes at $3.50 on the same day. Assume that on the next day September corn moves from $3.50 to $3.62. A nearest futures price series will show the following closing levels on these two successive days: $4, $3.62. In other words, the near­ est futures contract would imply a 38 ­cent loss on a day on which longs would have enjoyed (or shorts would have suffered) a price gain of 12 cents. This example is by no means artificial. In fact, it would be easy to find a plethora of similarly extreme situations in actual price histories. Moreover, even if the typical distortion at rollover is considerably less extreme, the point is that there is virtually always some distortion, and the cumulative effect of these errors would destroy the validity of any computer test. Fortunately, few traders are naive enough to use the nearest futures type of price series for computer testing. The two alternative linked price series described in the next sections have become the approaches employed by most traders wishing to use a single price series for each market in computer testing. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:299 SCORE: 19.00 ================================================================================ 281 SElECTINg THE BEST FuTurES PrICE SErIES For SySTEM TESTINg ■ Constant-Forward (“Perpetual”) Series The constant­forward (also known as “perpetual”) price series consists of quotes for prices a constant amount of time forward. The interbank currency market offers actual examples of constant­forward price series. For example, the three­month forward price series for the euro represents the quote for the euro three months forward from each given day in the series. This is in contrast to the standard u.S. futures contract, which specifies a fixed expiration date. A constant ­forward series can be constructed from futures price data through interpola­ tion. For example, if we were calculating a 90 ­day constant ­forward (or perpetual) series and the 90­day forward date fell exactly one ­third of the way between the expirations of the nearest two contracts, the constant ­forward price would be calculated as the sum of two ­thirds of the nearest contract price and one ­third of the subsequent contract price. As we moved forward in time, the nearer contract would be weighted less, and the weighting of the subsequent contract would increase proportionately. Eventually, the nearest contract would expire and drop out of the calculation, and the constant ­forward price would be based on an interpolation between the subsequent two contracts. As a more detailed example, assume you want to generate a 100­day forward price series based on euro futures, which are traded in March, June, September, and December contracts. T o illustrate the method for deriving the 100 ­day constant­forward price, assume the current date is January 20. In this case, the date 100 days forward is April 30. This date falls between the March and June contracts. Assume the last trading dates for these two contracts are March 14 and June 13, respectively. Thus, April 30 is 47 days after the last trading day for the March contract and 44 days before the last trad­ ing day for the June contract. T o calculate the 100 ­day forward price for January 20, an average price would be calculated using the quotes for March and June euro futures on January 20, weighting each quote in inverse proportion to its distance from the 100 ­day forward date (April 30). Thus, if on Janu­ ary 20 the closing price of March futures is 130.04 and the closing price of June futures is 130.77, the closing price for the 100 ­day forward series would be: 44 91 1300 4 130 77 130 42(. )( .) .+=47 91 Note that the general formula for the weighting factor used for each contract price is: W CF CC W FC CC1 2 21 2 1 21 = − − = − − where C1 = number of days until the nearby contract expiration C2 = number of days until the forward contract expiration F = number of days until forward quote date W1 = weighting for nearby contract price quote W2 = weighting for forward contract price quote ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:300 SCORE: 15.00 ================================================================================ 282 A Complete Guide to the Futures mArket So, for example, the weightings of the March and June quotes that would be used to derive a 100­day forward quote on March 2 would be as follows: Weighting for March quot e Weighting for = − − =1031 00 103 12 3 91 JJune quote = − − =100 12 103 12 88 91 As we move forward in time, the nearer contract is weighted less and less, but the weighting for the subsequent contract increases proportionately. When the number of days remaining until the expiration of the forward contract equals the constant ­forward time (100 days in this example), the quote for the constant ­forward series would simply be equal to the quote for the forward contract (June). Subsequent price quotes would then be based on a weighted average of the June and Septem­ ber prices. In this manner, one continuous price series could be derived. The constant ­forward price series eliminates the problem of huge price gaps at rollover points and is certainly a significant improvement over a nearest futures price series. However, this type of series still has major drawbacks. T o begin, it must be stressed that one cannot literally trade a constant ­ forward series, since the series does not correspond to any real contract. An even more serious deficiency of the constant ­forward series is that it fails to reflect the effect of the evaporation of time that exists in actual futures contracts. This deficiency can lead to major distortions—particularly in carrying ­charge markets. T o illustrate this point, consider a hypothetical situation in which spot gold prices remain stable at approximately $1,200/ounce for a one­year period, while forward futures maintain a constant pre­ mium of 1 percent per two­month spread. given these assumptions, futures would experience a steady downtrend, declining $73.82/ounce1 ($7,382 per contract) over the one­year period (the equivalent of the cumulative carrying­charge premiums). Note, however, the constant­forward series would com­ pletely fail to reflect this bear trend because it would register an approximate constant price. For example, a two ­month constant­forward series would remain stable at approximately $1,212/ounce (1.01 × $1,200 = $1,212). Thus, the price pattern of a constant ­forward series can easily deviate substantially from the pattern exhibited by the actual traded contracts—a highly undesirable feature. ■ Continuous (Spread-Adjusted) Price Series The spread­adjusted futures series, commonly known as continuous futures, is constructed to elimi­ nate the distortions caused by the price gaps between consecutive futures contracts at their transi­ tion points. In effect, the continuous futures price will precisely reflect the fluctuations of a futures position that is continuously rolled over to the subsequent contract N days before the last trading day, where N is a parameter that needs to be defined. If constructing their own continuous futures data series, traders should select a value of N that corresponds to their actual trading practices. 1 This is true since, given the assumptions, the one­year forward futures price would be approximately $1,273.82 (1.016 × $1,200 = $1,273.82) and would decline to the spot price ($1,200) by expiration. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:301 SCORE: 8.00 ================================================================================ 283 SElECTINg THE BEST FuTurES PrICE SErIES For SySTEM TESTINg For example, if a trader normally rolls a position over to a new contract approximately 20 days before the last trading day, N would be defined as 20. The scale of the continuous futures series is adjusted so the current price corresponds to a currently traded futures contract. Table 18.1 illustrates the construction of a continuous futures price for the soybean market. For simplicity, this example uses only two contract months, July and November; however, a continuous price could be formed using any number of traded contract months. For example, the continuous futures price could be constructed using the January, March, May, July, August, September, and November soybean contracts. table 18.1 Construction of a Continuous Futures price Using July and November Soybeans (cents/bushel)* Date Contract actual price Spread at rollover (Nearby Forward) Cumulative adjustment Factor Unadjusted Continuous Futures (Col. 3 + Col. 5) Continuous Futures price (Col. 6 – 772.5) 6/27/12 Jul ­12 1,471 1,471 698.5 6/28/12 Jul ­12 1,466 1,466 693.5 6/29/12 Jul ­12 1,512.75 1,512.75 740.25 7/2/12 Nov ­12 1,438 85 85 1,523 750.5 7/3/12 Nov ­12 1,474.75 85 1,559.75 787.25 *** 10/30/12 Nov ­12 1,533.75 85 1,618.75 846.25 10/31/12 Nov ­12 1,547 85 1,632 859.5 11/1/12 Jul ­13 1,474 86.25 171.25 1,645.25 872.75 11/2/12 Jul ­13 1,454 171.25 1,625.25 852.75 *** 6/27/13 Jul ­13 1,548.5 171.25 1,719.75 947.25 6/28/13 Jul ­13 1,564.5 171.25 1,735.75 963.25 7/1/13 Nov ­13 1,243.25 312.5 483.75 1,727 954.5 7/2/13 Nov ­13 1,242.5 483.75 1,726.25 953.75 *** 10/30/13 Nov ­13 1,287.5 483.75 1,771.25 998.75 10/31/13 Nov ­13 1,280.25 483.75 1,764 991.5 11/1/13 Jul ­14 1,224.5 45.5 529.25 1,753.75 981.25 11/4/13 Jul ­14 1,227.75 529.25 1,757 984.5 *** 6/27/14 Jul ­14 1,432 529.25 1,961.25 1,188.75 6/30/14 Jul ­14 1,400.5 529.25 1,929.75 1,157.25 7/1/14 Nov ­14 1,147.5 243.25 772.5 1,920 1,147.5 7/2/14 Nov ­14 1,141.5 772.5 1,914 1,141.5 *Assumes rollover on last day of the month preceding the contract month. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:302 SCORE: 14.00 ================================================================================ 284 A Complete Guide to the Futures mArket For the moment, ignore the last column in Table 18.1 and focus instead on the unadjusted con­ tinuous futures price (column 6). At the start of the period, the actual price and the unadjusted continuous futures price are identical. At the first rollover point, the forward contract (November 2012) is trading at an 85 ­cent discount to the nearby contract (July 2012). All subsequent prices of the November 2012 contract are then adjusted upward by this amount (the addition of a positive nearby/forward spread), yielding the unadjusted continuous futures prices shown in column 6. At the next rollover point, the forward contract (July 2013) is trading at an 86.25 ­cent discount to the nearby contract (November 2012). As a result, all subsequent actual prices of the July 2013 contract must now be adjusted by the cumulative adjustment factor—the total of all rollover gaps up to that point (171.25 cents)—in order to avoid any artificial price gaps at the rollover point. This cumulative adjustment factor is indicated in column 5. The unadjusted continuous futures price is obtained by adding the cumulative adjustment factor to the actual price. The preceding process is continued until the current date is reached. At this point, the final cumu­ lative adjustment factor is subtracted from all the unadjusted continuous futures prices (column 6), a step that sets the current price of the series equal to the price of the current contract (November 2014 in our example) without changing the shape of the series. This continuous futures price is indi­ cated in column 7 of Table 18.1. Note that although actual prices seem to imply a net price decline of 329.50 cents during the surveyed period, the continuous futures price indicates a 443 ­cent increase— the actual price change that would have been realized by a constant long futures position. In effect, the construction of the continuous series can be thought of as the mathematical equiva­ lent of taking a nearest futures chart, cutting out each individual contract series contained in the chart, and pasting the ends together (assuming a continuous series employing all contracts and using the same rollover dates as the nearest futures chart). In some markets, the spreads between nearby and forward contracts will range from premiums to discounts (e.g., cattle). However, in other markets, the spread differences will be unidirectional. For example, in the gold market, the forward month always trades at a premium to the nearby month. 2 In these types of markets, the spread­adjusted continuous price series can become increasingly disparate from actual prices. It should be noted that when nearby premiums at contract rollovers tend to swamp nearby dis ­ counts, it is entirely possible for the series to eventually include negative prices for some past periods as cumulative adjustments mount, as illustrated in the soybean continuous futures chart in Figure 18.1. The price gain that would have been realized by a continuously held futures position during this period 2 The reason for this behavioral pattern in gold spreads is related to the fact that world gold inventories exceed annual usage by many multiples, perhaps even by as much as a hundredfold. Consequently, there can never ac­ tually be a “shortage” of gold—and a shortage of nearby supplies is the only reason why a storable commodity would reflect a premium for the nearby contract. (Typically, for storable commodities, the fact that the forward contracts embed carrying costs will result in these contracts trading at a premium to more nearby months.) gold prices fluctuate in response to shifting perceptions of gold’s value among buyers and sellers. Even when gold prices are at extremely lofty levels, it does not imply any actual shortage, but rather an upward shift in the market’s perception of gold’s value. Supplies of virtually any level are still available—at some price. This is not true for most commodities, in which there is a definite relevant limit in total supplies. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:304 SCORE: 12.00 ================================================================================ 286 A Complete Guide to the Futures mArket series means that past prices in a continuous series will not match the actual historical prices that prevailed at the time. However, the essential point is that the continuous series is the only linked futures series that will exactly reflect price swings and hence equity fluctuations in an actual trading account. Consequently, it is the only linked series that can be used to generate accurate simulations in computer testing of trading systems. The preceding point is absolutely critical! Mathematics is not a matter of opinion. There is one right answer and there are many wrong answers. The simple fact is that if a continuous futures price series is defined so that rollovers occur on days consistent with rollovers in actual trading, results implied by using this series will precisely match results in actual trading (assuming, of course, accu­ rate commission and slippage cost estimates). In other words, the continuous series will exactly paral­ lel the fluctuations of a constantly held (i.e., rolled over) long position. All other types of linked series will not match actual market price movements. T o illustrate this statement, we compare the implications of various price series using the sideways gold market example cited earlier in this chapter (i.e., gold hovering near $1,200 and a forward/ nearby contract premium equal to 1 percent per two ­month spread). A trader buying a one­year for­ ward futures contract would therefore pay approximately $1,273.82 (1.016 × $1,200 = $1,273.82). The spot price would reflect a sideways pattern near $1,200. As previously seen, a 60­day constant­ forward price would reflect a sideways pattern near $1,212 (1.01 × $1,200). A nearest futures price series would exhibit a general sideways pattern, characterized by extended minor downtrends (reflecting the gradual evaporation of the carrying charge time premium as each nearby contract approached expiration), interspersed with upward gaps at rollovers between expiring and subsequent futures contracts. Thus the spot, constant ­forward, and nearest futures price series would all suggest that a long position would have resulted in a break­even trade for the year. In reality, however, the buyer of the futures contract pays $1,273.82 for a contract that eventually expires at $1,200. Thus, from a trading or real ­world viewpoint, the market actually witnesses a downtrend. The continuous futures price is the only price series that reflects the market decline—and real dollar loss—a trader would actually have experienced. I have often seen comments or articles by industry “experts” arguing for the use of constant ­ forward (perpetual) series instead of continuous series in order to avoid distortions. This argument has it exactly backwards. Whether these proponents of constant ­forward series adopt their stance because of naïveté or self ­interest (i.e., they are vendors of constant ­forward­type data), they are simply wrong. This is not a matter of opinion. If you have any doubts, try matching up fluctuations in an actual trading account with those that would be implied by constant ­forward­type price series. you will soon be a believer. Are there any drawbacks to the continuous futures time series? of course. It may be the best solution to the linked series problem, but it is not a perfect answer. A perfect alternative simply does not exist. one potential drawback, which is a consequence of the fact that continuous futures accurately reflect only price swings, not price levels, is that continuous futures cannot be used for any type of percentage calculations. This situation, however, can be easily remedied. If a system requires the calculation of a percentage change figure, use continuous futures to calculate the nominal price ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:458 SCORE: 19.00 ================================================================================ 440 A Complete Guide to the Futures mArket ■ Spreads—Definition and Basic Concepts A spread trade involves the simultaneous purchase of one futures contract against the sale of another futures contract either in the same market or in a related market. normally, the spread trader will initiate a position when he considers the price difference between two futures contracts to be out of line rather than when he believes the absolute price level to be too high or too low . in essence, the spread trader is more concerned with the difference between prices than the direction of price. For example, if a trader buys October cattle and sells February cattle, it would not make any difference to him whether October rose by 500 points and February by only 400 points or October fell by 400 and February fell by 500. in either case, October would have gained 100 points relative to February, and the trader’s profit would be completely independent of the overall market direction. However, this is not to say the spread trader will initiate a trade without having some definitive bias as to the future outright market direction. in fact, very often the direction of the market will determine the movement of the spread. in some instances, however, a spread trader may enter a posi- tion when he has absolutely no bias regarding future market direction but views a given price differ- ence as being so extreme that he believes the trade will work, or at worst allow only a modest loss, regardless of market direction. W e will elaborate on the questions of when and how market direction will affect spreads in later sections. ■ Why Trade Spreads? the following are some advantages to not exclusively restricting one’s trading to outright positions: 1. In highly volatile markets, the minimum outright commitment of one contract may offer excessive risk to small traders. in such markets, one-day price swings in excess of $1,500 per contract are not uncommon, and holding a one-contract position may well be overtrading for many traders. ironically, it is usually these highly volatile markets that provide the best potential trading opportunities. spreads offer a great flexibility in reducing risk to a desirable and manageable level, since a spread trade usually presents only a fraction of the risk involved in an outright position. 1 For example, assume a given spread is judged to involve approximately one-fifth the risk of an outright position. in such a case, traders for whom a one- contract outright position involves excessive risk may instead choose to initiate a one-, two-, three-, or four-contract spread position, depending on their desired risk level and objectives. 2. there are times when spreads may offer better reward/risk ratios than outright positions. Of course, the determination of a reward/risk ratio is a subjective matter. never- theless, given a trader’s market bias, in a given situation spreads may sometimes offer a better means of approaching the market. 1 For some markets, reduced-size contracts are available on one or more exchanges. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:459 SCORE: 35.00 ================================================================================ 441 tHe COnCepts And MeCHAniCs OF spreAd trAding 3. Spreads often offer some protection against sudden extreme losses due to dra- matic events that may spark a string of limit-up or limit-down moves counter to one’s position (e.g., freeze, large export deal). such situations are not all that infrequent, and traders can sometimes lose multiples of the maximum loss they intended to allow (i.e., as reflected by a protective stop) before they can even liquidate their positions. in contrast, during a time of successive limit moves, the value of a spread might not even change as both months may move the limit. Of course, eventually the spread will also react, but when it does, the market may well be past its frenzied panic stage, and the move may be gradual and moderate compared with the drastic price change of the outright position. 4. a knowledge and understanding of spreads can also be a valuable aid in trading outright positions. For example, a failure of the near months to gain sufficiently during a rally (in those commodities in which a gain can theoretically be expected) may signal the trader to be wary of an upward move as a possible technical surge vulnerable to retracement. in other words, the spread action may suggest that no real tightness exists. this scenario is merely one example of how close observation of spreads can offer valuable insights into outright market direction. naturally, at times, the inferences drawn from spread movements may be mislead- ing, but overall they are likely to be a valuable aid to the trader. A second way an understanding of spreads can aid an outright-position trader is by helping identify the best contract month in which to initiate a position. the trader with knowledge of spreads should have a distinct advan- tage in picking the month that offers the best potential versus risk. Over the long run, this factor alone could significantly improve trading performance. 5. trading opportunities may sometimes exist for spreads at a time when none is perceived for the outright commodity itself. ■ Types of Spreads there are three basic types of spreads: 1. the intramarket (or interdelivery) spread is the most common type of spread and con- sists of buying one month and selling another month in the same commodity. An example of an intramarket spread would be long december corn/short March corn. the intramarket spread is by far the most widely used type of spread and will be the focus of this chapter’s discussion. the intercrop spread is a special case of the intramarket spread involving two different crop years (e.g., long an old crop month and short a new crop month). the intercrop spread requires special consideration and extra caution. intercrop spreads can often be highly volatile, and price moves in opposite directions by new and old crop months are not particularly uncom- mon. the intercrop spread may often be subject to price ranges and patterns that distinctly separate it from the intracrop spread (i.e., standard intramarket spread). 2. the intercommodity spread consists of a long position in one commodity and a short position in a related commodity. in this type of spread the trader feels the price of a given ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:460 SCORE: 32.00 ================================================================================ 442 A Complete Guide to the Futures mArket commodity is too high or low relative to a closely related commodity. some examples of this type of spread include long december cattle/short december hogs and long July wheat/short July corn. The source/product spread, which involves a commodity and its by-product(s)—for example, soybeans versus soybean meal and/or soybean oil—is a specific type of intercommod- ity spread that is sometimes classified separately. usually, an intercommodity spread will involve the same month in each commodity, but this need not always be the case. ideally, traders should choose the month they consider the strongest in the market they are buying and the month they consider the weakest in the market they are selling. Obviously, these will not always be the same month. For example, assume the following price configuration: December February april Cattle 120.00 116.00 118.00 Hogs 84.00 81.00 81.00 given this price structure, a trader might decide the premium of cattle to hogs is too small and will likely increase. this trading bias would dictate the initiation of a long cattle/short hog spread. However, the trader may also believe February cattle is underpriced relative to other cattle months and that december hogs are overpriced relative to the other hog contracts. in such a case, it would make more sense for the trader to be long February cattle/short decem- ber hogs rather than long december cattle/short december hogs or long February cattle/short February hogs. One important factor to keep in mind when trading intercommodity spreads is that contract sizes may differ for each commodity. For example, the contract size for euro futures is 125,000 units, whereas the contract size for British pound futures is 62,500 units. thus, a euro/British pound spread consisting of one long contract could vary even if the price difference between the two markets remained unchanged. the difference in price levels is another important fac- tor relevant to contract ratios for intercommodity spreads. the criteria and methodology for determining appropriate contract ratios for intercommodity spreads are discussed in the next chapter. 3. the intermarket spread. this spread involves buying a commodity at one exchange and sell- ing the same commodity at another exchange, which will often be another country. An example of this type of spread would be long new Y ork March cocoa/short London March cocoa. trans- portation, grades deliverable, distribution of supply (total and deliverable) relative to location, and historical and seasonal basis relationships are the primary considerations in this type of spread. in the case of intermarket spreads involving different countries, currency fluctuations become a major consideration. intermarket spread trading is often referred to as arbitrage. As a rule, the intermarket spread requires a greater degree of sophistication and comprehensive familiarity with the commodity in question than other types of spreads. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:461 SCORE: 16.00 ================================================================================ 443 tHe COnCepts And MeCHAniCs OF spreAd trAding ■ The General Rule For many commodities, the intramarket spread can often, but not always, be used as a proxy for an outright long or short position. As a general rule, near months will gain ground relative to distant months in a bull market and lose ground in a bear market. the reason for this behavior is that a bull market usually reflects a current tight supply situation and often will place a premium on more imme- diately available supplies. in a bear market, however, supplies are usually burdensome, and distant months will have more value because they implicitly reflect the cost involved in storing the com- modity for a period of time. thus, if a trader expects a major bull move, he can often buy a nearby month and sell a more distant month. if he is correct in his analysis of the market and a bull move does materialize, the nearby contract will likely gain on the distant contract, resulting in a success- ful trade. it is critical to keep in mind that this general rule is just that, and is meant only as a rough guideline. there are a number of commodities for which this rule does not apply, and even in those commodities where it does apply, there are important exceptions. W e will elaborate on the question of applicability in the next section. At this point the question might legitimately be posed, “ if the success of a given spread trade is contingent upon forecasting the direction of the market, wouldn’t the trader be better off with an outright position?” Admittedly, the potential of an outright position will almost invariably be consid- erably greater. But the point to be kept in mind is that an outright position also entails a correspond- ingly greater risk. sometimes the outright position will offer a better reward/risk ratio; at other times the spread will offer a more attractive trade. A determination of which is the better approach will depend upon absolute price levels, prevailing price differences, and the trader’s subjective views of the risk and potential involved in each approach. ■ The General Rule—Applicability and Nonapplicability Commodities to Which the General rule Can Be applied Commodities to which the general rule applies with some regularity include corn, wheat, oats, soybeans, soybean meal, soybean oil, lumber, sugar, cocoa, cotton, orange juice, copper, and heating oil. ( the general rule will also usually apply to interest rate markets.) Although the general rule will usually hold in these markets, there are still important exceptions, some of which include: 1. At a given point in time the premium of a nearby month may already be excessively wide, and consequently a general price rise in the market may fail to widen the spread further. 2. s ince higher prices also increase carrying costs (see section entitled “the Limited-risk spread”), it is theoretically possible for a price increase to widen the discount of nearby months in a surplus market. Although such a spread response to higher prices is atypical, its probability of occurrence will increase in a high-interest-rate environment. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:462 SCORE: 19.00 ================================================================================ 444 A Complete Guide to the Futures mArket 3. s preads involving a spot month near expiration can move independently of, or contrary to, the direction implied by the general rule. the reason is that the price of an expiring position is criti- cally dependent upon various technical considerations involving the delivery situation, and wide distortions are common. 4. A bull move that is primarily technical in nature may fail to influence a widening of the nearby premiums since no real near-term tightness exists. ( such a price advance will usually only be temporary in nature.) 5. g overnment intervention (e.g., export controls, price controls, etc.), or even the expectation of government action, can completely distort normal spread relationships. therefore, it is important that when initiating spreads in these commodities, the trader keep in mind not only the likely overall market direction, but also the relative magnitude of existing spread differences and other related factors. Commodities Conforming to the Inverse of the General rule some commodities, such as gold and silver, conform to the exact inverse of the general rule: in a ris- ing market distant months gain relative to more nearby contracts, and in a declining market they lose relative to the nearby positions. In fact, in these markets, a long forward/short nearby spread is often a good proxy for an outright long position, and the reverse spread can be a substitute position for an outright short. in each of these markets nearby months almost invariably trade at a discount, which tends to widen in bull markets and narrow in bear markets. the reason for the tendency of near months in gold and silver to move to a wider discount in a bull market derives from the large worldwide stock levels of these metals. generally speaking, price fluctuations in gold and silver do not reflect near-term tightness or surplus, but rather the market’s changing perception of their value. in a bull market, the premium of the back months will increase because higher prices imply increased carrying charges (i.e., interest costs will increase as the total value of the contract increases). Because the forward months implicitly contain the cost of carrying the commodity, their premium will tend to widen when these costs increase. Although the preced- ing represents the usual pattern, there have been a few isolated exceptions due to technical factors. Commodities Bearing Little or No relationship to the General rule Commodities in which there is little correlation between general price direction and spread differ- ences usually fall into the category of nonstorable commodities (cattle and live hogs). W e will exam- ine the case of live cattle to illustrate why this there is no consistent correlation between price and spread direction in nonstorable markets. Live cattle, by definition, is a completely nonstorable commodity. When feedlot cattle reach mar- ket weight, they must be marketed; unlike most other commodities, they obviously cannot be placed in storage to await better prices. ( to be perfectly accurate, cattle feeders have a small measure of flexibility, in that they can market an animal before it reaches optimum weight or hold it for a while after. However, economic considerations will place strong limits on the extent of such marketing ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:463 SCORE: 20.00 ================================================================================ 445 tHe COnCepts And MeCHAniCs OF spreAd trAding shifts.) As a consequence of the intrinsic nature of this commodity, different months in live cattle are, in a sense, different commodities. June live cattle is a very different commodity from december live cattle. the price of each will be dependent on the market’s perception of the supply-demand picture that it expects to prevail at each given time period. it is not unusual for a key cattle on feed report to carry bullish implications for near months and bearish connotations for distant months, or vice versa. in such a case, the futures market can often react by moving in opposite directions for the near and distant contracts. the key point is that in a bullish (bearish) situation, the market will sometimes view the near-term supply/demand balance as being more bullish (bearish) and sometimes it will view the distant situation as being more bullish (bearish). A similar behavioral pattern prevails in hogs. thus, the general rule would not apply in these types of markets. in these markets, rather than being concerned about the overall price direction, the spread trader is primarily concerned with how he thinks the market will perceive the fundamental situation in dif- ferent time periods. For example, at a given point in time, June cattle and december cattle may be trading at approximately equal levels. if the trader believes that marketings will become heavy in the months preceding the June expiration, placing pressure on that contract, and further believes the market psychology will view the situation as temporary, expecting prices to improve toward year- end, he would initiate a long december/short June cattle spread. note that if he is correct in the development of near-term pressure but the market expects even more pronounced weakness as time goes on, the trade will not work even if his expectations for improved prices toward year-end also prove accurate. One must always remember that a spread’s life span is limited to the expiration of the nearer month, and substantiation of the spread idea after that point will be of no benefit to the trader. thus, the trader is critically concerned, not only with the fundamentals themselves, but also with the market’s perception of the fundamentals, which may or may not be the same. ■ Spread Rather Than Outright—An Example Frequently, the volatility of a given market may be so extreme that even a one-contract position may represent excessive risk for some traders. in such instances, spreads offer the trader an alternative approach to the market. For example, in early 2014, coffee futures surged dramatically, gaining more than 75 percent from late January to early March, with average daily price volatility more than tri- pling during that period. prices swung wildly for the next several months—pushing to a higher high in April, giving back more than half of the rally in the sell-off to the July low , and then rallying to yet another new high in October (see Figure 30.1). At that juncture, assume a low-risk trader believed that prevailing nearest futures prices near $2.22 in mid-October 2014 were unsustainable, but based on the market’s volatility (which was still around three times what it had been early in the year) and his money management rules felt he could not assume the risk of an outright position. such a trader could instead have entered a bear spread (e.g., short July 2015 coffee/long december 2015 coffee) and profited handsomely from the subsequent price slide. Figure 30.1 illustrates the close correspondence between the spread and the market. the fact that an outright position would have garnered a much larger profit is an irrelevant consideration, since the trader’s risk limitations would have prevented him from participating in the bear move altogether had his market view been confined to outright trades. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:464 SCORE: 17.00 ================================================================================ 446A COMpLete guide tO tHe Futures MArKet ■ The Limited-Risk Spread the limited-risk spread is a type of intracommodity spread involving the buying of a near month (relatively speaking) and the selling of a more distant month in a storable commodity in which the process of taking delivery, storing, and redelivering at a later date does not require reinspection or involve major transportation or storage complications. this defi nition would exclude such commodi- ties as live cattle, which by defi nition are nonstorable, and sugar, which involves major complications in taking delivery and storing. Commodities that fall into the limited-risk category include corn, wheat, oats, soybeans, soybean oil, copper, cotton, orange juice, cocoa, and lumber. 2 in a commodity fulfi lling the above specifi cations, the maximum premium that a more distant month can command over a nearby contract is roughly equal to the cost of taking delivery, holding the commodity for the length of time between the two expirations, and then redelivering. the cost for this entire operation is referred to as full carry. the term limited risk will be used only when the nearby month is at a discount. For example, assuming full carry in the October/december cotton FIGURE  30.1 July and december 2015 Coff ee Futures vs. July/december 2015 Coff ee spread Chart created using tradestation. ©tradestation t echnologies, inc. All rights reserved. 2 Although precious metals can easily be received in delivery, stored, and redelivered, they are not listed here because spreads in precious metals are almost entirely determined by carrying charges. thus, the only motivation for implementing an intramarket precious metals spread is an expectation for a change in carrying charges. in contrast, the purpose of a limited-risk spread is to profi t from an expected narrowing of the spread relative to the level implied by carrying charges (which are assumed to remain constant). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:465 SCORE: 29.00 ================================================================================ 447 tHe COnCepts And MeCHAniCs OF spreAd trAding spread is equal to 200 points, a long October/short december spread initiated at October 100 points under might be termed a limited-risk spread. However, the same long October/short december cotton spread would not be termed limited risk if, for example, October were at a 300-point pre- mium. nevertheless, it should be noted that even in this latter case, the maximum risk would still be defined—namely, 500 points—and in this respect the spread would still differ from spreads involving the selling of the nearby contract, or spreads in markets that do not fulfill the limited-risk specifica- tions detailed above. the best way to understand why it is unlikely for the premium of a distant month to exceed car- rying costs is to assume the existence of a situation where this is indeed the case. in such an instance, a trader who bought a nearby month and sold a more distant month would have an opportunity for speculative gain and, at worst, would have the option of taking delivery, storing, and redelivering at a likely profit (since we assumed a situation in which the premium of the distant month exceeded carrying charges). sounds too good to be true? Of course, and for this reason differences beyond full carry are quite rare unless there are technical problems in the delivery process. in fact, it is usually unlikely for a spread difference to even approach full carry since, as it does, the opportunity exists for a speculative trade that has very limited risk but, theoretically, no limit on upside potential. in other words, as spreads approach full carry, some traders will initiate long nearby/short forward spreads with the idea that there is always the possibility of gain, but, at worst, the loss will be minimal. For this reason, spreads will usually never reach full carry. At a surface glance, limited-risk spreads seem to be highly attractive trades, and indeed they often are. However, it should be emphasized that just because a spread is relatively near full carry does not neces- sarily mean it is an attractive trade. V ery often, such spreads will move still closer to full carry, resulting in a loss, or trade sluggishly in a narrow range, tying up capital that could be used elsewhere. How- ever, if the trader has reason to believe the nearby month should gain on the distant, the fact that the spread has a limited risk (the difference between full carry and the current spread differential) makes the trade particularly attractive. the components of carrying costs include interest, storage, insurance, and commission. W e will not digress into the area of calculating carrying charges. ( such information can be obtained either through the exchanges themselves or through commodity brokers or analysts specializing in the given commodity.) However, we would emphasize that the various components of carrying charges are variable rather than fixed, and consequently carrying charges can fluctuate quite widely over time. interest costs are usually the main component of carrying charges and are dependent on interest rates and price levels, both of which are sometimes highly volatile. it is critical to keep changes in carrying costs in mind when making historical comparisons. Can a trader ever lose more money in a limited-risk spread than the amount implied by the differ- ence between full carry and the spread differential at which the trade was initiated? the answer is that although such an occurrence is unlikely, it is possible. For one thing, as we indicated above, carrying charges are variable, and it is possible for the theoretical maximum loss of a spread trade to increase as a result of fluctuations in carrying costs. For example, a trader might enter a long October/short december cotton spread at 100 points October under, at a time when full carry approximates 200 points—implying a maximum risk of 100 points. However, in ensuing months, it is possible higher ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:466 SCORE: 37.00 ================================================================================ 448 A Complete Guide to the Futures mArket prices and rising interest rates could cause full carry to move beyond 200 points, increasing the trad- er’s risk correspondingly. in such an instance, it is theoretically possible for the given spread to move significantly beyond the point the trader considered the maximum risk point. Although such an event can occur, it should be emphasized that it is rather unusual, since in a limited-risk spread increased carrying costs due to sharply higher price levels will usually imply larger gains for the nearby months. As for interest rates, changes substantial enough to influence marked changes in carrying costs will usually take time to develop. Another example of a limited-risk spread that might contain hidden risk is the case in which the government imposes price ceilings on nearby contracts but not on the more distant contracts. Although highly unusual, this situation has happened before and represents a possible risk that the spread trader should consider in the unlikely event that the prevailing political environment is condu- cive to the enactment of price controls. Also, for short intervals of time, spread differences may well exceed full carry due to the absence of price limits on the nearby contract. For a number of commodities, price limits on the nearby contract are removed at some point before its expiration (e.g., first notice day, first trading day of the expiring month, etc.). Consequently, in a sharply declining market, the nearby month can move to a discount exceeding full carry as the forward month is contained by price limits. Although this situation will usually correct itself within a few days, in the interim, it can generate a substantial mar- gin call for the spread trader. it is important that spread traders holding their positions beyond the removal of price limits on the nearby contract are sufficiently capitalized to easily handle such possible temporary spread aberrations. As a final word, it should be emphasized that although there is a theoretical limit on the premium that a distant month can command over a nearby contract in carrying-charge markets, there is no similar limit on the premium that a nearby position can command. nearby premiums are usually indicative of a tight current supply situation, and there is no way of determining an upper limit to the premium the market will place on more immediately available supplies. ■ The Spread Trade—Analysis and Approach Step 1: Straightforward historical Comparison A logical starting point is a survey of the price action of the given spread during recent years. Histori- cal spread charts, if available, are ideal for this purpose. if charts (or historical price data that can be downloaded into a spreadsheet) are unavailable, the trader should, if possible, scan historical price data, checking the difference of the given spread on a biweekly or monthly basis for at least the past 5 to 10 years. this can prove to be a time-consuming endeavor, but a spread trade initiated without any concept of historical patterns is, in a sense, a shot in the dark. Although spreads can deviate widely from historical patterns, it is still important to know the normal range of a spread, as well as its “average” level. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:467 SCORE: 28.00 ================================================================================ 449 tHe COnCepts And MeCHAniCs OF spreAd trAding Step 2: Isolation of Similar Periods As a rule, spreads will tend to act similarly in similar situations. thus, the next step would be a refine- ment of step 1 by means of isolating roughly similar periods. For example, in a high-priced year, we might be interested in considering the spread action only in other past bull seasons, or we can cut the line still sharper and consider only bull seasons that were demand oriented or only those that were supply oriented. An examination of the spread’s behavior during different fundamental conditions in past years will usually reveal the relative comparative importance of similar and dissimilar seasons. Step 3: analysis of Spread Seasonality this step is a further refinement of step 1. sometimes a spread will tend to display a distinct seasonal pattern. For example, a given spread may tend to widen or narrow during a specific period. Knowledge of such a seasonality can be critically important in deciding whether or not to initiate a given spread. For example, if in nine of the past 10 seasons the near month of a given spread lost ground to the distant month during the March–June period, one should think twice about initiating a bull spread in March. Step 4: analysis and Implications of relevant Fundamentals this step would require the formulation of a concept of market direction (in commodities where applicable), or equivalent appropriate analysis in those commodities where it is not. this approach is fully detailed in the sections entitled “the general rule” and “the general rule—Applicability and nonapplicability.” Step 5: Chart analysis A key step before initiating a spread trade should be the examination of a current chart of the spread (or the use of some other technical input). As in outright positions, charts are an invaluable informa- tional tool and a critical aid to timing. ■ Pitfalls and Points of Caution ■ do not automatically assume a spread is necessarily a low-risk trade. in some instances, a spread may even involve greater risk than an outright position. specifically, in the case of intercommodity spreads, intercrop spreads, and spreads involving nonstorable commodities, the two legs of the spread can sometimes move in opposite directions. ■ Be careful not to overtrade a spread because of its lower risks or margin. A 5- to 10-contract spread position gone astray can often prove more costly than a bad one-contract outright trade. Overtrading is a very common error in spread trading. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:468 SCORE: 25.00 ================================================================================ 450 A Complete Guide to the Futures mArket ■ As a general rule, traders should avoid trading spreads in markets in which they are unfamiliar with the fundamentals. ■ Check the open interest of the months involved to ensure adequate liquidity, especially in spreads involving distant back months. A lack of liquidity can significantly increase the loss when getting out of a spread that has gone awry. At times, of course, a given spread may be sufficiently attrac- tive despite its less-than-desirable liquidity. nevertheless, even in such a case, it is important that traders be aware of the extra risk involved. ■ place a spread order on a spread basis rather than as two separate outright orders. some traders place their spread orders one leg at a time in the hopes of initiating their position at a better price than the prevailing market level. such an approach is inadvisable not only because it will often backfire, but also because it will increase commission costs. ■ When the two months of the spread are very close in price, extra care should be taken to specify clearly which month is the premium month in the order. ■ do not assume that current price quotations accurately reflect actual spread differences. time lags in the buying and selling of different contracts, as well as a momentary concentration of orders in a given contract month, can often result in outright price quotations implying totally unrepresen- tative spread values. ■ do not liquidate spreads one leg at a time. Failing to liquidate the entire spread position at one time is another common and costly error, which has caused many a good spread trade to end in a loss. ■ Avoid spreads involving soon-to-expire contracts. expiring contracts, aside from usually being free of any price limits, are subject to extremely wide and erratic price moves dependent on technical delivery conditions. ■ do not assume the applicability of prior seasons’ carrying charges before initiating a limited-risk spread. Wide price swings and sharply fluctuating interest costs can radically alter carrying costs. ■ try to keep informed of any changes in contract specifications, since such changes can substan- tially alter the behavior of a spread. ■ properly implemented intercommodity and intermarket spreads often require an unequal num- ber of contracts in each market. the methodology for determining the proper contract ratio be- tween different markets is discussed in the next chapter. ■ do not use spreads to protect an outright position that has gone sour—that is, do not initiate an opposite direction position in another contract as an alternative to liquidating a losing position. in most cases such a move amounts to little more than fooling oneself and often can exacerbate the loss. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:469 SCORE: 26.00 ================================================================================ 451 tHe COnCepts And MeCHAniCs OF spreAd trAding ■ Because it is especially easy to procrastinate in liquidating a losing spread position, the spread trader needs to be particularly vigilant in adhering to risk management principals. it is advisable that the spread trader determine a mental stop point (usually on the basis of closing values) prior to entering a spread and rigidly stick to liquidating the spread position if this mental stop point is reached. ■ Avoid excessively low-risk spreads because transaction costs (slippage as well as commission) will represent a significant percentage of the profit potential, reducing the odds of a net winning out- come. in short, the odds are stacked against the very-low-risk spread trader. ■ As a corollary to the prior item, a trader should choose the most widely spaced intramarket spread consistent with the desired risk level. generally speaking, the wider the time duration in an intramarket spread, the greater the volatility of the spread. this observation is as true for mar- kets conforming to the general rule as for markets unrelated or inversely related to the general rule. traders implementing a greater-than-one-unit intramarket spread position should be sure to choose the widest liquid spread consistent with the trading strategy. For example, it usually would make little sense to implement a two-unit March/May corn spread, since a one-unit March/July corn spread would offer a very similar potential/risk trade at half the transaction cost. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:471 SCORE: 11.00 ================================================================================ 453 . . . many more people see than weigh. —Philip Dormar Stanhope, Earl of Chesterfield B y definition, the intention of the spread trader is to implement a position that will reflect changes in the price difference between contracts rather than changes in outright price levels. T o achieve such a trade, the two legs of a spread must be equally weighted. As an obvious example, long 2 December corn/short 1 March corn is a spread in name only. Such a position would be far more dependent on fluctuations in the price level of corn than on changes in the price difference between December and March. The meaning of equally weighted, however, is by no means obvious. Many traders simply assume that a balanced spread position implies an equal number of contracts long and short. Such an assump- tion is usually valid for most intramarket spreads (although an exception will be discussed later in this chapter). However, for many intermarket and intercommodity 1 spreads, the automatic presumption of an equal number of contracts long and short can lead to severe distortions. Consider the example of a trader who anticipates that demand for lower quality Robusta coffee beans (London contract) will decline relative to higher quality Arabica beans (New Y ork contract) and Intercommodity Spreads: Determining Contract Ratios Chapter 31 1 The distinction between intermarket and intercommodity spreads was defined in Chapter 30. An intermarket spread involves buying and selling the same commodity at two different exchanges (e.g., New Y ork vs. London cocoa); the intercommodity spread involves buying and selling two different but related markets (e.g., wheat vs. corn, cattle vs. hogs). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:472 SCORE: 30.00 ================================================================================ 454 A Complete Guide to the Futures mArket attempts to capitalize on this forecast by initiating a 5-contract long New Y ork coffee/short London coffee spread. Assume the projection is correct, and London coffee prices decline from $0.80/lb to $0.65/lb, while New Y ork coffee prices simultaneously decline from $1.41/lb to $1.31/lb. At sur- face glance, it might appear this trade is successful, since the trader is short London coffee (which has declined by $0.15/lb) and long New Y ork coffee (which has lost only $0.10/lb). However, the trade actually loses money (even excluding commissions). The explanation lies in the fact that the contract sizes for the New Y ork and London coffee contracts are different: The size of the New Y ork coffee contract is 37,500 lb, while the size of the London coffee contract is 10 metric tonnes, or 22,043 lb. (Note: In practice, the London coffee contract is quoted in dollars/tonne; the calculations in this sec- tion reflect a conversion into $/pound for easier comparison with the New Y ork coffee contract.) Because of this disparity, an equal contract position really implies a larger commitment in New Y ork coffee. Consequently, such a spread position is biased toward gaining in bull coffee markets (assuming the long position is in New Y ork coffee) and losing in bear markets. The long New Y ork/short London spread position in our example actually loses $2,218 plus commissions, despite the larger decline in London coffee prices: Profit/los so f co ntractso f units per c ontrac tg ain/loss=× ×## per un it Profit/loss in long New York coffee positio n5 37 5000=× ×−,( $. .) $,10/lb1 8 750=− Profit/loss in short London coffee position = 52 20 43×× +,( $001 5/lb 16 532.) $,=+ Net profit/l oss in sprea d2 218=− $, The difference in contract size between the two markets could have been offset by adjusting the contract ratio of the spread to equalize the long and short positions in terms of units (lb). The gen- eral procedure would be to place U1/U2 contracts of the smaller-unit market (i.e., London coffee) against each contract of the larger-unit contract (i.e., New Y ork coffee). (U1 and U2 represent the number of units per contract in the respective markets—U1 = 37,500 lb and U2 = 22,043 lb.) Thus, in the New Y ork coffee/London coffee spread, each New Y ork coffee contract would be offset by 1.7 (37,500/22,043) London coffee contracts, implying a minimum equal-unit spread of five London coffee versus three New Y ork coffee (rounding down the theoretical 5.1-contract London coffee posi- tion to 5 contracts.) This unit-equalized spread would have been profitable in the above example: Profit/los so f co ntractso f units per c ontrac tg ain/loss=× ×## per un it Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,10/lb1 1 250=− Profit/loss in short London coffee position 52 20 43 0=× ×+,( $. 115/lb +1 6 532)$ ,= Net profit/l oss in sprea d+ 5 282= $, The unit-size adjustment, however, is not the end of our story. It can be argued that even the equalized-unit New Y ork coffee/London coffee spread is still unbalanced, since there is another signifi- cant difference between the two markets: London coffee prices are lower than New Y ork coffee prices. This observation raises the question of whether it is more important to neutralize the spread against equal price moves or equal-percentage price moves. The rationale for the latter approach is that, all else being equal, the magnitude of price changes is likely to be greater in the higher-priced market. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:473 SCORE: 34.00 ================================================================================ 455 IntercommodIty SpreadS: determInIng contract ratIoS The fact that percentage price change is a more meaningful measure than absolute price change is perhaps best illustrated by considering the extreme example of the gold/silver spread. The equal-unit approach, which neutralizes the spread against equal-dollar price changes in both markets, would imply the rather ludicrous spread position of 50 gold contracts versus 1 silver contract. (The contract size of silver is 5,000 oz; the contract size of gold is 100 oz.) Obviously, such a position would be almost entirely dependent upon changes in the price of gold rather than any movement in the gold/ silver spread. The disparity is due to the fact that since gold is far higher priced than silver (by a ratio of 32-101:1 based on the past 30-year range), its price swings will also be far greater. For example, if gold is trading at $1,400/oz and silver at $20/oz, a $2 increase in silver prices is likely to be accom- panied by far more than a $2 increase in gold prices. Clearly, the relevant criterion in the gold/silver spread is that the position should be indifferent to equal percentage price changes rather than equal absolute price changes. Although less obvious, the same principle would also appear preferable, even for intercommodity or intermarket spreads between more closely priced markets (e.g., New Y ork coffee/London coffee). Thus we adopt the definition that a balanced spread is a spread that is indifferent to equal percentage price changes in both markets. It can be demonstrated this condition will be fulfilled if the spread is initiated so the dollar values of the long and short positions are equal. 2 An equal-dollar-value spread 2 If the spread is implemented so that dollar values are equal, then: NU PN UPtt11 10 22 20,,== = where N1 = number of contracts in market 1 N2 = number of contracts in market 2 U1 = number of units per contract in market 1 U2 = number of units per contract in market 2 P1,t=0 = price of market 1 at spread initiation P2,t=0 = price of market 2 at spread initiation An equal-percentage price change implies that both prices change by the same factor k. Thus, Pk PP kPtt tt11 10 21 20,, ,,== ==== and where Pl,t = 1 = price of market 1 after equal-percentage price move P2,t = 1 = price of market 2 after equal-percentage price move And the equity changes (in absolute terms) are: Equity change in market 1 positio n =− ===NU kP PN UPtt11 10 10 11 1|| ,, ,t t tt k NU kP P = == − =− 0 22 20 20 1 | | ,, | Equity change in market 2 positio n| || ,=− =NU Pkt22 20 1 | Since, by definition, an equal-dollar-value spread at initiation implies that N1U1P1,t = 0 = N2U2P2,t = 0, the equity changes in the positions are equal. It should be noted that the equal-dollar-value spread only assures that equal-percentage price changes will not affect the spread if the percentage price changes are measured relative to the initiation price levels. However, equal-percentage price changes from subsequent price levels will normally result in different absolute dollar changes in the long and short positions (since the position values are not necessarily equal at any post-initiation points of reference). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:474 SCORE: 14.00 ================================================================================ 456 A Complete Guide to the Futures mArket can be achieved by using a contract ratio that is inversely proportional to the contract value (CV) ratio. This can be expressed as follows (see footnote 2 for symbol definitions): N N CV CV UP UP t t 2 1 1 2 11 0 22 0 == = = , , or, NN CV CV21 1 2 =       For example, if New Y ork coffee is trading at $1.41/lb and London coffee at $.80/lb, the equal-dollar- value spread would indicate a contract ratio of 1 New Y ork coffee/3 London coffee: NN CV CV N UP UP t t 21 1 2 1 11 0 22 0 =       =       = = , , If New York coffee contractN1 1= , N2 =× ×=37 5001 41/22 0430 80 3 London contracts,$ ., $. Thus, in an equal-dollar-value spread position, 3 New Y ork coffee contracts would be balanced by 9 (not 5) London contracts. It may help clarify matters to compare the just-defined equal-dollar-value approach to the equal-unit approach for the case of the New Y ork coffee/London coffee spread. Although the equal- unit spread is indifferent to equal absolute price changes, it will be affected by equal-percentage price changes (unless, of course, the price levels in both markets are equal, in which case the two approaches are equivalent). For example, given initiation price levels of New Y ork coffee = $1.41/lb and London coffee = $.80/lb, consider the effect of a 25 percent price decline on a long 3 New Y ork/ short 5 London coffee (equal unit) spread: Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,3525 39 656=− Profit/loss in short London coffee position 52 20 43 0=× ×−,( $. 220 +2 20 43)$ ,= Profit/loss in sprea d1 7 613=− $, The equal-dollar-value spread, however, would be approximately unchanged: Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,3525 39 656=− Profit/loss in short London coffee position 92 20 43 0=× ×+,( $. 220 +3 96 77)$ ,= Profit/loss in sprea d+ 21= $ Returning to our original example, if the trader anticipating price weakness in London coffee rela- tive to New Y ork coffee had used the equal-dollar-value approach (assuming a 3-contract position for New Y ork coffee), the results would have been as follows: Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,10 11 250=− Profit/loss in short London coffee position 92 20 43 +0=× ×,( $. 115 29 758) $,=+ Profit/loss in sprea d+ 18 508= $, ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:475 SCORE: 20.00 ================================================================================ 457 INTERCOMMODITY SPREADS: DETERMINING CONTRACT RATIOS Thus, while the naive placement of an equal contract spread actually results in a $2,218 loss despite the validity of the trade concept, the more appropriate equal-dollar-value approach results in a $18,508 gain. This example emphasizes the critical importance of determining appropriate contract ratios in intercommodity and intermarket spreads. An essential point to note is that if intercommodity and intermarket spreads are traded using an equal-dollar-value approach—as they should be—the price diff erence between the markets is no longer the relevant subject of analysis. Rather, such an approach is most closely related to the price ratio between the two markets. This fact means that chart analysis and the defi nition of historical ranges should be based on the price ratio, not the price diff erence. Figures 31.1 , 31.2 , and 31.3 illus- trate this point. Figure 31.1 depicts the September 2013 wheat/September 2013 corn spread in the standard form as a price diff erence. Figure 31.2 illustrates the price ratio of September 2013 wheat to September 2013 corn during the same period. Finally, Figure 31.3 plots the equity fl uctuations of the approximate equal-dollar-value spread: 3 wheat versus 4 corn. Note how much more closely the equal dollar position is paralleled by the ratio than by the price diff erence. 3 3 The equal-dollar-value spread would be precisely related to the price ratio only if the contract ratios in the spread were continuously adjusted to refl ect changes in the price ratio. (An analogous complication does not exist in equal-unit spreads, since the contract weightings are determined independent of price levels.) However, unless price levels change drastically during the holding period of the spread, the absence of theoretical readjust- ments in contract ratios will make little practical diff erence. In other words, equity fl uctuations in the equal- dollar-value spread will normally closely track the movements of the price ratio. FIGURE /uni00A031.1 September 2013 Wheat Minus September 2013 Corn Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:477 SCORE: 26.00 ================================================================================ 459 INTERCOMMODITY SPREADS: DETERMINING CONTRACT RATIOS In the preceding example, because wheat is a larger contract than corn (in dollar-value terms), a long 1 wheat/short 1 corn spread would be biased in the direction of the general price trend of grains. For example, during November 2012–August 2013, a period of declining grain prices (see Figure 31.4 ), the equal contract spread seems to suggest that wheat prices weakened signifi cantly relative to corn prices (see Figure 31.1 ). In reality, as indicated by Figures 31.2 and 31.3 , the wheat/corn relationship during this period was best characterized by a trading range. T o illustrate the trading implications of the spread ratio, consider a long wheat/short corn spread initiated at the late-November 2012 relative high and liquidated at the August 2013 peak. This trade would have resulted in a near breakeven trade if the spread were implemented on an equal-dollar-value basis (see Figure 31.2 or 31.3 ), but a signifi cant loss if an equal contract criterion were used instead (see Figure 31.1 ). It should now be clear why the standard assumption of an equal contract position is usually valid for intramarket spreads. In these spreads, contract sizes are identical, while price levels are normally close. Thus, the equal-dollar-value approach suggests a contract ratio very close to 1:1. If, however, two contracts in an intramarket spread are trading at signifi cantly diff erent price levels, the argument for using the equal-dollar-value approach (as opposed to equal contract positions) would be analogous to the intercommodity and intermarket case. Wide price diff erences between contracts in an intramarket spread can occur in extreme bull markets that place a large premium on FIGURE /uni00A031.4 September 2013 Wheat and September 2013 Corn ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:479 SCORE: 19.00 ================================================================================ 461 The stock market is but a mirror which . . . provides an image of the underlying or fundamental economic situation. —John Kenneth Galbraith ■ Intramarket Stock Index Spreads Spreads in carrying charge markets, such as gold, provide a good starting point for developing a theo- retical behavioral model for spreads in stock index futures. As is the case for gold, there can never be any near-term shortage in stock indexes, which means spreads will be entirely determined by carrying charges. As was explained in Chapter 30, gold spreads are largely determined by short-term interest rates. For example, since a trader could accept delivery of gold on an expiring contract and redeliver it against a subsequent contract, the price spread between the two months would primarily reflect financing costs and, hence, short-term rates. If the premium of the forward contract were sig- nificantly above the level implied by short-term rates, the arbitrageur could lock in a risk-free profit by performing a cash-and-carry operation. And if the premium were significantly lower, an arbitra- geur could lock in a risk-free profit by implementing a short nearby/long forward spread, borrowing gold to deliver against the nearby contract and accepting delivery at the expiration of the forward contract. These arbitrage forces will tend to keep the intramarket spreads within a reasonably well- defined band for any given combination of short-term interest rates and gold prices. The same arguments could be duplicated substituting a stock index for gold. In a broad sense this is true, but there is one critical difference between stock index spreads and gold spreads: Stocks pay Spread Trading in Stock Index Futures Chapter 32 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:480 SCORE: 29.00 ================================================================================ 462 A Complete Guide to the Futures mArket dividends. Thus, the interest rate cost of holding a stock position is offset (partially, or more than totally) by dividend income. The presence of dividends is easily incorporated into the framework of calculating a theoretical spread level. The spread would be in equilibrium if, based on current prices, interest rates, and dividends, there would be no difference between holding the actual equities in the index for the interim between the two spread months versus buying the forward index futures contract. Holding equities would incur an interest rate cost that does not exist in holding futures, but would also accrue the dividend yield the holder of futures does not receive. The theoretical spread level (P 2 − P1) at the expiration of P 1 at which these two alternative means of holding a long equity position—equity and stock index futures—would imply an equivalent outcome can be expressed symbolically as follows: PP P t id21 1 360−=     −() where P1 = price of nearby (expiring) futures contract P2 = price of forward futures contract t = number of days between expiration of nearby contract and expiration of forward contract i = short-term interest rate level at time of P1 expiration d = annualized dividend yield (%) As is evident from this equation, if short-term interest rates exceed dividend yields, forward futures will trade at a premium to nearby contracts. Conversely, if the dividend yield exceeds short- term interest rates, forward futures will trade at a discount. Since the dividend yield is not subject to sharp changes in the short run, for any given index (price) level, intramarket stock index spreads would primarily reflect expected future short-term rates (similar to gold spreads). If short-term interest rates exhibit low volatility, as characterized by the near-zero interest rate environment that prevailed in the years following the 2008 financial crisis, stock index spreads will tend to trade in relatively narrow range—a consequence of both major drivers of stock index spreads (interest rates and dividend yield) being stable. ■ Intermarket Stock Index Spreads As is the case with intercommodity and intermarket spreads trading at disparate price levels, stock index spreads should be traded as ratios rather than differences—an approach that will make the spread position indifferent to equal percentage price changes in both markets (indexes). As a reminder, to trade a ratio, the trader should implement each leg of the spread in approximately equal contract value positions, which, as was shown in Chapter 31, can be achieved by using a contract ratio that is inversely proportional to the contract value ratio. For example, if the E-mini Nasdaq 100 futures contract, which has a contract value of 20 times the index, is trading at 4,300 (a contract value of $86,000), and the Russell 2000 Mini futures contract, ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:481 SCORE: 14.00 ================================================================================ 463 SPREAd TRAdING IN SToCK INdEx FuTuRES which has a contract value of 100 times the index, is trading at 1,150 (a contract value of $115,000), the contract value ratio (CVR) of Nasdaq to Russell futures would be equal to: CVR2 04 ,300 /1 00 1,150 07 478=× ×=() () . Therefore, the contract ratio would be equal to the inverse of the contract value ratio: 1/0.7478 = 1.337. Thus, for example, a spread with 3 long (short) Russell contracts would be bal- anced by 4 Nasdaq short (long) contracts: 3 × 1.337 = 4.01. Because some stock indexes are inherently more volatile than other indexes—for example, smaller- cap indexes tend to be more volatile than larger-cap indexes—some traders may wish to make an additional adjustment to the contract ratio to neutralize volatility differences. If this were done, the contract ratio defined by the inverse of the contract value ratio would be further adjusted by multiply- ing by the inverse of some volatility measure ratio. one good candidate for such a volatility measure is the average true range (ATR), which was defined in Chapter 17. As an illustration, if in the aforemen- tioned example of the Nasdaq 100/Russell 2000 ratio, the prevailing ATR of the Nasdaq 100 is 0.8 times the ATR of the Russell 2000, then the Nasdaq/Russell 2000 contract ratio of 1.337 would be further adjusted by multiplying by the inverse of the ATR ratio (1 / 0.8 = 1.25), yielding a contract ratio of 1.671 instead of 1.337. If this additional adjustment is made, then a spread with 3 long (short) Russell contracts would be balanced by 5 short (long) Nasdaq contracts: 3 × 1.671= 5.01. It is up traders to decide whether they wish to further adjust the contract ratio for volatility. For the remainder of this chapter, we assume the more straightforward case of contract ratios being adjusted only for contract value differences (i.e., without any additional adjustment for volatility differences). The four most actively traded stock index futures contracts are the E-mini S&P 500, E-mini Nasdaq 100, E-mini dow , and the Russell 2000 Mini. There are six possible spread pairs for these four markets: ■ E-mini S&P 500 / E-mini dow ■ E-mini S&P 500 / E-mini Nasdaq 100 ■ E-mini S&P 500 / Russell 2000 Mini ■ E-mini Nasdaq 100 / E-mini dow ■ E-mini Nasdaq 100 / Russell 2000 Mini ■ E-mini dow / Russell 2000 Mini Traders who believe a certain group of stocks will perform better or worse than another group can express this view through stock index spreads. For example, a trader who expected large-cap stocks to outperform small-cap stocks could initiate long E-mini S&P 500/short Russell 2000 Mini spreads or long E-mini dow/short Russell 2000 Mini spreads. A trader expecting relative outperfor- mance by small-cap spreads would place the reverse spreads. As another example, a trader expecting relative outperformance by technology stocks might consider spreads that are long the tech-heavy Nasdaq 100 index and short another index, such as long E-mini Nasdaq 100/short E-mini S&P 500 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:482 SCORE: 22.00 ================================================================================ 464A CoMPLETE GuIdE To THE FuTuRES MARKET spreads. Again, to trade these types of spreads as price ratios, the spreads would be implemented so the contract values of each side are approximately equal, a condition that will be achieved when the contract ratio between the indexes is equal to the inverse of the contract value ratio. Figures 32.1 through 32.6 illustrate the contract value ratios for these six spread pairs during 2002–2015. In some cases, such as the S&P 500/dow spread, the contract value ratio does not vary much. As can be seen in Figure 32.1 , the contract value ratio for this pair ranged by a factor of only about 1.2 from low to high over the entire period. For other index pairs, however, the contract value ratio ranged widely. For example, Figure 32.4 shows that during the same period, the high Nasdaq/ dow contract value ratio was nearly 2.5 times the low ratio. Since the contract ratio required to keep the trade neutral to equal percentage price changes in both markets is equal to the inverse of the prevailing contract value ratio, the appropriate contract ratio for these spreads can range widely over time. For example, for the aforementioned Nasdaq 100/dow ratio, a three-contract dow position would have been balanced by a seven-contract Nasdaq position when the contract value ratio was at its low versus only a three-contract position (rounding up) when the ratio was at its high. Figures 32.7 through 32.12 illustrate the price ratios for the six stock index pairs during the same period, along with an overlay of one of the indexes to facilitate visually checking of the relationships between the index price ratio and the overall stock market direction. Note that the price ratios in Figures 32.7 through 32.12 are identical in pattern to the contract value ratios in Figures 32.1 through 32.6 , which is a consequence of the contract value ratio being equal to the price ratio times a constant—the constant being equal to the ratio of the multipliers for the indexes. FIGURE  32.1 Contract Value Ratio: S&P 500/dow E-Mini Futures ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:489 SCORE: 14.00 ================================================================================ 471 Spread Trading in Currency Futures Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency. The process engages all the hidden forces of economic law on the side of destruction, and does it in a manner which not one man in a million is able to diagnose. —John Maynard Keynes ■ Intercurrency Spreads Conceptually, intercurrency spreads are identical to outright currency trades. After all, a net long or short currency futures position is also a spread in that it implies an opposite position in the dollar. For example, a net long Japanese yen (JY) position means that one is long the JY versus the U.S. dollar (USD). If the JY strengthens against the USD, the long JY position will gain. If the JY strengthens against the Swiss franc (SF) and euro but remains unchanged against the USD, the long JY position will also remain unchanged. In an intercurrency spread, the implied counterposing short in the USD is replaced by another currency. For example, in a long JY/short euro spread, the position will gain when the JY strengthens relative to the euro, but will be unaffected by fluctuations of the JY relative to the dollar. The long JY/short euro spread is merely the combination of a long JY/short USD and a long USD short euro position, in which the opposite USD positions offset each other. (T o be precise, the implied USD posi- tions will only be completely offset if the dollar values of the JY and euro positions are exactly equal.) There are two possible reasons for implementing an intercurrency spread: 1. The trader believes currency 1 will gain against the USD, while currency 2 will lose against the USD. In this case, a long currency 1/short currency 2 spread is best thought of as two separate outright trades. 2. The trader believes that one foreign currency will gain on another, but has no strong opinion regarding the movement of either currency against the USD. In this case, the intercurrency spread is analogous to an outright currency trade, with the implied short or long in the USD replaced by another currency. If, however, the two currencies are far more closely related to each other than to the USD, the connotation normally attributed to a spread might be at least partially appropriate. Chapter 33 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:490 SCORE: 25.00 ================================================================================ 472 A Complete Guide to the Futures mArket If an intercurrency spread is motivated by the second of these factors, the position should be balanced in terms of equal dollar values. (This may not always be possible for the small trader.) Otherwise, equity losses can occur, even if the exchange rate between the two currencies remains unchanged. For example, consider a long 4 December SF/short 4 December euro spread position imple- mented when the December SF = $1.000 and the December euro = $1.250. At the trade initiation, the exchange rate between the SF and euro is 1 euro = 1.25 SF. If the SF rises to $1.100 and the euro climbs to $1.375, the exchange rate between the SF and euro is unchanged: 1 euro = 1.25 SF. However, the spread position will have lost $12,500: Equity change numbe ro fc ontrac ts number of unitsp er contra ct ga=× × iin/loss peru nit Equity change in long SF 41 25 000 01 0= 50 000=× ×,$ .$ , Equity change in short euro 4 125 000 01 25 62 500=× ×− =−,$ .$ , Netp rofit/loss 12 500=− $, The reason the spread loses money even though the SF/euro exchange rate remains unchanged is that the original position was unweighted. At the initiation prices, the spread represented a long SF position of $500,000 but a short euro position of $625,000. Thus, the spread position was biased toward gaining if the dollar weakened against both currencies and losing if the dollar strengthened. If, however, the spread were balanced in terms of equal dollar values, the equity of the position would have been unchanged. For example, if the initial spread position were long 5 December SF/short 4 December euro (a position in which the dollar value of each side = $625,000), the aforementioned price shift would not have resulted in an equity change: Equity change in long SF 51 25 000 01 06 25 00=× ×=,$ .$ , Equity change in short euro 4 125 000 01 25 62 500=× ×− =−,( $. )$ , Netprofit/loss 0= The general formula for determining the equal-dollar-value spread ratio (number of contracts of currency 1 per contract of currency 2) is: Equal-dollar-spread rati o numbe ro f units per contra ct of currenc= yy2 priceo f currenc y2 numbe ro f units per contra ct of currenc y1 () () (() () priceo f currenc y1 For example, if currency 1, the British pound (BP) = $1.50, and currency 2, the euro = $1.20, and the BP futures contract consists of 62,500 units, while the euro futures contract consists of 125,000 units, the implied spread ratio would be: (, )($ .) (, )($ .) .125 0001 20 62 5001 50 16= ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:491 SCORE: 13.00 ================================================================================ 473 SPreAD TrADINg IN CUrreNCY FUTUreS Thus, the equal dollar value spread would consist of 1.6 BP contracts per euro contract, or 8 BP to 5 euro. equity fluctuations in an equal-dollar-value intercurrency spread position will mirror the price ratio (or exchange rate) between currencies. It should be emphasized that price ratios (as opposed to price spreads) are the only meaningful means of representing intercurrency spreads. For example, if the BP = $1.50 and SF = $1.00, an increase of $0.50 in both the currencies will leave the price spread between the BP and SF unchanged, even though it would drastically alter the relative values of the two currencies: a decline of the BP vis-à-vis the SF from 1.5 SF to 1.33 SF. ■ Intracurrency Spreads An intracurrency spread—the price difference between two futures contracts for the same currency— directly reflects the implied forward interest rate differential between dollar-denominated accounts and accounts denominated in the given currency. For example, the June/December euro spread indicates the expected relationship between six-month eurodollar and euro rates in June. 1 T o demonstrate the connection between intracurrency spreads and interest rate differentials, we compare the alternatives of investing in dollar-denominated versus euro-denominated accounts: S = spot exchange rate ($/euro) F = current forward exchange rate for date at end of investment period ($/euro) r 1 = simple rate of return on dollar-denominated account for investment period (nonannualized) r2 = simple rate of return on euro-denominated account for investment period (nonannualized) alternative a: Invest in Dollar-Denominated account alternative B: Invest in euro-Denominated account 1. Invest $1 in dollar-denominated account. 1. Convert $1 to euro at spot. 2. Funds at end of period = $1 (1 + r1) exchange rate is S, which yields 1/S euro. (By definition, if S equals dollars per euro, 1/S = euro per dollar.) 2. Invest 1/S euro in euro-denominated account at r 2. 3. Lock in forward exchange rate by selling the anticipated euro proceeds at end of investment period at current forward rate F.2 4. Funds at end of period = 1/S (1 + r2) euro. 5. Converted to dollars at rate F, funds at end of period = $F/S (1 + r2) (since F = dollars per euro). 1 The eurocurrency rates are interest rates on time deposits for funds outside the country of issue and hence free of government controls. For example, interest rates on dollar-denominated deposits in London are eurodollar rates, while rates on sterling-denominated deposits in Frankfurt are eurosterling rates. The quoted eurocurrency rates represent the rates on transactions between major international banks. 2 A short forward position can be established in one of two ways: (1) selling futures that are available for forward dates at three-month intervals; and (2) initiating a long spot/short forward position in the foreign exchange (FX) swap market and simultaneously selling spot. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:493 SCORE: 29.00 ================================================================================ 475 SPreAD TrADINg IN CUrreNCY FUTUreS Of course, the market forces just described would come into play well before the forward/spot ratio increased to 0.82/0.80 = 1.025. The intervention of arbitrageurs will assure the six-month forward/spot ratio would not rise significantly above 1 + r 1/1 + r2 = 1.0099. A similar argument could be used to demonstrate that arbitrage intervention would keep the forward/spot ratio from declining significantly below 1.0099. In short, arbitrage activity will assure that the forward/spot ratio will be approximately defined by the above equation. This relationship is commonly referred to as the interest rate parity theorem. Since currency futures must converge with spot exchange rates at expiration, the price spread between a forward futures contract and a nearby expiring contract must reflect the prevailing interest rate ratio (between the eurodollar rate and the given eurocurrency rate). 4 Hence, a spread between two forward futures contracts can be interpreted as reflecting the market’s expectation for the inter- est rate ratio at the time of the nearby contract expiration. Specifically, if P 1 = price of the more nearby futures expiring at t1 and P2 = price of the forward futures contract expiring at time t 2, then P2/P1 will equal the expected interest rate ratio (expressed as 1+r1/1+r2) for term rates of duration t2 − t1 at time t1. It should be stressed that the forward interest rate ratio implied by spreads in futures will usually differ from the prevailing interest rate ratio. If the market expects the eurodollar rate to be greater than the foreign eurocurrency rate, forward futures for that currency will trade at a premium to more nearby futures—the wider the expected differential, the wider the spread. Conversely, if the foreign eurocurrency rate is expected to be greater than the eurodollar rate, forward futures will trade at a discount to nearby futures. The above relationships suggest that intracurrency spreads can be used to trade expectations regarding future interest rate differentials between different currencies. If a trader expected eurodol- lar rates to gain (move up more or down less) on a foreign eurocurrency rate (relative to the expected interest rate ratio implied by the intracurrency futures spread), this expectation could be expressed as a long forward/short nearby spread in that currency. Conversely, if the trader expected the foreign eurocurrency rate to gain on the eurodollar rate, the implied trade would be a long nearby/short forward intracurrency spread. As a technical point, a 1:1 spread ratio would fluctuate even if the implied forward interest rate ratio were unchanged. For example, if P 2 = $0.81/euro and P1 = $0.80/euro, a 10-percent increase in both rates would result in a 810-point price gain in the forward contract and only a 800-point gain in the nearby contract, even though the implied forward interest rate ratio would be unchanged (since an equal percentage change in each month would leave F/S unchanged). In order for the spread posi- tion to be unaffected by equal percentage price changes in both contracts, a development that would not affect the implied forward interest rate ratio, the spread would have to be implemented so that the dollar value of the long and short positions were equal. This parity will be achieved when the contract ratio is equal to the inverse of the price ratio. For example, given the above case of P 2 = $0.81 and 4 All references to interest rate ratios in this section should be understood to mean (1 + r1)/(l + r2) where r1 and r2 are the nonannualized rates of return for the time interim between S and F. Thus, in the above example, the interest rate ratio for the six-month period given annualized rates of 4.04 percent and 2.01 percent is equal to 1.02/1.01 = 1.0099. The reader should be careful not to misconstrue the intended definition of interest rate ratio with a literal interpretation, which in the above example would suggest a figure of 0.02/0.01 = 2. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:494 SCORE: 37.00 ================================================================================ 476 A Complete Guide to the Futures mArket P1 = $0.80, an 80-contract forward/81-contract nearby spread would not be affected by equal price changes (e.g., a 10-percent price increase would cause a total 64,800-point change in both legs of the spread). As can be seen in this example, a balanced spread will only be possible for extremely large positions. This fact, however, does not present a problem, since the distortion is sufficiently small so that a 1:1 contract ratio spread serves as a reasonable approximation. Intracurrency spreads can also be combined to trade expectations regarding two foreign euro- currency rates. In this case, the trader would implement a long nearby/short forward spread in the currency with the expected relative rate gain, and a long forward/short nearby spread in the other currency. For example, assume that in February the June/December euro spread implies that the June six-month eurodollar rate will be 1 percent above the euro rate, while the June/December JY spread implies that the June eurodollar rate will be 2 percent above the euroyen rate. In combina- tion, these spreads imply that the June euro rate will be higher than the June euroyen rate. If a trader expected euroyen rates to be higher than euro rates in June, the following combined spread positions would be implied: long June JY/short December JY plus long December euro/short June euro. T o summarize, intracurrency spreads can be used to trade interest rate differentials in the follow- ing manner: expectation Indicated trade eurodollar rate will gain on given eurocurrency rate (relative to rate ratio implied by spread). Long forward/short nearby spread in given currency eurodollar rate will lose on given eurocurrency rate (relative to rate ratio implied by spread). Long nearby/short forward spread in given currency eurocurrency rate 1 will gain on eurocurrency rate 2 (relative to rate ratio implied by spreads in both markets). Long nearby/short forward spread in market 1 and long forward/short nearby spread in market 2 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:495 SCORE: 49.00 ================================================================================ 477 A put might more properly be called a stick. For the whole point of a put—its purpose, if you will—is that it gives its owner the right to force 100 shares of some godforsaken stock onto someone else at a price at which he would very likely rather not take it. So what you are really doing is sticking it to him. —Andrew T obias Getting By on $100,000 a Year (and Other Sad T ales) ■ Preliminaries There are two basic types of options: calls and puts. The purchase of a call option on futures1 provides the buyer with the right, but not the obligation, to purchase the underlying futures contract at a speci- fied price, called the strike or exercise price, at any time up to and including the expiration date. 2 A put option provides the buyer with the right, but not the obligation, to sell the underlying futures contract at the strike price at any time prior to expiration. (Note, therefore, that buying a put is a bearish trade, while selling a put is a bullish trade.) The price of an option is called the premium, and is quoted in An Introduction to Options on Futures Chapter 34 1 Chapters 34 and 35 deal specifically with options on futures contracts. However, generally speaking, analogous concepts would apply to options on cash (physical) goods or instruments (e.g., bullion versus gold futures). Some of the advantages of basing an option contract on futures as opposed to the cash asset are discussed in the next section. 2 For some markets, the expiration date on the option and the underlying futures contract will be the same; for other markets, the expiration date on the option will be a specified date prior to the expiration of the futures contract. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:496 SCORE: 125.00 ================================================================================ 478 A Complete Guide to the Futures mArket either dollars (or cents) per unit or points. Table 34.1 illustrates how to calculate the dollar value of a premium. As a specific example, a trader who buys a $1,000 August gold call at a premium of $50 pays $50/oz ($5,000 per contract) for the right to buy an August gold futures contract at $1,000 (regardless of how high its price may rise) at any time up to the expiration date of the August option. Because options are traded for both puts and calls and a number of strike prices for each futures contract, the total number of different options traded in a market will far exceed the number of futures contracts—often by a factor of 10 to 1 or more. This broad variety of listed options provides the trader with myriad alternative trading strategies. Like their underlying futures contracts, options are exchange-traded, standardized contracts. Consequently, option positions can be offset prior to expiration simply by entering an order opposite to the position held. For example, the holder of a call could liquidate his position by entering an order to sell a call with the same expiration date and strike price. The buyer of a call seeks to profit from an anticipated price rise by locking in a specific purchase price. His maximum possible loss will be equal to the dollar amount of the premium paid for the option. This maximum loss would occur on an option held until expiration if the strike price were above the prevailing futures price. For example, if August gold futures were trading at $990 upon the expiration of the August option, a $1,000 call would be worthless because futures could be purchased more cheaply at the existing market price. 3 If the futures were trading above the strike price at expira- tion, then the option would have some value and hence would be exercised. However, if the difference table 34.1 Determining the Dollar Value of Option premiums Contracts Quoted on an Index Option premium (in points) × $ value per point = $ value of the option premium Examples: E-mini S&P 500 options 8.50 (option premium) × $50 per point = $425 (option premium $ value) U.S. dollar index options 2.30 (option premium) × $1,000 per point = $2,300 (option premium $ value) Contracts Quoted in Dollars Option premium (in dollars or cents per unit) × No. of units in futures contract = $ value of the option premium Examples: Gold options $42 (option premium) × 100 (ounces in futures contract) = $4,200 (option premium $ value) WTI crude oil options $1.24 (option premium) × 1,000 (barrels in futures contract) = $1,240 (option premium $ value) 3 However, it should be noted that even in this case, the call buyer could have recouped part of the premium if he had sold the option prior to expiration. This is true since the option will maintain some value (i.e., premium greater than zero) as long as there is some possibility of the futures price rising above the strike price prior to the expiration of the option. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:497 SCORE: 90.00 ================================================================================ 479 AN INTrOduCTION TO OPTIONS ON FuTureS between the futures price and the strike price were less than the premium paid for the option, the net result of the trade would still be a loss. In order for the call buyer to realize a net profit, the dif- ference between the futures price and the strike price would have to exceed the premium at the time the call was purchased (after adjusting for commission cost). The higher the futures price, the greater the resulting profit. Of course, if the futures reach the desired objective, or the call buyer changes his market opinion, he could sell his call prior to expiration. 4 The buyer of a put seeks to profit from an anticipated price decline by locking in a sales price. Similar to the call buyer, his maximum possible loss is limited to the dollar amount of the premium paid for the option. In the case of a put held until expiration, the trade would show a net profit if the strike price exceeded the futures price by an amount greater than the premium of the put at purchase (after adjusting for commission cost). While the buyer of a call or put has limited risk and unlimited potential gain, 5 the reverse is true for the seller. The option seller (“writer”) receives the dollar value of the premium in return for undertaking the obligation to assume an opposite position at the strike price if an option is exercised. For example, if a call is exercised, the seller must assume a short position in futures at the strike price (since by exercising the call, the buyer assumes a long position at that price). upon exercise, the exchange’s clearinghouse will establish these opposite futures positions at the strike price. After exercise, the call buyer and seller can either maintain or liquidate their respective futures positions. The seller of a call seeks to profit from an anticipated sideways to modestly declining market. In such a situation, the premium earned by selling a call will provide the most attractive trading oppor- tunity. However, if the trader expected a large price decline, he would usually be better off going short futures or buying a put—trades with open-ended profit potential. In a similar fashion, the seller of a put seeks to profit from an anticipated sideways to modestly rising market. Some novices have trouble understanding why a trader would not always prefer the buy side of an option (call or put, depending on his market opinion), since such a trade has unlimited potential and limited risk. Such confusion reflects the failure to take probability into account. Although the option seller’s theoretical risk is unlimited, the price levels that have the greatest probability of occurring (i.e., prices in the vicinity of the market price at the time the option trade occurs) would result in a net gain to the option seller. roughly speaking, the option buyer accepts a large probability of a small loss in return for a small probability of a large gain, whereas the option seller accepts a small probability of a large loss in exchange for a large probability of a small gain. In an efficient market, neither the consistent option buyer nor the consistent option seller should have any advantage over the long run. 6 4 even if the call is held until the expiration date, it will usually still be easier to offset the position in the options market rather than exercising the call. 5 T echnically speaking, the gains on a put would be limited, since prices cannot fall below zero; but for practical purposes, it is entirely reasonable to speak of the maximum possible gain on a long put position as being unlimited. 6 T o be precise, this statement is not intended to imply that the consistent option buyer and consistent option seller would both have the same expected outcome (zero excluding transactions costs). Theoretically, on average, it is rea- sonable to expect the market to price options so there is some advantage to the seller to compensate option sellers for providing price insurance—that is, assuming the highly undesirable exposure to a large, open-ended loss. So, in effect, option sellers would have a more attractive return profile and a less attractive risk profile than option buyers, and it is in this sense that the market will, on average, price options so that there is no net advantage to the buyer or seller. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:498 SCORE: 149.00 ================================================================================ 480 A Complete Guide to the Futures mArket ■ Factors That Determine Option Premiums An option’s premium consists of two components: Premiu mi ntri nsic v aluet imev alue=+ The intrinsic value of a call option is the amount by which the current futures price is above the strike price. The intrinsic value of a put option is the amount by which the current futures price is below the strike price. In effect, the intrinsic value is that part of the premium that could be realized if the option were exercised and the futures contract offset at the current market price. For example, if July crude oil futures were trading at $74.60, a call option with a strike price of $70 would have an intrinsic value of $4.60. The intrinsic value serves as a floor price for an option. Why? Because if the premium were less than the intrinsic value, a trader could buy and exercise the option, and immediately offset the resulting futures position, thereby realizing a net gain (assuming this profit would at least cover the transaction costs). Options that have intrinsic value (i.e., calls with strike prices below the current futures price and puts with strike prices above the current futures price) are said to be in-the-money. Options with no intrinsic value are called out-of-the-money options. An option whose strike price equals the futures price is called an at-the-money option. The term at-the-money is also often used less restrictively to refer to the specific option whose strike price is closest to the futures price. An out-of-the-money option, which by definition has an intrinsic value of zero, nonetheless retains some value because of the possibility the futures price will move beyond the strike price prior to the expi- ration date. An in-the-money option will have a value greater than the intrinsic value because a position in the option will be preferred to a position in the underlying futures contract. reason: Both the option and the futures contract will gain equally in the event of favorable price movement, but the option’s maximum loss is limited. The portion of the premium that exceeds the intrinsic value is called the time value. It should be emphasized that because the time value is almost always greater than zero, one should avoid exercising an option before the expiration date. Almost invariably, the trader who wants to offset his option position will realize a better return by selling the option, a transaction that will yield the intrinsic value plus some time value, as opposed to exercising the option, an action that will yield only the intrinsic value. The time value depends on four quantifiable factors 7: 1. the relationship between the strike price and the current futures price. As illus- trated in Figure 34.1, the time value will decline as an option moves more deeply in-the-money or out-of-the-money. deeply out-of-the-money options will have little time value, since it is unlikely the futures will move to (or beyond) the strike price prior to expiration. deeply in- the-money options have little time value because these options offer very similar positions to the underlying futures contracts—both will gain and lose equivalent amounts for all but an extreme adverse price move. In other words, for a deeply in-the-money option, the fact that the 7 Theoretically, the time value will also be influenced by price expectations, which are a non-quantifiable factor. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:499 SCORE: 76.00 ================================================================================ 481 AN INTrOduCTION TO OPTIONS ON FuTureS risk is limited is not worth very much, because the strike price is so far away from the prevailing futures price. As Figure 34.1 shows, the time value will be at a maximum at the strike price. 2. time remaining until expiration. The more time remaining until expiration, the greater the time value of the option. This is true because a longer life span increases the probability of the intrinsic value increasing by any specifi ed amount prior to expiration. In other words, the more time until expiration, the greater the probable price range of futures. Figure 34.2 illustrates the standard theoretical assumption regarding the relationship between time value and time remaining until expiration for an at-the-money option. Specifi cally, the time value is FIGURE  34.1 Theoretical Option Premium Curve Source: Chicago Board of Trade, Marketing department. Call Option Strike price Intrinsic value T -bond futures price130 132 134 136 138 140 Time value premium 8 6 4 2 Option premium Strike price Intrinsic value T-bond futures price 124 126 128 130 8 6 4 2 Option premium Put Option Time value premium FIGURE  34.2 Time Value decay Source: Options on Comex Gold Futures, published by Commodity exchange, Inc. (COMeX), 1982. Time value decay 94 10 Time remaining until expiration (months) Time value premium ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:500 SCORE: 76.00 ================================================================================ 482 A Complete Guide to the Futures mArket table 34.2 Option prices as a Function of V olatility in e-Mini S&p 500 Futures pricesa annualized V olatility put or Call premium 10 22.88 ($1,144) 20 45.75 ($2,288) 30 68.62 ($3,431) 40 91.46 ($4,573) 50 114.29 ($5,715) a At-the-money options at a strike price of 2000 with 30 days to expiration. 8 James Bowe, Option Strategies T rading Handbook (New Y ork, NY: Coffee, Sugar, and Cocoa exchange, 1983). assumed to be a function of the square root of time. (This relationship is a consequence of the typical assumption regarding the shape of the probability curve for prices of the underlying futures contract.) Thus, an option with nine months until expiration would have 1.5 times the time value of a four-month option with the same strike price (; ;. )93 42 32 15== ÷= and three times the time value of a one-month option (; ;)93 11 31 3== ÷= . 3. V olatility. Time value will vary directly with the estimated volatility of the underlying futures contract for the remaining lifespan of the option. This relationship is the result of the fact that greater volatility raises the probability the intrinsic value will increase by any specified amount prior to expiration. In other words, the greater the volatility, the larger the probable range of futures prices. As Table 34.2 shows, volatility has a strong impact on theoretical option pre- mium values. Although volatility is an extremely important factor in determining option premium values, it should be stressed that the future volatility of the underlying futures contract is never pre- cisely known until after the fact. (In contrast, the time remaining until expiration and the rela - tionship between the current price of futures and the strike price can be exactly specified at any juncture.) Thus, volatility must always be estimated on the basis of historical volatility data. As will be explained, this factor is crucial in explaining the deviation between theoretical and actual premium values. 4. Interest rates. The effect of interest rates on option premiums is considerably smaller than any of the above three factors. The specific nature of the relationship between interest rates and premiums was succinctly summarized by James Bowe 8: The effect of interest rates is complicated because changes in rates affect not only the underlying value of the option, but the futures price as well. Taking it in steps, a buyer of any given option must pay the premium up front, and of course the seller receives the money. If interest rates go up and everything else stays constant, the opportunity cost to the option buyer of giving up the use of his money increases, and so he is will- ing to bid less. Conversely, the seller of options can make more on the premiums by ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:501 SCORE: 43.00 ================================================================================ 483 AN INTrOduCTION TO OPTIONS ON FuTureS investing the cash received and so is willing to accept less; the value of the options fall. However, in futures markets, part of the value of distant contracts in a carry market reflects the interest costs associated with owning the commodity. An increase in the interest rate might cause the futures price to increase, leading to the value of existing calls going up. The net effect on calls is ambiguous, but puts should decline in value with increasing interest rates, as the effects are reinforcing. ■ Theoretical versus Actual Option Premiums There is a variety of mathematical models available that will indicate the theoretical “fair value” for an option, given specific information regarding the four factors detailed in the previous section. Theoret- ical values will approximate, but by no means coincide with, actual premiums. does the existence of such a discrepancy necessarily imply that the option is mispriced? definitely not. The model-implied premium will differ from the actual premium for two reasons: 1. The model’s assumption regarding the mathematical relationship between option prices (premi- ums) and the factors that affect option prices may not accurately describe market behavior. This is always true because, to some extent, even the best option-pricing models are only theoretical approximations of true market behavior. 2. The volatility figure used by an option-pricing model will normally differ somewhat from the market’s expectation of future volatility. This is a critical point that requires further elaboration. recall that although volatility is a crucial input in any option pricing formula, its value can only be estimated. The theoretical “fair value” of an option will depend on the specific choice of a volatility figure. Some of the factors that will influence the value of the volatility estimate are the length of the prior period used to estimate volatility, the time interval in which volatility is mea- sured, the weighting scheme (if any) used on the historical volatility data, and adjustments (if any) to reflect relevant influences (e.g., the recent trend in volatility). It should be clear that any specific volatility estimate will implicitly reflect a number of unavoidably arbitrary decisions. different assumptions regarding the best procedure for estimating future volatility from past volatility will yield different theoretical premium values. Thus, there is no such thing as a single, well-defined fair value for an option. All that any option pricing model can tell you is what the value of the option should be given the specific assumptions regarding expected volatility and the form of the mathematical relationship between option prices and the key factors affecting them. If a given mathematical model provides a close approximation of market behavior, a discrepancy between the theoretical value and the actual premium means the market expectation for volatility, called the implied volatility, differs from the historically based volatility estimate used in the model. The question of whether the volatility assump- tions of a specific pricing model provide more accurate estimates of actual volatility than the implied volatility figures (i.e., the future volatility suggested by actual premiums) can only be answered empirically. A bias toward buying “underpriced” options (relative to the theoretical model fair value) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:502 SCORE: 90.00 ================================================================================ 484 A Complete Guide to the Futures mArket and selling “overpriced” options would be justified only if empirical evidence supported the conten- tion that, on balance, the model’s volatility assumptions proved to be better than implied volatility in predicting actual volatility levels. If a model’s volatility estimates were demonstrated to be superior to implied volatility estimates, it would suggest, from a strict probability standpoint, a bullish trader would be better off selling puts than buying calls if options were overpriced (based on the fair value figures indicated by the model), and buying calls rather than selling puts if options were underpriced. Similarly, a bearish trader would be better off selling calls than buying puts if options were overpriced, and buying puts rather than selling calls if options were underpriced. The best strategy for any individual trader, however, would depend on the specific profile of his price expectations (i.e., the probabilities the trader assigns to various price outcomes). ■ Delta (the Neutral Hedge Ratio) Delta, also called the neutral hedge ratio, is the expected change in the option price given a one-unit change in the price of the underlying futures contract. For example, if the delta of an August gold call option is 0.25, it means that a $1 change in the price of August futures can be expected to result in a $0.25 change in the option premium. Thus, the delta value for a given option can be used to determine the number of options that would be equivalent in risk to a single futures contract for small changes in price. It should be stressed that delta will change rapidly as prices change. Thus, the delta value cannot be used to compare the relative risk of options versus futures for large price changes. Table 34.3 illustrates the estimated delta values for out-of-the-money, at-the-money, and in-the- money call options for a range of times to expiration. Where did these values come from? They are derived from the same mathematical models used to determine a theoretical value for an option pre- mium given the relationship between the strike price and the current price of futures, time remaining table 34.3 Change in the premium of an e-Mini S&p 500 Call Option for 20.00 ($1000) Move in the Underlying Futures Contracta Increase in the 2000 call option premium if the futures price rises: From 1900 to 1920 From 2000 to 2020 From 2100 to 2120 Time to expiration $ Delta $ Delta $ Delta 1 week $10 0.01 $500 0.5 $1,000 1 1 month $120 0.12 $510 0.51 $870 0.87 3 months $260 0.26 $510 0.51 $750 0.75 6 months $330 0.33 $520 0.52 $690 0.69 12 months $390 0.39 $520 0.52 $650 0.65 aAssumed volatility: 15 percent; assumed interest rate: 2 percent per year. Source: CMe Group (www .cmegroup.com). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:503 SCORE: 101.00 ================================================================================ 485 AN INTrOduCTION TO OPTIONS ON FuTureS until expiration, estimated volatility, and interest rates. For any given set of values for these factors, delta will equal the absolute difference between the option premium indicated by the model and the model-indicated premium if the futures price changes by one point. Table 34.3 illustrates a number of important observations regarding theoretical delta values: 1. Delta values for out-of-the-money options are low. This relationship is a result of the fact that there is a high probability that any given price increase 9 will not make any actual differ- ence to the value of the option at expiration (i.e., the option will probably expire worthless). 2. Delta values for in-the-money options are relatively high, but less than one. In- the-money options have high deltas because there is a high probability that a one-point change in the futures price will mean a one-point change in the option value at expiration. However, since this probability must always be equal to less than one, the delta value will also always be equal to less than one. 3. Delta values for at-the-money options will be near 0.50. Since there is a 50/50 chance that an at-the-money option will expire in-the-money, there will be an approximately 50/50 chance that a one-point increase in the price of futures will result in a one-point increase in the option value at expiration. 4. Delta values for out-of-the-money options will increase as time to expiration increases. A longer time to expiration will increase the probability that a price increase in futures will make a difference in the option value at expiration, since there is more time for futures to reach the strike price. 5. Delta values for in-the-money options will decrease as time to expiration increases. A longer time to expiration will increase the probability that a change in the futures price will not make any difference to the option value at expiration since there is more time for futures to fall back to the strike price by the time the option expires. 6. Delta values for at-the-money options are not substantially affected by time to maturity until near expiration. This behavioral pattern is true because the probability that an at-the-money option will expire in-the-money remains close to 50/50 until the option is near expiration. 9 This section implicitly assumes that the option is a call. If the option is a put, read “price decrease” for all refer- ences to “price increase.” ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:505 SCORE: 24.00 ================================================================================ 487 Brokers are fond of pointing out to possible buyers of options that they are a splendid thing to buy, and pointing out to sellers that they are a splendid thing to sell. They believe implicitly in this paradox. Thus the buyer does well, the seller does well, and it is not necessary to stress the point that the broker does well enough. Many examples can be cited showing all three of them emerging from their adventures with a profit. One wonders why the problem of unemployment cannot be solved by having the unemployed buy and sell each other options, instead of mooning around on those park benches. —Fred Schwed Where Are the Customers’ Yachts? ■ Comparing Trading Strategies The existence of options greatly expands the range of possible trading strategies. For example, in the absence of an option market, a trader who is bullish can either go long or initiate a bull spread (in those markets in which spread movements correspond to price direction). However, if option-related trad- ing approaches are included, the bullish trader can consider numerous alternative strategies including: long out-of-the-money calls, long in-the-money calls, long at-the-money calls, short out-of-the-money puts, short in-the-money puts, short at-the-money puts, “synthetic” long positions, combined positions in futures and options, and a variety of bullish option spreads. Frequently, one of these option-related strategies will offer significantly better profit potential for a given level of risk than an outright futures position. Thus, the trader who considers both option-based strategies and outright positions should have a decided advantage over the trader who restricts his trades to only futures. Option Trading Strategies Chapter 35 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:506 SCORE: 34.00 ================================================================================ 488 A Complete Guide to the Futures mArket There is no single best trading approach. The optimal trading strategy in any given situation will depend on the prevailing option premium levels and the specific nature of the expected price sce- nario. How does one decide on the best strategy? This chapter will attempt to answer this critical question in two steps. First, we will examine the general profit/loss characteristics (profiles) of a wide range of alternative trading strategies. Second, we will consider how price expectations can be combined with these profit/loss profiles to determine the best trading approach. The profit/loss profile is a diagram indicating the profit or loss implied by a position (vertical axis) for a range of market prices (horizontal axis). The profit/loss profile provides an ideal means of understanding and comparing different trading strategies. The following points should be noted regarding the profit/loss profiles detailed in the next section: 1. All illustrations are based on a single option series, for a single market, on a single date: the August 2015 gold options on April 13, 2015. This common denominator makes it easy to com- pare the implications of different trading strategies. The choice of April 13, 2015, was not arbi- trary. On that date, the closing price of August futures (1,200.20) was almost exactly equal to one of the option strike prices ($1,200/oz), thereby providing a nearly precise at-the-money option—a factor that greatly facilitates the illustration of theoretical differences among out-of- the-money, in-the-money, and at-the-money options. The specific closing values for the option premiums on that date were as follows ($/oz): Strike price august Calls august puts 1,050 155.2 5.1 1,100 110.1 10.1 1,150 70.1 19.9 1,200 38.8 38.7 1,250 19.2 68.7 1,300 9.1 108.7 1,350 4.5 154.1 Option pricing data in this chapter courtesy of OptionVue (www .optionvue.com). The reader should refer to these quotes when examining each of the profit/loss profiles in the next section. 2. In order to avoid unnecessarily cluttering the illustrations, the profit/loss profiles do not include transaction costs and interest income effects, both of which are very minor. (Note the assump- tion that transaction costs equal zero imply that commission costs equal zero and that positions can be implemented at the quoted levels—in this case, the market close.) 3. The profit/loss profiles reflect the situation at the time of the option expiration. This assumption simplifies the exposition, since the value of an option can be precisely determined at that point in time. At prior times, the value of the option will depend on the various factors discussed in the previous chapter (e.g., time until expiration, volatility, etc.). Allowing for an evaluation of each option strategy at interim time stages would introduce a level of complexity that would place the discussion beyond the scope of this book. However, the key point to keep in mind ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:507 SCORE: 46.00 ================================================================================ 489 OPTION TrAdINg STrATegIeS is that the profit/loss profile for strategies that include a net long options position will shift upward as the time reference point is further removed from the expiration date. The reason is that at expiration, options have only intrinsic value; at points prior to expiration, options also have time value. Thus, prior to expiration, the holder of an option could liquidate his position at a price above its intrinsic value—the liquidation value assumed in the profit/loss profile. Simi- larly, the profit/loss profile would be shifted downward for the option writer (seller) at points in time prior to expiration. This is true since at such earlier junctures, the option writer would have to pay not only the intrinsic value but also the time value if he wanted to cover his position. 4. It is important to keep in mind that a single option is equivalent to a smaller position size than a single futures contract (see section entitled “ delta—the Neutral Hedge ratio” in the previous chapter). Similarly, an out-of-the-money option is equivalent to a smaller position size than an in-the-money option. Thus, the trader should also consider the profit/loss profiles consisting of various multiples of each strategy. In any case, the preference of one strategy over another should be based entirely on the relationship between reward and risk rather than on the absolute profit (loss) levels. In other words, strategy preferences should be totally independent of posi- tion size. 5. Trading strategies are evaluated strictly from the perspective of the speculator. Hedging applica- tions of option trading are discussed separately at the end of this chapter. ■ Profit/Loss Profiles for Key Trading Strategies Strategy 1: Long Futures exAMPle. Buy August gold futures at $1,200. (See Table 35.1 and Figure 35.1.) Comment. The simple long position in futures does not require much explanation and is included primarily for purposes of comparison to other less familiar trading strategies. As every trader knows, the long futures position is appropriate when one expects a significant price advance. However, as will tabLe 35.1 profit/Loss Calculations: Long Futures Futures price at expiration ($/oz) Futures price Change ($/oz) profit/Loss on position 1,000 –200 –$20,000 1,050 –150 –$15,000 1,100 –100 –$10,000 1,150 –50 –$5,000 1,200 0 $0 1,250 50 $5,000 1,300 100 $10,000 1,350 150 $15,000 1,400 200 $20,000 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:508 SCORE: 10.00 ================================================================================ 490A COMPleTe gUIde TO THe FUTUreS MArKeT be illustrated later in this section, for any given price scenario, some option-based strategy will often provide a more attractive trade in terms of reward/risk characteristics. Strategy 2: Short Futures exAMPle . Sell August gold futures at $1,200. (See Table 35.2 and Figure 35.2 .) tabLe 35.2 profit/Loss Calculations: Short Futures Futures price at expiration ($/oz) Futures price Change ($/oz) profit/Loss on position 1,000 200 $20,000 1,050 150 $15,000 1,100 100 $10,000 1,150 50 $5,000 1,200 0 $0 1,250 –50 –$5,000 1,300 –100 –$10,000 1,350 –150 –$15,000 1,400 –200 –$20,000 FIGURE  35.1 Profi t/loss Profi le: long Futures Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 20,000 15,000 10,000 5,000 −5,000 −10,000 −15,000 −20,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:509 SCORE: 41.00 ================================================================================ 491 OPTION TrAdINg STrATegIeS Comment. Once again, this strategy requires little explanation and is included primarily for com- parison to other strategies. As any trader knows, the short futures position is appropriate when one is expecting a signifi cant price decline. However, as will be seen later in this chapter, for any given expected price scenario, some option-based strategy will often off er a more attractive trading oppor- tunity in terms of reward/risk characteristics. Strategy 3a: Long Call (at-the-Money) exAMPle . Buy August $1,200 gold futures call at a premium of $38.80/oz ($3,880), with August gold futures trading at $1,200/oz. (See Table 35.3 a and Figure 35.3 a.) Comment. The long call is a bullish strategy in which maximum risk is limited to the premium paid for the option, while maximum gain is theoretically unlimited. However, the probability of a loss is greater than the probability of a gain, since the futures price must rise by an amount exceeding the option premium (as of the option expiration) in order for the call buyer to realize a profi t. Two spe- cifi c characteristics of the at-the-money option are the following: 1. The maximum loss will only be realized if futures are trading at or below their current level at the time of the option expiration. 2. For small price changes, each $1 change in the futures price will result in approximately a $0.50 change in the option price. (At-the-money options near expiration, which will change by a greater amount, are an exception.) Thus, for small price changes, a net long futures position is equivalent to approximately two call options in terms of risk. FIGURE  35.2 Profi t/loss Profi le: Short Futures Price of August gold futures at option expiration ($/oz) 1,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Profit/loss at expiration ($) 20,000 15,000 10,000 5,000 −5,000 −10,000 −15,000 −20,000 0 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:510 SCORE: 23.00 ================================================================================ 492A COMPleTe gUIde TO THe FUTUreS MArKeT tabLe 35.3a profit/Loss Calculations: Long Call (at-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of premium paid Call Value at expiration profit/Loss of position [(4) – (3)] 1,000 38.8 $3,880 $0 –$3,880 1,050 38.8 $3,880 $0 –$3,880 1,100 38.8 $3,880 $0 –$3,880 1,150 38.8 $3,880 $0 –$3,880 1,200 38.8 $3,880 $0 –$3,880 1,250 38.8 $3,880 $5,000 $1,120 1,300 38.8 $3,880 $10,000 $6,120 1,350 38.8 $3,880 $15,000 $11,120 1,400 38.8 $3,880 $20,000 $16,120 FIGURE  35.3a Profi t/loss Profi le: long Call (At-the-Money) Price of August gold futures at option expiration ($/oz) Futures at time of position initiation and strike price Breakeven price = $1,238.80 Profit/loss at expiration ($) 1,000 15,000 17,500 12,500 10,000 7 ,500 2,500 0 −2,500 −5,000 5,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:511 SCORE: 45.00 ================================================================================ 493 OPTION TrAdINg STrATegIeS Strategy 3b: Long Call (Out-of-the-Money) exAMPle. Buy August $1,300 gold futures call at a premium of $9.10/oz ($910), with August gold futures trading at $1,200/oz. (See Table 35.3b and Figure 35.3b.) Comment. The buyer of an out-of-the-money call reduces his maximum risk in exchange for accept- ing a smaller probability that the trade will realize a profit. By definition, the strike price of an out-of- the-money call is above the current level of futures. In order for the out-of-the-money call position to realize a profit, the futures price (as of the time of the option expiration) must exceed the strike price by an amount greater than the premium ($9.10/oz in this example). Note that in the out-of- the-money call position, price increases that leave futures below the option strike price will still result in a maximum loss on the option. The long out-of-the-money call might be a particularly appropriate position for the trader expecting a large price advance, but also concerned about the possibility of a large price decline. It should be emphasized that the futures price need not necessarily reach the strike price in order for the out-of-the-money call to be profitable. If the market rises quickly, the call will increase in value and hence can be resold at a profit. (However, this characteristic will not necessarily hold true for slow price advances, since the depressant effect of the passage of time on the option premium could more than offset the supportive effect of the increased price level of futures.) For small price changes, the out-of-the-money call will change by less than a factor of one-half for each dollar change in the futures price. Thus, for small price changes, each long futures position will be equivalent to several long out-of-the-money calls in terms of risk. tabLe 35.3b profit/Loss Calculations: Long Call (Out-of-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,300 Call at Initiation ($/oz) $ amount of premium paid Call Value at expiration profit/Loss on position [(4) – (3)] 1,000 9.1 $910 $0 –$910 1,050 9.1 $910 $0 –$910 1,100 9.1 $910 $0 –$910 1,150 9.1 $910 $0 –$910 1,200 9.1 $910 $0 –$910 1,250 9.1 $910 $0 –$910 1,300 9.1 $910 $0 –$910 1,350 9.1 $910 $5,000 $4,090 1,400 9.1 $910 $10,000 $9,090 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:512 SCORE: 39.00 ================================================================================ 494A COMPleTe gUIde TO THe FUTUreS MArKeT FIGURE  35.3b Profi t/loss Profi le: long Call (Out-of-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Strike price Breakeven price = $1,309.10 Profit/loss at expiration ($) 1,000 10,000 5,000 7 ,500 2,500 −2,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strategy 3c: Long Call (In-the-Money) example . Buy August $1,100 gold futures call at a premium of $110.10 /oz ($11,010), with August gold futures trading at $1,200/oz. (See Table 35.3 c and Figure 35.3 c.) Comment. In many respects, a long in-the-money call position is very similar to a long futures posi- tion. The three main diff erences between these two trading strategies are: 1. The long futures position will gain slightly more in the event of a price rise—an amount equal to the time value portion of the premium paid for the option ($1,010 in the above example). 2. For moderate price declines, the long futures position will lose slightly less. (Once again, the diff erence will be equal to the time value portion of the premium paid for the option.) 3. In the event of a large price decline, the loss on the in-the-money long call position would be lim- ited to the total option premium paid, while the loss on the long futures position will be unlimited. In a sense, the long in-the-money call position can be thought of as a long futures position with a built-in stop. This characteristic is an especially important consideration for speculators who typically employ protective stop-loss orders on their positions—a prudent trading approach. A trader using a protective sell stop on a long position faces the frustrating possibility of the market declining suffi ciently to activate his stop and subsequently rebounding. The long in-the-money call position off ers the spec- ulator an alternative method of limiting risk that does not present this danger. Of course, this benefi t does not come without a cost; as mentioned above, the buyer of an in-the-money call will gain slightly less than the outright futures trader if the market advances, and will lose slightly more if the market declines moderately. However, if the trader is anticipating volatile market conditions, he might very ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:513 SCORE: 27.00 ================================================================================ 495 OPTION TrAdINg STrATegIeS well prefer a long in-the-money call position to a long futures position combined with a protective sell stop order. In any case, the key point is that the trader who routinely compares the strategies of buying an in-the-money call versus going long futures with a protective sell stop should enjoy an advantage over those traders who never consider the option-based alternative. FIGURE  35.3c Profi t/loss Profi le: long Call (In-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiationStrike price Breakeven price = $1210.10 Profit/loss at expiration ($) 1,000 10,000 −10,000 −15,000 5,000 −5,000 0 15,000 20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 tabLe 35.3c profit/Loss Calculations: Long Call (In-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,100 Call at Initiation ($/oz) $ amount of premium paid Call Value at expiration profit/Loss on position [(4) – (3)] 1,000 110.1 $11,010 $0 –$11,010 1,050 110.1 $11,010 $0 –$11,010 1,100 110.1 $11,010 $0 –$11,010 1,150 110.1 $11,010 $5,000 –$6,010 1,200 110.1 $11,010 $10,000 –$1,010 1,250 110.1 $11,010 $15,000 $3,990 1,300 110.1 $11,010 $20,000 $8,990 1,350 110.1 $11,010 $25,000 $13,990 1,400 110.1 $11,010 $30,000 $18,990 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:514 SCORE: 45.00 ================================================================================ 496 A Complete Guide to the Futures mArket Table 35.3d summarizes the profit/loss implications of various long call positions for a range of price assumptions. Note that as calls move deeper in-the-money, their profit and loss characteristics increasingly resemble a long futures position. The very deep in-the-money $1,050 call provides an interesting apparent paradox: The profit/loss characteristics of this option are nearly the same as those of a long futures position for all prices above $1,050, but the option has the advantage of limited risk for lower prices. How can this be? Why wouldn’t all traders prefer the long $1,050 call to the long futures position and, therefore, bid up its price so that its premium also reflected more time value? (The indicated premium of $15,520 for the $1,050 call consists almost entirely of intrinsic value.) There are two plausible explanations to this apparent paradox. First, the option price reflects the market’s assessment that there is a very low probability of gold prices moving to this deep in- the-money strike price, and therefore the market places a low value on the time premium. In other words, the market places a low value on the loss protection provided by an option with a strike price so far below the market. Second, the $1,050 call represents a fairly illiquid option position, and the quoted price does not reflect the bid/ask spread. No doubt, a potential buyer of the call would have had to pay a higher price than the quoted premium in order to assure an execution. tabLe 35.3d profit/Loss Matrix for Long Calls with Different Strike prices Dollar amount of premiums paid $1,050 $1,100 $1,150 $1,200 $1,250 $1,300 $1,350 Call Call a Call Call a Call Call a Call $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450 position profit/Loss at expiration Futures price at expiration ($/oz) Long Futures at $1,200 In-the-Money at-the-Money Out-of-the-Money $1,050 Call $1,100 Calla $1,150 Call $1,200 Calla $1,250 Call $1,300 Calla $1,350 Call 1,000 –$20,000 –$15,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450 1,050 –$15,000 –$15,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450 1,100 –$10,000 –$10,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450 1,150 –$5,000 –$5,520 –$6,010 –$7,010 –$3,880 –$1,920 –$910 –$450 1,200 $0 –$520 –$1,010 –$2,010 –$3,880 –$1,920 –$910 –$450 1,250 $5,000 $4,480 $3,990 $2,990 $1,120 –$1,920 –$910 –$450 1,300 $10,000 $9,480 $8,990 $7,990 $6,120 $3,080 –$910 –$450 1,350 $15,000 $14,480 $13,990 $12,990 $11,120 $8,080 $4,090 –$450 1,400 $20,000 $19,480 $18,990 $17,990 $16,120 $13,080 $9,090 $4,550 aThese calls are compared in Figure 35.3d. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:515 SCORE: 29.00 ================================================================================ 497 OPTION TrAdINg STrATegIeS Figure 35.3 d compares the three types of long call positions to a long futures position. It should be noted that in terms of absolute price changes, the long futures position represents the largest position size, while the out-of-the-money call represents the smallest position size. Figure 35.3 d suggests the following important observations: 1. As previously mentioned, the in-the-money call is very similar to an outright long futures position. 2. The out-of-the-money call will lose the least in a declining market, but will also gain the least in a rising market. 3. The at-the-money call will lose the most in a steady market and will be the middle-of-the-road performer (relative to the other two types of calls) in advancing and declining markets. Again, it should be emphasized that these comparisons are based upon single-unit positions that may diff er substantially in terms of their implied position size (as suggested by their respective delta values). A comparison that involved equivalent position size levels for each strategy (i.e., equal delta values for each position) would yield diff erent observations. This point is discussed in greater detail in the section entitled “Multiunit Strategies.” FIGURE  35.3d Profi t/loss Profi le: long Futures and long Call Comparisons (In-the-Money, At-the-Money, and Out-of-the-Money) Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Long futures At-the-money call (strike price = $1,200) Out-of-the-money call (strike price = $1,300) In-the-money call (strike price = $1,100) Profit/loss at expiration ($) 1,000 10,000 −10,000 −15,000 5,000 −5,000 0 15,000 20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:516 SCORE: 25.00 ================================================================================ 498A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 4a: Short Call (at-the-Money) example . Sell August $1,200 gold futures call at a premium of $38.80 /oz ($3,880), with August gold futures trading at $1,200/oz. (See Table 35.4 a and Figure 35.4 a.) tabLe 35.4a profit/Loss Calculations-Short Call (at-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of premium received Call Value at expiration profit/Loss on position [(3) – (4)] 1,000 38.8 $3,880 $0 $3,880 1,050 38.8 $3,880 $0 $3,880 1,100 38.8 $3,880 $0 $3,880 1,150 38.8 $3,880 $0 $3,880 1,200 38.8 $3,880 $0 $3,880 1,250 38.8 $3,880 $5,000 –$1,120 1,300 38.8 $3,880 $10,000 –$6,120 1,350 38.8 $3,880 $15,000 –$11,120 1,400 38.8 $3,880 $20,000 –$16,120 FIGURE  35.4a Profi t/loss Profi le: Short Call (At-the-Money) Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike price Breakeven price = $1,238.80 Profit/loss at expiration ($) 1,000 5,000 2,500 −5,000 −2,500 0 −10,000 −7,500 −17,500 −15,000 −12,500 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:517 SCORE: 65.00 ================================================================================ 499 OPTION TrAdINg STrATegIeS Comment. The short call is a bearish position with a maximum potential gain equal to the premium received for selling the call and unlimited risk. However, in return for assuming this unattractive maximum reward/maximum risk relationship, the seller of a call enjoys a greater probability of realizing a profit than a loss. Note the short at-the-money call position will result in a gain as long as the futures price at the time of the option expiration does not exceed the futures price at the time of the option initiation by an amount greater than the premium level ($38.80/oz in our example). However, the maximum possible profit (i.e., the premium received on the option) will only be real- ized if the futures price at the time of the option expiration is below the prevailing market price at the time the option was sold (i.e., the strike price). The short call position is appropriate if the trader is modestly bearish and views the probability of a large price rise as being very low . If, however, the trader anticipated a large price decline, he would probably be better off buying a put or going short futures. Strategy 4b: Short Call (Out-of-the-Money) example. Sell August $1,300 gold futures call at a premium of $9.10/oz ($910), with August gold futures trading at $1,200/oz. (See Table 35.4b and Figure 35.4b.) Comment. The seller of an out-of-the-money call is willing to accept a smaller maximum gain (i.e., premium) in exchange for increasing the probability of a gain on the trade. The seller of an out-of- the-money call will retain the full premium received as long as the futures price does not rise by an amount greater than the difference between the strike price and the futures price at the time of the option sale. The trade will be profitable as long as the futures price at the time of the option expiration is not above the strike price by more than the option premium ($9.10/oz in this example). The short out-of-the-money call represents a less bearish posture than the short at-the-money call position. Whereas the short at-the-money call position reflects an expectation that prices will either decline or increase only slightly, the short out-of-the-money call merely reflects an expectation that prices will not rise sharply. tabLe 35.4b profit/Loss Calculations: Short Call (Out-of-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,300 Call at Initiation ($/oz) $ amount of premium received Value of Call at expiration profit/Loss on position [(3) – (4)] 1,000 9.1 $910 $0 $910 1,050 9.1 $910 $0 $910 1,100 9.1 $910 $0 $910 1,150 9.1 $910 $0 $910 1,200 9.1 $910 $0 $910 1,250 9.1 $910 $0 $910 1,300 9.1 $910 $0 $910 1,350 9.1 $910 $5,000 –$4,090 1,400 9.1 $910 $10,000 –$9,090 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:518 SCORE: 25.00 ================================================================================ 500A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 4c: Short Call (In-the-Money) example . Sell August $1,100 gold futures call at a premium of $110.10 /oz ($11,010), with August gold futures trading at $1,200/oz. (See Table 35.4 c and Figure 35.4 c.) FIGURE  35.4b Profi t/loss Profi le: Short Call (Out-of-the-Money) Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Strike price Breakeven price = $1,309.10 Profit/loss at expiration ($) 1,000 2,500 −5,000 −2,500 0 −10,000 −7,500 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 tabLe 35.4c profit/Loss Calculations: Short Call (In-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,100 Call at Initiation ($/oz) Dollar amount of premium received Value of Call at expiration profit/Loss on position [(3) – (4)] 1,000 110.1 $11,010 $0 $11,010 1,050 110.1 $11,010 $0 $11,010 1,100 110.1 $11,010 $0 $11,010 1,150 110.1 $11,010 $5,000 $6,010 1,200 110.1 $11,010 $10,000 $1,010 1,250 110.1 $11,010 $15,000 –$3,990 1,300 110.1 $11,010 $20,000 –$8,990 1,350 110.1 $11,010 $25,000 –$13,990 1,400 110.1 $11,010 $30,000 –$18,990 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:519 SCORE: 25.00 ================================================================================ 501 OPTION TrAdINg STrATegIeS Comment. For most of the probable price range, the profi t/loss characteristics of the short in-the- money call are fairly similar to those of the outright short futures position. There are three basic dif- ferences between these two positions: 1. The short in-the-money call will lose modestly less than the short futures position in an advancing market because the loss will be partially off set by the premium received for the call. 2. The short in-the-money call will gain modestly more than the short futures position in a mod- erately declining market. 3. In a very sharply declining market, the profi t potential on a short futures position is open-ended, whereas the maximum gain in the short in-the-money call position is limited to the total pre- mium received for the call. In eff ect, the seller of an in-the-money call chooses to lock in modestly better results for the prob- able price range in exchange for surrendering the opportunity for windfall profi ts in the event of a price collapse. generally speaking, a trader should only choose a short in-the-money call over a short futures position if he believes that the probability of a sharp price decline is extremely small. Table 35.4 d summarizes the profi t/loss results for various short call positions for a range of price assumptions. As can be seen, as calls move more deeply in-the-money, they begin to resemble FIGURE  35.4c Profi t/loss Profi le: Short Call (In-the-Money) Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Strike price Breakeven price = $1210.10 Profit/loss at expiration ($) 1,000 10,000 15,000 −10,000 5,000 −5,000 0 −20,000 −15,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:520 SCORE: 50.00 ================================================================================ 502 A Complete Guide to the Futures mArket a short futures position more closely. (Sellers of deep in-the-money calls should be aware that longs may choose to exercise such options well before expiration. early exercise can occur if the poten- tial interest income on the premium is greater than the theoretical time value of the option for a zero interest rate assumption.) Short positions in deep out-of-the-money calls will prove profitable for the vast range of prices, but the maximum gain is small and the theoretical maximum loss is unlimited. Figure 35.4d compares each type of short call to a short futures position. The short at-the-money call position will be the most profitable strategy under stable market conditions and the middle-of- the-road strategy (relative to the other two types of calls) in rising and declining markets. The short out-of-the-money call will lose the least in a rising market, but it will also be the least profitable strategy if prices decline. The short in-the-money call is the type of call that has the greatest potential and risk and, as mentioned above, there is a strong resemblance between this strategy and an outright short position in futures. It should be emphasized that the comparisons in Figure 35.4d are based upon single-unit positions. However, as previously explained, these alternative strategies do not represent equivalent position sizes. Comparisons based on positions weighted equally in terms of some risk measure (e.g., equal delta values) would yield different empirical conclusions. tabLe 35.4d profit/Loss Matrix for Short Calls with Different Strike prices Dollar amount of premium received $1,050 $1,100 $1,150 $1,200 $1,250 $1,300 $1,350 Call Call Call Call Call Call Call $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450 position profit/Loss at expiration Futures price at expiration ($/oz) Short Futures at $1,200 In-the-Money at-the- Money Out-of-the Money $1,050 Call $1,100 Call a $1,150 Call $1,200 Call a $1,250 Call $1,300 Call a $500 Call 1,000 $20,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450 1,050 $15,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450 1,100 $10,000 $10,520 $11,010 $7,010 $3,880 $1,920 $910 $450 1,150 $5,000 $5,520 $6,010 $7,010 $3,880 $1,920 $910 $450 1,200 $0 $520 $1,010 $2,010 $3,880 $1,920 $910 $450 1,250 –$5,000 –$4,480 –$3,990 –$2,990 –$1,120 $1,920 $910 $450 1,300 –$10,000 –$9,480 –$8,990 –$7,990 –$6,120 –$3,080 $910 $450 1,350 –$15,000 –$14,480 –$13,990 –$12,990 –$11,120 –$8,080 –$4,090 $450 1,400 –$20,000 –$19,480 –$18,990 –$17,990 –$16,120 –$13,080 –$9,090 –$4,550 aThese calls are compared in Figure 35.4d. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:521 SCORE: 31.00 ================================================================================ 503 OPTION TrAdINg STrATegIeS Strategy 5a: Long put (at-the-Money) example . Buy August $1,200 gold futures put at a premium of $38.70/oz ($3,870), with August gold futures trading at $1,200/oz. (See Table 35.5 a and Figure 35.5 a.) FIGURE  35.4d Profi t/loss Profi le: Short Futures and Short Call Comparisons (In-the-Money, At-the-Money, and Out-of-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Short futures At-the-money call (strike price = $1,200) Out-of-the-money call (strike price = $1,300) In-the-money call (strike price = $1,100) Profit/loss at expiration ($) 1,000 10,000 15,000 −10,000 5,000 −5,000 0 −15,000 −20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 tabLe 35.5a profit/Loss Calculations: Long put (at-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of premium paid put Value at expiration profit/Loss on position [(4) – (3)] 1,000 38.7 $3,870 $20,000 $16,130 1,050 38.7 $3,870 $15,000 $11,130 1,100 38.7 $3,870 $10,000 $6,130 1,150 38.7 $3,870 $5,000 $1,130 1,200 38.7 $3,870 $0 –$3,870 1,250 38.7 $3,870 $0 –$3,870 1,300 38.7 $3,870 $0 –$3,870 1,350 38.7 $3,870 $0 –$3,870 1,400 38.7 $3,870 $0 –$3,870 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:522 SCORE: 48.00 ================================================================================ 504A COMPleTe gUIde TO THe FUTUreS MArKeT Comment. The long put is a bearish strategy in which maximum risk is limited to the premium paid for the option, while maximum gain is theoretically unlimited. However, the probability of a loss is greater than the probability of a gain, since the futures price must decline by an amount exceeding the option premium (as of the option expiration) in order for the put buyer to realize a profi t. Two specifi c characteristics of the at-the-money option are: 1. The maximum loss will be realized only if futures are trading at or above their current level at the time of the option expiration. 2. For small price changes, each $1 change in the futures price will result in approximately a $0.50 change in the option price (except for options near expiration). Thus, for small price changes, a net short futures position is equivalent to approximately 2 put options in terms of risk. Strategy 5 b: Long put (Out-of-the-Money) example . Buy August $1,100 gold futures put at a premium of $10.10 /oz ($1,010). (The current price of August gold futures is $1,200/oz.) (See Table 35.5 b and Figure 35.5 b.) Comment. The buyer of an out-of-the-money put reduces his maximum risk in exchange for accept- ing a smaller probability that the trade will realize a profi t. By defi nition, the strike price of an out-of- the-money put is below the current level of futures. In order for the out-of-the-money put position Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike price Breakeven price = $1,161.30 Profit/loss at expiration ($) 1,000 10,000 7,500 −5,000 5,000 −2,500 2,500 0 17,500 15,000 12,500 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 FIGURE  35.5a Profi t/loss Profi le: long Put (At-the-Money) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:523 SCORE: 41.00 ================================================================================ 505 OPTION TrAdINg STrATegIeS to realize a profi t, the futures price (as of the time of the option expiration) must penetrate the strike price by an amount greater than the premium ($10.10/oz in the above example). Note that in the out-of-the-money put position, price decreases that leave futures above the option strike price will still result in a maximum loss on the option. The long out-of-the-money put might be a particularly appropriate position for the trader expecting a large price decline, but also concerned about the pos- sibility of a large price rise. tabLe 35.5b profit/Loss Calculations: Long put (Out-of-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,100 put at Initiation ($/oz) $ amount of premium paid Value of put at expiration profit/Loss on position [(4) – (3)] 1,000 10.1 $1,010 $10,000 $8,990 1,050 10.1 $1,010 $5,000 $3,990 1,100 10.1 $1,010 $0 –$1,010 1,150 10.1 $1,010 $0 –$1,010 1,200 10.1 $1,010 $0 –$1,010 1,250 10.1 $1,010 $0 –$1,010 1,300 10.1 $1,010 $0 –$1,010 1,350 10.1 $1,010 $0 –$1,010 1,400 10.1 $1,010 $0 –$1,010 Price of August gold futures at option expiration Futures price at time of position initiation Breakeven price = $1,089.90 Profit/loss at expiration ($) 1,000 7,500 10,000 5,000 −2,500 2,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strike price FIGURE  35.5b Profi t/loss Profi le: long Put (Out-of-the-Money) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:524 SCORE: 46.00 ================================================================================ 506 A Complete Guide to the Futures mArket It should be emphasized that the futures price need not necessarily reach the strike price in order for the out-of-the-money put to be profitable. If the market declines quickly, the put will increase in value, and hence can be resold at a profit. (However, this behavior will not necessarily hold for slow price declines, since the depressant effect of the passage of time on the option premium could well more than offset the supportive effect of the decreased price level of futures.) For small price changes, the out-of-the-money put will change by less than a factor of one-half for each dollar change in the futures price. Thus, for small price changes, each short futures position will be equivalent to several short out-of-the-money puts in terms of risk. Strategy 5c: Long put (In-the-Money) example. Buy August $1,300 gold futures put at a premium of $108.70/oz ($10,870), with August gold futures trading at $1,200/oz. (See Table 35.5c and Figure 35.5c.) Comment. In many respects, a long in-the-money put option is very similar to a short futures posi- tion. The three main differences between these two trading strategies are: 1. The short futures position will gain slightly more in the event of a price decline—an amount equal to the time value portion of the premium paid for the option ($870 in this example). 2. For moderate price advances, the short futures position will lose slightly less. (Once again, the difference will be equal to the time value portion of the premium paid for the option.) 3. In the event of a large price advance, the loss on the in-the-money long put position would be limited to the total option premium paid, while the loss on the short futures position would be unlimited. tabLe 35.5c profit/Loss Calculations: Long put (In-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,300 put at Initiation ($/oz) Dollar amount of premium paid Value of put at expiration profit/Loss on position [(3) – (4)] 1,000 108.7 $10,870 $30,000 $19,130 1,050 108.7 $10,870 $25,000 $14,130 1,100 108.7 $10,870 $20,000 $9,130 1,150 108.7 $10,870 $15,000 $4,130 1,200 108.7 $10,870 $10,000 –$870 1,250 108.7 $10,870 $5,000 –$5,870 1,300 108.7 $10,870 $0 –$10,870 1,350 108.7 $10,870 $0 –$10,870 1,400 108.7 $10,870 $0 –$10,870 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:525 SCORE: 22.00 ================================================================================ 507 OPTION TrAdINg STrATegIeS In a sense, the long in-the-money put position can be thought of as a short futures position with a built-in stop. This characteristic is an especially important consideration for speculators who typically employ protective stop loss orders on their positions—a prudent trading approach. A trader using a protective buy stop on a short position faces the frustrating possibility of the market advancing suffi ciently to activate his stop and subsequently breaking. The long in-the-money put position off ers the speculator an alternative method of limiting risk that does not present this danger. Of course, this benefi t does not come without a cost: as mentioned earlier, the buyer of an in-the-money put will gain slightly less than the outright short futures trader if the market declines and lose slightly more if the market advances moderately. However, if the trader is anticipating volatile market conditions, he might very well prefer a long in-the-money put position to a short futures position combined with a protective buy stop order. In any case, the key point is that the trader who routinely compares the strategies of buying an in-the-money put versus going short futures with a protective buy stop should enjoy an advantage over those traders who never consider the option-based alternative. Table 35.5 d summarizes the profi t/loss implications of various long put positions for a range of price assumptions. Note that as puts move deeper in-the-money, their profi t and loss characteristics increasingly resemble a short futures position. FIGURE  35.5c Profi t/loss Profi le: long Put (In-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Strike price Breakeven price = $1,191.30 Profit/loss at expiration ($) 1,000 10,000 −10,000 −15,000 5,000 −5,000 0 15,000 20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:526 SCORE: 30.00 ================================================================================ 508 A Complete Guide to the Futures mArket tabLe 35.5d profit/Loss Matrix for Long puts with Different Strike prices Dollar amount of premium paid $1,350 put $1,300 put $1,250 put $1,200 put $1,150 put $1,100 put $1,050 put $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510 position profit/Loss at expiration Futures price at expiration ($/oz) Short Futures at $1,200 In-the-Money at-the-Money Out-of-the-Money $1,350 put $1,300 puta $1,250 put $1,200 puta $1,150 put $1,100 puta $1,050 put 1,000 $20,000 $19,590 $19,130 $18,130 $16,130 $13,010 $8,990 $4,490 1,050 $15,000 $14,590 $14,130 $13,130 $11,130 $8,010 $3,990 –$510 1,100 $10,000 $9,590 $9,130 $8,130 $6,130 $3,010 –$1,010 –$510 1,150 $5,000 $4,590 $4,130 $3,130 $1,130 –$1,990 –$1,010 –$510 1,200 $0 –$410 –$870 –$1,870 –$3,870 –$1,990 –$1,010 –$510 1,250 –$5,000 –$5,410 –$5,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510 1,300 –$10,000 –$10,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510 1,350 –$15,000 –$15,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510 1,400 –$20,000 –$15,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510 aThese puts are compared in Figure 35.5d. Figure 35.5d compares the three types of long put positions to a short futures position. It should be noted that in terms of absolute price changes, the short futures position represents the largest position size, while the out-of-the-money put represents the smallest position size. Figure 35.5d sug- gests the following important observations: 1. As previously mentioned, the in-the-money put is very similar to an outright short futures position. 2. The out-of-the-money put will lose the least in a rising market, but will also gain the least in a declining market. 3. The at-the-money put will lose the most in a steady market and will be the middle-of- the-road performer (relative to the other two types of puts) in declining and advancing markets. Again, it should be emphasized that these comparisons are based on single-unit positions that may differ substantially in terms of their implied position size (as suggested by their respective delta values). A comparison that involved equivalent position size levels for each strategy (i.e., equal delta values for each position) would yield different observations. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:527 SCORE: 30.00 ================================================================================ 509 OPTION TrAdINg STrATegIeS example . Sell August $1,200 gold futures put at a premium of $38.70/oz ($3,870), with August gold futures trading at $1,200/oz. (See Table 35.6 a and Figure 35.6 a.) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Short futures At-the-money put (strike price = $1,200) Out-of-the-money put (strike price = $1,100) In-the-money put (strike price = $1,300) Price/loss at expiration ($) 1,000 10,000 −10,000 −15,000 5,000 −5,000 0 15,000 20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 FIGURE  35.5d Profi t/loss Profi le: Short Futures and long Put Comparisons (In-the-Money, At-the-Money, and Out-of-the-Money) tabLe 35.6a profit/Loss Calculations: Short put (at-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of premium received put Value at expiration profit/Loss on position [(3) – (4)] 1,000 38.7 $3,870 $20,000 –$16,130 1,050 38.7 $3,870 $15,000 –$11,130 1,100 38.7 $3,870 $10,000 –$6,130 1,150 38.7 $3,870 $5,000 –$1,130 1,200 38.7 $3,870 $0 $3,870 1,250 38.7 $3,870 $0 $3,870 1,300 38.7 $3,870 $0 $3,870 1,350 38.7 $3,870 $0 $3,870 1,400 38.7 $3,870 $0 $3,870 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:528 SCORE: 46.00 ================================================================================ 510A COMPleTe gUIde TO THe FUTUreS MArKeT Comment. The short put is a bullish position with a maximum potential gain equal to the premium received for selling the put and unlimited risk. However, in return for assuming this unattractive maximum reward/maximum risk relationship, the seller of a put enjoys a greater probability of real- izing a profi t than a loss. Note that the short at-the-money put position will result in a gain as long as the futures price at the time of the option expiration is not below the futures price at the time of the option initiation by an amount greater than the premium level ($38.70/oz in our example). However, the maximum possible profi t (i.e., the premium received on the option) will only be realized if the futures price at the time of the option expiration is above the prevailing market price at the time the option was sold (i.e., the strike price). The short put position is appropriate if the trader is modestly bullish and views the probability of a large price decline as being very low . If, however, the trader anticipated a large price advance, he would probably be better off buying a call or going long futures. Strategy 6b: Short put (Out-of-the-Money) example . Sell August $1,100 gold futures put at a premium of $10.10 /oz ($1,010), with August gold futures trading at $1,200/oz. (See Table 35.6 b and Figure 35.6 b .) Comment. The seller of an out-of-the-money put is willing to accept a smaller maximum gain (i.e., premium) in exchange for increasing the probability of gain on the trade. The seller of an out-of-the- money put will retain the full premium received as long as the futures price does not decline by an FIGURE  35.6a Profi t/loss Profi le: Short Put (At-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike price Breakeven price = $1,161.30 Profit/loss at expiration ($) 1,000 −10,000 −12,500 5,000 2,500 −2,500 −5,000 −7,500 0 −15,000 −17,500 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:529 SCORE: 39.00 ================================================================================ 511 OPTION TrAdINg STrATegIeS amount greater than the diff erence between the futures price at the time of the option sale and the strike price. The trade will be profi table as long as the futures price at the time of the option expira- tion is not below the strike price by more than the option premium ($10.10/oz in this example). The short out-of-the-money put represents a less bullish posture than the short at-the-money put tabLe 35.6b profit/Loss Calculations: Short put (Out-of-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,100 put at Initiation ($/oz) Dollar amount of premium received Value of put at expiration profit/Loss on position [(3) – (4)] 1,000 10.1 $1,010 $10,000 –$8,990 1,050 10.1 $1,010 $5,000 –$3,990 1,100 10.1 $1,010 $0 $1,010 1,150 10.1 $1,010 $0 $1,010 1,200 10.1 $1,010 $0 $1,010 1,250 10.1 $1,010 $0 $1,010 1,300 10.1 $1,010 $0 $1,010 1,350 10.1 $1,010 $0 $1,010 1,400 10.1 $1,010 $0 $1,010 Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Breakeven price = $1,089.90 Profit/loss at expiration ($) 1,000 −10,000 2,500 −2,500 −5,000 −7,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strike price FIGURE  35.6b Profi t/loss Profi le: Short Put (Out-of-the-Money) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:530 SCORE: 25.00 ================================================================================ 512 A Complete Guide to the Futures mArket position. Whereas the short at-the-money put position reflects an expectation that prices will either rise or decline only slightly, the short out-of-the-money put merely reflects an expectation that prices will not decline sharply. Strategy 6c: Short put (In-the-Money) example. Sell August $1,300 gold futures put at a premium of $108.70/oz ($10,870), with August gold futures trading at $1,200/oz. (See Table 35.6c and Figure 35.6c.) Comment. For most of the probable price range, the profit/loss characteristics of the short in-the- money put are fairly similar to those of the outright long futures position. There are three basic dif- ferences between these two positions: 1. The short in-the-money put will lose modestly less than the long futures position in a declining market because the loss will be partially offset by the premium received for the put. 2. The short in-the-money put will gain modestly more than the long futures position in a moder- ately advancing market. 3. In a very sharply advancing market, the profit potential on a long futures position is open-ended, whereas the maximum gain in the short in-the-money put position is limited to the total pre- mium received for the put. In effect, the seller of an in-the-money put chooses to lock in modestly better results for the probable price range in exchange for surrendering the opportunity for windfall profits in the event of a price explosion. generally speaking, a trader should only choose a short in-the-money put over a long futures position if he believes that the probability of a sharp price advance is extremely small. tabLe 35.6c profit/Loss Calculations: Short put (In-the-Money) (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,300 put at Initiation ($/oz) Dollar amount of premium received put Value at expiration profit/Loss on position [(3) – (4)] 1,000 108.7 $10,870 $30,000 –$19,130 1,050 108.7 $10,870 $25,000 –$14,130 1,100 108.7 $10,870 $20,000 –$9,130 1,150 108.7 $10,870 $15,000 –$4,130 1,200 108.7 $10,870 $10,000 $870 1,250 108.7 $10,870 $5,000 $5,870 1,300 108.7 $10,870 $0 $10,870 1,350 108.7 $10,870 $0 $10,870 1,400 108.7 $10,870 $0 $10,870 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:531 SCORE: 27.00 ================================================================================ 513 OPTION TrAdINg STrATegIeS Table 35.6 d summarizes the profi t/loss results for various short put positions for a range of price assumptions. As can be seen, as puts move more deeply in the money, they begin to more closely resemble a long futures position. (As previously explained in the case of calls, sellers of deep in-the- money options should be cognizant of the real possibility of early exercise.) Short positions in deep out-of-the-money puts will prove profi table for the vast range of prices, but the maximum gain is small and the theoretical maximum loss is unlimited. Figure 35.6 d compares each type of short put to a long futures position. The short at-the-money put position will be the most profi table strategy under stable market conditions and the middle-of- the-road strategy (relative to the other two types of puts) in declining and rising markets. The short out-of-the-money put will lose the least in a declining market, but it will also be the least profi table strategy if prices advance. The short in-the-money put is the type of put that has the greatest potential and risk and, as mentioned above, there is a strong resemblance between this strategy and an outright long position in futures. It should be emphasized that the comparisons in Figure 35.6 d are based upon single-unit positions. However, as previously explained, these alternative strategies do not represent equivalent position sizes. Comparisons based on positions weighted equally in terms of some risk measure (e.g., equal delta values) would yield diff erent empirical conclusions. FIGURE  35.6c Profi t/loss Profi le: Short Put (In-the-Money) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Breakeven price =$1,191.30 Profit/loss at expiration ($) 1,000 10,000 15,000 −10,000 5,000 −5,000 −15,000 −20,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strike price ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:532 SCORE: 38.00 ================================================================================ 514A COMPleTe gUIde TO THe FUTUreS MArKeT tabLe 35.6d profit/Loss Matrix for Short puts with Different Strike prices Dollar amount of premium received $1,350 put $1,300 put $1,250 put $1,200 put $1,150 put $1,100 put $1,050 put $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510 position profit/Loss at expiration Futures price at expiration ($/oz) Long Futures at $1,200 In-the- Money at-the- Money Out-of- the-Money $1,350 put $1,300 put a $1,250 put $1,200 put a $1,150 put $1,100 put a $1,050 put 1,000 –$20,000 –$19,590 –$19,130 –$18,130 –$16,130 –$13,010 –$8,990 –$4,490 1,050 –$15,000 –$14,590 –$14,130 –$13,130 –$11,130 –$8,010 –$3,990 $510 1,100 –$10,000 –$9,590 –$9,130 –$8,130 –$6,130 –$3,010 $1,010 $510 1,150 –$5,000 –$4,590 –$4,130 –$3,130 –$1,130 $1,990 $1,010 $510 1,200 $0 $410 $870 $1,870 $3,870 $1,990 $1,010 $510 1,250 $5,000 $5,410 $5,870 $6,870 $3,870 $1,990 $1,010 $510 1,300 $10,000 $10,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510 1,350 $15,000 $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510 1,400 $20,000 $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510 a These puts are compared in Figure 35.6 d. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Long futures At-the-money put (strike price = $1,200) Out-of-the money put (strike price = $1,100) In-the-money put (strike price = $1,300) Profit/loss at expiration ($) 1,000 10,000 15,000 −10,000 5,000 −5,000 0 −15,000 −20,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 FIGURE  35.6d Profi t/loss Profi le: long Futures and Short Put Comparisons (In-the-Money, At-the-Money, and Out-of-the-Money) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:533 SCORE: 62.00 ================================================================================ 515 OPTION TrAdINg STrATegIeS Strategy 7: Long Straddle (Long Call + Long put) example. Buy August $1,200 gold futures call at a premium of $38.80/oz ($3,880) and simultane- ously buy an August $1,200 gold futures put at a premium of $38.70/oz ($3,870). (See Table 35.7 and Figure 35.7.) Comment. The long straddle position is a volatility bet. The buyer of a straddle does not have any opinion regarding the probable price direction; he merely believes that option premiums are underpriced relative to the potential market volatility. Andrew T obias once offered a some - what more cynical perspective of this type of trade 1: “Indeed, if you haven’t any idea of which way the [market] is headed but feel it is headed someplace, you can buy both a put and a call on it. That’s called a straddle and involves enough commissions to keep your broker smiling all week.” As can be seen in Figure 35.7, the long straddle position will be unprofitable for a wide price range centered at the current price. Since this region represents the range of the most probable price outcomes, the long straddle position has a large probability of loss. In return for accepting a large probability of loss, the buyer of a straddle enjoys unlimited profit potential in the event of either a large price rise or a large price decline. The maximum loss on a long straddle position is equal to the total premium paid for both the long call and long put and will only be experienced if the expiration price is equal to the futures price at the time the options were purchased. (Implicit assumption: both the call and put are at-the-money options.) tabLe 35.7 profit/Loss Calculations: Long Straddle (Long Call + Long put) (1) (2) (3) (4) (5) (6) (7) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of total premium paid Call Value at expiration put Value at expiration profit/Loss on position [(5) + (6) – (4)] 1,000 38.8 38.7 $7,750 $0 $20,000 $12,250 1,050 38.8 38.7 $7,750 $0 $15,000 $7,250 1,100 38.8 38.7 $7,750 $0 $10,000 $2,250 1,150 38.8 38.7 $7,750 $0 $5,000 –$2,750 1,200 38.8 38.7 $7,750 $0 $0 –$7,750 1,250 38.8 38.7 $7,750 $5,000 $0 –$2,750 1,300 38.8 38.7 $7,750 $10,000 $0 $2,250 1,350 38.8 38.7 $7,750 $15,000 $0 $7,250 1,400 38.8 38.7 $7,750 $20,000 $0 $12,250 1 Andrew T obias, Getting By on $100,000 a Year (and Other Sad T ales) (New Y ork, NY: Simon & Schuster, 1980). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:534 SCORE: 52.00 ================================================================================ 516A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 8: Short Straddle (Short Call + Short put) example . Sell August $1,200 gold futures call at a premium of $38.80/oz ($3,880 ) and simultane- ously sell an August $1,200 put at a premium of $38.70/oz ($3,870). (See Table 35.8 and Figure 35.8 .) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and call and put strike prices Breakeven price = $1,122.50 Breakeven price = 1,277.50 Profit/loss at expiration ($) 1,000 5,000 10,000 15,000 –10,000 –5,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 FIGURE  35.7 Profi t/loss Profi le: long Straddle (long Call + long Put) tabLe 35.8 profit/Loss Calculations: Short Straddle (Short Call + Short put) (1) (2) (3) (4) (5) (6) (7) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of total premium received Call Value at expiration put Value at expiration profit/Loss on position [(4) – (5) – (6)] 1,000 38.8 38.7 $7,750 $0 $20,000 –$12,250 1,050 38.8 38.7 $7,750 $0 $15,000 –$7,250 1,100 38.8 38.7 $7,750 $0 $10,000 –$2,250 1,150 38.8 38.7 $7,750 $0 $5,000 $2,750 1,200 38.8 38.7 $7,750 $0 $0 $7,750 1,250 38.8 38.7 $7,750 $5,000 $0 $2,750 1,300 38.8 38.7 $7,750 $10,000 $0 –$2,250 1,350 38.8 38.7 $7,750 $15,000 $0 –$7,250 1,400 38.8 38.7 $7,750 $20,000 $0 –$12,250 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:535 SCORE: 62.00 ================================================================================ 517 OPTION TrAdINg STrATegIeSComment. The short straddle position will be profi table over a wide range of prices. The best outcome for a seller of a straddle is a totally unchanged market. In this circumstance, the seller will realize his maximum profi t, which is equal to the total premium received for the sale of the call and put. The short straddle position will remain profi table as long as prices do not rise or decline by more than the combined total premium of the two options. The seller of the straddle enjoys a large probability of a profi table trade, in exchange for accepting unlimited risk in the event of either a very sharp price advance or decline. This strategy is appropriate if the speculator expects prices to trade within a moderate range, but has no opinion regarding the probable market direction. A trader anticipating nonvolatile market con- ditions, but also having a price-directional bias, would be better off selling either calls or puts rather than a straddle. For example, a trader expecting low volatility and modestly declining prices should sell 2 calls instead of selling a straddle. Strategy 9: bullish “texas Option hedge” (Long Futures + Long Call) 2 example . Buy August gold futures at $1,200 and simultaneously buy an August $1,200 gold futures call at a premium of $38.80 /oz ($3,880). (See Table 35.9 and Figure 35.9 .) FIGURE  35.8 Profi t/loss Profi le: Short Straddle (Short Call + Short Put) Profi t/loss Profi le: Short Straddle (Short Call + Short Put) Price of August gold futures at option expiration ($/oz) Breakeven price = $1,122.50 Breakeven price = 1,277.50 Profit/loss at expiration ($) 1,000 5,000 10,000 –10,000 –15,000 –5,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Futures price at time of position initiation and call and put strike prices 2 By defi nition, a hedge implies a futures position opposite to an existing or anticipated actual position. In com- modity trading, T exas hedge is a facetious reference to so-called “hedgers” who implement a futures position in the same direction as their cash position. The classic example of a T exas hedge would be a cattle feeder who goes long cattle futures. Whereas normal hedging reduces risk, the T exas hedge increases risk. There are many option strate- gies that combine off setting positions in options and futures. This strategy is unusual in that it combines reinforcing positions in futures and options. Consequently, the term T exas option hedge seems to provide an appropriate label. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:536 SCORE: 28.00 ================================================================================ 518A COMPleTe gUIde TO THe FUTUreS MArKeT tabLe 35.9 profit/Loss Calculations: bullish “texas Option hedge” (Long Futures + Long Call) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of premium paid profit/Loss on Long Futures position Call Value at expiration profit/Loss on position [(4)+(5)–(3)] 1,000 38.8 $3,880 –$20,000 $0 –$23,880 1,050 38.8 $3,880 –$15,000 $0 –$18,880 1,100 38.8 $3,880 –$10,000 $0 –$13,880 1,150 38.8 $3,880 –$5,000 $0 –$8,880 1,200 38.8 $3,880 $0 $0 –$3,880 1,250 38.8 $3,880 $5,000 $5,000 $6,120 1,300 38.8 $3,880 $10,000 $10,000 $16,120 1,350 38.8 $3,880 $15,000 $15,000 $26,120 1,400 38.8 $3,880 $20,000 $20,000 $36,120 FIGURE  35.9 Profi t/loss Profi le: Bullish “T exas Option Hedge” (long Futures + long Call) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike price Breakeven price = $1,219.40 Profit/loss at expiration ($) 1,000 37,500 50,000 25,000 −25,000 −37,500 12,500 −12,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Long 2 futures Long futures + long call ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:537 SCORE: 28.00 ================================================================================ 519 OPTION TrAdINg STrATegIeS Comment. This strategy provides an interesting alternative method of pyramiding—that is, increas- ing the size of a winning position. For example, a trader who is already long a futures contract at a profit and believes the market is heading higher may wish to increase his position without doubling his risk in the event of a price reaction—as would be the case if he bought a second futures contract. Such a speculator could choose instead to supplement his long position with the purchase of a call, thereby limiting the magnitude of his loss in the event of a price retracement, in exchange for real- izing a moderately lower profit if prices continued to rise. Figure 35.9 compares the alternative strategies of buying two futures versus buying a futures con- tract and a call. (For simplicity of exposition, the diagram assumes that both the futures contract and the call are purchased at the same time.) As can be seen, the long two futures position will always do moderately better in a rising market (by an amount equal to the premium paid for the call), but will lose more in the event of a significant price decline. The difference in losses between the two strate- gies will widen as larger price declines are considered. Strategy 10: bearish “texas Option hedge” (Short Futures + Long put) example. Sell August gold futures at $1,200 and simultaneously buy an August $1,200 gold put at a premium of $38.70/oz ($3,870). (See Table 35.10 and Figure 35.10.) Comment. This strategy is perhaps most useful as an alternative means of increasing a short position. As illustrated in Figure 35.10, the combination of a short futures contract and a long put will gain moderately less than 2 short futures contracts in a declining market, but will lose a more limited amount in a rising market. tabLe 35.10 profit/Loss Calculations: bearish “texas Option hedge” (Short Futures + Long put) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1200 put at Initiation ($/oz) $ amount of premium paid profit/Loss on Short Futures position put Value at expiration profit/Loss on position [(4) + (5) – (3)] 1,000 38.7 $3,870 $20,000 $20,000 $36,130 1,050 38.7 $3,870 $15,000 $15,000 $26,130 1,100 38.7 $3,870 $10,000 $10,000 $16,130 1,150 38.7 $3,870 $5,000 $5,000 $6,130 1,200 38.7 $3,870 $0 $0 –$3,870 1,250 38.7 $3,870 –$5,000 $0 –$8,870 1,300 38.7 $3,870 –$10,000 $0 –$13,870 1,350 38.7 $3,870 –$15,000 $0 –$18,870 1,400 38.7 $3,870 –$20,000 $0 –$23,870 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:538 SCORE: 30.00 ================================================================================ 520A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 11a: Option-protected Long Futures (Long Futures + Long at-the-Money put) example . Buy August gold futures at $1,200/oz and simultaneously buy an August $1200 gold put at a premium of $38.70/oz ($3,870). (See Table 35.11 a and Figure 35.11 a.) Comment. A frequently recommended strategy is that the trader implementing (or holding) a long futures position can consider buying a put to protect his downside risk. The basic idea is that if the market declines, the losses in the long futures position will be off set dollar for dollar by the long put position. Although this premise is true, it should be stressed that such a combined position represents nothing more than a proxy for a long call. The reader can verify the virtually identical nature of these two alternative strategies by comparing Figure 35.11 a to Figure 35.3 a. If prices increase, the long futures position will gain, while the option will expire worthless. On the other hand, if prices decline, the loss in the combined position will equal the premium paid for the put. In fact, if the call and put premiums are equal, a long futures plus long put position will be precisely equivalent to a long call. In most cases, the trader who fi nds the profi t/loss profi le of this strategy attractive would be better off buying a call, because the transaction costs are likely to be lower. However, if the trader already holds a long futures position, buying a put may be a reasonable alternative to liquidating this position and buying a call. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike price Breakeven price = $1,180.65 Profit/loss at expiration ($) 1,000 37,500 50,000 25,000 −25,000 −37,500 12,500 −12,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Short 2 futures Short futures + long put FIGURE  35.10 Profi t/loss Profi le: Bearish “T exas Option Hedge” (Short Futures + long Put) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:539 SCORE: 31.00 ================================================================================ 521 OPTION TrAdINg STrATegIeS tabLe 35.11a profit/Loss Calculations: Option-protected Long Futures—Long Futures + Long at-the- Money put (Similar to Long at-the-Money Call) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of premium paid profit/Loss on Long Futures position put Value at expiration profit/Loss on position [(4) + (5) – (3)] 1,000 38.7 $3,870 –$20,000 $20,000 –$3,870 1,050 38.7 $3,870 –$15,000 $15,000 –$3,870 1,100 38.7 $3,870 –$10,000 $10,000 –$3,870 1,150 38.7 $3,870 –$5,000 $5,000 –$3,870 1,200 38.7 $3,870 $0 $0 –$3,870 1,250 38.7 $3,870 $5,000 $0 $1,130 1,300 38.7 $3,870 $10,000 $0 $6,130 1,350 38.7 $3,870 $15,000 $0 $11,130 1,400 38.7 $3,870 $20,000 $0 $16,130 FIGURE  35.11a Profi t/loss Profi le: Option-Protected long Futures—long Futures + long at-the-Money Put (Similar to long At-the-Money Call) Price of August gold futures at option expiration ($/oz) Futures at time of position initiation and strike price Breakeven price = $1,238.70 Profit/loss at expiration ($) 1,000 10,000 7,500 12,500 15,000 17,500 5,000 −5,000 −2,500 2,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:540 SCORE: 33.00 ================================================================================ 522A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 11b: Option-protected Long Futures (Long Futures + Long Out-of-the-Money put) example . Buy August gold futures at $1,200/oz and simultaneously buy an August $1,100 gold futures put at a premium of $10.10/oz ($1,010). (See Table 35.11 b and Figure 35.11 b.) tabLe 35.11b profit/Loss Calculations: Option-protected Long Futures—Long Futures + Long Out-of- the-Money put (Similar to Long In-the-Money Call) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,100 put at Initiation ($/oz) $ amount of premium paid profit/Loss on Long Futures position put Value at expiration profit/Loss on position [(4) + (5) – (3)] 1,000 10.1 $1,010 –$20,000 $10,000 –$11,010 1,050 10.1 $1,010 –$15,000 $5,000 –$11,010 1,100 10.1 $1,010 –$10,000 $0 –$11,010 1,150 10.1 $1,010 –$5,000 $0 –$6,010 1,200 10.1 $1,010 $0 $0 –$1,010 1,250 10.1 $1,010 $5,000 $0 $3,990 1,300 10.1 $1,010 $10,000 $0 $8,990 1,350 10.1 $1,010 $15,000 $0 $13,990 1,400 10.1 $1,010 $20,000 $0 $18,990 FIGURE  35.11b Profi t/loss Profi le: Option-Protected long Futures—long Futures + long Out-of-the-Money Put (Similar to long In-the-Money Call) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Breakeven price = $1,210.10 Profit/loss at expiration ($) 1,000 10,000 15,000 20,000 5,000 −5,000 −10,000 −15,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strike price ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:541 SCORE: 37.00 ================================================================================ 523 OPTION TrAdINg STrATegIeS Comment. As can be verified by comparing Figure 35.11b to Figure 35.3c, this strategy is virtually equivalent to buying an in-the-money call. Supplementing a long futures position with the purchase of an out-of-the-money put will result in slightly poorer results if the market advances, or declines moderately, but will limit the magnitude of losses in the event of a sharp price decline. Thus, much like the long in-the-money call position, this strategy can be viewed as a long position with a built- in stop. In most cases, it will make more sense for the trader to simply buy an in-the-money call since the transaction cost will be lower. However, if a speculator is already long futures, the purchase of an out-of-the-money put might present a viable alternative to liquidating this position and buying an in-the-money call. Strategy 12a: Option-protected Short Futures (Short Futures + Long at-the-Money Call) example. Sell August gold futures at $1,200/oz and simultaneously buy an August $1,200 gold call at a premium of $38.80/oz ($3,880). (See Table 35.12a and Figure 35.12a.) Comment. A frequently recommended strategy is that the trader implementing (or holding) a short futures position can consider buying a call to protect his upside risk. The basic idea is that if the mar- ket advances, the losses in the short futures position will be offset dollar for dollar by the long call position. Although this premise is true, it should be stressed that such a combined position represents nothing more than a proxy for a long put. The reader can verify the virtually identical nature of these two alternative strategies by comparing Figure 35.12a to Figure 35.5a. If prices decline, the short futures position will gain, while the option will expire worthless. And if prices advance, the loss in the combined position will equal the premium paid for the call. In fact, if the put and call premiums are equal, a short futures plus long call position will be precisely equivalent to a long put. tabLe 35.12a profit/Loss Calculations: Option-protected Short Futures—Short Futures + Long at-the- Money Call (Similar to Long at-the-Money put) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of premium paid profit/Loss on Short Futures position Call Value at expiration profit/Loss on position [(4)+ (5) – (3)] 1,000 38.8 $3,880 $20,000 $0 $16,120 1,050 38.8 $3,880 $15,000 $0 $11,120 1,100 38.8 $3,880 $10,000 $0 $6,120 1,150 38.8 $3,880 $5,000 $0 $1,120 1,200 38.8 $3,880 $0 $0 –$3,880 1,250 38.8 $3,880 –$5,000 $5,000 –$3,880 1,300 38.8 $3,880 –$10,000 $10,000 –$3,880 1,350 38.8 $3,880 –$15,000 $15,000 –$3,880 1,400 38.8 $3,880 –$20,000 $20,000 –$3,880 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:542 SCORE: 19.00 ================================================================================ 524A COMPleTe gUIde TO THe FUTUreS MArKeT In most cases, the trader who fi nds the profi t/loss profi le of this strategy attractive would be better off buying a put, because the transaction costs are likely to be lower. However, if the trader already holds a short futures position, buying a call may be a reasonable alternative to liquidating this position and buying a put. Strategy 12b: Option-protected Short Futures (Short Futures + Long Out-of-the-Money Call) example . Sell August gold futures at $1,200/oz and simultaneously buy an August $1,300 gold futures call at a premium of $9.10/oz ($910). (See Table 35.12 b and Figure 35.12 b.) Comment. As can be verifi ed by comparing Figure 35.12 b to Figure 35.5 c, this strategy is virtually equivalent to buying an in-the-money put. Supplementing a short futures position with the purchase of an out-of-the-money call will result in slightly poorer results if the market declines or advances moderately, but will limit the magnitude of losses in the event of a sharp price advance. Thus, much as with the long in-the-money put position, this strategy can be viewed as a short position with a built-in stop. Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation and strike priceBreakeven price = $1,161.20 Profit/loss at expiration ($) 1,000 10,000 17,500 15,000 12,500 7,500 5,000 2,500 −5,000 −2,500 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 FIGURE  35.12a Profi t/loss Profi le: Option-Protected Short Futures—Short Futures + long At-the-Money Call (Similar to long At-the-Money Put) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:543 SCORE: 34.00 ================================================================================ 525 OPTION TrAdINg STrATegIeS In most cases, it will make more sense for the trader simply to buy an in-the-money put since the transaction costs will be lower. However, if a speculator is already short futures, the purchase of an out-of-the-money call might present a viable alternative to liquidating this position and buying an in-the-money put. tabLe 35.12b profit/Loss Calculations: Option-protected Short Futures—Short Futures + Long Out- of-the-Money Call (Similar to Long In-the-Money put) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,300 Call at Initiation ($/oz) $ amount of premium paid profit/Loss on Short Futures position Call Value at expiration profit/Loss on position [(4) + (5) – (3)] 1,000 9.1 $910 $20,000 $0 $19,090 1,050 9.1 $910 $15,000 $0 $14,090 1,100 9.1 $910 $10,000 $0 $9,090 1,150 9.1 $910 $5,000 $0 $4,090 1,200 9.1 $910 $0 $0 –$910 1,250 9.1 $910 –$5,000 $0 –$5,910 1,300 9.1 $910 –$10,000 $0 –$10,910 1,350 9.1 $910 –$15,000 $5,000 –$10,910 1,400 9.1 $910 –$20,000 $10,000 –$10,910 FIGURE  35.12b Profi t/loss Profi le: Option-Protected Short Futures—Short Futures + long Out-of-the-Money Call (Similar to long In-the-Money Put) Price of August gold futures at option expiration ($/oz) Futures price at time of position initiation Breakeven price = $1,190.90 Profit/loss at expiration ($) 1,000 10,000 15,000 20,000 5,000 −5,000 −10,000 −15,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 Strike price ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:544 SCORE: 77.00 ================================================================================ 526 A Complete Guide to the Futures mArket Strategy 13: Covered Call Write (Long Futures + Short Call) example. Buy August gold futures at $1,200/oz and simultaneously sell an August $1,200 gold futures call at a premium of $38.80/oz ($3,880). (See Table 35.13 and Figure 35.13.) Comment. There has been a lot of nonsense written about covered call writing. In fact, even the term is misleading. The implication is that covered call writing—the sale of calls against long positions—is somehow a more conservative strategy than naked call writing—the sale of calls without any offsetting long futures position. This assumption is absolutely false. Although naked call writing implies unlimited risk, the same statement applies to covered call writing. As can be seen in Figure 35.13, the covered call writer merely exchanges unlimited risk in the event of a market advance (as is the case for the naked call writer) for unlimited risk in the event of a market decline. In fact, the reader can verify that this strategy is virtually equivalent to a “naked” short put position (see Strategy 35.6a). One frequently mentioned motivation for covered call writing is that it allows the holder of a long position to realize a better sales price. For example, if the market is trading at $1,200 and the holder of a long futures contract sells an at-the-money call at a premium of $38.80/oz instead of liquidating his position, he can realize an effective sales price of $1,238.80 if prices move higher (the $1,200 strike price plus the premium received for the sale of the call). And, if prices move down by no more than $38.80/oz by option expiration, he will realize an effective sales price of at least $1,200. Pre- sented in this light, this strategy appears to be a “heads you win, tails you win” proposition. However, there is no free lunch. The catch is that if prices decline by more than $38.80, the trader will realize a lower sales price than if he had simply liquidated the futures position. And, if prices rise substantially higher, the trader will fail to participate fully in the move as he would have if he had maintained his long position. The essential point is that although many motivations are suggested for covered call writing, the trader should keep in mind that this strategy is entirely equivalent to selling puts. tabLe 35.13 profit/Loss Calculations: Covered Call Write—Long Futures + Short Call (Similar to Short put) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of premium received profit/Loss on Long Futures position Call Value at expiration profit/Loss on position [(3) + (4) – (5)] 1,000 38.8 $3,880 –$20,000 $0 –$16,120 1,050 38.8 $3,880 –$15,000 $0 –$11,120 1,100 38.8 $3,880 –$10,000 $0 –$6,120 1,150 38.8 $3,880 –$5,000 $0 –$1,120 1,200 38.8 $3,880 $0 $0 $3,880 1,250 38.8 $3,880 $5,000 $5,000 $3,880 1,300 38.8 $3,880 $10,000 $10,000 $3,880 1,350 38.8 $3,880 $15,000 $15,000 $3,880 1,400 38.8 $3,880 $20,000 $20,000 $3,880 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:545 SCORE: 44.00 ================================================================================ 527 OPTION TrAdINg STrATegIeS Strategy 14: Covered put Write (Short Futures + Short put) example . Sell August futures at $1,200 and simultaneously sell an August $1,200 gold futures put at a premium of $38.70/oz ($3,870). (See Table 35.14 and Figure 35.14 .) FIGURE  35.13 Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to Short Put) Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 5,000 2,500 0 −2,500 −7 ,500 −10,000 −12,500 −15,000 −5,000 1,050 1,100 1,150 1,200 1,250 Futures price at time of position initiation and strike price Breakeven price = $1,161 .20 1,300 1,350 1,400 −17 ,500 tabLe 35.14 profit/Loss Calculations: Covered put Write—Short Futures + Short put (Similar to Short Call) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 put at Initiation ($/oz) $ amount of premium received profit/Loss on Short Futures position put Value at expiration profit/Loss on position [(3) + (4) – (5)] 1,000 38.7 $3,870 $20,000 $20,000 $3,870 1,050 38.7 $3,870 $15,000 $15,000 $3,870 1,100 38.7 $3,870 $10,000 $10,000 $3,870 1,150 38.7 $3,870 $5,000 $5,000 $3,870 1,200 38.7 $3,870 $0 $0 $3,870 1,250 38.7 $3,870 –$5,000 $0 –$1,130 1,300 38.7 $3,870 –$10,000 $0 –$6,130 1,350 38.7 $3,870 –$15,000 $0 –$11,130 1,400 38.7 $3,870 –$20,000 $0 –$16,130 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:546 SCORE: 48.00 ================================================================================ 528A COMPleTe gUIde TO THe FUTUreS MArKeT Comment. Comments analogous to those made for Strategy 13 would apply here. The sale of a put against a short futures position is equivalent to the sale of a call. The reader can verify this by compar- ing Figure 35.14 to Figure 35.4 a. The two strategies would be precisely equivalent (ignoring transac- tion cost diff erences) if the put and call premiums were equal. Strategy 15: Synthetic Long Futures (Long Call + Short put) example . Buy an August $1,150 gold futures call at a premium of $70.10/oz ($7,010) and simultane- ously sell an August $1,150 gold futures put at a premium of $19.90/oz ($1,990). (See Table 35.15 and Figure 35.15 .) Comment. A synthetic long futures position can be created by combining a long call and a short put for the same expiration date and the same strike price. For example, as illustrated in Table 35.15 and Figure 35.15 , the combined position of a long August $1,150 call and a short August $1,150 put is virtually identical to a long August futures position. The reason for this equivalence is tied to the fact that the diff erence between the premium paid for the call and the premium received for the put is approxi- mately equal to the intrinsic value of the call. each $1 increase in price will raise the intrinsic value of the call by an equivalent amount and each $1 decrease in price will reduce the intrinsic value of the FIGURE  35.14 Profi t/loss Profi le: Covered Put Write—Short Futures + Short Put (Similar to Short Call) Price of August gold futures at option expiration ($/oz) 1,000 1,050 1,100 1,150 1,200 1,250 Futures price at time of position initiation and strike price Breakeven price = $1,238.70 1,300 1,350 1,400 Profit/loss at expiration ($) 5,000 2,500 0 −2,500 −7 ,500 −10,000 −12,500 −17 ,500 −15,000 −5,000 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:547 SCORE: 33.00 ================================================================================ 529 OPTION TrAdINg STrATegIeS tabLe 35.15 profit/Loss Calculations: Synthetic Long Futures (Long Call + Short put) (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,150 Call at Initiation ($/oz) $ amount of premium paid premium of august $1,150 put at Initiation ($/oz) $ amount of premium received Call Value at expiration put Value at expiration profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 70.1 $7,010 19.9 $1,990 $0 $15,000 −$20,020 1,050 70.1 $7,010 19.9 $1,990 $0 $10,000 −$15,020 1,100 70.1 $7,010 19.9 $1,990 $0 $5,000 −$10,020 1,150 70.1 $7,010 19.9 $1,990 $0 $0 −$5,020 1,200 70.1 $7,010 19.9 $1,990 $5,000 $0 −$20 1,250 70.1 $7,010 19.9 $1,990 $10,000 $0 $4,980 1,300 70.1 $7,010 19.9 $1,990 $15,000 $0 $9,980 1,350 70.1 $7,010 19.9 $1,990 $20,000 $0 $14,980 1,400 70.1 $7,010 19.9 $1,990 $25,000 $0 $19,980 FIGURE  35.15 Profi t/loss Profi le: Synthetic long Futures (long Call + Short Put) Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 20,000 15,000 10,000 5,000 −5,000 −10,000 −15,000 −20,000 0 1,050 1,100 1,150 1,200 1,250 Futures price at time of position initiation Breakeven price = $1,200.20 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:548 SCORE: 39.00 ================================================================================ 530 A Complete Guide to the Futures mArket call (or if prices decline below $1,150, increase the value of the put) by an equivalent amount. Thus, as long as the expiration date and strike price of the two options are identical, a long call/short put position acts just like a long futures contract. The futures equivalent price implied by a synthetic position is given by the following formula: Synthetic futures pos itio n prices trike pricec all prem ium=+ − −put premi um It should be noted there will be one synthetic futures position price corresponding to each strike price for which options are traded for the given futures contract. In this example, the synthetic long position is the same price as a long futures contract. (Synthetic futures position price = $1,150 + $70.10 − $19.90 = $1,200.20.) Thus, ignoring transaction costs and interest income effects, buying the August $1,150 call and simultaneously selling the August $1,150 put would be equivalent to buying an August futures contract. Of course, the trader consider- ing this strategy as an alternative to an outright long futures position must incorporate transaction costs and interest income effects into the calculation. In this example, the true cost of the synthetic futures position would be raised vis-à-vis a long futures contract as a result of the following three factors: 1. Because the synthetic futures position involves two trades, in a less liquid market, it is reason- able to assume the execution costs will also be greater. In other words, the option-based strategy will require the trader to give up more points (relative to quoted levels) in order to execute the trade. 2. The synthetic futures position will involve greater commission costs. 3. The dollar premium paid for the call ($7,010) exceeds the dollar premium received for the put ($1,990). Thus, the synthetic futures position will involve an interest income loss on the differ- ence between these two premium payments ($5,020). This factor, however, would be offset by the margin requirements on a long futures position. Once the above differences are accounted for, the apparent relative advantage a synthetic futures position will sometimes seemingly offer will largely, if not totally, disappear. Nonetheless, insofar as some market inefficiencies may exist, the synthetic long futures position will sometimes offer a slight advantage over the direct purchase of a futures contract. In fact, the existence of such discrepancies would raise the possibility of pure arbitrage trades. 3 For example, if the price implied by the synthetic long futures position was less than the futures price, even after accounting for transaction costs and interest income effects, the arbitrageur could lock in a profit by buying the call, selling the put, and selling futures. Such a trade is called a reverse conversion. Alternately, if after adjusting for transaction costs and interest income effects, the implied price of the synthetic long futures position were greater than the futures price, the arbitrageur could lock in a profit by buying futures, selling the call, and buying the put. Such a trade is called a conversion. 3 Pure arbitrage implies a risk-free trade in which the arbitrageur is able to lock in a small profit by exploiting temporary price distortions between two related markets. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:549 SCORE: 39.00 ================================================================================ 531 OPTION TrAdINg STrATegIeS It should be obvious that such risk-free profit opportunities will be limited in terms of both duration and magnitude. generally speaking, conversion and reverse conversion arbitrage will normally only be feasible for professional arbitrageurs who enjoy much lower transac- tion costs (commissions plus execution costs) than the general public. The activity of these arbitrageurs will tend to keep synthetic futures position prices about in line with actual futures prices. Strategy 16: Synthetic Short Futures (Long put + Short Call) example. Buy an August $1,300 gold futures put at a premium of $108.70/oz ($10,870) and simul- taneously sell an August $1,300 gold futures call at a premium of $9.10/oz ($910). (See Table 35.16 and Figure 35.16.) Comment. As follows directly from the discussion of the previous strategy, a synthetic short futures position can be created by combining a long put and a short call with the same expiration date and the same strike price. In this example, the synthetic futures position based upon the $1,300 strike price options is $0.40 higher priced than the underlying futures contract. (Synthetic futures position = $1,300 + $9.10 − $108.70 = $1,200.40.) However, for reasons similar to those discussed in the previous strategy, much of the advantage of an implied synthetic futures position price versus the actual futures price typically disappears once transaction costs and interest income effects are incorporated into the evaluation. An arbitrage employing the synthetic short futures position is called a conversion and was detailed in the previous strategy. tabLe 35.16 profit/Loss Calculations: Synthetic Short Futures (Long put + Short Call) (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,300 Call at Initiation ($/oz) Dollar amount of premium received premium of august $1,300 put at Initiation ($/oz) Dollar amount of premium paid Value of Call at expiration Value of put at expiration profit/Loss on position [(3) − (5) + (7) − (6)] 1,000 9.1 $910 108.7 $10,870 $0 $30,000 $20,040 1,050 9.1 $910 108.7 $10,870 $0 $25,000 $15,040 1,100 9.1 $910 108.7 $10,870 $0 $20,000 $10,040 1,150 9.1 $910 108.7 $10,870 $0 $15,000 $5,040 1,200 9.1 $910 108.7 $10,870 $0 $10,000 $40 1,250 9.1 $910 108.7 $10,870 $0 $5,000 –$4,960 1,300 9.1 $910 108.7 $10,870 $0 $0 –$9,960 1,350 9.1 $910 108.7 $10,870 $5,000 $0 –$14,960 1,400 9.1 $910 108.7 $10,870 $10,000 $0 –$19,960 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:550 SCORE: 26.00 ================================================================================ 532A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 17: the ratio Call Write (Long Futures + Short 2 Calls) example . Buy August gold futures at $1,200 and simultaneously sell two August $1,200 gold futures calls at a premium of $38.80/ oz. ($7,760). (See Table 35.17 and Figure 35.17 .) FIGURE  35.16 Profi t/loss Profi le: Synthetic Short Futures (long Put + Short Call). Futures price at time of position initiation Breakeven price = $1,210.40 Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 20,000 15,000 10,000 5,000 −5,000 −10,000 −15,000 −20,000 0 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400 tabLe 35.17 profit/Loss Calculations: ratio Call Write—Long Futures + Short 2 Calls (Similar to Short Straddle) (1) (2) (3) (4) (5) (6) Futures price at expiration ($/oz) premium of august $1,200 Call at Initiation ($/oz) $ amount of total premium received profit/Loss on Long Futures position Value of 2 Calls at expiration profit/Loss on position [(3) + (4) − (5)] 1,000 38.8 $7,760 –$20,000 $0 –$12,240 1,050 38.8 $7,760 –$15,000 $0 –$7,240 1,100 38.8 $7,760 –$10,000 $0 –$2,240 1,150 38.8 $7,760 –$5,000 $0 $2,760 1,200 38.8 $7,760 $0 $0 $7,760 1,250 38.8 $7,760 $5,000 $10,000 $2,760 1,300 38.8 $7,760 $10,000 $20,000 –$2,240 1,350 38.8 $7,760 $15,000 $30,000 –$7,240 1,400 38.8 $7,760 $20,000 $40,000 –$12,240 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:551 SCORE: 47.00 ================================================================================ 533 OPTION TrAdINg STrATegIeS Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 10,000 5,000 −5,000 −10,000 0 1,050 1,100 1,150 1,200 1,250 Breakeven price = $1,122.40 Breakeven price = $1,277 .60 1,300 1,350 1,400 −15,000 Futures price at time of position initiation FIGURE  35.17 Profi t/loss Profi le: ratio Call Write—long Futures + Short 2 Calls (Similar to Short Straddle) Comment. The combination of 1 long futures contract and 2 short at-the-money calls is a balanced position in terms of delta values. In other words, at any given point in time, the gain or loss in the long futures contract due to small price changes (i.e., price changes in the vicinity of the strike price) will be approximately off set by an opposite change in the call position. (Over time, however, a mar- ket characterized by small price changes will result in the long futures position gaining on the short call position due to the evaporation of the time value of the options.) The maximum profi t in this strategy will be equal to the premium received for the 2 calls and will occur when prices are exactly unchanged. This strategy will show a net profi t for a wide range of prices centered at the prevailing price level at the time the position was initiated. However, the position will imply unlimited risk in the event of very sharp price increases or declines. The profi t/loss profi le for this strategy should look familiar—it is virtually identical to the short straddle position (see Strategy 35.8). The virtual equivalence of this strategy to the short straddle position follows directly from the previously discussed structure of a synthetic futures position: Ratio call wr itel ong f utures short calls =+ 2 However, from the synthetic futures position relationship, we know that: Long f utures long call short put ≈+ ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:552 SCORE: 71.00 ================================================================================ 534 A Complete Guide to the Futures mArket Thus: Ratio call writ el ong c all short put short c alls or Rati ≈+ + 2, oo call wr ite short put short call≈+ The right-hand term of this last equation is, in fact, the definition of a short straddle. In similar fashion, it can be demonstrated that a short put write (short futures + short 2 puts) would also yield a profit/loss profile nearly identical to the short straddle position. Strategy 18: bull Call Money Spread (Long Call with Lower Strike price/Short Call with higher Strike price) example. Buy an August $1,250 gold futures call at a premium of $19.20/oz ($1,920) and simultaneously sell an August $1,300 call at a premium of $9.10 ($910). (See Table 35.18 and Figure 35.18.) Comment. This type of spread position is also called a debit spread because the amount of premium paid for the long call is greater than the amount of the premium received for the short call. The maxi- mum risk in this type of trade is equal to the difference between these two premiums. The maximum possible gain in this spread will be equal to the difference between the two strike prices minus the net difference between the two premiums. The maximum loss will occur if prices fail to rise at least beyond the lowest strike price. The maximum gain will be realized if prices rise above the higher strike price. Note that although the maximum profit exceeds the maximum risk by a factor of nearly 4 to 1, the probability of a loss is significantly greater than the probability of a gain. This condition is true since prices must rise $60.10/oz before the strategy proves profitable. tabLe 35.18 profit/Loss Calculations: bull Call Money Spread (Long Call with Lower Strike price/ Short Call with higher Strike price) (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,250 Call ($/oz) $ amount of premium paid premium of august $1,300 Call ($/oz) Dollar amount of premium received $1,250 Call Value at expiration $1,300 Call Value at expiration profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,050 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,100 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,150 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,200 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,250 19.2 $1,920 9.1 $910 $0 $0 -$1,010 1,300 19.2 $1,920 9.1 $910 $5,000 $0 $3,990 1,350 19.2 $1,920 9.1 $910 $10,000 $5,000 $3,990 1,400 19.2 $1,920 9.1 $910 $15,000 $10,000 $3,990 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:553 SCORE: 62.00 ================================================================================ 535 OPTION TrAdINg STrATegIeS This strategy can perhaps be best understood by comparing it to the long call position (e.g., long August $1,250 gold futures call). In eff ect, the spread trader reduces the premium cost for the long call position by the amount of premium received for the sale of the more deeply out-of-the-money call. This reduction in the net premium cost of the trade comes at the expense of sacrifi cing the pos- sibility of unlimited gain in the event of a large price rise. As can be seen in Figure 35.18 , in contrast to the outright long call position, price gains beyond the higher strike price will cease to aff ect the profi tability of the trade. Strategy 19a: bear Call Money Spread (Short Call with Lower Strike price/Long Call with higher Strike price)—Case 1 example . Buy August $1,150 gold futures call at a premium of $70.10/oz ($7,010) and simultane- ously sell an August $1,100 gold futures call at a premium of $110.10/oz ($11,010), with August gold futures trading at $1,200/oz. (See Table 35.19 a and Figure 35.19 a.) Comment. This type of spread is called a credit spread, since the amount of premium received for the short call position exceeds the premium paid for the long call position. The maximum possible gain on the trade is equal to the net diff erence between the two premiums. The maximum possible loss is equal to the diff erence between the two strike prices minus the diff erence between the two premiums. The maximum gain would be realized if prices declined to the lower strike price. The maximum loss would occur if prices failed to decline to at least the higher strike price. Although FIGURE  35.18 Profi t/loss Profi le: Bull Call Money Spread (long Call with lower Strike Price/ Short Call with Higher Strike Price) Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 3,750 5,000 2,500 0 −1,250 1,250 1,050 1,100 1,150 1,200 1,250 Breakeven price = $1,260.10 1,300 1,350 1,400 −2,500 Futures price at time of position initiation ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:554 SCORE: 45.00 ================================================================================ 536A COMPleTe gUIde TO THe FUTUreS MArKeT tabLe 35.19a profit/Loss Calculations: bear Call Money Spread (Short Call with Lower Strike price/ Long Call with higher Strike price); Case 1—both Calls In-the-Money (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,150 Call ($/oz) $ amount of premium paid premium of august $1,100 Call ($/oz) $ amount of premium received $1,150 Call Value at expiration $1,100 Call Value at expiration profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 70.1 $7,010 110.1 $11,010 $0 $0 $4,000 1,050 70.1 $7,010 110.1 $11,010 $0 $0 $4,000 1,100 70.1 $7,010 110.1 $11,010 $0 $0 $4,000 1,150 70.1 $7,010 110.1 $11,010 $0 $5,000 –$1,000 1,200 70.1 $7,010 110.1 $11,010 $5,000 $10,000 –$1,000 1,250 70.1 $7,010 110.1 $11,010 $10,000 $15,000 –$1,000 1,300 70.1 $7,010 110.1 $11,010 $15,000 $20,000 –$1,000 1,350 70.1 $7,010 110.1 $11,010 $20,000 $25,000 –$1,000 1,400 70.1 $7,010 110.1 $11,010 $25,000 $30,000 –$1,000 Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 3,750 5,000 2,500 0 −1,250 1,250 1,050 1,100 1,150 1,200 1,250 Breakeven price = $1,140 1,300 1,350 1,400 Futures price at time of position initiation FIGURE  35.19a Profi t/loss Profi le: Bear Call Money Spread (Short Call with lower Strike Price/long Call with Higher Strike Price); Case 1—Both Calls In-the-Money ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:555 SCORE: 62.00 ================================================================================ 537 OPTION TrAdINg STrATegIeS in the above example the maximum gain exceeds the maximum risk by a factor of 4 to 1, there is a greater probability of a net loss on the trade, since prices must decline by $60/oz before a profit is realized. In this type of spread, the trader achieves a bearish position at a fairly low premium cost at the expense of sacrificing the potential for unlimited gains in the event of a very sharp price decline. This strategy might be appropriate for the trader expecting a price decline but viewing the possibility of a very large price slide as being very low . Strategy 19b: bear Call Money Spread (Short Call with Lower Strike price/Long Call with higher Strike price)—Case 2 example. Buy an August $1,300 gold futures call at a premium of $9.10/oz ($9.10) and simultane- ously sell an August $1,200 gold futures call at a premium of $38.80/oz ($3,880), with August gold futures trading at $1,200/oz. (See Table 35.19b and Figure 35.19b.) Comment. In contrast to the previous strategy, which involved two in-the-money calls, this illustra- tion is based on a spread consisting of a short at-the-money call and a long out-of-the-money call. In a sense, this type of trade can be thought of as a short at-the-money call position with built-in stop-loss protection. (The long out-of-the-money call will serve to limit the risk in the short at-the- money call position.) This risk limitation is achieved at the expense of a reduction in the net premium received by the seller of the at-the-money call (by an amount equal to the premium paid for the out- of-the-money call). This trade-off between risk exposure and the amount of net premium received is illustrated in Figure 35.19b, which compares the outright short at-the-money call position to the above spread strategy. tabLe 35.19b profit/Loss Calculations: bear Call Money Spread (Short Call with Lower Strike price/Long Call with higher Strike price); Case 2—Short at-the-Money Call/Long Out-of-the-Money Call (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,300 Call ($/oz) $ amount of premium paid premium of august $1,200 Call ($/oz) $ amount of premium received Value of $1,300 Call at expiration Value of $1,200 Call at expiration profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 9.1 $910 38.8 $3,880 $0 $0 $2,970 1,050 9.1 $910 38.8 $3,880 $0 $0 $2,970 1,100 9.1 $910 38.8 $3,880 $0 $0 $2,970 1,150 9.1 $910 38.8 $3,880 $0 $0 $2,970 1,200 9.1 $910 38.8 $3,880 $0 $0 $2,970 1,250 9.1 $910 38.8 $3,880 $0 $5,000 –$2,030 1,300 9.1 $910 38.8 $3,880 $0 $10,000 –$7,030 1,350 9.1 $910 38.8 $3,880 $5,000 $15,000 –$7,030 1,400 9.1 $910 38.8 $3,880 $10,000 $20,000 –$7,030 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:556 SCORE: 59.00 ================================================================================ 538A COMPleTe gUIde TO THe FUTUreS MArKeT Strategy 20a: bull put Money Spread (Long put with Lower Strike price/Short put with higher Strike price)—Case 1 example . Buy an August $1,250 gold futures put at a premium of $68.70/oz ($6,870) and simulta- neously sell an August $1,300 put at a premium of $108.70/oz ($10,870), with August gold futures trading at $1,200/oz. (See Table 35.20 a and Figure 35.20 a.) Comment. This is a net credit bull spread that uses puts instead of calls. The maximum gain in this strategy is equal to the diff erence between the premium received for the short put and the premium paid for the long put. The maximum loss is equal to the diff erence between the strike prices minus the diff erence between the premiums. The maximum gain will be achieved if prices rise to the higher strike price, while the maximum loss will occur if prices fail to rise at least to the lower strike price. The profi t/loss profi le of this trade is very similar to the profi le of the net debit bull call money spread illustrated in Figure 35.18 . Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 5,000 2,500 0 −2,500 −5,000 −7 ,500 −10,000 −12,500 −17 ,500 1,050 1,100 1,150 1,200 1,250 Bear call money spread Short at-the-money call Breakeven price on spread = $1,229.70 Breakeven price on short call = $1,238.80 1,300 1,350 1,400 −15,000 Futures price at time of position initiation FIGURE  35.19b Profi t/loss Profi le: Bear Call Money Spread (Short Call with lower Strike Price/long Call with Higher Strike Price); Case 2—Short At-the-Money Call/long Out-of-the- Money Call with Comparison to Short At-the-Money Call ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:557 SCORE: 47.00 ================================================================================ 539 OPTION TrAdINg STrATegIeS tabLe 35.20a profit/Loss Calculations: bull put Money Spread (Long put with Lower Strike price/ Short put with higher Strike price); Case 1—both puts In-the-Money (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,250 put ($/oz) $ amount of premium paid premium of august $1,300 put ($/oz) $ amount of premium received $1,250 put Value at expiration $1,300 put Value at expiration profit/Loss on position [(5) − (3) + (6) −(7)] 1,000 68.7 $6,870 108.7 $10,870 $25,000 $30,000 –$1,000 1,050 68.7 $6,870 108.7 $10,870 $20,000 $25,000 –$1,000 1,100 68.7 $6,870 108.7 $10,870 $15,000 $20,000 –$1,000 1,150 68.7 $6,870 108.7 $10,870 $10,000 $15,000 –$1,000 1,200 68.7 $6,870 108.7 $10,870 $5,000 $10,000 –$1,000 1,250 68.7 $6,870 108.7 $10,870 $0 $5,000 –$1,000 1,300 68.7 $6,870 108.7 $10,870 $0 $0 $4,000 1,350 68.7 $6,870 108.7 $10,870 $0 $0 $4,000 1,400 68.7 $6,870 108.7 $10,870 $0 $0 $4,000 FIGURE  35.20a Profi t/loss Profi le: Bull Put Money Spread (long Put with lower Strike Price/ Short Put with Higher Strike Price); Case 1—Both Puts In-the-Money Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 3,750 5,000 2,500 0 1,250 1,050 1,100 1,150 1,200 1,250 Breakeven price = $1,260 1,300 1,350 1,400 −1,250 Futures price at time of position initiation ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:558 SCORE: 83.00 ================================================================================ 540 A Complete Guide to the Futures mArket Strategy 20b: bull put Money Spread (Long put with Lower Strike price/Short put with higher Strike price)—Case 2 example. Buy an August $1,100 gold futures put at a premium of $10.10/oz ($1,010) and simul- taneously sell an August $1,200 put at a premium of $38.70/oz ($3,870), with August gold futures trading at $1,200/oz. (See Table 35.20b and Figure 35.20b.) Comment. In contrast to Case 1, which involved two in-the-money puts, this strategy is based on a long out-of-the-money put versus a short at-the-money put spread. In a sense, this strategy can be viewed as a short at-the-money put position with a built-in stop. (The purchase of the out-of- the-money put serves to limit the maximum possible loss in the event of a large price decline.) This risk limitation is achieved at the expense of a reduction in the net premium received. This trade-off between risk exposure and the amount of premium received is illustrated in Figure 35.20b, which compares the outright short at-the-money put position to this spread strategy. Strategy 21: bear put Money Spread (Short put with Lower Strike price/Long put with higher Strike price) example. Sell an August $1,100 gold futures put at a premium of $10.10/oz ($1,010) and simul- taneously buy an August $1,150 put at a premium of $19.90/oz ($1,990), with August gold futures trading at $1,200/oz. (See Table 35.21 and Figure 35.21.) Comment. This is a debit bear spread using puts instead of calls. The maximum risk is equal to the difference between the premium paid for the long put and the premium received for the short put. The maximum gain equals the difference between the two strike prices minus the difference between the premiums. The maximum loss will occur if prices fail to decline to at least the higher strike price. The maximum gain will be achieved if prices decline to the lower strike price. The profit/loss profile of this spread is approximately equivalent to the profile of the bear call money spread (see Figure 35.19a). tabLe 35.20b profit/Loss Calculations: bull put Money Spread (Long put with Lower Strike price/Short put with higher Strike price); Case 2—Long Out-of-the-Money put/Short at-the-Money put (1) (2) (3) (4) (5) (6) (7) (8) Futures price at expiration ($/oz) premium of august $1,100 put ($/oz) Dollar amount of premium paid premium of august $1,200 put ($/oz) Dollar amount of premium received Value of $1,100 put at expiration Value of $1,200 put at expiration profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 10.1 $1,010 38.7 $3,870 $10,000 $20,000 –$7,140 1,050 10.1 $1,010 38.7 $3,870 $5,000 $15,000 –$7,140 1,100 10.1 $1,010 38.7 $3,870 $0 $10,000 –$7,140 1,150 10.1 $1,010 38.7 $3,870 $0 $5,000 –$2,140 1,200 10.1 $1,010 38.7 $3,870 $0 $0 $2,860 1,250 10.1 $1,010 38.7 $3,870 $0 $0 $2,860 1,300 10.1 $1,010 38.7 $3,870 $0 $0 $2,860 1,350 10.1 $1,010 38.7 $3,870 $0 $0 $2,860 1,400 10.1 $1,010 38.7 $3,870 $0 $0 $2,860 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:559 SCORE: 56.00 ================================================================================ 541 OPTION TrAdINg STrATegIeS FIGURE  35.20b Profi t/loss Profi le: Bull Put Money Spread (long Put with lower Strike Price/ Short Put with Higher Strike Price); Case 2—long Out-of-the-Money Put/Short At-the-Money Put with Comparison to Short At-the-Money Put Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 5,000 2,500 0 −2,500 −5,000 −7 ,500 −10,000 −12,500 −15,000 1,050 1,100 1,150 1,200 1,250 Bull put money spread Short at-the-money put Breakeven price on spread = $1,171.40 Breakeven price on short put $1,161.30 1,300 1,350 1,400 −17 ,500 Futures price at time of position initiation tabLe 35.21 profit/Loss Calculations: bear put Money Spread (Short put with Lower Strike price/Long put with higher Strike price) (1) (2) (3) (4) (5) (6) (7) Futures price at expiration ($/oz) premium of august $1,150 put ($/oz) $ amount of premium paid premium of august $1,100 put ($/oz) $ amount of premium received Value of $1,150 put Value of $1,100 put profit/Loss on position [(5) − (3) + (6) − (7)] 1,000 19.9 $1,990 10.1 $1,010 $15,000 $10,000 $4,020 1,050 19.9 $1,990 10.1 $1,010 $10,000 $5,000 $4,020 1,100 19.9 $1,990 10.1 $1,010 $5,000 $0 $4,020 1,150 19.9 $1,990 10.1 $1,010 $0 $0 –$980 1,200 19.9 $1,990 10.1 $1,010 $0 $0 –$980 1,250 19.9 $1,990 10.1 $1,010 $0 $0 –$980 1,300 19.9 $1,990 10.1 $1,010 $0 $0 –$980 1,350 19.9 $1,990 10.1 $1,010 $0 $0 –$980 1,400 19.9 $1,990 10.1 $1,010 $0 $0 –$980 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:560 SCORE: 76.00 ================================================================================ 542A COMPleTe gUIde TO THe FUTUreS MArKeT Other Spread Strategies Money spreads represent only one class of option spreads. A complete discussion of option spread strategies would require a substantial extension of this section—a degree of detail beyond the scope of this presentation. The following are examples of some other types of spreads. time spread. A time spread is a spread between two calls or two puts with the same strike price, but a diff erent expiration date. An example of a time spread would be: long 1 August $1,300 gold futures call/short 1 december $1,300 gold futures call. Time spreads are more complex than the other strategies discussed in this section, because the profi t/loss profi le at the time of expiration cannot be precisely predetermined, but rather must be estimated on the basis of theoretical valuation models. Diagonal spread. This is a spread between two calls or two puts that diff er in terms of both the strike price and the expiration date. An example of a diagonal spread would be: long 1 August $1,200 gold futures call/short 1 december $1,250 gold futures call. In eff ect, this type of spread combines the money spread and the time spread into one trade. butterfl y spread. This is a three-legged spread in which the options have the same expiration date but diff er in strike prices. A butterfl y spread using calls consists of two short calls at a given strike price, one long call at a higher strike price, and one long call at a lower strike price. The list of types of option spreads can be significantly extended, but the above examples should be sufficient to give the reader some idea of the potential range of complexity of spread Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 3,750 5,000 2,500 0 −1,250 −2,500 1,250 1,050 1,100 1,150 1,200 1,250 Breakeven price = $1,140.20 1,300 1,350 1,400 Futures price at time of position initiation FIGURE  35.21 Profi t/loss Profi le; Bear Put Money Spread (Short Put with lower Strike Price/ long Put with Higher Strike Price) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:561 SCORE: 35.00 ================================================================================ 543 OPTION TrAdINg STrATegIeS strategies. One critical point that must be emphasized regarding option spreads is that these strategies are normally subject to a major disadvantage: the transaction costs (commissions plus cumulative bid/asked spreads) for these trades are relatively large compared to the profit poten- tial. This consideration means that the option spread trader must be right a large percentage of the time if he is to come out ahead of the game. The importance of this point cannot be overem - phasized. In short, as a generalization, other option strategies will usually offer better trading opportunities. Multiunit Strategies The profit/loss profile can also be used to analyze multiple-unit option strategies. In fact, multiple- unit option positions may often provide the more appropriate strategy for purposes of comparison. For example, as previously detailed, a long futures position is more volatile than a long or short call position. In fact, for small price changes, each $1 change in a futures price will only result in approxi- mately a $0.50 change in the call price (the delta value for an at-the-money call is approximately equal to 0.5). As a result, in considering the alternatives of buying futures and buying calls, it probably makes more sense to compare the long futures position to two long calls (see Table 35.22) as opposed to one long call. Figure 35.22 compares the strategies of long futures versus long two calls, which at the time of initiation are approximately equivalent in terms of delta values. Note this comparison indicates that the long futures position is preferable if prices change only moderately, but that the long two-call position will gain more if prices rise sharply, and lose less if prices decline sharply. In contrast, the comparison between long futures and a long one-call position would indicate that futures provide the better strategy in the event of a price advance of any magnitude (see Figure 35.3d). For most purposes, the comparison employing two long calls will be more meaningful because it comes much closer to matching the risk level implicit in the long futures position. tabLe 35.22 profit/Loss Calculations: Long two at-the-Money Calls (1) (2) (3) (4) (5) Futures price at expiration ($/oz) premium of august $1,200 Call ($/oz) $ amount of total premium paid Value of 2 Calls at expiration profit/Loss on position [(4) − (3)] 1,000 38.8 $7,760 $0 –$7,760 1,050 38.8 $7,760 $0 –$7,760 1,100 38.8 $7,760 $0 –$7,760 1,150 38.8 $7,760 $0 –$7,760 1,200 38.8 $7,760 $0 –$7,760 1,250 38.8 $7,760 $10,000 $2,240 1,300 38.8 $7,760 $20,000 $12,240 1,350 38.8 $7,760 $30,000 $22,240 1,400 38.8 $7,760 $40,000 $32,240 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:562 SCORE: 17.00 ================================================================================ 544A COMPleTe gUIde TO THe FUTUreS MArKeT Choosing an Optimal Strategy It the previous sections we examined a wide range of alternative trading strategies. Now what? How does a trader decide which of these alternatives provides the best trading opportunity? This ques- tion can be answered only if probability is incorporated into the analysis. The selection of an optimal option strategy will depend entirely on the trader’s price and volatility expectations. Insofar as these expectations will diff er from trader to trader, the optimal option strategy will also vary, and the success of the selected option strategy will depend on the accuracy of the trader’s expectations. In order to select an optimal option strategy, the trader needs to translate his price expectations into probabilities. The basic approach requires the trader to assign estimated probability levels for the entire range of feasible price intervals. Figure 35.23 illustrates six diff erent types of probability distributions for August gold futures. These distributions can be thought of as representing six diff erent hypothetical expectations. (The charts in Figure 35.23 implicitly assume that the current price of August gold futures is $1,200.) Several important points should be made regarding these probability distributions: 1. The indicated probability distributions only represent approximations of traders’ price expec- tations. In reality, any reasonable probability distribution would be represented by a smooth curve. The stair-step charts in Figure 35.23 are only intended as crude models that greatly sim- plify calculations. (The use of smooth probability distributions would require integral calculus in the evaluation process.) Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 25,000 12,500 −12,500 −25,000 0 1,050 1,100 1,150 1,200 1,250 Breakeven price on long 2 calls = $1,238.80 Long futures Long 2 calls 1,300 1,350 1,400 37 ,500 +37 ,500 Futures price at time of position initiation FIGURE  35.22 Profi t/loss Profi le: Two long Calls vs. long Futures ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:564 SCORE: 8.00 ================================================================================ 546 A Complete Guide to the Futures mArket 5. The probability distributions in Figure 35.23 represent sample hypothetical illustrations of personal price expectations. The indicated optimal strategy in any given situation will depend upon the specific shape of the expected price distribution, an input that will differ from trader to trader. The general nature of the price expectations implied by each of the distributions in Figure 35.23 can be summarized as follows: Expected Probability Distribution 1. Higher prices and low volatility. This interpretation follows from the fact that there is a greater probability of higher prices and that the probabilities are heavily weighted toward intervals close to the current price level. Expected Probability Distribution 2. Higher prices and high volatility. This distribution reflects the same 60/40 probability bias toward higher prices as was the case for distribution 1, but the assumed probability of a substantially higher or lower price is much greater. Expected Probability Distribution 3. lower prices and low volatility. This distribution is the bearish counterpart of distribution 1. Expected Probability Distribution 4. lower prices and high volatility. This distribution is the bearish counterpart of distribution 2. Expected Probability Distribution 5. Neutral price assumptions and low volatility. This distribution is symmetrical in terms of higher and lower prices, and probability levels are heavily weighted toward prices near the current level. Expected Probability Distribution 6. Neutral price assumptions and high volatility. This distribution is also symmetrical in terms of high and low prices, but substantially higher and lower prices have a much greater probability of occurrence than in distribution 5. Figure 35.24 combines expected Probability distribution 1 with three alternative bullish strat- egies. (Since it is assumed that there is a greater probability of higher prices, there is no need to consider bearish or neutral trading strategies.) Insofar as the assumed probability distribution is very heavily weighted toward prices near the current level, the short put position appears to offer the best strategy. Figure 35.25 combines the same three alternative bullish strategies with the bull - ish/volatile price scenario suggested by expected Probability distribution 2. In this case, the long call position appears to be the optimal strategy, since it is by far the best performer for large price advances and declines—price outcomes that account for a significant portion of the overall prob - ability distribution. In analogous fashion, Figure 35.26 suggests the preferability of the short call position given the bearish/nonvolatile price scenario assumption, while Figure 35.27 suggests that the long put position is the optimal strategy given the bearish/volatile price scenario. Finally, two alternative neutral strategies are compared in Figures 35.28 and 35.29 for two neutral price distributions that differ in terms of assumed volatility. The short straddle appears to offer the better strategy in the low volatility distribution assumption, while the reverse conclusion is suggested in the volatile price case. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:565 SCORE: 14.00 ================================================================================ 547 OPTION TrAdINg STrATegIeS FIGURE  35.24 “Bullish/Nonvolatile” expected Probability distribution and Profi t/loss Profi les for Three Alternative Bullish Strategies Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 25,000 12,500 −12,500 −25,000 0 1,050 1,100 1,150 1,200 1,250 Long futures Short 2 puts Long 2 calls .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 FIGURE  35.25 “Bullish/V olatile” expected Probability distribution and Profi t/loss Profi les for Three Alternative Bullish Strategies Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 25,000 12,500 −12,500 −25,000 0 1,050 1,100 1,150 1,200 1,250 Long futures Short 2 puts Long 2 calls .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:566 SCORE: 12.00 ================================================================================ 548A COMPleTe gUIde TO THe FUTUreS MArKeT FIGURE  35.26 “Bearish/Nonvolatile” expected Probability distribution and Profi t/loss Profi les for Three Alternative Bearish Strategies “Bearish/Nonvolatile” expected Probability distribution and Profi t/loss Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 25,000 12,500 −12,500 −25,000 0 1,050 1,100 1,150 1,200 1,250 Short futures Short 2 calls Long 2 puts .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 FIGURE  35.27 “Bearish/V olatile” expected Probability distribution and Profi t/loss Profi les for Three Alternative Bearish Strategies Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 25,000 12,500 −12,500 −25,000 0 1,050 1,100 1,150 1,200 1,250 .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 Short futures Short 2 calls Long 2 puts ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:567 SCORE: 30.00 ================================================================================ 549 OPTION TrAdINg STrATegIeS FIGURE  35.28 “Neutral/Nonvolatile” expected Probability distribution and Profi t/loss Profi les for Two Alternative Neutral Strategies “Neutral/Nonvolatile” expected Probability distribution and Profi t/loss Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 10,000 5,000 −5,000 −10,000 0 1,050 1,100 1,150 1,200 1,250 .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 Long straddle Short straddle FIGURE  35.29 “Neutral/V olatile” expected Probability distribution and Profi t/loss Profi les for Two Alternative Neutral Strategies Price of August gold futures at option expiration ($/oz) Profit/loss at expiration ($) 1,000 10,000 5,000 −5,000 −10,000 −15,000 0 1,050 1,100 1,150 1,200 1,250 .20 .18 .16 .14 .12 .10 Probability .08 .06 .04 .02 1,300 1,350 1,400 Long straddle Short straddle ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:571 SCORE: 12.00 ================================================================================ 553 OPTION TrAdINg STrATegIeS tabLe 35.26 probability-W eighted profit/Loss ratio Comparisons for “bearish/V olatile” expected probability Distribution Short Futures Short Call Long put price range ($/oz) average price ($/oz) assumed probability Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) 950–999.9 975 0.06 22,500 1,350 3,880 233 18,630 1,117.8 1,000–1,049.9 1,025 0.1 17,500 1,750 3,880 388 13,630 1,363 1,050–1,099.9 1,075 0.12 12,500 1,500 3,880 466 8,630 1,035.6 1,100–1,149.9 1,125 0.14 7,500 1,050 3,880 543 3,630 508.2 1,150–1,199.9 1,175 0.18 2,500 450 3,880 698 –1,370 –246.6 1,200–1,249.9 1,225 0.12 –2,500 –300 1,380 166 –3,870 –464.4 1,250–1,299.9 1,275 0.1 –7,500 –750 –3,620 –362 –3,870 –387 1,300–1,349.9 1,325 0.08 –12,500 –1,000 –8,620 –690 –3,870 –309.6 1,350–1,399.9 1,375 0.06 –17,500 –1,050 –13,620 –817 –3,870 –232.2 1,400–1,449.9 1,425 0.04 –22,500 –900 –18,620 –745 –3,870 –154.8 Probability-weighted profit/loss ratio: 6,100/4,000 = 1.53 2,494/2,614 = 0.95 4,025/1,795 = 2.24 tabLe 35.27 probability-W eighted profit/Loss ratio Comparisons for “Neutral/Nonvolatile” expected probability Distribution Long Straddle Short Straddle price range ($/oz) average price ($/oz) assumed probability Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) 1,000–1,049.9 1,025 0.05 9750 488 –9,750 –488 1,050–1,099.9 1,075 0.1 4,750 475 –4,750 –475 1,100–1,149.9 1,125 0.15 –250 –38 250 38 1,150–1,199.9 1,175 0.2 –5,250 –1,050 5,250 1,050 1,200–1,249.9 1,225 0.2 –5,250 –1,050 5,250 1,050 1,250–1,299.9 1,275 0.15 –250 –38 250 38 1,300–1,349.9 1,325 0.1 4,750 475 –4,750 –475 1,350–1,399.9 1,375 0.05 9,750 488 –9,750 –488 Probability-weighted profit/loss ratio: 1,925/2,175 = 0.89 2,175/1,925 = 1.13 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:572 SCORE: 25.00 ================================================================================ 554 A Complete Guide to the Futures mArket hedging applications The entire discussion in this chapter has been approached from the vantage point of the speculator. However, option-based strategies can also be employed by the hedger. T o illustrate how options can be used by the hedger, we compare five basic alternative strategies for the gold jeweler who anticipates a requirement for 100 ounces of gold in August. The assumed date in this illustration is April 13, 2015, a day on which the relevant price quotes were as follows: spot gold = $1,198.90, August gold futures = $1,200, August $1,200 gold call premium = $38.80, August $1,200 gold put premium = $38.70. The five purchasing alternatives are: 5 1. Wait until time of requirement. In this approach, the jeweler simply waits until August before purchasing the gold. In effect, the jeweler gambles on the interim price movement of gold. If gold prices decline, he will be better off. However, if gold prices rise, his purchase price will increase. If the jeweler has forward-contracted for his products, he may need to lock in his raw material purchase costs in order to guarantee a satisfactory profit margin. Consequently, the price risk inherent in this approach may be unacceptable. tabLe 35.28 probability-W eighted profit/Loss ratio Comparisons for “Neutral/V olatile” expected probability Distribution Long Straddle Short Straddle price range ($/oz) average price ($/oz) assumed probability Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) Gain/Loss at average price ($) probability- W eighted Gain/Loss ($) 950–999.9 975 0.05 14,750 738 –14,750 –738 1,000–1,049.9 1,025 0.08 9,750 780 –9,750 –780 1,050–1,099.9 1,075 0.1 4,750 475 –4,750 –475 1,100–1,149.9 1,125 0.12 –250 –30 250 30 1,150–1,199.9 1,175 0.15 –5,250 –788 5,250 788 1,200–1,249.9 1,225 0.15 –5,250 –788 5,250 788 1,250–1,299.9 1,275 0.12 –250 –30 250 30 1,300–1,349.9 1,325 0.1 4,750 475 –4,750 –475 1,350–1,399.9 1,375 0.08 9,750 780 –9,750 –780 1,400–1,449.9 1,425 0.05 14,750 738 –14,750 –738 Probability-weighted profit/loss ratio: 3,985/1,635 = 2.44 1,635/3,985 = 0.41 5 There is no intention to imply that the following list of alternative hedging strategies is all-inclusive. Many other option-based strategies are also possible. For example, the jeweler could buy a call and sell a put at the same strike price—a strategy similar to buying a futures contract (see Strategy 15). ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:573 SCORE: 36.00 ================================================================================ 555 OPTION TrAdINg STrATegIeS 2. buy spot gold. The jeweler can buy spot gold and store it until August. In this case, he locks in a purchase price of $1,198.90/oz plus carrying costs (interest, storage, and insurance). This approach eliminates price risk, but also removes the potential of benefiting from any possible price decline. 3. buy gold futures. The jeweler can purchase one contract of August gold futures, thereby locking in a price of $1,200/oz. The higher price of gold futures vis-à-vis spot gold reflects the fact that futures embed carrying costs. Insofar as the price spread between futures and spot gold will be closely related to the magnitude of carrying costs, the advantages and disadvantages of this approach will be very similar to those discussed in the above strategy. 4. buy an at-the-money call. Instead of purchasing spot gold or gold futures, the jeweler could instead buy an August $1,200 gold futures call at a premium of $38.80/oz. The disadvantage of this approach is that if prices advance the jeweler locks in a higher purchase price: $1,238.80/ oz. However, by purchasing the call, the jeweler retains the potential for a substantially lower purchase price in the event of a sharp interim price decline. Thus, if, for example, spot prices declined to $1,050/oz by the time of the option expiration, the jeweler’s purchase price would be reduced to $1,088.80/oz (the spot gold price plus the option premium). 6 In effect, the pur- chase of the call can be viewed as a form of price risk insurance, with the cost of this insurance equal to the “premium.” 7 5. buy an out-of-the-money call. As an example, the jeweler could purchase an August $1,300 gold futures call at a premium of $9.10/oz. In this case, the jeweler forgoes protection against moderate price advances in exchange for reducing the premium costs. Thus, the jeweler assures he will have to pay no more than $1,309.10/oz. The cost of this price protection is $910 as opposed to the $3,880 premium for the at-the-money call. In a sense, the purchase of the out-of-the-money call can be thought of as a price risk insurance policy with a “deductible.” As in the case of purchasing an at-the-money call, the jeweler would retain the potential of benefit- ing from any interim price decline. As should be clear from the above discussion, options meaningfully expand the range of choices open to the hedger. As was the case for speculative applications, the choice of an optimal strategy will depend on the trader’s (hedger’s) individual expectations and preferences. It should be stressed that this section is only intended as an introduction to the concept of using options for hedging. A compre- hensive review of hedging strategies would require a far more extensive discussion. 6 T echnically speaking, since gold futures options expire before the start of the contract month, the effective purchase price would be raised by the amount of carrying costs for the remaining weeks until August. 7 The use of futures for hedging is also often described as “insurance.” However, in this context, the term is misapplied. In standard application, the term insurance implies protection against a catastrophic event for a cost that is small relative to the potential loss that is being insured. In using futures for hedging, the potential cost is equivalent to the loss protection. For example, if the jeweler buys gold futures, he will protect himself against a $10,000 increase in purchase cost if prices increase by $100/oz, but he will also realize a $10,000 loss on his hedge if prices decline by $100/oz. In this sense, the use of the call for hedging comes much closer to the standard concept of insurance: the magnitude of the potential loss being insured is much greater than the cost of the insurance. ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:703 SCORE: 24.00 ================================================================================ 685 Achievement, elements of, 586–587 Acreage figures, 355 Action, taking, 583 Actual contract series, 279–280 Adjusted R 2, 642 Adjusted rate mortgages (ARMs), 423, 424 Advice, seeking, 580 Agricultural markets. See also U.S. Department of Agriculture (USDA) acreage figures, 355 cattle (see Cattle) corn (see Corn) cotton (see Cotton) grain prices and, 351 hogs (see Hog production) production costs and, 351 seasonal considerations and, 356 wheat (see Wheat market) AMR. See Average maximum retracement (AMR) Analogous season method, 374 Analysis of regression equation: autocorrelation and (see Autocorrelation) dummy variables and, 659–663 Durbin-Watson statistic, as measure of autocorrelation, 652–654 heteroscedasticity and, 672–673 missing variables, time trend and, 655–658 multicollinearity and, 663–666 outliers and, 649–673 residual plot, 650–651 topics, advanced, 666–671 a priori restriction, 660 Arbitrage, pure, 530 ARMs. See Adjusted rate mortgages (ARMs) At-of-the-money call, buying, 555 At-of-the-money options definition of, 480 delta values and, 485 ATR. See Average true range (ATR) Autocorrelation: definition of, 651 Durbin-Watson statistic as measure of, 652–654 implications of, 654–655 transformations to remove, 670–671 Availability of substitutes, 361 Average maximum retracement (AMR), 331 Average parameter set performance, 311 Average percentage method, seasonal index, 391–394 Average return, 323, 326 Average true range (ATR), 262, 463 Backward elimination, stepwise regression, 682 Bad luck insurance, 257 Balanced spread, 455 Balance table, 373–374 Bar charts, 35–39 Bear call money spread, 535–538 case 1: short call with lower strike price/long call with higher strike price, 535–536 case 2: short call with lower strike price/long call with higher strike price, 537–538 Index ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:704 SCORE: 40.00 ================================================================================ 686 Index Bullishness: bullish put trade, 477 fundamentals and, 349 market response analysis and, 404, 405 Bullish T exas option hedge, 517–519 Bull market: flags, pennants and, 131–132 intramarket spreads and, 460 run days in, 118 spread trades and, 443 thrust days and, 116, 117 Bull put money spread: case 1: long put with lower strike price/short put with higher strike price, 538–539 case 2: long put with lower strike price/short put with higher strike price, 540 “Bull trap”: about, 205–211 confirmation conditions, 208, 209 Butterfly spread, 542 Buy and sell signals, trend-following systems and, 252 Buy hedge, cotton mill, 12–13 Call options, 477 Calmar ratio, 331 Calmness, 585 Cancel if close order. See CIC (cancel if close) order. Candlestick charts, 43–44 “real body,” 43, 44 “shadows,” 43 Carrying-charge markets, 282 Carrying charges, limited-risk spread and, 446, 447–448 Carryover stocks, 355, 432–433 Case-Shiller Home Price Index, 423, 424 Cash settlement process, 4 Cash versus futures price seasonality, 389–390 Cattle: cattle-on-feed numbers, 352–354 futures, 348, 385 inflation and, 385 production loss, 351 spread trades and, 444–445 Central limit theorem, 609–612 Change of market opinion, 204 Bearishness: bearish put trade, 477 fundamentals and, 349 market response analysis and, 404, 406 Bearish T exas option hedge, 519–520 Bear market: of 1980-1982, 366–367 flags, pennants and, 133–134 run days in, 118, 119 spread trades and, 443 thrust days and, 116 “Bear trap”: about, 205–211 confirmation conditions, 208, 210 Beat the Dealer, 587 Bell-shaped curve, 601 Benchmark, 327 Bernanke, Ben, 431–432 Best fit, regression analysis and, 591–593 deviations, 591–592 least-squares approach, 592–593, 594 “Best linear unbiased estimators” (BLUE), 621 Bet size, variation in, 581 “Black box” system, 576 Blind simulation approach, system optimization, 311 BLASH approach, 27–28 BLUE. See “Best linear unbiased estimators” (BLUE) Bottom formations. See T op and bottom formations Bowe, James, 482–483 Box size, 42 Breakout(s), 86–89 confirmation of, 86 continuation patterns and, 180–181 counter-to-anticipated, flag or pennant, 219–222 definition of, 33 downside, 87, 88 false signals for, 151, 153 false trend-line, 211–213 flags, pennants and, 128 opposite direction breakout of flag or pennant following normal, 222–225 upside, 87, 89 winning signals for, 152, 153 Breakout systems, 243–244 British pound (BP), intercurrency spreads and, 472–473 Bull call money spread, 534–535 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:705 SCORE: 12.00 ================================================================================ 687 Index Comfortable choices, trading principles and, 584 Comfort zone, trading within, 577 Commissions, 19 Commodities: bearing little or no relationship to general rule, 444–445 conforming to inverse of general rule, 444 demand curves and, 361 general spread trade rule and, 443–444 intercommodity spread and, 441–442 nonstorable, 351, 360, 444 perishable, 360, 364 Commodities, 357 Commodity T raders Consumers Report, 434 Commodity trading advisors (CTAs), 23, 578 Comparing indicators, 157–165 difference indicators, 158, 159 indicator correlations, 161–162, 163 popular comparisons, 164 Comparisons: nominal price levels, 355 one-year, 350 two managers, 320–322 Compounded return, 323 Computer testing of trading systems. See T esting/ optimizing trading systems Confidence, 579–580 Confidence interval(s), 612–614 for an individual forecast, 627–629 multiple regression model and, 642 Confirmation conditions, 247–250 bull or bear trap, 208 pattern, 249, 250 penetration as, 248 time delay and, 248–249 Confirmation myth, 170 Congestion phases. See Continuation patterns Consistency, 582 Constant-forward (“perpetual”) series, 281–282 Consumer price index (CPI), 383 Consumption: definition of, 363 demand and, 357, 363–366 price and, 364 as proxy for inelastic demand, 370 Contingent order, 18 Chart(s): BLASH approach, 27–28 equity, 566 linked-contract (see Linked-contract charts) Random Walkers and, 29–34 types of (see Chart types) Chart analysis, 149–154 confirmation conditions and, 150 false breakout signals, 151, 153 long-term chart, 152, 154 most important rules in, 205–231 spread trades and, 449 trading range and, 150 winning breakout signals, 152, 153 Chart-based objectives, 189 Chart patterns, 109–147 continuation patterns, 123–134 flags and pennants (see Flags and pennants) head and shoulders, 138–141 one-day patterns (see One-day patterns) reversal days, 113–116, 147 rounding tops and bottoms, 141–143 run days, 116, 118–119 spikes (see Spikes) thrust days, 116, 117 T op and bottom formations (see T op and bottom formations) Triangles (see Triangles) wedge, 146–147 wide-ranging days (see Wide-ranging days) Chart types, 35–44 bar charts, 35–39 candlestick charts, 43–44 close-only (“line”) charts, 40–42 linked contract series: nearest futures versus continuous futures, 39–40 point-and-figure charts, 42–43 CIC (cancel if close) order, 188 Close-only (“line”) charts, 40–42 CME/COMEX contract, 459 Cochrane-Orcutt procedure, 671 Code parameter, 293 Coefficient of determination (r 2), 630–633 Coffee: intercommodity spreads and, 453–454, 456 seasonal index and, 400 spread trade example, 445–446 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:706 SCORE: 15.00 ================================================================================ 688 Index Countertrend systems, 254–256 contrary opinion, 256 definition of, 236 fading minimum move, 255 fading minimum move with confirmation delay, 255 general considerations, 254–255 oscillators, 255 types of, 255–256 Countertrend trade entry signals, 182 Covered call write, 526–527 Covered put write, 527–528 CPI. See Consumer price index (CPI) CR 2 (corrected R2), 642–643 CRB Commodity Yearbook, 414 Credit spread, 535 Crop reports, 434 Crop years, intercrop spread and, 441 Crossover points, moving averages and, 182 Crude oil market. See also WTI crude oil money stop and, 185 poor timing and, 425 seasonal index and, 399 CTAs. See Commodity trading advisors (CTAs) Currency futures, 471–476 intercurrency spreads, 471–473 intracurrency spreads, 473–476 Curvature, breaking of, 229, 230 Daily price limit, 8–9 Data errors, 679 Data insufficiency, conclusions and, 357 Data vendors, futures price series selection and, 287 Day versus good-till-canceled (GTC) order, 16 Degrees of freedom (df), 615, 640, 644 Deliverable grade, 9 Delivery, 4 Delta (neutral hedge ratio), 484–485 Demand: consumption and, 357, 363–366 definition of, 359–362, 363 elasticity of, 361–362 highly inelastic, 370–371 incorporation of (see Incorporation of demand) increase in, 364 inflation and, 355 price and, 362–363 quantifying, 362–363 stable, 368 Continuation patterns, 123–134 flags and pennants (see Flags and pennants) trading range breakouts and, 180–181 triangles (see Triangles) Continuous (spread-adjusted) price series, 282–285 Continuous distribution, 600–601 Continuous futures. See also Nearest vs. continuous futures price gaps and, 282 rule of seven and, 194–196 Continuous futures charts: creation of, 47 measured moves and, 190–193 nearest futures vs., 39–40 Continuous parameter, 292–293 Contract months, 5, 8 Contract rollovers. See Rollover dates Contract size, 5 Contract specifications: about, 5–9 sample, 6–7 Contrary opinion, 203–204, 256 Conversion, 530 Copper: inflation and, 385 price-forecasting model, 366–367 price moves and, 428, 429 Corn: ethanol production and, 680 intercommodity spreads and, 457–459 major resistance area and, 427 price movements and, 430 production, 348 seasonal index and, 401 unexpected developments and, 419, 420, 421 Corrected R 2 (CR2), 642–643 Correlation coefficient (r), independent variables and, 665–666 Correlation matrix, 666 Costs. See also Carrying charges production, price declines and, 351–352 transaction, 295–296, 313 Cotton: carryover and, 432–433 unexpected developments and, 418 yields, 355 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:707 SCORE: 12.00 ================================================================================ 689 Index Dummy variables, 659–663 Durbin-Watson statistic, as measure of autocorrelation, 652–654 Eckardt, Bill, 578, 584 Edge, having an, 576 Efficient market hypothesis, 428, 431 Elasticity of demand, 361–362 Elementary statistics, 597–618 central limit theorem, 609–612 confidence intervals, 612–614 measures of dispersion, 597–599 normal curve (Z) table, reading, 604–606 population mean, 607 populations and samples, 606 probability distributions, 599–604 sampling distribution, 608–609 standard deviation, 599, 607 t-test, 614–618 E-Mini Dow: descending triangle, 127 futures, uptrend line, 60 intermarket stock index spreads, 461–470 E-Mini Nasdaq 100: double bottom, 135, 137 downtrend lines and, 67 flags and pennants, 130 intermarket stock index spreads, 461–470 uptrend lines and, 59, 61 wide-ranging down bar, 123 E-Mini S&P 500: intermarket stock index spreads, 461–470 market response analysis and, 408, 409 options on futures and, 482, 484 price envelope bands and, 107, 108 seasonal index and, 399 trend lines and, 74 upthrust/downthrust days and, 117 Employment report: stock index futures response to, 408–409 T -Note futures response to monthly, 404–407 ENPPT . See Expected net profit per trade (ENPPT) Equal-dollar-spread ratio, 472 Equal-dollar-value spread, 455–460 Equally weighted term, 453 Equilibrium, 363, 365 Equity change, intercurrency spreads and, 472–473 Equity chart, 566 Demand curve, 359, 361 Demand-influencing variables, 368–370 DeMark, Thomas, 66, 69, 199 DeMark sequential, 199–203 Dependent variable, determining, 675–676 Detrended seasonal index, 394 Deviation: definition of, 623 total, 630–631 Diagonal spread, 542 Diary, maintaining trader’s, 565 Difference indicators: Close – Close vs. Close – MA, 158 ratio versions, 159 Discipline, 578 Discrete parameter, 293 Discrete variable, 600 Discretionary traders, losing period adjustments, 562–563 Disloyalty/loyalty, 583–584 Dispersion, measures of, 597–599 Disturbance, definition of, 623 Diversification: planned trading approach and, 560, 561–562 trend-following systems and, 256–258 Dividends, 462 Dollar: equal-dollar-value spread, 455–460 intercurrency spreads and, 471 price, 383 Dollar value, option premiums and, 477–478 Double top, penetration of, 227–229 curvature, breaking of, 229 Double tops and bottoms: double bottom, 137–138 double top, 136 triple top, 129 Down run day, 118, 268 Downthrust day, 116 Downtrend channels, 62, 63 Downtrend lines: definition of, 57 examples of, 59, 61, 65 false breakout signals, 211, 213 Driehaus, Richard, 578, 585 Druckenmiller, Stanley, 581, 584 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:709 SCORE: 10.00 ================================================================================ 691 Index Generic trading systems: breakouts (see Breakout systems) moving averages and, 237–243 Gold: fundamental analysis and, 347, 371 futures (see Gold futures) intramarket stock index spreads and, 461 market response analysis and, 410 prices, 284 seasonal index and, 400 spot, buying, 555 Gold futures: buying, 555 volume shift in, 10 Gold/silver spread, 454 Good-till-canceled (GTC) orders. See GTC orders Government regulations, potential impact of, 415 Government reports, unexpected developments and, 420 GPR (gain-to-pain ratio), 328–329 Grain prices, 351 Great Recession, 423 Gresham’s law of money, 312 Grinder, John, 586 Gross domestic product (GDP): deflator, 383 independent variables and, 677 GTC orders: about, 16 order placement and, 568 stop-loss points and, 183, 188 trade exit and, 569 Hard work, skill versus, 576–577 Head and shoulders: about, 138–141 failed top pattern, 227–229 Heating oil: alternative approach, 396–397 average percentage method, 391, 392–394, 398 link relative method, 394–396, 398 Hedge, definition of, 517 Hedge ratio, neutral (delta), 484–485 Hedging, 11–13 applications, 554–555 buy hedge, 12–13 Fundamental analysis: about, 16 analogous season method, 374 balance table, 373–374 danger in using, 417 discounting and, 428–430 expectations, role of, 379–381 fallacies. see Fallacies forecasting model, building, 413–415 gold market and, 371 index models, 376–377 inflation, incorporation of, 383–388 long-term implications versus short-term response, 432–435 market response analysis (see Market response analysis) money management and, 426–427 “old hand” approach, 373 pitfalls in, 418–426 reasons to use, 427–428 regression analysis, 374–375 seasonal analysis and, 389–401 spread trades and, 449 supply-demand analysis, 359–371 technical analysis and, 21–24, 417–418, 426–427 trading and, 417–435 types of, 373–377 FundSeeder.com, 343 Futures markets, nature of, 3–4 Futures price series selection, 279–288 actual contract series, 279–280 comparing the series, 285–287 constant-forward (“perpetual”) series, 281–282 continuous (spread-adjusted) price series, 282–285 nearest futures, 280 Gain(s): expected, 550, 551 maximization of, 583 Gain-to-pain ratio (GPR), 328–329 Gardner, John, 314 GDP . See Gross domestic product (GDP) General rule, spreads, 443–445 about, 443 applicability and nonapplicability, 443–444 commodities bearing little or no relationship to, 444–445 commodities conforming to inverse of, 444 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:710 SCORE: 15.00 ================================================================================ 692 Index Intercurrency spreads, 471–473 equity change and, 472–473 reasons for implementing, 471–472 Interest rate differentials, intracurrency spreads and, 473, 476 Interest rate parity theorem, 475 Interest rate ratios, intracurrency spreads and, 475 Interest rates: option premiums and, 482–483 recession and, 367 Intermarket spreads, 442, 453, 462–470 Internal trend lines, 73–78 alternate, 75 versus conventional, 74, 76–77 support and resistance and, 106 International Cocoa Agreement, 356 International Sugar Agreement, 356 In-the-money options: definition of, 480 delta values and, 485 Intracurrency spreads, 473–476 interest rate differentials and, 473, 476 interest rate ratios and, 475 Intramarket (or interdelivery) spread, 441 Intramarket stock index spreads, 461–462 Intrinsic value, of options, 489 Intuition, 586 Investment insights, 343 Japanese stock market, 22 Japanese yen (JY), intercurrency spreads and, 471 Jobs report. See Employment report Kitchen sink approach, 312 Kuwait, 1990 invasion of, 420 Last notice day, 9 Last trading day, 9 Leading Indicator myth, 171–172 Least-squares approach, 592–593, 594 Lefèvre, Edwin, 178, 570, 580–581 Lessons, trader’s diary and, 565 Leverage: negative, 320 risk and, 320 through borrowing. see Notional funding Limit days, automatic trading systems and, 296 financial markets and, 13–14 general observations on, 13–15 sell hedge, 11–12 Heteroscedasticity, 672–673 Hidden risk, 320 Hildreth-Lu procedure, 671 Hite, Larry, 585 Hog production: fundamentals and, 348, 350, 356 regression analysis and, 374, 589–591 regression equation and, 633 supply-demand analysis and, 360, 365 Hope, as four-letter word, 584 Housing market: Case-Shiller Home Price Index, 423 housing bubble, 2003-2006, 423, 425 Implied volatility, 483–484 Incorporation of demand: demand change, growth pattern in, 368 demand-influencing variables, identification of, 368–370 highly inelastic demand (and supply elastic relative to demand), 370–371 methods for, 367–371 need for, 366–367 stable demand, 368 Independence, 579 Independent variables: forecasting model, building, 415 multicollinearity and, 665 regression analysis and, 677, 679 Index models, 376–377 Individual contract series, 279–280 Inflation: adjustments, 355 price data for, 414 price-forecasting models and, 383–388 Inflationary boom, 422 Inflation indexes, 383 Information, viewing old as new , 349–350 Intelligence, 582–583 Intercommodity spreads, 441–442. See also Limited- risk spread about, 441–442 contract ratios and, 453–460 Intercrop spreads, 441, 460 Hedging (continued) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:711 SCORE: 15.00 ================================================================================ 693 Index Market(s): agricultural, 351 bear (see Bear market) bull (see Bull market) correlated, leverage reduction and, 562 excitement and, 585 exiting position and, 584–585 free, 357 housing (see Housing market) nonrandom prices and, 587 planned trading approach and, 560 trading results and, 317 Market characteristic adjustments, trend-following systems and, 251–252 Market direction, 449 Market hysteria, 585 Market-if-touched (MIT) order, 18 Market observations. See Rules, trading Market opinion: appearances and, 582–583 change of, 204 Market order, 16 Market patterns, trading rules and, 572–573 Market Profile trading technique, 585 Market psychology, shift in, 429 Market response analysis, 403–411 isolated events and, 409–410 limitations of, 410–411 repetitive events and, 403–410 stock index futures response to employment reports, 408–409 T -Note futures response to monthly U.S. employment report, 404–407 Market Sense and Nonsense: How the Markets Really Work, 319 Market statistics, balance table and, 373–374 Market wizard lessons, 575–587 Market Wizards books, 575, 579, 580, 581, 585, 586 MAR ratio, 330, 335 MBSs. See Mortgage-backed securities (MBSs) McKay, Randy, 576, 581, 583 Measured moves (MM), 190–193 Measures of dispersion, 597–599 Mechanical systems. See T echnical trading systems Metals. See Copper; Gold market Method: determination of, 576 development of, 576 Limited-risk spread, 446–448 Limit order, 17 “Line” (close-only) charts, 40–42 Linearity, transformations to achieve, 666–669 Linearly weighted moving average (LWMA), 239–240 Linked-contract charts, 45–56 comparing the series, 48 continuous (spread-adjusted) price series, 47 creation of, methods for, 46–48 nearest futures, 46–47 nearest vs. continuous futures, 39–40, 48–51, 52–56 necessity of, 45–46 Linked contract series: nearest futures versus continuous futures, 39–40 Link relative method, seasonal index, 394–396 Liquidation information, 564 Live cattle. See Cattle Livestock markets, 287. See also Cattle; Hog production Long call (at-the-money) trading strategy, 491–492 Long call (out-of-the-money) trading strategy, 493–494 Long futures trading strategy, 489–490 Long put (at-the-money), 503–504 Long put (in-the-money), 506–508 Long put (out-of-the-money), 504–506 Long straddle, 515–516 Long-term implications versus short-term response, 432–435 Long-term moving average, reaction to, 181–182 Look-back period, 173 Losing period adjustments, planned trading approach and, 562–563 Losing trades, overlooking, 313 Losses: partial, taking, 583 temporary large, 245 Loyalty/disloyalty, 583–584 Lumber, inflation and, 384 “Magic number” myth, 170 Managers: comparison of two, 320–322 negative Sharpe ratios and, 325 MAR. See Minimum acceptable return (MAR) Margins, 19 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:713 SCORE: 41.00 ================================================================================ 695 Index Option trading strategies, 487–555 comparing, 487–489 hedging applications and, 554–555 multiunit strategies, 543–544 optimal, choosing, 544–554 profit/loss profiles (see Profit/loss profile) spread strategies, other, 542–543 Orders, types of, 16–19 Ordinary least squares (OLS), 654 Organization of the Petroleum Exporting Countries (OPEC), 356, 425 Original trading systems, 261–278 run-day breakout system, 268–273 run-day consecutive count system, 273–278 wide-ranging-day system (see Wide-ranging-day system) Oscillators, 167–170, 255 Out-of-the-money call, buying, 555 Out-of-the-money options: definition of, 480 delta values and, 485 Outright positions, spread tables and, 440, 441 Overbought/oversold indicators, 198–199 Parabolic price moves, 585 Parameter(s): definition of, 291, 606 types of, 292–293 Parameter set: average performance, 311 definition of, 291 Parameter shift, trend-following systems and, 247 Parameter stability, optimizing systems and, 297 Past performance, evaluation, 319–341 investment insights, 343 return alone, 319–322 risk-adjusted return measures, 323–335 visual (see Visual performance evaluation) Patience, virtue of, 580–581 Pattern(s). See also Chart patterns; Continuation patterns; One-day patterns market, 572–573 seasonal, 415 Pattern recognition systems, definition of, 237 Penetration of top and bottom formations, 225–229 Observations, market. See Rules, trading OCO (one-cancels-other) order, 18 Oil. See Crude oil market; Heating oil; WTI crude oil “Old hand” approach, 373 OLS (Ordinary least squares), 654 One-cancels-other (OCO) order, 18 One-day patterns: about, 109–123 spikes, 109–113 One-tailed test, 614, 617 One-year comparisons, 350 OPEC. See Organization of the Petroleum Exporting Countries’ (OPEC) Open interest, volume and, 9–10 Open-mindedness, 585 Optimization: definition of, 297 past performance and, 313 Optimization myth, 298–310 Optimizing systems, 297–298 Option(s): fair value of, theoretical, 483 qualities of, 489 Option premium curve, theoretical, 481 Option premiums, 480–483 components of, 480 interest rates and, 482–483 intrinsic value and, 480 strike price and current futures price, 480–481 theoretical versus actual, 483–484 time remaining until expiration, 481–482 time value and, 480–483 volatility and, 482 Option-protected long futures: long futures + long at-the-money put, 520–521 long futures + long out-of-the-money put, 522–523 Option-protected short futures: short futures + long at-the-money call, 523–524 short futures + long out-of-the-money call, 524–525 Options on futures, 477–485 about, 477–479 delta and (neutral hedge ratio), 484–485 option premiums and (see Option premiums) ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:714 SCORE: 8.00 ================================================================================ 696 Index Preforecast period (PFP) price, 677–678 Premium(s): definition of, 477 dollar value of option, 477–478 Price(s): consumption and, 364 dollar price, 383 grain, 351 nonrandom, 587 preforecast period (PFP) price, 677–678 strike or exercise, 477 supply, demand and swings (see Price swings) target levels and, 356–357 Price changes, price series and, 285 Price envelope bands, 107–108 Price-forecasting models: adding expectations as variable in, 380 demand and, 366–367 inflation and, 383 Price-indicator divergences, 171–172 Price levels: nearest futures and, 91, 101 nearest futures price series and, 48 nominal, comparing, 355 price series and, 285 Price movements: dramatic, 428 fitting news to, 431–432 linked series and, 286 parabolic, 585 trend-following systems and, 245, 246 Price oscillator, 163 Price quoted in, 5 Price reversals, 229 Price seasonality, cash versus futures, 389–390 Price-supporting organizations, 356 Price swings: nearest futures and, 101 nearest futures price series and, 48 Price trigger range (PTR), 262 Probability: distributions, 599–604 heads and tails coin tosses, 390 real versus, 390–391 Probability-weighted profit/loss ratio (PWPLR), 550–551 Producer price index (PPI), 383 Pennants. See Flags and pennants People’s Republic of China (PRC), 418 Percent retracement, reversal of minor reaction, 179–180 Percent return, optimizing systems and, 297 Performance evaluation, visual. See Visual performance evaluation Perishable commodities, 360 “Perpetual” (constant-forward) series, 281–282 Personality, trading method and, 576 Personal trading, analysis of, 565–566 Perspective: keeping, 587 lack of, 351 Petroleum. See Crude oil market; Heating oil; Organization of the Petroleum Exporting Countries’ (OPEC); WTI crude oil Philosophy, trading, 559, 578 Pivotal events, 422 Planned trading approach, 559–566 markets to be traded, 560 personal trading, analysis of, 565–566 planning time routine and, 563 risk control plan (see Risk control plan) trader’s diary, maintaining, 565 trader’s spreadsheet, maintaining, 563–564 trading philosophy and, 559 Point-and-figure charts, 42–43 Population, definition of, 598 Population mean, estimation of, 607 Population regression line, 619–620 Populations and samples, 606 Position, trading around, 581–582 Position exit criteria, 189–204 change of market opinion, 204 chart-based objectives, 189 contrary opinion, 203–204 DeMark sequential, 199–203 measured moves, 190–193 overbought/oversold indicators, 198–199 rule of seven, 194–196 support and resistance levels, 196–197 trailing stops, 204 PPI. See Producer price index (PPI) PRC. See People’s Republic of China (PRC) Precious metals market. See also Gold market carrying charges and, 446 demand and, 362 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:715 SCORE: 51.00 ================================================================================ 697 Index Prudence, 583 PTR. See Price trigger range (PTR) Pure arbitrage, 530 PWPLR. See Probability-weighted profit/loss ratio (PWPLR) Pyramiding: midtrend entry and, 182 rejected signals and, 251 trend-following systems and, 252–253 Quantum Fund, 22 Random error, 628, 679 Random sample, definition of, 608 Random variable, 599 Random Walkers, 29–34 Rate of change, 163 Ratio call write, 532–534 Reaction count, 179–180 Recession, severe, 367. See also Great Recession Regression analysis, 589–595, 675–683 about, 374–375, 589–591 assumptions of, basic, 620 best fit, meaning of, 591–593 dependent variable, determining, 675–676 example, practical, 593 forecast error and, 679–680 independent variables, selecting, 677 least-squares approach, 592–593, 594 practical considerations in applying, 675–683 preforecast period (PFP) price and, 677–678 regression forecast, reliability of, 593–595 simulation, 680–681 step-by-step procedure, sample, 682–683 stepwise regression, 681–682 survey period length and, 678–679 Regression coefficients: computing t-value for, 626 multicollinearity and, 665 sampling distribution of, 621 testing significance of, 620–626 Regression equation, 619–635 analyzing (see Analysis of regression equation) coefficient of determination R 2, 630–633 confidence interval for an individual forecast, 627–629 extrapolation, 630 misspecification and, 679 Production costs, price declines and, 351–352 Profit(s): partial, pulling out, 584 slow systems and, 245, 246 winning trades and, 570–571 Profit/loss matrix, short puts with different strike prices, 514 Profit/loss profile: alternative bearish strategies, three, 548 alternative bullish strategies, three, 547 alternative neutral strategies, two, 549 bear call money spread, 536, 538 bearish “T exas option hedge,” 520 bear put money spread, 539, 542 bull call money spread, 535 bullish “T exas option hedge,” 518 bull put money spread, 541 covered call write, 527 covered put write, 528 definition of, 488 key option trading strategies and, 489–542 key trading strategies and, 489–542 long call (at-the-money), 492, 495 long call (out-of-the-money), 494 long futures, 490 long futures and long call comparisons, 497 long futures and short put comparisons, 514 long put (at-the-money), 504 long put (in-the-money), 507 long put (out-of-the-money), 505 long straddle, 516 option-protected long futures, 521, 522 option-protected short futures, 524, 525 ratio call write, 533 short call (at-the-money), 498 short call (in-the-money), 501 short call (out-of-the-money), 500 short futures, 491 short futures and long put comparisons, 509 short futures and short call comparisons, 503 short put (at-the-money), 510 short put (in-the-money), 513 short put (out-of-the-money), 511 short straddle, 517 synthetic long futures, 529 synthetic short futures, 532 trading strategies and, 488–489 two long calls vs. long futures, 544 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:717 SCORE: 10.00 ================================================================================ 699 Index detrended, 394 link relative method, 394–396, 398 Seasonal patterns, forecasting model, 415 Securitizations, 423 SEE. See Standard error of the estimate (SEE) Segmented trades, analysis of, 565–566 Sell hedge, cotton producer, 11–12 Sell signals, trend-following systems and, 252 SER. See Standard error of the regression (SER) Series selection. See Futures price series selection Settlement type, 9 Sharpe ratio, 323–325, 334, 343. See also Symmetric downside-risk (SDR) Sharpe ratio Short call (at-the-money) trading strategy, 498–499 Short call (in-the-money) trading strategy, 500–502 Short call (out-of-the-money) trading strategy, 499–500 Short futures trading strategy, 490–491 Short put (at-the-money), 509–510 Short put (in-the-money), 512–513 Short put (out-of-the-money), 510–512 Short straddle, 516–517 Short-term response versus long-term implications, 432–435 Sideways market, moving averages and, 79, 81 Signal price, limit days and, 296 Signals, failed, 205, 206 Simple moving average (SMA), 165–167 Simple regression, 625 Simulated results, 312–313 fabrication, 313 kitchen sink approach, 312 losing trades, overlooking, 313 optimization and, 317 risk, ignoring, 312–313 terminology and, 311 transaction costs, 313 well-chosen example, 312 Simulation, blind, 311 Single market system variation (SMSV), 256–257 Skill, hard work versus, 576–577 Sklarew , Arthur, 194 Slippage: automatic trading systems and, 295 sampling distribution and, 608 transaction costs and, 291 trend-following systems and, 247 Rules, trading, 567–574 analysis and review of, 573–574 market patterns and, 572–573 miscellaneous, 571–572 risk control (money management), 569–570 trade entry, 568–569 trade exit, 569–570 winning trades, holding/exiting, 570–571 Run-day breakout system, 268–273 basic concept, 268 daily checklist, 269 illustrated example, 270–273 parameters, 269 parameter set list, 270 trading signals, 269 Run-day consecutive count system, 273–278 basic concept, 273 daily checklist, 274 definitions, 273 illustrated example, 275–278 parameters, 274 parameter set list, 274 trading signals, 273–274 Run days, 116, 118–119, 268 Russell 2000 Mini, intermarket stock index spreads, 461–470 Samples, populations and, 598, 606 Sampling distribution, 608–609 Sands, Russell, 434 Saucers. See Rounding tops and bottoms Saudi Arabia, 425 Scale order, 18 Schwager, Jack, 319 Schwartz, Marty, 22, 585 SDR Sharpe ratio, 327–328, 334 SE. See Standard error (SE) Seasonal analysis, 389–401 cash versus futures price seasonality, 389–390 expectations, role of, 390 real or probability, 390–391 seasonal index (see Seasonal index) seasonal trading, 389 Seasonal considerations, ignoring, 356 Seasonal index, 391–401 alternative approach, 396–401 average percentage method, 391–394 ================================================================================ SOURCE: eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf#page:718 SCORE: 17.00 ================================================================================ 700 Index stock index futures and (see Stock index futures) time, 542 types of, 441–442 Spread seasonality, 449 Spreadsheet, maintaining traders, ’ 563–564 Stability: of return, 338 time (see Time stability) Standard deviation: calculation of, 323, 599 estimation of, 607 Standard error (SE), 612, 627 Standard error of the estimate (SEE), 627 Standard error of the mean, 612 Standard error of the regression (SER): about, 627 multiple regression model and, 641–642 simulation and, 681 Standardized residuals, regression run analysis and, 647 Statistic, definition of, 606 Statistics: elementary (see Elementary statistics) forecasting model, building, 414 influence of expectations on actual, 381 using prior-year estimates rather than revised, 379–380 Steidlmayer, Peter, 585 Stepwise regression, 681–682 Stochastic indicator, 199 Stock index futures: dividends and, 462 intermarket stock index spreads, 462–470 intramarket stock index spreads, 461–462 most actively traded contracts, 463 response to employment reports, 408–409 spread pairs, 463 spread trading in, 461–470 Stock market collapse, 425 Stop, trailing. See Trailing stop Stop close only, 18 Stop-limit order, 17 Stop-loss points, 183–188 flags and pennants and, 184–185 money stop and, 185, 187 relative highs and relative lows, 185, 186 relative lows and, 185, 186 selecting, 183–188 SMSV . See Single market system variation (SMSV) Soros, George, 22 Source/product spread, 442 Soybeans, inflation and, 384 Spike(s), 109–113 definition of, 112–113 reversal days and, 147 “spike days,” 237 Spike days. See Spike(s) Spike extremes, return to, 213–216 Spike highs: penetration of, 214–215 qualifying conditions and, 110–111 significance of, 109 spike extremes and, 213–216 Spike lows: penetration of, 215 price declines, 109 significance of, 110 Spike penetration signals negated, 216 Spike reversal days, 115–116 Spot gold, 555 Spread-adjusted (continuous) price series, 282–285 Spread order, 15, 19 Spreads: about, 439–440 analysis and approach, 448–449 balanced, 455 butterfly, 542 chart analysis and, 449 credit, 535 currency futures and (see Currency futures) definition of, 440 diagonal, 542 equal-dollar-value spread, 455–460 fundamentals and, 449 general rule (see General rule, spreads) historical comparison and, 448 intercommodity (see Intercommodity spreads) intercrop, 441, 460 intermarket, 442, 453 intramarket (or interdelivery), 441 limited-risk, 446–448 pitfalls and points of caution, 449–451 rather than outright - example, 445–446 reason for trading, 440–441 seasonality and, 449 similar periods, isolation of, 449 ================================================================================ SOURCE: eBooks\Branden Turner - Options Trading (azw3 epub mobi)\Branden Turner - Options Trading.epub#section:c003.xhtml SCORE: 11.00 ================================================================================ Introduction C ongratulations on downloading “ Options Trading,” and thank you for doing so. The world of options trading is growing increasingly chaotic, and downloading this book is the first step you can take towards actually doing something about it. The first step is also always the easiest. However, the information you find in the following chapters is so important to take to heart as they are not concepts that can be put into action immediately. If you file them away for when they are really needed, then when the time comes that you actually use them, you will be glad you did. To that end, the following chapters will discuss the primary preparedness principals that you will need to consider if you ever hope to really be successful in the investing world. This means you will want to consider the quality of your options—including the potential issues raised by their current value, how they can be best utilized in an emergency case to drive in quick cash, and how to operate with them properly. With stock selection out of the way, you will then learn everything you need to know about trading in a wide variety of markets including stocks, forex, and commodities (using the options instrument in each market). Rounding out the three primary requirements for successful options trading, you will then learn about crucial risk management principles and what they will mean for you. Finally, you will learn how investing is the quickest way to reach financial freedom. There are plenty of books on this subject on the market, thanks again for choosing this one! Every effort was made to ensure it is full of as much useful information as possible, so please enjoy! ================================================================================ SOURCE: eBooks\Branden Turner - Options Trading (azw3 epub mobi)\Branden Turner - Options Trading.epub#section:c016.xhtml SCORE: 11.00 ================================================================================ CFD T his is a key point that actually explains why there is much less bureaucracy for forex trading than for buying and selling bank shares. CFDs (Contract for Difference) are contracts for differences that follow the performance of a given underlying (share, currency, index, etc.) and that can be exchanged, that is, bought or sold. CFDs differ from shares because they are not co-owned by a company and therefore do not give voting rights to those holding them. However, CFDs offer the same economic benefits as equities, such as profits, dividends, and splits. In even more technical terms, the CFD exchanges the difference in value between the opening price of the certain underlying security (e.g., share) and its closing price. Following this mechanism, the trader who negotiates CFDs: Gets a positive result if it buys before the underlying goes up Gets a negative result if it sells before the underlying goes down The mechanism is very simple, and we are sure that it is already clear. We need to buy if we think that a stock is close to the upside, we need to sell it if we think that a stock is close to the downside. CFDs follow the values of the underlying assets so you can get positive results just like shareholders, but playing at home from the comfort of your home. ================================================================================ SOURCE: eBooks\Branden Turner - Options Trading (azw3 epub mobi)\Branden Turner - Options Trading.epub#section:c042.xhtml SCORE: 13.00 ================================================================================ Chapter 5: Ways to Trade T he main method for investing in the forex market, therefore, remains the classic forex market. When you operate on the forex market, you are actually buying and selling currencies. However, over the years, other financial instruments have been introduced to invest in forex and currencies indices on the forex exchange. We are talking about CFD (contract for difference) and binary options. The main feature of these two financial instruments is the following: when you use them to invest in forex, you will not actually own the lots you are investing in. That said, for those who do not intend to trade online, it could make little sense. Let's try to clarify. Both CFDs and binary options are contracts between investors and brokers. It's not like the classic forex market, where traders buy and sell among themselves. In CFDs and binary options, the asset movement (in this case the buying and selling of currencies) does not take place. CFDs and binary options are used to speculate on the performance of the value of equity securities. If the trader's forecast is correct, the operation will lead to a profit; vice versa, if the trader's prediction is wrong, the operation will lead to a loss. So, the mode of operation is similar to the stock market: if I invest on the upside, whether I do it with CFDs or actually buy currencies, I only earn money if the value increases. As we explained in the previous paragraphs, CFDs are also derivative instruments, so they are used to speculate on the performance of asset values. This means that when you buy and sell CFDs, you will never own the asset traded (as opposed to classic forex trading). Moreover, as with binary options, with CFDs it is possible to trade on: Equity securities Equity indices Forex currencies pairs Commodities ETF Leverage plays an important role in CFD trading: through leverage, we can literally multiply the value of our investment. Just to give an example, if you use a lever of 1: 100 and invest € 100, thanks to this lever you can move well € 10,000 (using only your hundred!). All this is made possible thanks to the leverage, which is a sort of "loan" (if we can define it) by the broker, thanks to which you can invest more money than you really have. But if we talk about eToro, we can't avoid talking about Social Trading. For those who do not know, eToro was the first broker to have introduced Social Trading in CFDs. Thanks to Social trading it is possible to invest by copying (automatically) the operations carried out by the other traders registered on the eToro platform. All you need is a couple of clicks to find the traders to follow, choose the amount to invest, and you're done. In this way, even novice traders can exploit the knowledge and experience of professional traders, copying their operations. The online trading strategies are based on the study of mathematical and graphic analysis that can suggest the trader the best moment to buy and sell. As we have seen today, it is possible to invest in the stock market thanks to online trading, choosing between trading binary options and trading with the forex market. Precise right away that there is no suitable trading strategy for all traders, but there are different trading strategies, based on traders and their style of trading. Therefore, it is possible to customize different online trading strategies on the basis of their trading objectives, their intellectual and psychological abilities. We also recommend using 2 proven techniques not to turn winnings into losses: stop loss: it establishes a maximum loss that you are willing to suffer; take profit: you place a dynamic exit level that rises slowly. ================================================================================ SOURCE: eBooks\Branden Turner - Options Trading (azw3 epub mobi)\Branden Turner - Options Trading.epub#section:c079.xhtml SCORE: 23.00 ================================================================================ Chapter 10: Swing Trading Options S wing trading with options can be extremely difficult. This is why we decided to create this chapter, in which we go through some of the main ideas and concepts to always keep in mind, to be profitable from the start. Now, it is clear that at the beginning it is not easy to take money out of the market. However, with the right guidelines, it is not that difficult to achieve success in a short period of time. Anyway, let's get into some of the key factors to consider when it comes to swing trading with options. “ If you are undecided, stay still.” It is not necessary to invest continuously. If you do not have precise ideas, it is better to do nothing and wait for clearer signs. Often times, the market is full of indecision: keep calm and stack up money for the future. "Cut losses and let profits run.” This is perhaps the best known and most important rule for those investing in the stock market. An indispensable factor for the application of this rule is the identification, immediately after the purchase, of the stop loss. This is how much you are willing to lose on that investment (consider when determining the average daily excursion of the stock). The cold and systematic application, even if painful, of the stop loss will preserve you from huge losses that would make the sale more and more traumatic, freezing capital that could be invested elsewhere. “Learn from your mistakes.” Errors are not always negative: if you follow a strategy with a method, if you apply the stop losses, you will not make particularly serious mistakes. Errors are an integral part of stock trading: you need to analyze why you made them and what you can learn from them. In this way, a small loss can become a good investment lesson for the future. “Take profit and invest them back.” If one of our titles is on the rise, take profit will be applied as the stock grows. A stock cannot grow indefinitely, when the trend is reversed, selling at the top, we will have had a profit avoiding further descents. If then the title should go up again, it does not matter, it will go better next time. You cannot always sell at the top since you cannot time the market. "Buy on the rumor and sell on the news." When positive news on a certain title officially comes out, pay attention. It may already be too late to invest in that title since the market could already have priced it in. Do not believe in “safe investments.” If someone tells you that a title will certainly reach a certain price, he either does not understand much of the stock market or is only doing his own interests. “Never become emotionally attached to a stock.” Some investors always follow a limited number of companies that they consider more reliable than others. There are no titles better than others, but only favorable situations and unfavorable situations. Often, instead of admitting an error, one perseveres on it with the consequence of being heavily unbalanced on a stock. This is really bad, especially if you are overcommitted to a stock in which, at that moment, the market does not believe in. "Always maintain certain liquidity available." Cyclically we find ourselves in situations of several days of generalized decline of the whole stock exchange and often, for lack of liquidity, we cannot grasp excellent buying opportunities. Keep some money aside to jump on big opportunities. “Choose the right platform .” One important rule for investing in the stock market is that the platform makes a difference. Carefully selecting safe, honest and reliable trading platforms is the first step to make money. Those who start investing in the stock market for the first time must be careful to choose platforms that are really simple to use, perhaps with high-quality educational support. Some platforms also offer add-on tools, such as notifications, social trading and free analysis tools to guide less experienced traders. “Invest only in what you understand.” As the "guru" of finance Warren Buffett said, "never, never, invest in something that you do not understand, and above all, that you do not know.” The overwhelming majority of investors can achieve their capital growth goals by using the most common financial instruments, which are almost always simple to understand. The complex tools are best left to the great experts in the field. “Diversify your portfolio.” When investing, the word to keep in mind is “diversification.” Never invest in a single title, because if that sinks, your money will come to the same end. It is always better to have diversified investments to minimize the specific risks of a company, a market, an asset class or a currency. The more you diversify and the lower the probability of having drastic falls. “Understand and evaluate the risk.” The risk is an intrinsic component of every investment. If it does not exist, there is no return. Whether they are government bonds, stocks or mutual funds, they all have a risk component, which will obviously be greater if you want to hope for higher returns. So, if someone tells you that there is an investment without risk, it means that it is better to get advice from someone else. “Look beyond direct investment .” As an alternative to direct purchase of shares, it is possible to invest in the stock market indexes, through ETFs (listed mutual funds, which replicate the performance of equity and bond indices), or in mutual funds, that offer a high diversification even with minimum amounts, allow you to invest small periodic shares, for example 100 euros per month, and may even provide a monthly coupon. “Do not follow the masses.” The typical decision of who buys stocks by investing in the stock market is usually strongly influenced by the advice of acquaintances, neighbors, or relatives. So, if everyone around is investing in a particular company, a beginner investor tends to do the same. But this strategy is bound to fail in the long run, and it is not the right approach. There should be no need to say that you should always avoid having a herd mentality if you do not want to lose hard-earned money on the stock market. The world's biggest investor, Warren Buffett, is right when he says, "Be fearful when others are greedy, and be greedy when others are fearful!" “ Do not try to time the market .” One thing that Warren Buffett does not do is try to time the stock market, even if he has a very strong understanding of the key price levels of the single shares. Most investors, however, do exactly the opposite, which often causes losses of money. So, you should never try to give timing to the market a chance. In reality, no one has ever succeeded in doing so successfully and consistently over multiple market cycles. “Be disciplined.” Historically, it has often happened that during periods of a high market upswing, we first caused moments of panic. Market volatility has inevitably made investors poorer, even if the market moved in the intended direction. Therefore, it is prudent to have patience and follow a disciplined investment approach as well as keeping a long-term general picture in mind. “ Be realistic and do not hope .” There is nothing wrong with hoping to make the best investment, but you could be in trouble if the financial goals are not based on realistic assumptions. For example, many stocks have generated more than 50 percent of returns during the big uptrend in recent years. However, this does not mean that we can always expect the same kind of return from the stock exchange. “ Keep your portfolio under control .” We live in a connected world. Every important event that happens anywhere in the world also has an impact on our money. So, we have to monitor our portfolio and make adjustments constantly. “ Be sure to be on the legal side of things .” If someone proposes an investment, it must be verified as an “authorized project.” In our country, those who offer financial investments must be authorized by law, and this is an important safeguard for savers. In fact, the authorization is issued only in the presence of the requested requisites and, once authorized, the financial intermediaries are subject to constant supervision. Checking this is not particularly demanding: if you have internet you can even directly access the information held by the supervisory authorities; otherwise you can contact the authorities themselves using traditional means. “ Be skeptical and do your own research ." Nobody gives anything for nothing: be wary of investment proposals that ensure a very high return. At the promise of high returns, there are usually very high risks or, in some cases, even attempts of fraud. Be wary of the "Ponzi schemes." These "operations," in fact, cannot guarantee any kind of return, as they are normally supplied exclusively by the continuity of the accessions. In other words, when the new signatures are no longer sufficient to pay the "interests" to the previous subscribers, the schemes are destined to fail. Be wary of the vague and generic investment proposals, for which the methods for using the money collected are not explained in detail (what kind of securities will be purchased, at what prices, on which markets, with which risk profiles - interest rate, foreign exchange or counterparty - and whether and which hedging instruments will be used to cover such risks). “ Have a long-term mindset .” According to Warren Buffett, the shares once bought, are not to be sold. It is, therefore, better to evaluate the industrial trends in the long term and then buy them, leaving aside the passengers' enthusiasm. “ When investing in real estate, know the area you are investing in .” To start with, it is good that you put your focus on your area of residence or, if you live in a big city, even on your neighborhood or on one that you know well. If you think to act on a field of action too large, you risk dispersing too much energy towards something that can present totally different solutions. Dedicate yourself only to residential buildings, apartments or houses. The commercial ones, even if they can be very profitable, have other rules and in general greater difficulties. The same for the land: you can do big business, but it is not something suitable for those who start. “ Choose the right leverage and use it to your advantage .” Real estate investments must be done with leverage. If you want to make an investment only with your money, then the essence of real estate investment is not clear to you. In fact, the concept of financial leverage allows you to invest with money that is not yours but to make money directly for you. Leverage an economic tool that allows you to get where you would not get only with your own strength. You can take out a mortgage (if you can afford it) or engage financial partners. It may seem strange to you, but it is not at all: even the richest need partners and remember that a figure that seems almost unimaginable to you, it may be normal to somebody else. " Verba volant, scripta manent " the Latins used to say. So never make verbal agreements, even if it is a relative or a childhood friend. Consult a lawyer to have the templates of the documents to be used. Like everything, at first it will seem difficult, but after a few times you will become an expert in basic legal practices for the sale of real estate, and you will be able to create documents in a very short time even by yourself. “ Consider shorter positions .” In the fixed income universe, a short duration approach is potentially able to reduce sensitivity to rising interest rates, while optimizing the returns/risk rations “ Know your risk/reward ratio .” A higher return may be tempting, but you must be sure not to take too many risks about the remuneration you would get. In bond markets, this means avoiding lengthening duration in a context of rising interest rates. Increasing investments in riskier assets may seem appropriate at the moment (when the macroeconomic scenario is quite positive), but it could turn out to be a rather risky choice if the situation should change. For example, the yields offered by high yield debt, on average 3% in Europe and 5.5% in the United States, would not be sufficient to compensate investors if insolvencies passed from their current level of 2% to a more normal one of the 5%. Conversely, market areas with a good risk/return profile, with high-rated issuers offering attractive returns, include emerging market debt, subordinated financial bonds, and hybrid corporate bonds. Aiming at long-term quality makes it possible to take on fair risks, helping to limit the impact of any negative macroeconomic event. “Take the currency pairing into account.” Global investments are exposed to currency risks. High yield bonds and emerging market funds, for example, are usually denominated in US dollars, but the underlying bonds they hold may be issued in another currency. Fund managers may choose to include currency risk in the overall portfolio risk as exchange rates fluctuate or decide to contain this risk through currency hedging. “ Stay flexible, keep some cash aside .” It is important to have the flexibility to underwrite and liquidate investments to seize the best opportunities. However, trades are expensive and can quickly erode earnings. This happens above all in the bond markets, given the relatively low levels of returns. The bid-ask spread is on average 30-40% of the yield, so an excess of trades erodes this margin and obviously reduces the total return. Even holding portfolios with structurally short duration, allowing short-term bonds to come to maturity naturally, can improve returns because you will effectively pay the bid-ask spread once. “ Build up your portfolio over time .” If investing a small sum such as 5000 Euro, will not allow you to live on that income, it can certainly represent an opportunity, to make money. Also, even if you have good economic availability, the ideal is always "to make it safe," start to invest from small figures and then fuel the investment over time. “The past does not equal the future.” The story is not indicative of how an investment will result in the future and investors should always try to weigh the potential risks associated with a particular investment, as well as its possible returns. Once you have established a profitable options trading strategy that generates a passive income every single month, you cannot fly to Thailand and live the laptop lifestyle just yet. As the millionaire Tony Robbins said, just because it works, it does not mean it will last forever . I really want this to sink in as it is one of the most important notions of the entire book. When things are moving in the right direction, it is time to triple down on your effort and truly commit yourself to mastery. In particular, there is one thing that I'd like you to do once the first profits start to come. Find a mentor One of the great things about success is that it leaves footsteps: almost anything you would like to do to improve your life has already been done by someone else. It does not matter whether you are starting a business, beginning your trading journey, having a happy marriage, losing weight, quitting smoking, running a marathon or simply organizing a perfect lunch. There is certainly someone who did it very well and has left some clues. When you are able to take advantage of these precious clues, you will discover that life is like a game in which you must connect the dots, and all the dots have already been identified and organized by others. All you have to do is follow their project and use their system. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:14 SCORE: 18.00 ================================================================================ xiii IntroduCtIon You have a tremendous advantage over algorithmic trading models, investment bank trading desks, hedge funds, and anyone who appears on or pays attention to cable business news shows. This book is written to show where that advantage lies and how to exploit it to make confident and suc- cessful investment choices. In doing so, it explains how options work and what they can tell you about the market’s estimation of the value of stocks. even if, after reading it, you decide to stick with straight stock in- vesting and never make an option transaction, understanding how options work will give you a tremendous advantage as an investor. The reason for this is simple: by understanding options, you can understand what the rest of the market is expecting the future price of a stock to be. Understanding what future stock prices are implied by the market is like playing cards with an opponent who always leaves his or her hand face up on the table. Y ou can look at the cards you are dealt, compare them with your opponent’s, and play the round only when you are sure that you have the winning hand. By incorporating options into your portfolio, you will enjoy an even greater advantage because of a peculiarity about how option prices are determined. Option prices are set by market participants making trans- actions, but those market participants all base their sale and purchase decisions on the same statistical models. These models are like sausage grinders. They contain no intelligence or insight but rather take in a few simple inputs, grind them up in a mechanical way, and spit out an option price of a specific form. An option model does not, for instance, care about the operational details of a company. This oversight can lead to situations that seem to be too good to be true. For instance, I have seen a case in which an investor ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:15 SCORE: 30.00 ================================================================================ could commit to buy a strong, profitable company for less than the amount of cash it held—in effect, allowing the investor to pay $0.90 to receive a dollar plus a share of the company’s future profits! Although it is true that these kinds of opportunities do not come along every day, they do indeed come along for patient, insightful investors. This example lies at the heart of intelligent option investing, the es- sence of which can be expressed as a three-step process: 1. Understanding the value of a stock 2. Comparing that intelligently estimated value with the mechani- cally derived one implied by the option market 3. Tilting the risk-reward balance in one’s favor by investing in the best opportunities using a combination of stocks and options The goal of this book is to provide you with the knowledge you need to be an intelligent option investor from the standpoint of these three steps. There is a lot of information contained within this book but also a lot of information left out. This is not meant to be an encyclopedia of option equations, a handbook of colorfully named option strategies, or a treatise on financial statement analysis. Unlike academic books covering options, such as hull’s excellent book, 1 not a single integration symbol or mathematical proof is found between this book’s covers. Understanding how options are priced is an important step in being an intelligent option investor; doing dif- ferential partial equations or working out mathematical proofs is not. Unlike option books written for professional practitioners, such as natenberg’s book,2 you will not find explanations about complex strategies or graphs about how “the greeks”3 vary under different conditions. Floor traders need to know these things, but intelligent option investors—those making considered long-term investments in the financial outcomes of companies—have very different motivations, resources, and time horizons from floor traders. Intelligent option investors, it turns out, do better not even worrying about the great majority of things that floor traders must consider every day. Unlike how-to books about day trading options, this book does not have one word to say about chart patterns, market timing, get-rich-quick schemes, or any of the many other delusions popular among people who xiv  •   Introduction ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:16 SCORE: 24.00 ================================================================================ Introduction    • xv will soon be paupers. Making good decisions is a vital part of being an intelligent option investor; frenetic, haphazard, and unconsidered trading is most certainly not. Unlike books about securities analysis, you will not find detailed dis- cussions about every line item on a financial statement. Understanding how a company creates value for its owners and how to measure that value is an important step in being an intelligent option investor; being able to rattle off information about arcane accounting conventions is not. To paraphrase Warren Buffett, 4 this book aims to provide you with a sound intellectual framework for assessing the value of a company and making rational, fact-based decisions about how to invest in them with the help of the options market. The book is split into three parts: • part I provides an explanation of what options are, how they are priced, and what they can tell you about what the market thinks the future price of a stock will be. This part corresponds to the second step of intelligent option investing listed earlier. • part II sets forth a model for determining the value of a company based on only a handful of drivers. It also discusses some of the behavioral and structural pitfalls that can and do affect investors’ emotions and how to avoid them to become a better, more rational investor. This part corresponds to the first step of intelligent option investing listed earlier. • part III turns theory into practice—showing how to read the nec- essary information on an option pricing screen; teaching how to measure and manage leverage in a portfolio containing cash, stocks, and options; and going into detail about the handful of op- tion strategies that an intelligent option investor needs to know to generate income, boost growth, and protect gains in an equity port- folio. This part corresponds to the final step of intelligent option investing listed earlier. no part of this book assumes any prior knowledge about options or stock valuation. That said, it is not some sort of “Options for Beginners” or “My First Book of valuation” treatment either. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:17 SCORE: 12.00 ================================================================================ Investing beginners will learn all the skills—soup to nuts—they need to successfully and confidently invest in the stock and options market. peo- ple who have some experience in options and who may have used covered calls, protective puts, and the like will find out how to greatly improve their results from these investments and how to use options in other ways as well. professional money managers and analysts will develop a thorough understanding of how to effectively incorporate option investments into their portfolio strategies and may in fact be encouraged to consider ques- tions about valuation and behavioral biases in a new light as well. The approach used here to teach about valuation and options is unique, simple without being simpleminded, and extremely effective in communicating these complex topics in a memorable, vivid way. r ead- ers used to seeing option books littered with hockey-stick diagrams and partial differential equations may have some unlearning to do, but no mat- ter your starting point—whether you are a novice investor or a seasoned hedge fund manager—by the end of this book, I believe that you will look at equity investing in a new light. xvi  •   Introduction ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:18 SCORE: 17.00 ================================================================================ 1 Part I OptiOns FOr the intelligent invest Or Don’t believe anything you have heard or read about options. If you listen to media stories, you will learn that options are modern financial innovations so complex that only someone with an advanced degree in mathematics can properly understand them. Every contention in the preceding sentence is wrong. If you listen to the pundits and traders blabbing on the cable business channels, you will think that you will never be successful using options unless you understand what “put backspreads, ” “iron condors, ” and count- less other colorfully named option strategies are. Y ou will also learn that options are short-term trading tools and that you’ll have to be a razor-sharp “technical analyst” who can “read charts” and jump in and out of positions a few times a week (if not a few times a day) to do well. Every contention in the preceding paragraph is so wrong that believing them is liable to send you to the poor house. The truth is that options are simple, directional instruments that we understand perfectly well from countless encounters with them in our daily lives. They are the second-oldest financial instrument known to humanity—in a quite literal sense, modern economic life would not be possible without them. Options are instruments that not only can be used but should be used in long-term strategies; they most definitely should be traded in and out of as infrequently as possible. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:19 SCORE: 20.00 ================================================================================ 2  •   The Intelligent Option Investor The first part of this book will give you a good understanding of what options are, how their prices are determined, and how those prices fluctuate based on changes in market conditions. There is a good reason to develop a solid understanding of this theoretical background: the framework the option market uses to determine the price of options is based on provably faulty premises that, while “approximately right” in certain circumstances, are laughably wrong in other circumstances. The faults can be exploited by intelligent, patient inves- tors who understand which circumstances to avoid and which to seek out. Without understanding the framework the market uses to value options and where that framework breaks down, there is no way to exploit the faults. Part I of this book, in a nutshell, is designed to give you an understanding of the framework the market uses to value options. This book makes extensive use of diagrams to explain option theory, pricing, and investment strategies. Those readers of the printed copy of this book are encouraged to visit the Intelligent Option Investor website (www .IntelligentOptionInvestor.com) to see the full-color versions of the type of illustrations listed here. Doing so will allow you to visualize options even more effectively in the distinctive intelligent option investing way. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:20 SCORE: 44.00 ================================================================================ 3 Chapter 1 OptiOn Fundamentals This chapter introduces what an option is and how to visualize options in an intelligent way while hinting at the great flexibility and power a sensible use of options gives an investor. It is split into three sections: 1. Option Overview: Characteristics, everyday options, and a brief option history. 2. Option Directionality: An investigation of similarities and differ - ences between stocks and options. This section also contains an introduction to the unique way that this book visualizes options and to the inescapable jargon used in the options world and a bit of intelligent option investor–specific jargon as well. 3. Option Flexibility: An explanation of why options are much more investor-friendly than stocks, as well as examples of the handful of strategies an intelligent option investor uses most often. Even those of you who know something about options should at the very least read the last section. Y ou will find that the intelligent option investor makes very close to zero use of the typical hockey-stick diagrams shown in other books. Instead, this book uses the concept of a range of exposure. The rest of the book—discussing option pricing, corporate valuation, and option strategies—builds on this range-of-exposure concept, so skipping it is likely to lead to confusion later. This chapter is an important first step in being an intelligent option investor. Someone who knows how options work does not qualify as be- ing an intelligent option investor, but certainly, one cannot become an ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:21 SCORE: 33.00 ================================================================================ 4  •   The Intelligent Option Investor intelligent option investor without understanding these basic facts. The concepts discussed here will be covered in greater detail and depth later in this book. For now, it is enough to get a sense for what options are, how to think about them, and why they might be useful investment tools. Characteristics and History By the end of this section, you should know the four key characteristics of options, be able to name a few options that are common in our daily lives, and understand a bit about the long history of options as a financial product and how modern option markets operate. Jargon introduced in this section is as follows: Black-Scholes-Merton model (BSM) Listed look-alike Central counterparty Characteristics of Options Rather than giving a definition for options, I’ll list the four most important characteristics that all options share and provide a few common examples. Once you understand the basic characteristics of options, have seen a few examples, and have spent some time thinking about them, you will start to see elements of optionality in nearly every situation in life. An option 1. Is a contractual right 2. Is in force for a specified time 3. Allows an investor to profit from the change in value of another asset 4. Has value as long as it is still in force This definition is broad enough that it applies to all sorts of options— those traded on a public exchange such as the Chicago Board Options Exchange and those familiar to us in our daily lives. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:22 SCORE: 23.00 ================================================================================ Option Fundamentals   • 5 Options in Daily Life The type of option with which people living in developed economies are most familiar is an insurance contract. Let’s say that you want to fully insure your $30,000 car. Y ou sign a contract (option characteristic number 1) with your insurance company that covers you for a specified amount of time (option characteristic number 2)—let’s say one year. If during the coverage period your car is totaled, your insurance company buys your wreck of a car (worth $0 or close to it) for $30,000—allowing you to buy an identical car. When this happens, you as the car owner (or investor in a real asset) realize a profit of $30,000 over the market value of your destroyed car (option characteristic number 3). Obviously, the insurance company is bound to uphold its promise to indemnify you from loss for the entire term of the contract; the fact that you have a right to sell a worthless car to your insurance company for the price you paid for it implies that the insurance has value during its entire term (option characteristic number 4). Another type of option, while perhaps not as widely used by everyday folks, is easily recognizable. Imagine that you are a struggling author who has just penned your first novel. The novel was not a great seller, but one day you get a call from a movie producer offering you $50,000 for the right to draft a screenplay based on your work. This payment will grant the producer exclusive right (option characteristic number 1) to turn the novel into a movie, as well as the right to all proceeds from a potential future movie for a specific period of time (option characteristic number 2)—let’s say 10 years. After that period is up, you as the author are free to renegotiate an- other contract. As a struggling artist working in an unfulfilling day job, you happily agree to the deal. Three weeks later, a popular daytime talk show host features your novel on her show, and suddenly, you have a New York Times bestseller on your hands. The value of your literary work has gone from slight to great in a single week. Now the movie producer hires the Cohen brothers to adapt your film to the screen and hires George Clooney, Matt Damon, and Julia Roberts to star in the movie. When it is released, the film breaks records at the box office. How much does the producer pay to you? Nothing. The producer had a contractual right to profit from the screenplay based on your work. When the producer bought this right, your literary work was not worth much; suddenly, it is worth a great deal, and ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:23 SCORE: 24.00 ================================================================================ 6  •   The Intelligent Option Investor the producer owns the upside potential from the increase in value of your story (option characteristic number 3). Again, it is obvious that the right to the literary work has value for the entire term of the contract (option characteristic number 4). Keep these characteristics in mind, and we will go on to look at how these defining elements are expressed in financial markets later in this chapter. Now that you have an idea of what an option looks like, let’s turn briefly to a short history of these financial instruments. A Brief History of Options Many people believe that options are a new financial invention, but in fact, they have been in use for more than two millennia—one of the first historically attested uses of options was by a pre-Socratic philosopher named Miletus, who lived in ancient Greece. Miletus the philosopher was accused of being useless by his fellow citizens because he spent his time considering philosophical matters (which at the time included a study of natural phenomena as well) rather than putting his nose to the grindstone and weaving fishing nets or some such thing. Miletus told them that his knowledge was in fact not useless and that he could apply it to something people cared about, but he simply chose not to. As proof of his contention, when his studies related to weather revealed to him that the area would enjoy a bumper crop of olives in the upcoming season, he went around to the owners of all the olive presses and paid them a fee to reserve the presses (i.e., he entered into a contractual agreement— option characteristic number 1) through harvest time (i.e., the contract had a prespecified life—option characteristic number 2). Indeed, Miletus’s prediction was correct, and the following season yielded a bumper crop of olives. The price of olives must have fallen because of the huge surge of supply, and demand for olive presses skyrocketed (because turning the olive fruit into oil allowed the produce to be stored longer). Because Miletus had cornered the olive press market, he was able to generate huge profits, turning the low-value olives into high-value oil (i.e., he profited from the change in value of an underlying asset—option characteristic number 3). His rights to the olive presses ended after the har- vest but not before he had become very wealthy thanks to his philosophical ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:24 SCORE: 24.00 ================================================================================ Option Fundamentals   • 7 studies (i.e., his contractual rights had value through expiration—option characteristic number 4). This is only one example of an ancient option transaction (a few thou- sand years before the first primitive common stock came into existence), but as long as there has been insurance, option contracts have been a well- understood and widely used financial instrument. Can you imagine how little cross-border trade would occur if sellers and buyers could not shift the risk of transporting goods to a third party such as an insurance company? How many ships would have set out for the Spice Islands during the Age of Exploration, for instance? Indeed, it is hard to imagine what trade would look like today if buyers and sellers did not have some way to mitigate the risks associated with uncertain investments. For hundreds of years, options existed as private contracts specifying rights to an economic exposure of a certain quantity of a certain good over a given time period. Frequently, these contracts were sealed between the producers and sellers of a commodity product and wholesale buyers of that commodity. Both sides had an existing exposure to the commodity (the producer wanted to sell the commodity, and the wholesaler wanted to buy it), and both sides wanted to insure themselves against interim price movements in the underlying commodity. But there was a problem with this system. Let’s say that you were a Renaissance merchant who wanted to insure your shipment of spice from India to Europe, and so you entered into an agreement with an insurer. The insurer asked you to pay a certain amount of premium up front in return for guaranteeing the value of your cargo. Y our shipment leaves Goa but is lost off Madagascar, and all your investment capital goes down with the ship to the bottom of the Indian Ocean. However, when you try to find your option counterparty—your insurer—it seems that he has absconded with your premium money and is living a life of pleasure and song in another country. In the parlance of modern financial markets, your option investment failed because of counterparty risk. Private contracts still exist today in commodity markets as well as the stock market (the listed look-alike option market—private contracts specifying the right to upside and downside exposure to single stocks, exchange-traded funds, and baskets is one example that institutional investors use heavily). However, private contracts still bring with them a ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:25 SCORE: 36.00 ================================================================================ 8  •   The Intelligent Option Investor risk of default by one’s counterparty, so they are usually only entered into after both parties have fully assessed the creditworthiness of the other. Obviously, individual investors—who might simply want to speculate on the value of an underlying stock or exchange-traded fund (ETF)—cannot spend the time doing a credit check on every counterparty with whom they might do business. 1 Without a way to make sure that both parties are financially able to keep up their half of the option bargain, public option markets simply could not exist. The modern solution to this quandary is that of the central counter - party. This is an organization that standardizes the terms of the option con- tracts transacted and ensures the financial fulfillment of the participating counterparties. Central counterparties are associated with securities exchanges and regulate the parties with which they deal. They set rules regarding collateral that must be placed in escrow before a transaction can be made and request additional funds if market price changes cause a counterparty’s account to become undercollateralized. In the United States, the central counterparty for options transactions is the Options Clearing Corporation (OCC). The OCC is an offshoot of the oldest option exchange, the Chicago Board Option Exchange (CBOE). In the early 1970s, the CBOE itself began as an offshoot of a large futures exchange—the Chicago Mercantile Exchange—and subsequently started the process of standardizing option contracts (i.e., specifying the exact per-contract quantity and quality of the underlying good and the expiration date of the contract) and building the other infrastructure and regulatory framework necessary to create and manage a public market. Although market infrastructure and mechanics are very important for the brokers and other professional participants in the options market, most aspects are not terribly important from an investor’s point of view (the things that are—such as margin—will be discussed in detail later in this book). The one thing an investor must know is simply that the option market is transparent, well regulated, and secure. Those of you who have a bit of extra time and want to learn more about market mechanics should take a look through the information on the CBOE’s and OCC’s websites. Listing of option contracts on the CBOE meant that investors needed to have a sense for what a fair price for an option was. Three academics, Fischer Black, Myron Scholes, and Robert Merton, were responsible for ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:26 SCORE: 33.00 ================================================================================ Option Fundamentals   • 9 developing and refining an option pricing model known as the Black- Scholes or Black-Scholes-Merton model, which I will hereafter abbreviate as the BSM. The BSM is a testament to human ingenuity and theoretical elegance, and even though new methods and refinements have been developed since its introduction, the underlying assumptions for new option pricing methods are the same as the BSM. In fact, throughout this book, when you see “BSM, ” think “any statistically based algorithm for determining option p r i c e s .” The point of all this background information is that options are not only not new-fangled financial instruments but in fact have a long and proud history that is deeply intertwined with the development of modern economies themselves. Those of you interested in a much more thorough coverage of the history of options would do well to read the book, Against the Gods: The Remarkable History of Risk, by Peter Bernstein (New Y ork: Wiley, 1998). Now that you have a good sense of what options are and how they are used in everyday life, let’s now turn to the single most important thing for a fundamental investor to appreciate about these financial instruments: their inherent ability to exploit directionality. Directionality The key takeaway from this section is evident from the title. In addition to demonstrating the directional power inherent in options, this section also introduces the graphic tools that I will use throughout the rest of this book to show the risk and reward inherent in any investment—whether it is an investment in a stock or an option. For those of you who are not well versed in options yet, this is the section in which I explain most of the jargon that you simply cannot escape when transacting in options. However, even readers who are familiar with options should at least skim through this explanation. Doing so will likely increase your appreciation for the characteristics of options that make them such powerful investment tools and also will introduce you to this novel way of visualizing them. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:27 SCORE: 16.00 ================================================================================ 10  •   The Intelligent Option Investor Jargon introduced in this section is as follows: Call option Moneyness Put option In the money (ITM) Range of exposure At the money (ATM) Strike price Out of the money (OTM) Gain exposure Premium Accept exposure American style Canceling exposure European style Exercise (an option) Visual Representation of a Stock Visually, a good stock investment looks like this: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 Future Stock Price Last Stock Price Y ou can make a lot of mistakes when investing, but as long as you are right about the ultimate direction a stock will take and act accordingly, all those mistakes will be dwarfed by the success of your position. Good investing, then, is essentially a process of recognizing and exploiting the directionality of mispriced stocks. Usually, investors get exposure to a stock’s directionality by buying, or going long, that stock. This is what the investor’s risk and reward profile looks like when he or she buys the stock: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:28 SCORE: 20.00 ================================================================================ Option Fundamentals   • 11 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 GREEN RED As soon as the “Buy” button is pushed, the investor gains expo- sure to the upside potential of the stock—this is the shaded region la- beled “green” in the figure. However, at the same time, the investor also must accept exposure to downside risk—this is the shaded region labeled “red. ” Anyone who has invested in stocks has a visceral understanding of stock directionality. We all know the joy of being right as our investment soars into the green and we’ve all felt the sting as an investment we own falls into the red. We also know that to the extent that we want to gain exposure to the upside potential of a stock, we must necessarily simultane- ously accept its downside risk. Options, like stocks, are directional instruments that come in two types. These two types can be defined in directional terms: Call option A security that allows an investor exposure to a stock’s upside potential (remember, “Call up”) Put option A security that allows an investor exposure to a stock’s downside potential (remember, “Put down”) The fact that options split the directionality of stocks in half—up and down—is a great advantage to an investor that we will investigate more in a moment. Right now, let’s take a look at each of these directional instruments— call options and put options—one by one. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:29 SCORE: 30.00 ================================================================================ 12  •   The Intelligent Option Investor Visual Representation of Call Options In a similar way that we created a diagram of the risk-reward profile of owner- ship in a common stock, a nice way of understanding how options work is to look at a visual representation. The following diagram represents a call option. There are a few things to note about this representation: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 GREEN 1. The shaded area (green) represents the price and time range over which the investor has economic exposure—I term this the range of exposure. Because we are talking about call options, and because call options deal with the upside potential of a stock, you see that the range of exposure lies higher than the present stock price (remember, “Call up”). 2. True to one of the defining characteristics of an option mentioned earlier, our range of exposure is limited by time; the option pictured in the preceding figure expires 500 days in the future, after which we have no economic exposure to the stock’s upside potential. 3. The present stock price is $50 per share, but our upside exposure only begins at $60 per share. The price at which economic exposure begins is called the strike price of an option. In this case, the strike price is $60 per share, but we could have picked a strike price at the market price of the stock, further above the market price of the stock (e.g., a strike price of $75), or even below the market price of the stock. We will inves- tigate optimal strike prices for certain option strategies later in this book. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:30 SCORE: 48.00 ================================================================================ Option Fundamentals   • 13 4. The arrow at the top of the shaded region in the figure indicates that our exposure extends infinitely upward. If, for some reason, this stock suddenly jumped not from $50 to $60 per share but from $50 to $1,234 per share, we would have profitable exposure to all that upside. 5. Clearly, the diagram showing a purchased call option looks a great deal like the top of the diagram for a purchased stock. Look back at the top of the stock purchase figure and compare it with the preceding figure: the inherent directionality of options should be completely obvious. Any time you see a green region on diagrams like this, you should take it to mean that an investor has the potential to realize a gain on the investment and that the investor has gained exposure. Any time an option investor gains exposure, he or she must pay up front for that potential gain. The money one pays up front for an option is called premium (just like the fee you pay for insurance coverage). In the preceding diagram, then, we have gained exposure to a range of the stock’s upside potential by buying a call option (also known as a long call). If the stock moves into this range before or at option expiration, we have the right to buy the stock at our $60 strike price (this is termed exer - cising an option) or simply sell the option in the option market. It is almost always the wrong thing to exercise an option for reasons we discuss shortly. 2 If, instead, the stock is trading below our strike price at expiration, the option is obviously worthless—we owned the right to an upside scenario that did not materialize, so our ownership right is worth nothing. It turns out that there is special jargon that is used to describe the relationship between the stock price and the range of option exposure: Jargon Situation In the money (ITM) Stock price is within the option’s range of exposure Out of the money (OTM) Stock price is outside the option’s range of exposure At the money (ATM) Stock price is just at the border of the option’s range of exposure Each of these situations is said to describe the moneyness of the option. Graphically, moneyness can be represented by the following diagram: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:31 SCORE: 13.00 ================================================================================ 14  •   The Intelligent Option Investor 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 ITM ATM OTM Date/Day Count Stock Price 749 999 GREEN As we will discuss in greater detail later, not only can an investor use options to gain exposure to a stock, but the investor also can choose to accept exposure to it. Accepting exposure means running the risk of a financial loss if the stock moves into an option’s range of exposure. If we were to accept expo- sure to the stock’s upside potential, we would graphically represent it like this: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 RED Any time you see a shaded region labeled “red” on diagrams like this, you should take it to mean that the investor has accepted the risk of realizing a loss on the investment and should say that the investor has accepted exposure. Any time an option investor accepts exposure, he or she gets to receive premium up front in return for accepting the risk. In the preceding example, the investor has accepted upside exposure by selling a call option (a.k.a. a short call). ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:32 SCORE: 31.00 ================================================================================ Option Fundamentals   • 15 In this sold call example, we again see the shaded area representing the exposure range. We also see that the exposure is limited to 500 days and that it starts at the $60 strike price. The big difference we see between this diagram and the one before it is that when we gained upside exposure by buying a call, we had potentially profitable exposure infinitely upward; in the case of a short call, we are accepting the possibility of an infinite loss. Needless to say, the decision to accept such risk should not be taken lightly. We will discuss in what circumstances an investor might want to accept this type of risk and what techniques might be used to manage that risk later in this book. For right now, think of this diagram as part of an explanation of how options work, not why someone might want to use this particular strategy. Let’s go back to the example of a long call because it’s easier for most people to think of call options this way. Recall that you must pay a premium if you want to gain exposure to a stock’s directional potential. In the diagrams, you will mark the amount of premium you have to pay as a straight line, as can be seen here: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 Breakeven Line: $62.50 499 Date/Day Count Stock Price 749 999 GREEN I have labeled the straight line the “Breakeven line” for now and have as- sumed that the option’s premium totals $2.50. Y ou can think of the breakeven line as a hurdle the stock must cross by expiration time. If, at expiration, the stock is trading for $61, you have the right to purchase the shares for $60. Y ou make a $1 profit on this trans- action, which partially offsets the original $2.50 cost of the option. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:33 SCORE: 31.00 ================================================================================ 16  •   The Intelligent Option Investor It is important to note that a stock does not have to cross this line for your option investment to be profitable. We will discuss this dynamic in Chapter 2 when we learn more about the time value of options. Visual Representation of Put Options Now that you understand the conventions we use for our diagrams, let’s think about how we might represent the other type of option, dealing with downside exposure—the put. First, let’s assume that we want to gain expo- sure to the downside potential of a stock. Graphically, we would represent this in the following way: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 GREEN First, notice that, in contrast to the diagram of the call option, the directional exposure of a put option is bounded on the downside by $0, so we do not draw an arrow indicating infinite exposure. This is the same downside exposure of a stock because a stock cannot fall below zero dollars per share. In this diagram, the time range for the put option is the same 500 days as for our call option, but the price range at which we have exposure starts at a strike price of $50—the current market price of the stock—making this an at-the-money (ATM) put. If you think about moneyness in terms of a range of exposure, the difference between out of the money (OTM) and in the money (ITM) becomes easy and sensible. Here are examples of differ- ent moneyness cases for put options: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:34 SCORE: 16.00 ================================================================================ Option Fundamentals   • 17 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 OTM ATM ITMGREEN We are assuming that this put option costs $5, leading to a breakeven line of $45. This breakeven line is like an upside-down hurdle in that we would like the stock to finish below $45; if it expires below $50 but above $45, again, we will be able to profit from the exercise, but this profit will not be great enough to cover the cost of the option. 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 Breakeven Line: $45.00 GREEN Obviously, if we can gain downside exposure to a stock, we must be able to accept it as well. We can accept downside exposure by selling a put; this book represents a sold put graphically like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:35 SCORE: 9.00 ================================================================================ 18  •   The Intelligent Option Investor 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 Breakeven Line: $45.00 RED In this diagram, we are receiving a $5 premium payment in return for accepting exposure to the stock’s downside. As such, as long as the stock expires above $45, we will realize a profit on this investment. Visual Representation of Options Canceling Exposure Let’s take a look again at our visual representation of the risk and reward of a stock: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 GREEN RED We bought this stock at $50 per share and will experience an unreal- ized gain if the stock goes up and an unrealized loss if it goes down. What might happen if we were to simultaneously buy a put, expiring in 365 days and struck at $50, on the same stock? Because we are purchasing a put, we know that we are gaining expo- sure to the downside. Any time we gain exposure, we shade the exposure ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:37 SCORE: 19.00 ================================================================================ 20  •   The Intelligent Option Investor Any time a gain of exposure overlaps another gain of exposure, the potential gain from an investment if the stock price moves into that region rises. We will not represent this in the diagrams of this book, but you can think of overlapping gains as deeper and deeper shades of green (when gaining exposure) and deeper and deeper shades of red (when accepting it). Now that you understand how to graphically represent gaining and accepting exposure to both upside and downside directionality and how to represent situations when opposing exposures overlap, we can move onto the next section, which introduces the great flexibility options grant to an investor and discusses how that flexibility can be used as a force of either good or evil. Flexibility Again, the main takeaway of this section should be obvious from the title. Here we will see the only two choices stock investors have with regard to risk and return, and we will contrast that with the great flexibility an option investor has. We will also discuss the concept of an effective buy price and an effective sell price—two bits of intelligent option investor jargon. Last, we will look at a typical option strategy that might be recommended by an option “guru” and note that these types of strategies actually are at cross-purposes with the directional nature of options that makes them so powerful in the first place. Jargon introduced in this chapter is as follows: Effective buy price (EBP) Covered call Effective sell price (ESP) Long strangle Leg Stocks Give Investors Few Choices A stock investor only has two choices when it comes to investing: going long or going short. Using our visualization technique, those two choices look like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:38 SCORE: 8.00 ================================================================================ Option Fundamentals   • 21 - 20 40 60 80 100 120 140 160 180 200 - 20 40 60 80 100 120 140 160 180 200 GREEN GREEN RED RED Going long a stock (i.e., buying a stock). Going short a stock (i.e., short selling a stock). If you want to gain exposure to a stock’s upside potential by going long (left-hand diagram), you also must simultaneously accept exposure to the stock’s downside risk. Similarly, if you want to gain exposure to a stock’s downside potential by going short (right-hand diagram), you also must ac- cept exposure to the stock’s upside risk. In contrast, option investors are completely unrestrained in their ability to choose what directionality to accept or gain. An option investor could, for example, very easily decide to establish exposure to the direc- tionality of a stock in the following way: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 GREEN GREEN GRAY GRAY GREEN RED RED RED Why an investor would want to do something like this is completely beyond me, but the point is that options are flexible enough to allow this type of a crazy structure to be built. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:39 SCORE: 15.00 ================================================================================ 22  •   The Intelligent Option Investor The beautiful thing about this flexibility is that an intelligent option in- vestor can pick and choose what exposure he or she wants to gain or accept in order to tailor his or her risk-return profile to an underlying stock. By tailoring your risk-return profile, you can increase growth, boost income, and insure your portfolio from downside shocks. Let’s take a look at a few examples. Options Give Investors Many Choices Buying a Call for Growth - 50 100 150 200 BE = $55 GREEN Above an investor is bullish on the prospects of the stock and is using a call op- tion to gain exposure to a stock’s upside potential above $50 per share. Rather than accepting exposure to the stock’s entire downside potential (maximum of a $50 loss) as he or she would have by buying the stock outright, the call- option investor would pay an upfront premium of, in this case, $5. Selling a Put for Income 50 100 150 200 - BE = $45 RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:40 SCORE: 19.00 ================================================================================ Option Fundamentals   • 23 Here an investor is bullish on the prospects of the stock, so he or she doesn’t mind accepting exposure to the stock’s downside risk below $50. In return for accepting this risk, the option investor receives a premium—let’s say $5. This $5 is income to the investor—kind of like a do-it-yourself dividend payment. By the way, as you will discover later in this book, this is also the risk- return profile of a covered call. Buying a Put for Protection 50 100 150 200 - GREEN REDGRAY Above an investor wants to enjoy exposure to the stock’s upside potential while limiting his or her losses in case of a market fall. By buying a put option struck a few dollars under the market price of the stock, the investor cancels out the downside exposure he or she accepted when buying the stock. With this protective put overlay in place, any loss on the stock will be compensated for through a gain on the put contract. The investor can use these gains to buy more of the stock at a lower price or to buy another put contract as protection when the first contract expires. Tailoring Exposure with Puts and Calls - 20 40 60 80 100 120 140 160 180 200 BE = $60.50 GREEN RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:41 SCORE: 26.00 ================================================================================ 24  •   The Intelligent Option Investor Here an investor is bullish on the prospects of the stock and is tailor - ing where to gain and accept exposure by selling a short-term put and simultaneously buying a longer-term call. By doing this, the investor basically subsidizes the purchase of the call option with the sale of the put option, thereby reducing the level the stock needs to exceed on the upside before one breaks even. In this case, we’re assuming that the call option costs $1.50 and the put option trades for $1.00. The cash inflow from the put option partially offsets the cash outflow from the call op- tion, so the total breakeven amount is just the call’s $60 strike price plus the net of $0.50. Effective Buy Price/Effective Sell Price One thing that I hope you realized while looking at each of the preceding diagrams is how similar each of them looks to a particular part of our long and short stock diagrams: Buying a stock. - 20 40 60 80 100 120 140 160 180 200 - 20 40 60 80 100 120 140 160 180 200 RED GREEN GREEN RED Short selling a stock. For example, doesn’t the diagram labeled “Buying a call for growth” in the preceding section look just like the top part of the buying stock diagram? ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:42 SCORE: 27.00 ================================================================================ Option Fundamentals   • 25 In fact, many of the option strategies I will introduce in this book simply represent a carving up of the risk-reward profile of a long or short stock position and isolating one piece of it. To make it more clear and easy to remember the rules for breaking even on different strategies, I will actu- ally use a different nomenclature from breakeven. If a diagram has one or both of the elements of the risk-return profile of buying a stock, I will call the breakeven line the effective buy price and abbreviate it EBP. For example, if we sell a put option, we accept downside risk in the same way that we do when we buy a stock: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 EBP = $45 RED Basically, what we are saying when we accept downside risk is that we are willing to buy the stock if it goes below the strike price. In return for accepting this risk, we are paid $5 in premium, and this cash inflow effectively lowers the buying price at which we own the stock. If, when the option expires, the stock is trading at $47, we can think of the situation not as “being $3 less than the strike price” but rather as “being $2 over the b u y p r i c e .” Conversely, if a diagram has one or both of the elements of the risk- return profile of short selling a stock, I will call the breakeven line the effective sell price and abbreviate it ESP. For example, if we buy a put option anticipating a fall in the stock, we would represent it graphically like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:43 SCORE: 16.00 ================================================================================ 26  •   The Intelligent Option Investor 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 ESP = $45 GREEN When a short seller sells a stock, he or she gets immediate profit exposure to the stock’s downside potential. The seller is selling at $50 and hopes to make a profit by buying the shares back later at a lower price—let’s say $35. When we get profit exposure to a stock’s downside potential using options, we are getting the same exposure as if we sold the stock at $50, except that we do not have to worry about losing our shirts if the stock moves up instead of down. In order to get this peace of mind, though, we must spend $5 in premium. This means that if we hold the position to expiration, we will only realize a net profit if the stock is trading at the $50 mark less the money we have already paid to buy that ex- posure—$5 in this case. As such, we are effectively selling the stock short at $45. There are some option strategies that end up not looking like one of the two stock positions—the flexibility of options allows an investor to do things a stock investor cannot. For example, here is the graphic representa- tion of a strategy commonly called a long strangle: 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 BE 1 = $80.75 BE 2 = $19.25 GREEN GREEN ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:44 SCORE: 44.00 ================================================================================ Option Fundamentals   • 27 Here we have a stock trading at $50 per share, and we have bought one put option and one call option. The put option is struck at $20 and is trading for $0.35. The call option is struck at $80 and is trading for $0.40. Note that the top part of the diagram looks like the top part of the long-stock diagram and that the bottom part looks like the bottom part of the short-stock diagram. Because a stock investor cannot be simulta- neously long and short the same stock, we cannot use such terminology as effective buy or effective sell price. In this case, we use breakeven and abbreviate it BE. This option strategy illustrates one way in which options are much more flexible than stocks because it allows us to profit if the stock moves up (into the call’s range of exposure) or down (into the put’s range of exposure). If the stock moves up quickly, the call option will be in the money, but the put option will be far, far, far out of the money . Thus, if we are ITM on the call, the premium paid on the puts probably will end up a total loss, and vice versa. For this reason, we calculate both break- even prices as the sum of both legs of our option structure (where a leg is defined as a single option in a multioption strategy). As long as the leg that winds up ITM is ITM enough to cover the cost of the other leg, we will make a profit on this investment. The only way we can fail to make a profit is if the stock does not move one way or another enough before the options expire. Flexibility without Directionality Is a Sucker’s Game Despite this great flexibility in determining what directional invest- ments one wishes to make, as I mentioned earlier, option market mak- ers and floor traders generally attempt to mostly (in the case of floor traders) or wholly (in the case of market makers) insulate themselves against large moves in the underlying stock or figure out how to lim- it the cost of the exposure they are gaining and do so to such an ex- tent that they severely curtail their ability to profit from large moves. I do not want to belabor the point, but I do want to leave you with one graphic illustration of a “typical” complex option strategy sometimes called a condor : ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:45 SCORE: 21.00 ================================================================================ 28  •   The Intelligent Option Investor 5/18/2012 - 20 40 60 80 100 120 140 160 180 200 5/20/2013 249 499 Date/Day Count Stock Price 749 999 BE 1 BE 2 RED RED There are a few important things to notice. First, notice how much shorter the time frame is—we have moved from a 500-day time exposure to a two-week exposure. In general, a floor trader has no idea of what the long-term value of a stock should be, so he or she tries to protect himself or herself from large moves by limiting his or her time exposure as much as possible. Second, look at how little price exposure the trader is accepting! He or she is attempting to control his or her price risk by making several simultaneous option trades (which, by the way, puts the trader in a worse position in terms of breakeven points) that end up canceling out most of his or her risk exposure to underlying moves of the stock. With this position, the trader is speculating that over the next short time period, this stock’s market price will remain close to $50 per share; what basis the trader has for this belief is beyond me. In my mind, winning this sort of bet is no better than going to Atlantic City and betting that the marble on the roulette wheel will land on red—completely random and with only about a 50 percent chance of success. 3 It is amazing to me that, after reading books, subscribing to newslet- ters, and listening to TV pundits advocating positions such as this, inves- tors continue to have any interest in option investing whatsoever! With the preceding explanation, you have a good foundation in the concept of options, their inherent directionality, and their peerless flex- ibility. We will revisit these themes again in Part III of this book when we investigate the specifics of how to set up specific option investments. However, before we do that, any option investor must have a good sense of how options are priced in the open market. We cover the topic of option pricing in Chapter 2. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:46 SCORE: 21.00 ================================================================================ 29 Chapter 2 The black-scholes- merTon model As you can tell from Chapter 1, options are in fact simple financial instru- ments that allow investors to split the financial exposure to a stock into upside and downside ranges and then allow investors to gain or accept that expo- sure with great flexibility. Although the concept of an option is simple, trying to figure out what a fair price is for an option’s range of exposure is trickier. The first part of this chapter details how options are priced according to the Black- Scholes-Merton model (BSM)—the mathematical option pricing model mentioned in Chapter 1—and how these prices predict future stock prices. Many facets of the BSM have been identified by the market at large as incorrect, and you will see in Part III of this book that when the rubber of theory meets the road of practice, it is the rubber of theory that gets deformed. The second half of this chapter gives a step-by-step refutation to the principles underlying the BSM. Intelligent investors should be very, very happy that the BSM is such a poor tool for pricing options and pre- dicting future stock prices. It is the BSM’s shortcomings and the general market’s unwillingness or inability to spot its structural deficiencies that allow us the opportunity to increase our wealth. Most books that discuss option pricing models require the reader to have a high level of mathematical sophistication. I have interviewed candidates with master’s degrees in financial engineering who indeed had a very high level of mathematical competence and sophistication yet could not translate that sophistication into the simple images that you will see over the next few pages. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:47 SCORE: 27.00 ================================================================================ 30  •   The Intelligent Option Investor This chapter is vital to someone aspiring to be an intelligent options investor. Contrary to what you might imagine, option pricing is in itself something that intelligent option investors seldom worry about. Much more important to an intelligent option investor is what option prices im- ply about the future price of a stock and in what circumstances option prices are likely to imply the wrong stock prices. In terms of our intelligent option investing process, we need two pieces of information: 1. A range of future prices determined mechanically by the option market according to the BSM 2. A rationally determined valuation range generated through an insightful valuation analysis This chapter gives the theoretical background necessary to derive the former. The BSM’s Main Job is to Predict Stock Prices By the end of this section, you should have a big-picture sense of how the BSM prices options that is put in terms of an everyday example. Y ou will also understand the assumptions underlying the BSM and how, when combined, these assumptions provide a prediction of the likely future value of a stock. Jargon introduced in this section includes the following: Stock price efficiency Forward price (stock) Lognormal distribution Efficient market hypothesis (EMH) Normal distribution BSM cone Drift The Big Picture Before we delve into the theory of option pricing, let me give you a general idea of the theory of option prices. Imagine that you and your spouse or significant other have reservations at a nice restaurant. The reservation time is coming up quickly, and you are still at home. The restaurant is extremely hard to get reservations for, and if you are not there at your reservation time, ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:49 SCORE: 15.00 ================================================================================ 32  •   The Intelligent Option Investor This example illustrates precisely the process on which the BSM and all other statistically based option pricing formulas work. The BSM has a fixed number of inputs regarding the underlying asset and the contract itself. Inputting these variables into the BSM generates a range of likely future values for the price of the underlying security and for the statistical probability of the security reaching each price. The statistical probability of the security reach- ing a certain price (that certain price being a strike price at which we are inter- ested in buying or selling an option) is directly tied to the value of the option. Now that you have a feel for the BSM on a conceptual dining- reservation level, let’s dig into a specific stock-related example. Step-by-Step Method for Predicting Future Stock Price Ranges—BSM-Style In order to understand the process by which the BSM generates stock price predictions, we should first look at the assumptions underlying the model. We will investigate the assumptions, their tested veracity, and their impli- cations in Chapter 3, but first let us just accept at face value what Messrs. Black, Scholes, and Merton take as axiomatic. According to the BSM, • Securities markets are “efficient” in that market prices perfectly reflect all publicly available information about the securities. This implies that the current market price of a stock represents its fair value. New information regarding the securities is equally likely to be positive as negative; as such, asset prices are as likely to move up as they are to move down. • Stock prices drift upward over time. This drift cannot exceed the risk-free rate of return or arbitrage opportunities will be available. • Asset price movements are random and their percentage returns follow a normal (Gaussian) distribution. • There are no restrictions on short selling, and all hedgers can bor - row at the risk-free rate. There are no transaction costs or taxes. Trading never closes (24/7), and stock prices are mathematically continuous (i.e., they never gap up or down), arbitrage opportuni- ties cannot persist, and you can trade infinitely small increments of shares at infinitely small increments of prices. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:50 SCORE: 9.00 ================================================================================ The Black-Scholes-Merton Model  • 33 Okay, even if the last assumption is a little hard to swallow, the first three sound plausible, especially if you have read something about the efficient market hypothesis (EMH). Suffice it to say that these assumptions express the “orthodox” opinion held by financial economists. Most finan- cial economists would say that these assumptions describe correctly, in broad-brush terms, how markets work. They acknowledge that there may be some exceptions and market frictions that skew things a bit in the real world but that on the whole the assumptions are true. Let us now use these assumptions to build a picture of the future stock price range predicted by the BSM. Start with an Underlying Asset First, imagine that we have a stock that is trading at exactly $50 right now after having fluctuated a bit in the past. Advanced Building Corp. (ABC) 5/18/2012 5/20/2013 249 499 749 999 100 90 80 70 60 50 40 30 20 Date/Day Count Stock Price I am just showing one year of historical trading data and three years of calendar days into the future. Let’s assume that we want to use the BSM to predict the likely price of this asset, Advanced Building Corp. (ABC), three years in the future. The BSM’s first assumption—that markets are efficient and stock prices are perfect reflections of the worth of the corporation—means that if ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:64 SCORE: 15.00 ================================================================================ The Black-Scholes-Merton Model  • 47 The fact that the theoretical basis of option pricing is provably wrong is very good news for intelligent investors. The essence of intelligent option investing involves comparing the mechanically determined and unreason- able range of stock price predictions made by the BSM with an intelligent and rational valuation range made by a human investor. Because the BSM is using such ridiculous assumptions, it implies that intelligent, rational investors will have a big investing advantage. Indeed, I believe that they do. Now that we have seen how the BSM forecasts future price ranges for stocks and why the predictions made by the BSM are usually wrong, let us now turn to an explanation of how the stock price predictions made by the BSM tie into the option prices we see on an option exchange such as the Chicago Board Option Exchange (CBOE). ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:66 SCORE: 21.00 ================================================================================ 49 Chapter 3 The InTellIgenT InvesTor’s guIde To opTIon prIcIng By the end of this chapter, you should understand how changes in the follow- ing Black-Scholes-Merton model (BSM) drivers affect the price of an option: 1. Moneyness 2. Forward volatility 3. Time to expiration 4. Interest rates and dividend yields Y ou will also learn about the three measures of volatility—forward, im- plied, and statistical. Y ou will also understand what drivers affect option prices the most and how simultaneous changes to more than one variable may work for or against an option investment position. In this chapter and throughout this book in general, we will not try to figure out a precise value for any options but just learn to realize when an op- tion is clearly too expensive or too cheap vis-à-vis our rational expectations for a fair value of the underlying stock. As such, we will discuss pricing in general terms; for example, “This option will be much more expensive than that one. ” This generality frees us from the computational difficulties that come about when one tries to calculate too precise a price for a given op- tion. The BSM is designed to give a precise answer, but for investing, simply knowing that the price of some security is significantly different from what it should be is enough to give one an investing edge. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:67 SCORE: 26.00 ================================================================================ 50  •   The Intelligent Option Investor In terms of how this chapter fits in with the goal of being an intelligent option investor, it is in this chapter that we start overlaying the range of exposure introduced in Chapter 1 with the implied stock price range given by the BSM cone that was introduced in Chapter 2. This perspective will allow us to get a sense of how expensive it will be to gain exposure to a given range or, conversely, to see how much we are likely to be able to generate in revenue by accepting exposure to that range. Understanding the value of a given range of exposure as perceived by the marketplace will allow us to determine what option strategy will be best to use after we determine our own intelligent valuation range for a stock. Jargon introduced in this chapter is as follows: Strike–stock price ratio Volatility (Vol) Time value Forward volatility Intrinsic value Implied volatility Tenor Statistical volatility Time decay Historical volatility How Option Prices are Determined In Chapter 1, we saw what options looked like from the perspective of ranges of exposure. One of the takeaways of that chapter was how flexible options are in comparison with stocks. Thinking about it a moment, it is clear that the flexibility of options must be a valuable thing. What would it be worth to you to only gain upside to a stock without having to worry about losing capital as a result of a stock price decline? The BSM, the principles of which we discussed in detail in Chapter 2, was intended to answer this question precisely—“What is the fair value of an option?” Let us think about option prices in the same sort of probabilis- tic sense that we now know the BSM is using. First, let’s assume that we want to gain exposure to the upside poten- tial of a $50 stock by buying a call option with a strike price of $70 and a time to expiration of 365 days. Here is the risk-return profile of this option position merged with the image of the BSM cone: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:68 SCORE: 12.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  51 5/18/2012 20 30 40 50 60 70 80 90 100 5/20/2013 249 499 999749 Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN Notice that because this call option is struck at $70, the upside po- tential we have gained lies completely outside the cone of values the BSM sees as reasonably likely. This option, according to the BSM, is something like the bet that a seven-year-old might make with another seven-year- old: “If you can [insert practically impossible action here], I’ll pay you a zillion dollars. ” The action is so risky or impossible that in order to entice his or her classmate to take the bet, the darer must offer a phenomenal return. Off the playground and into the world of high finance, the way to offer someone a phenomenal return is to set the price of a risky asset very low. Following this logic, we can guess that the price for this option should be very low. In fact, we can quantify this “very low” a bit more by thinking about the probabilities surrounding this call option investment. Remembering back to the contention in Chapter 2 that the lines of the BSM cone represent around a 16 percent probability of occurrence, we can see that the range of exposure lies outside this, so the chance of the stock making it into this range is lower than 16 percent. Let’s say that the range of exposure sits at just the 5 percent probability level. What this means is that if you can find 20 identical investments like this and invest in all of them, only one will pay off (1/20 = 5 percent). ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:69 SCORE: 17.00 ================================================================================ 52  •   The Intelligent Option Investor Thus, if you thought that you would win $1 for each successful invest- ment you made, you might only be willing to pay $0.04 to play the game. In this case, you would be wagering $0.04 twenty times in the hope of making $1 once—paying $0.80 total to net $0.20 for a (probabilistic) 25 percent return. Now how much would you be willing to bet if the perceived chance of success was not 1 in 20 but rather 1 in 5? With options, we can increase the chance of success simply by altering the range of exposure. Let’s try this now by moving the strike price down to $60: 5/18/2012 5/20/2013 249 499 749 20 30 40 50 60 70 80 90 100 999 Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN After moving the strike price down, one corner of the range of exposure we have gained falls within the BSM probability cone. This option will be significantly more expensive than the $70 strike option because the perceived probability of the stock moving into this range is material. If we say that the chance of this call option paying its owner $1 is 1 in 5 rather than 1 in 20 (the range of exposure is within the 16 percent line, so we’re estimating it as a 20 percent chance—1 in 5, in other words), we should be willing to pay more to make this investment. If we expected to win $1 for every five tries, we should be willing to spend $0.16 per bet. Here we would again expect to pay $0.80 in total to net $0.20, and again our expected percentage return would be 25 percent. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:70 SCORE: 28.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  53 Notice that by moving the strike down from an expected 5 percent chance of success to an expected 20 percent chance of success, we have agreed that we would pay four times the amount to play. What would happen if we lowered the strike to $50 so that the exposure range started at the present price of the stock? Obviously, this at-the-money (ATM) option would be more expensive still: 5/18/2012 30 20 40 50 60 70 80 90 100 5/20/2013 249 499 749 999 Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN The range of upside exposure we have gained with this option is not only well within the BSM probability cone, but in fact it lies across the dotted line in- dicating the “most likely” future stock value as predicted by the BSM. In other words, this option has a bit better than a 50 percent chance of paying off, so it should be proportionally more expensive than either of our previous options. The payouts and probabilities I provided earlier are completely made up in order to show the principles underlying the probabilistic pricing of option contracts. However, by looking at an option pricing screen, it is very easy to extrapolate annualized prices associated with each of the probabil- ity levels I mentioned—5, 20, and 50 percent. The following table lists the relative market prices of call options cor- responding to each of the preceding diagrams. 1 The table also shows the calculation of the call price as a percentage of the present price of the stock ($50) as well as the strike–stock price ratio , which shows how far above or below the present stock price a given strike price is. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:71 SCORE: 28.00 ================================================================================ 54  •   The Intelligent Option Investor Strike Price Strike–Stock Price Ratio Call Price Call Price as a Percent of Stock Price 70 140% $0.25 0.5 60 120% $1.15 2.3 50 100% $4.15 8.3 Notice that each time we lowered the strike price in successive examples, we lowered the ratio of the strike price to the stock price. This relationship (sometimes abbreviated as K/S, where K stands for strike price and S stands for stock price) and the change in option prices associated with it are easy for stock investors to understand because of the obvious tie to directionality. This is precisely the reason why we have used changes in the strike–stock price ratio as a vehicle to explain option pricing. There are other variables that can cause option prices to change, and we will discuss these in a later section. I will not make such a long-winded explanation, but, of course, put options are priced in just the same way. In other words, this put option, 5/18/2012 - 10 20 30 40 50 60 70 80 90 100 5/20/2013 249 499 749 999 Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:72 SCORE: 13.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  55 would be more expensive than the following put option, which looks like this: 5/18/2012 5/20/2013 249 499 749 999 - 10 20 30 40 50 60 70 80 90 100 Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN The former would be more expensive than the latter simply because the range of exposure for the first lies further within the BSM cone of prob- ability than the latter. We can extrapolate these lessons regarding calls and puts to come up with a generalized rule about comparing the prices of two or more op- tions. Options will be more expensive in proportion to the total range of exposure that lies within the BSM cone. Graphically, we can represent this rule as follows: This call option will be much less expensive… GREEN GREEN than this call option. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:73 SCORE: 63.00 ================================================================================ 56  •   The Intelligent Option Investor This is so because the area of the range of exposure for the option on the left that is bounded by the BSM probability cone is much smaller than the range of exposure for the option on the right that is bounded by the same BSM probability cone. Time Value versus Intrinsic Value One thing that I hope you will have noticed is that so far we have talked about options that are either out of the money (OTM) or at the money (ATM). In-the-money (ITM) options—options whose range of exposure already contains the present stock price—may be bought and sold in just the same way as ATM and OTM options, and the pricing principle is ex- actly the same. That is, an ITM option is priced in proportion to how much of its range of exposure is contained within the BSM probability cone. However, if we think about the case of an OTM call option, we realize that the price we are paying to gain access to the stock’s upside potential is based completely on potentiality. Contrast this case with the case of an ITM call option, where an investor is paying not only for potential upside exposure but also for actual upside as well. It makes sense that when we think about pricing for an ITM call option, we divide the total option price into one portion that represents the poten- tial for future upside and another portion that represents the actual upside. These two portions are known by the terms time value and intrinsic value, respectively. It is easier to understand this concept if we look at a specific example, so let’s consider the case of purchasing a call option struck at $40 and having it expire in one year for a stock presently trading at $50 per share. We know that a call option deals with the upside potential of a stock and that buying a call option allows an investor to gain exposure to that up- side potential. As such, if we buy a call option struck at $40, we have access to all the upside potential over that $40 mark. Because the stock is trading at $50 right now, we are buying two bits of upside: the actual bit and the potential bit. The actual upside we are buying is $10 worth (= $50 − $40) and is termed the intrinsic value of the option. A simple way to think of intrinsic value that is valid for both call options and put options is the amount by which an option is ITM. However, the option’s cost will be greater than only the intrinsic value as long as there is still time ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:74 SCORE: 40.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  57 before the option expires. The reason for this is that although the intrinsic value represents the actual upside of the stock’s price over the option strike price, there is still the possibility that the stock price will move further upward in the future. This possibility for the stock to move further upward is the potential bit mentioned earlier. Formally, this is called the time value of an option. Let us say that our one-year call option struck at $40 on a $50 stock costs $11.20. Here is the breakdown of this example’s option price into in- trinsic and time value: $10.00 Intrinsic value: the amount by which the option is ITM + $1.20 Time value: represents the future upside potential of the stock = $11.20 Overall option price Recall that earlier in this book I mentioned that it is almost always a mis- take to exercise a call option when it is ITM. The reason that it is almost always a mistake is the existence of time value. If we exercised the preceding option, we would generate a gain of exactly the amount of intrinsic value—$10. How- ever, if instead we sold the preceding option, we would generate a gain totaling both the intrinsic value and the time value—$11.20 in this example—and then we could use that gain to purchase the stock in the open market if we wanted. Our way of representing the purchase of an ITM call option from a risk-reward perspective is as follows: Advanced Building Corp. (ABC) 5/18/2012 5/20/2013 249 499 749 EBP = $51.25 999 100 90 80 70 60 50 40 30 20 Date/Day Count Stock Price GREEN ORANGE ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:75 SCORE: 30.00 ================================================================================ 58  •   The Intelligent Option Investor Usually, our convention is to shade a gain of exposure in green, but in the case of an ITM option, we will represent the range of exposure with intrinsic value in orange. This will remind us that if the stock falls from its present price of $50, we stand to lose the intrinsic value for which we have already paid. Notice also that our (two-tone) range of exposure completely over - laps with the BSM probability cone. Recalling that each upper and lower line of the cone represents about a 16 percent chance of going higher or lower, respectively, we can tell that according to the option market, this stock has a little better than an 84 percent chance of trading for $40 or above in one year’s time. 2 Again, the pricing used in this example is made up, but if we take a look at option prices in the market today and redo our earlier table to in- clude this ITM option, we will get the following: Strike Price ($) Strike–Stock Price Ratio (%) Call Price ($) Call Price as a Percent of Stock Price 70 140 $0.25 0.5 60 120 $1.15 2.3 50 100 $4.15 8.3 40 80 10.85 21.7 Again, it might seem confounding that anyone would want to use the ITM strategy as part of their investment plan. After all, you end up paying much more and being exposed to losses if the stock price drops. I ask you to suspend your disbelief until we go into more detail regarding option investment strategies in Part III of this book. For now, the important points are (1) to understand the difference between time and intrinsic value, (2) to see how ITM options are priced, and (3) to understand our convention for diagramming ITM options. From these diagrams and examples it is clear that moving the range of exposure further and further into the BSM probability cone will increase the price of the option. However, this is not the only case in which options will change price. Every moment that time passes, changes can occur to ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:76 SCORE: 21.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  59 the size of the BSM’s probability cone itself. When the cone changes size, the range-of-exposure area within the cone also changes. Let’s explore this concept more. How Changing Market Conditions Affect Option Prices At the beginning of Chapter 2, I started with an intuitive example related to a friendly bet on whether a couple would make it to a restaurant in time for a dinner reservation. Let’s go back to that example now and see how the inputs translate into the case of stock options. Dinner Reservation Example Stock Option Equivalent How long before seating time Tenor 3 of the option Distance between home and restaurant Difference between strike price and present market price (i.e., strike–stock price ratio) Amount of traffic/likelihood of getting caught at a stoplight How much the stock returns are thought likely to vary up and down Average traveling speed Stock market drift Gas expenditure Dividend payout Looking at these inputs, it is clear that the only input that is not known with certainty when we start for the restaurant is the amount of traffic/ number of stoplights measure. Similarly, when the BSM is figuring a range of future stock prices, the one input factor that is unknowable and that must be estimated is how much the stock will vary over the time of the option contract. It is no surprise, then, that expectations regarding this variable become the single most important factor for determining the price of an option and the factor that people talk most about when they talk about options— volatility (vol). This factor is properly known as forward volatility and is formally defined as the expected one-standard-deviation fluctuation up and down around the forward stock price. If this definition sounds familiar, ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:77 SCORE: 22.00 ================================================================================ 60  •   The Intelligent Option Investor it is because it is also the definition of the BSM cone. To the extent that expectations are not directly observable, forward volatility can only be guessed at. The option market’s best guess for the forward volatility, as expressed through the option prices themselves, is known as implied volatility. We will discuss implied volatility in more detail in the next section and will see how to build a BSM cone using option market prices and the forward volatility they imply in Part III. The one other measure of volatility that is sometimes mentioned is sta- tistical volatility (a.k.a. historical volatility). This is a purely descriptive statis- tic that measures the amount the stock price actually fluctuated in the past. Because it is simply a backward-looking statistic, it does not directly affect option pricing. Although the effect of statistical volatility on option prices is not direct, it can have an indirect effect, thanks to a behavioral bias called anchoring. Volatility is a hard concept to understand, let alone a quantity to attempt to predict. Rather than attempt to predict what forward volatility should be, most market participants simply look at the recent past statistical volatility and tack on some cushion to come to what they think is a reason- able value for implied volatility. In other words, they mentally anchor on the statistical volatility and use that anchor as an aid to decide what forward vola- tility should be. The amount of cushion people use to pad statistical volatility differs for different types of stocks, but usually we can figure that the market’s implied volatility will be about 10 percentage points higher than statistical volatility. It is important to realize that this is a completely boneheaded way of figuring what forward volatility will be (so don’t emulate it yourself), but people do boneheaded things in the financial markets all the time. However people come to an idea of what forward volatility is rea- sonable for a given option, it is certain that changing perceptions about volatility are one of the main drivers of option prices in the market. To understand how this works, let’s take a look at what happens to the BSM cone as our view of forward volatility changes. Changing Volatility Assumptions Let’s say that we are analyzing an option that expires in two years, with a strike price of $70. Further assume that the market is expecting a forward ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:78 SCORE: 16.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  61 volatility of 20 percent per year for this stock. Visually, our assumptions yield the following: Advanced Building Corp. (ABC) 5/18/2012 5/20/2013 249 499 749 999 100 90 80 70 60 50 40 30 20 Date/Day Count Stock Price GREEN A forward volatility of 20 percent per year suggests that after three years, the most likely range for the stock’s price according to the BSM will be around $41 on the low side to around $82 on the high side. Furthermore, we can tell from our investigations in Chapter 2 that this option will be worth something, but probably not much—about the same as or maybe a little more than the one-year, $60 strike call option we saw in Chapter 2. 4 Now let’s increase our assumption for volatility over the life of the contract to 40 percent per year. Increasing the volatility means that the BSM probability cone becomes wider at each point. In simple terms, what we are saying is that it is likely for there to be many more large swings in price over the term of the option, so the range of the possible outcomes is wider. Here is what the graph looks like if we double our assumptions regarding implied volatility from 20 to 40 percent: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:80 SCORE: 55.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  63 With this change in assumptions, we can see that the most likely range for the stock’s price three years in the future is between about $50 and about $70. As such, the chance of the stock price hitting $70 in two years moves from somewhat likely (20 percent volatility in the first example) to very likely (40 percent volatility in the second example) to very unlikely (10 percent volatility in the third example) in the eyes of the BSM. This characterization of “very unlikely” is seen clearly by the fact that the BSM probability cone contains not one whit of the call option’s exposure range. In each of these cases, we have drawn the graphs by first picking an assumed volatility rate and then checking the worth of an option at a cer - tain strike price. In actuality, option market participants operate in reverse order to this. In other words, they observe the price of an option being transacted in the marketplace and then use that price and the BSM model to mathematically back out the percentage volatility implied by the option price. This is what is meant by the term implied volatility and is the process by which option prices themselves display the best guesses of the option market’s participants regarding forward volatility. Indeed, many short-term option speculators are not interested in the range of stock prices implied by the BSM at all but rather the dramatic change in price of the option that comes about with a change in the width of the volatility cone. For example, a trader who saw the diagram representing 10 percent annu- alized forward volatility earlier might assume that the company should be trad- ing at 20 percent volatility and would buy options hoping that the price of the options will increase as the implied volatility on the contracts return to normal. This type of market participant talks about buying and selling volatility as if implied volatility were a commodity in its own right. In this style of option trad- ing, investors assume that option contracts for a specific stock or index should always trade at roughly the same levels of implied volatility. 5 When implied vola- tilities change from the normal range—either by increasing or decreasing—an option investor in this vein sells or buys options, respectively. Notice that this style of option transaction completely ignores not only the ultimate value of the underlying company but also the very price of the underlying stock. It is precisely this type of strategy that gives rise to the complex short- term option trading strategies we mentioned in Chapter 1—the ones that are set up in such a way as to shield the investor transacting options from any of the directionality inherent in options. Our take on this kind of trading is that ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:81 SCORE: 31.00 ================================================================================ 64  •   The Intelligent Option Investor although it is indeed possible to make money using these types of strategies, because multiple options must be transacted at one time (in order to control directional risk), and because in the course of one year many similar trades will need to be made, after you pay the transaction costs and assuming that you will not be able to consistently win these bets, the returns you stand to make using these strategies are low when one accounts for the risk undertaken. Of course, because this style of option trading benefits brokers by allowing them to profit from the bid-ask spread and from a fee on each transaction, they tend to encourage clients to trade in this way. What is good for the goose is most definitely not good for the gander in the case of brokers and investors, so, in general, strategies that will benefit the investor relatively more than they benefit the investor’s broker—like the intelligent option investing we will discuss in Part III—are greatly preferable. The two drivers that have the most profound day-to-day impact on option prices are the ones we have already discussed: a change in the strike–stock price ratio and a change in forward volatility expectations. However, over the life of a contract, the most consistent driver of option value change is time to expiration. We discuss this factor next. Changing Time-to-Expiration Assumptions To see why time to expiration is important to option pricing, let us leave our volatility assumptions fixed at 20 percent per year and assume that we are buying a call option struck at $60 and expiring in two years. First, let’s look at our base diagram—two years to expiration: Advanced Building Corp. (ABC) 5/18/2012 5/20/2013 249 499 749 999 100 90 80 70 60 50 40 30 20 Date/Day Count Stock Price GREEN ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:82 SCORE: 23.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  65 It is clear from the large area of the exposure range bordered by the BSM probability cone that this option will be fairly expensive. Let’s now look at an option struck at the same price on the same un- derlying equity but with only one year until expiration: Advanced Building Corp. (ABC) 5/18/2012 5/20/2013 249 499 749 999 100 90 80 70 60 50 40 30 20 Date/Day Count Stock Price GREEN Consistent with our expectations, shortening the time to expiration to 365 days from 730 days does indeed change the likelihood as calculated by the BSM of a call option going above $60 from quite likely to just barely likely. Again, this can be confirmed visually by noting the much smaller area of the exposure range bounded by the BSM probability cone in the case of the one-year option versus the two-year one. Indeed, even without drawing two diagrams, we can see that the chance of this stock rising above $60 decreases the fewer days until expira- tion simply because the outline of the BSM probability cone cuts diagonal- ly through the exposure range. As the cone’s outline gets closer to the edge of the exposure range and finally falls below it, the perceived chance falls to 16 percent and then lower. We would expect, just by virtue of the cone’s shape, that options would lose value with the passage of time. This effect has a special name in the options world—time decay. Time decay means that even if neither a stock’s price nor its volatility change very much over the duration of an option contract, the value of that option will ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:83 SCORE: 23.00 ================================================================================ 66  •   The Intelligent Option Investor still fall slowly. Time decay is governed by the shape of the BSM cone and the degree to which an option’s range of exposure is contained within the BSM cone. The two basic rules to remember are: 1. Time decay is slowest when more than three months are left before expiration and becomes faster the closer one moves toward expiration. 2. Time decay is slowest for ITM options and becomes faster the closer to OTM the option is. Visually, we can understand the first rule—that time decay increases as the option nears expiration—by observing the following: Slope is shallow here... But steep here... The steepness of the slope of the curve at the two different points shows the relative speed of time decay. Because the slope is steeper the less time there is on the contract, time decay is faster at this point as well. Visually, we can understand the second rule—that OTM options lose value faster than ITM ones—by observing the following: Time BT ime A Time BT ime A GREEN GREEN ORANGE OTM option ITM option ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:84 SCORE: 23.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  67 At time A for the OTM option, we see that there is a bit of the range of exposure contained within the cone; however, after some time has passed and we are at time B, none of the range of exposure is contained within the BSM cone. In contrast, at times A and B for the ITM option, the entire range of exposure is contained within the BSM cone. Granted, the area of the range of exposure is not as great at time B as it was at time A, but still, what there is of the area is completely contained within the cone. Theoretically, time decay is a constant thing, but sometimes actual market pricing does not conform well to theory, especially for thinly traded options. For example, you might not see any change in the price of an option for a few days and then see the quoted price suddenly fall by a nickel even though the stock price has not changed much. This is a function of the way prices are quoted—often moving in 5-cent increments rather than in 1-cent increments—and lack of “interest” in the option as measured by liquidity. Changing Other Assumptions The other input assumptions for the BSM (stock market drift and dividend yield) have very small effects on the range of predicted future outcomes in what I would call “normal” economic circumstances. The reason for this is that these assumptions do not change the width of the BSM cone but rather change the tilt of the forward stock price line. Remember that the effect of raising interest rates by a few points is simply to tilt the forward stock price line up by a few degrees; increasing your dividend assumptions has the opposite effect. As long as interest rates and dividend yields stay within typical limits, you hardly see a difference in predicted ranges (or option prices) on the basis of a change in these variables. Simultaneous Changes in Variables In all the preceding examples, we have held all variables but one constant and seen how the option price changes with a change in the one “free” variable. The thing that takes some time to get used to when one is first dealing with options is that, in fact, the variables don’t all hold still when another variable changes. The two biggest determinants of option price are, as we’ve seen, the strike–stock price ratio and the forward volatility ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:85 SCORE: 12.00 ================================================================================ 68  •   The Intelligent Option Investor assumption. Because these are the two biggest determinants, let’s take a look at some common examples in which a change in one offsets or exac- erbates a change in the other. Following are a few examples of how interactions between the variables sometimes appear. For each of these examples, I am assuming a shorter investment time horizon than I usually do because most people who get hurt by some adverse combination of variables exacerbate their pain by trading short-term contracts, where the effect of time value is particularly severe. Falling Volatility Offsets Accurate Directional Prediction Let’s say that we are expecting Advanced Building Corp. to announce that it will release a new product and that we believe that this product announcement will generate a significant short-term boost in the stock price. We think that the $50 stock price could pop up to $55, so we buy some short-dated calls struck at $55, figuring that if the price does pop, we can sell the calls struck at $55 for a handsome profit. Here’s a diagram of what we are doing: 20 25 30 35 40Stock Price 45 50 55 60 Advanced Building Corp. (ABC) 65 GREEN As you should be able to tell by this diagram, this call option should be pretty cheap—there is a little corner of the call option’s range of expo- sure within the BSM cone, but not much. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:86 SCORE: 25.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  69 Now let’s say that our analysis is absolutely right. Just after we buy the call options, the company makes its announcement, and the shares pop up by 5 percent. This changes the strike–stock price ratio from 1.05 to 1.00. All things being held equal, this should increase the price of the option because there would be a larger portion of the range of exposure contained within the BSM cone. However, as the stock price moves up, let’s assume that not everything remains constant but that, instead, implied volatility falls. This does hap- pen all the time in actuality; the option market is full of bright, insightful people, and as they recognize that the uncertainty surrounding a product announcement or whatever is growing, they bid up the price of the options to try to profit in case of a swift stock price move. In the preceding diagram, we’ve assumed an implied volatility of 35 percent per year. Let’s say that the volatility falls dramatically to 15 percent per year and see what happens to our diagram: 20 25 30 35 40Stock Price 45 50 55 60 Advanced Building Corp. (ABC) 65 Stock price jumps Implied volatility drops GREEN The stock price moves up rapidly, but as you can see, the BSM cone shrinks as the market reassesses the uncertainty of the stock’s price range in the short term. The tightening of the BSM cone is so drastic that it more than offsets the rapid price change of the underlying stock, so now the option is actually worth less! ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:87 SCORE: 13.00 ================================================================================ 70  •   The Intelligent Option Investor We, of course, know that it is worth less because after the announce- ment, there is only the smallest sliver of the call’s range of exposure con- tained within the BSM cone. Volatility Rise Fails to Offset Inaccurate Directional Prediction Let’s say that we are bullish on the Antelope Bicycle Co. (ABC) and, noting that the volatility looks “cheap, ” buy call options on the shares. In this case, an investor would be expecting to make money on both the stock price and the implied volatility increasing—a situation that would indeed create an amplification of investor profits. We buy a 10 percent OTM call on ABC that expires in 60 days when the stock is trading for $50. 20 25 30 35 40Stock Price 45 50 55 Antelope Bicycle Corp. (ABC) 60 GREEN The next morning, while checking our e-mail and stock alerts, we find that ABC has been using a metal alloy in its crankshafts that spontaneously combusts after a certain number of cranks. This process has led to severe burn injuries to some of ABC’s riders, and the possibility of a class-action lawsuit is high. The market opens, and ABC’s shares crash by 10 percent. At the same time, the volatility on the options skyrocket from 15 to 35 percent ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:88 SCORE: 16.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  71 because of the added uncertainty surrounding product liability claims. Here is what the situation looks like now: 20 25 30 35 40Stock Price 45 50 55 Antelope Bicycle Corp. (ABC) 60 GREEN This time we were right that ABC’s implied volatility looked too cheap, but because we were directionally wrong, our correct volatility prediction does us no good financially. The stock has fallen heavily, and even with a large increase in the implied volatility, our option is likely worth less than it was when we bought it. Also, because the option is now further OTM than it originally was, time decay is more pronounced. Thus, to the extent that the stock price stays at the new $45 level, our option’s value will slip away quickly with each passing day. Rise in Volatility Amplifies Accurate Directional Prediction These examples have shown cases in which changes in option pricing variables work to the investor’s disadvantage, but it turns out that changes can indeed work to an investor’s advantage as well. For instance, let’s say that we find a company—Agricultural Boron Co. (ABC)—that we think, because of its patented method of producing agricultural boron com- pounds, is relatively undervalued. We decide to buy 10 percent OTM calls on it. Implied volatility is sitting at around 25 percent, but our option is far enough OTM that it is not very expensive. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:90 SCORE: 22.00 ================================================================================ The Intelligent Investor’s Guide to Option Pricing  •  73 With this happy news story, our call options went from nearly worthless to worth quite a bit—the increase in volatility amplified the rising stock price and allowed us to profit from changes to two drivers of option pricing. There is an important follow-up to this happy story that is well worth keeping in the back of your mind when you are thinking about investing in possible takeover targets using options. That is, our BSM cone widened a great deal when the announcement was made because the market be- lieved that there might be a higher counteroffer or that the deal would fall through. If instead the announcement from DuPont was that it had made a friendly approach to the ABC board of directors and that its offer had already been accepted, uncertainty surrounding the future of ABC would fall to zero (i.e., the market would know that barring any antitrust con- cerns, DuPont would close on this deal when it said it would). In this case, implied volatility would simply fall away, and the call option’s value would become the intrinsic value (in other words, there is no potential or time value left in the option). The situation would look like this: 20 30 40 Stock Price 50 60 70 Agricultural Boron Co. (ABC) 80 GREEN We would still make $5 worth of intrinsic value on an invested base that must have been very small (let’s say $0.50 or so), but were the situation to remain uncertain, we would make much more. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:92 SCORE: 15.00 ================================================================================ 75 Part II A sound intellectuAl frAmework for Assessing vAlue After reading Part I, you should have a very good theoretical grasp on how options work and how option prices predict the future prices of stocks. This takes us partway to the goal of becoming intelligent option investors. The next step is to understand how to make intelligent, rational es- timates of the value of a company. It makes no sense at all for a person to invest his or her own capital buying or selling an option if he or she does not have a good understanding of the value of the underlying stock. The problem for most investors—both professional and individual— is that they are confused about how to estimate the value of a stock. As such, even those who understand how the Black-Scholes-Merton model (BSM) predicts future stock prices are not confident that they can do any better. There is a good reason for the confusion among both professional and private investors: they are not taught to pay attention to the right things. Individual investors, by and large, do not receive training in the basic tools of valuation analysis—discounted cash flows and how economic transac- tions are represented in a set of financial statements. Professional investors are exquisitely trained in these tools but too often spend time spinning their wheels considering immaterial details simply because that is what they have been trained to do and because their compensation usually relies on short- rather than long-term performance. They have all the tools in the world but are taught to apply them to answering the wrong questions. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:95 SCORE: 8.00 ================================================================================ 78  •   The Intelligent Option Investor money and discount rates, but even being unacquainted with these terms right now will not be a handicap. Business is essentially a collection of very simple transactions—pro- ducing, selling, and investing excess profits. In my experience, one of the biggest investing mistakes occurs when people forget to think about busi- ness in terms of these simple transactions. Having a firm grasp of valuation is an essential part of being an in- telligent option investor. The biggest drawback of the BSM is its initial as- sumption that all stock prices represent the true values of the stocks in question. It follows that the best opportunity for investors comes when a stock’s present price is far from its true intrinsic value. In order to assess how attractive an investment opportunity is, we must have a good under- standing of the source of value for a firm and the factors that contribute to it. These are the topics of this chapter and the next. In terms of our intelligent option investing process, we need two pieces of information: 1. A range of future prices determined mechanically by the option market according to the BSM 2. A rationally determined valuation range generated through an in- sightful valuation analysis This chapter and the next give the theoretical background necessary to de- rive the latter. Jargon to be introduced in this chapter is as follows: Asset Structural constraints Demand-side constraints Supply-side constraints Owners’ cash profit (OCP) Expansionary cash flow Free cash flow to owner(s) (FCFO) Working capital The Value of an Asset The meaning of asset , in financial terms, is different from the vernacular meaning of “something I’ d be upset about if it broke or was stolen. ” In financial terms, an asset is anything that can be owned that (1) was created ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:119 SCORE: 12.00 ================================================================================ 102  •   The Intelligent Option Investor Another case in which the normal profit range of a company may change is through improvements in productivity. And although improve- ments to productivity can take a long time to play out, they can be ex- tremely important. The reason for this is that even if a company is in a stage in which revenues do not grow very quickly, if profit margins are in- creasing, profit that can flow to the owner(s) will grow at a faster rate than revenues. Y ou can see this very clearly in the following table: Year 0 1 2 3 4 5 6 7 8 9 10 Revenues ($) 1,234 1,271 1,309 1,348 1,389 1,431 1,473 1,518 1,563 1,610 1,658 Revenue growth (%) — 3 3 3 3 3 3 3 3 3 3 OCP ($) 4 432 445 497 485 514 544 560 637 625 708 746 OCP margin (%) 35 35 38 36 37 38 38 42 40 44 45 OCP growth rate (%) — 3 12 –2 6 6 3 14 –2 13 5 Even though revenues grew by a constant 3 percent per year over this time, OCP margin (owner’s cash profit/revenues) increased from 35 to 45 percent, and the compound annual growth in OCP was nearly twice that of revenue growth—at 6 percent. Thinking back to the earlier discussion of the life cycle of a company, recall that the rate at which a company’s cash flows grew was a very important determinant of the value of the firm. The dynamic of a company with a rela- tively slow-growing revenue line and an increasing profit margin is common. A typical scenario is that a company whose revenues have been increasing quickly may be more focused on meeting demand by any means possible rath- er than in the most efficient way. As revenue growth slows, attention starts to turn to increasing the efficiency of the production processes. As that efficiency increases, so does the profit margin. As the profit margin increases, as long as the revenue line has some positive growth, profit growth will be even faster. This dynamic is worth keeping in mind when analyzing companies and in the next section, where I discuss the next driver of company value— investment level and efficacy. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:122 SCORE: 8.00 ================================================================================ The Four Drivers of Value  •  105 Over this very long period, the nominal GDP growth in the United States averaged just over 6 percent per year. If the investment projects of a company are generally successful, the company will be able to dependably grow its profits at a rate faster than this 6 percent (or so) benchmark. The length of time it will be able to grow faster than this benchmark will depend on various factors related to the competitive- ness of the industry, the demand environment, and the investing skill of its managers. Seeing whether or not investments have been successful over time is a simple matter of comparing OCP growth with nominal GDP . Let’s look at a few actual examples. Here is a graph of my calculation of Walmart’s OCP and OCP margin over the last 13 years: 2000 2005 2010 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00%20,000 18,000 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 - Estimated Owners’ Cash Profit and OCP Margin for Walmart Total Estimated OCP (LH) OCP Margin (RH) As one might expect with such a large, mature firm, OCP margin (shown on the right-hand axis) is very steady—barely breaking from the 3.5 to 4.5 percent range over the last 10 years. At the same time, its to- tal OCP (shown on the left-hand axis) grew nicely as a result of increases in revenues. Over the last seven years, Walmart has spent an average of around 2 percent of its revenues on expansionary projects, implying that ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:158 SCORE: 33.00 ================================================================================ 141 Part III IntellIgent OptIOn InvestIng Now that you understand how options work and how to value companies, it is time to move from the theoretical to the practical to see how to apply this knowledge to investing in the market. With Part III of this book, we make the transition from theoretical to practical, and by the time you finish this part, you will be an intelligent option investor. To invest in options, you must know how to transact them; this is the subject of Chapter 7. In it, you will see how to interpret an option pricing screen and to break down the information there so that you can under - stand what the option market is predicting for the future price of a stock. I also talk about the only one of the Greeks that an intelligent option investor needs to understand well—delta. Chapter 8 deals with a subject that is essential for option investors— leverage. Not all option strategies are levered ones, but many are. As such, without understanding what leverage is, how it can be measured and used, and how it can be safely and sanely incorporated into a portfolio, you can- not be said to truly understand options. Chapters 9–11 deal with specific strategies to gain, accept, and mix exposure. In these chapters I offer specific advice about what strike prices are most effective to select and what tenors, what to do when the expected outcomes of an investment materially change, and how to incorporate each strategy into your portfolio. Chapter 11 also gives guidance on so- called option overlay strategies, where a position in a stock is overlain by an option to modify the stock’s risk-reward profile (e.g., protective puts for hedging and covered calls for generating income). ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:159 SCORE: 13.00 ================================================================================ 142  •   The Intelligent Option Investor Unlike some books, this book includes only a handful of strategies, and most of those are very simple ones. I shun complex positions for two reasons. First, as you will see, transacting in options can be very expensive. The more complex an option strategy is, the less attractive the potential returns become. Second, the more complex a strategy is, the less the inher- ent directionality of options can be used to an investor’s advantage. Simple strategies are best. If you understand these simple strategies well, you can start modifying them yourself to meet specific investing sce- narios when and if the need arises. Perhaps by using these simple strategies you will not be able to chat with the local investment club option guru about the “gamma on an iron condor, ” but that will be his or her loss and not yours. Chapter 12 looks at what it means to invest intelligently while under- standing the two forms of risk you assume by selecting stocks in which to invest: market risk and valuation risk. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:160 SCORE: 39.00 ================================================================================ 143 Chapter 7 FIndIng MIsprIced OptIOns All our option-related discussions so far have been theoretical. Now it is time to delve into the practical to see how options work in the market. After finishing this chapter, you should understand 1. How to read an option chain pricing screen 2. Option-specific pricing features such as a wide bid-ask spread, volatility smile, bid and ask volatility, and limited liquidity/ availability 3. What delta is and why it is important to intelligent option investors 4. How to compare what the option market implies about future stock prices to an intelligently determined range In terms of where this chapter fits into our goal of becoming intelligent option investors, obviously, even if you have a perfect understanding of option and valuation theory, if you do not understand the practical steps you must take to find actual investment opportunities in the real world, all the theory will do you no good. New jargon introduced in this chapter includes the following: Closing price Bid implied volatility Settlement price Ask implied volatility Contract size Volatility smile Round-tripping Greeks Bid-ask spread Delta ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:161 SCORE: 20.00 ================================================================================ 144  •   The Intelligent Option Investor Making Sense of Option Quotes Let’s start our practical discussion by taking a look at an actual option pricing screen. These screens can seem intimidating at first, but by the end of this chapter, they will be quite sensible. Last 0.86 -0.23 -0.14 -0.04 -0.17 -0.14 -0.06 -0.13 -0.12 -0.07 -0.09 -0.14 -0.06 -0.20 -0.26 -0.10 +0.01 0.91 0.94 21.672% 24.733% 0.8387 0.4313 0.0631 0.0000 0.0000 0.0000 0.9580 0.9598 0.9620 0.7053 0.4743 0.2461 0.0357 0.0392 0.0482 21.722% 22.988% 62.849% 72.188% 81.286% 201.771% 192.670% 175.779% 20.098% 18.997% 18.491% 25.587% 29.201% 35.855% 55.427% 123.903% 64.054% 23.311% 22.407% 21.813% 21.147% 22.144% 23.409% 54.689% 66.920% 35.642% 23.656% 23.072% 22.553% 21.460% 21.374% 21.581% 32.597% 24.854% 23.426% 20.380% 19.627% N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 0.26 0.04 0.02 0.02 0.02 13.30 12.40 11.35 1.19 0.58 0.22 0.01 0.01 0.02 11.90 12.35 10.10 1.68 1.10 0.67 0.05 0.03 0.02 0.24 0.02 10.35 9.30 8.40 1.17 19.408% 18.405% 17.721% 0.56 0.20 11.75 10.70 9.50 1.65 1.08 0.65 0.04 0.01 0.01 11.55 12.30 12.00 10.00 2.48 1.93 1.48 0.41 0.29 0.21 12.20 3.60 1.75 10.05 9.85 2.44 1.91 1.45 0.39 0.27 0.18 12.10 3.50 1.70 0.00 0.23 0.02 C0.00 C0.00 C0.00 0.09 0.45 1.15 C4.99 C5.99 C6.99 C4.99 C5.99 C6.99 C12.01 C11.01 C10.01 1.16 0.54 0.22 C0.00 C0.00 C0.00 C0.00 C0.00 C0.00 0.33 0.76 1.40 C5.03 C6.00 C6.99 C0.00 C0.01 C0.03 0.84 1.23 1.88 C12.02 C11.03 C10.04 1.65 1.06 0.66 C0.06 0.03 0.02 C12.05 C11.07 C10.10 C2.58 1.93 12.10 3.40 1.69 0.68 4.25 C7.27 1.42 0.38 C0.30 C0.22 C0.11 C0.15 C0.19 1.80 2.27 2.73 C5.57 C6.43 C7.35 Chng Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta JUL 26 ´13 31 32 33 37 38 39 20 21 22 31 32 33 37 38 39 Description Call Last Chng Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta Put 0.9897 0.9869 0.9834 0.6325 0.4997 0.3606 0.0463 0.0266 0.0155 0.9712 0.9628 0.9535 0.5890 0.5118 0.4324 0.1664 0.1258 0.0923 0.9064 0.5354 0.3336 +0.01 +0.10 +0.11 0.07 0.09 22.812%2 4.853% -0.1613 -0.5689 -0.9373 -1.0000 -1.0000 -1.0000 22.469% 24.612% 85.803% 203.970% 267.488% 20.456% 19.851% N/A N/A N/A 0.42 1.20 5.25 7.25 8.90 0.39 1.17 4.90 4.85 5.40 +0.02 +0.09 +0.14 -0.0420 -0.0402 -0.0380 -0.2948 -0.5261 -0.7545 -0.9652 -0.9616 -0.9524 77.739% 70.681% 63.514% 20.303% 19.170% 19.011% 41.423% 61.602% 52.378% N/A N/A N/A N/A N/A N/A 0.02 0.02 0.02 0.34 0.73 1.38 5.30 6.55 7.30 0.33 0.71 1.35 4.95 19.958% 18.577% 17.954% 4.65 6.70 22.720% 22.019% 21.378% 20.455% 19.050% 21.354% 0.000% 23.193% 22.845% 22.218% 21.148% 20.913% 20.899% +0.07 +0.05 +0.16 +0.09 +0.12 +0.04 50.831% 48.233% 46.993% 23.384% 22.672% 22.106% 36.111% 30.947% 44.342% N/A N/A N/A N/A 0.02 0.03 0.05 0.82 1.25 1.82 5.55 6.30 7.55 0.01 0.80 1.23 1.79 4.95 6.15 6.85 -0.0103 -0.0131 -0.0166 -0.3679 -0.5008 -0.6402 -0.9558 -0.9757 -0.9871 22.989% 22.284% 21.453% 17.134% 37.572% 38.919% 37.587% 35.246% 23.914% 23.485% 22.925% 22.967% 26.265% 28.715% 0.11 0.13 0.17 0.19 1.78 2.25 2.80 5.80 6.85 7.85 0.13 0.17 1.75 2.22 2.76 5.70 6.50 7.40 -0.0318 -0.0406 -0.0503 -0.4120 -0.4879 -0.5665 -0.8294 -0.8690 -0.9025 34.172% 23.567% 23.145% 22.479% 21.404% 19.420% 18.411% 37.790% 35.385% 30.523% 24.198% 23.081% 0.00 +0.09 33.497% 26.033% 24.745% 0.68 4.25 7.40 0.66 4.15 7.30 -0.0906 -0.4520 -0.6521 33.203% 25.378% 24.054% AUG 16 ´13 20 21 22 31 32 33 37 38 39 SEP 20 ´13 20 21 22 31 32 33 37 38 39 20 32 37 JAN 17 ´14 JAN 16 ´15 I pulled this screen—showing the prices for options on Oracle (ORCL)— on the weekend of July 20–21, 2013, when the market was closed. The last trade of Oracle’s stock on Friday, July 19, was at $31.86, down $0.15 from the Thursday’s close. Y our brokerage screen may look different from this one, but you should be able to pull back all the data columns shown here. I have limited the data I’m pulling back on this screen in order to increase its readability. More strikes were available, as well as more expiration dates. The expirations shown here are 1 week and 26, 60, 180, and 544 days in the future—the 544-day expiry being the longest tenor available on the listed market. Let’s first take a look at how the screen itself is set up without paying attention to the numbers listed. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:162 SCORE: 20.00 ================================================================================ Finding Mispriced Options    • 145 Calls are on the left, puts on the right. Strike prices and expirations are listed here. You can tell the stock was down on this day because most of the call options are showing losses and all the put options are showing gains. All the strikes for each selected expiry are listed grouped together. This query was set up to pull back three strikes at the three moneyness regions (20–22, 29–31, 37–39). The 1-week options and the LEAPS did not have strikes at each of the prices I requested. Now that you can see what the general setup is, let’s drill down and look at only the calls for one expiration to see what each column means. Last C12.02 11.75 10.70 9.50 1.65 1.08 0.65 0.04 0.01 0.01 0.02 0.03 0.05 0.67 1.10 1.68 10.10 12.35 11.90 N/A N/A N/A 22.720% 55.427% 20 SEP 20 ´13 21 22 31 32 33 37 38 39 0.9869 0.9834 0.6325 0.4997 0.3606 0.0463 0.0266 0.0155 123.903% 64.054% 23.311% 22.407% 21.813% 21.147% 22.144% 23.409% 22.019% 21.378% 20.455% 19.050% 21.354% C11.03 C10.04 1.65 1.06 -0.13 -0.12 -0.07 0.00 +0.01 0.66 C0.06 0.03 0.02 Chnq Bid AskA skImpl.I mpl.Bid Vol. Vol. Delta Description Call 0.9897 Red (loss) Green (gain) ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:163 SCORE: 22.00 ================================================================================ 146  •   The Intelligent Option Investor Last This is the last price at which the associated contract traded. Notice that the last price associated with the far in-the-money (ITM) strikes ($20, $21, $22) and one of the far out-of-the-money (OTM) strikes ($37) have the letter “C” in front of them. This is just my broker’s way of showing that the contract did not trade during that day’s trading session and that the last price listed was the closing price of the previous day. Closing prices are not necessarily market prices. At the end of the day, if a contract has not traded, the exchange will give an indicative closing price (or settlement price ) for that day. The Oracle options expiring on August 16, 2013, and struck at $20 may not have traded for six months or more, with the exchange simply “marking” a closing price every day. One important fact to understand about option prices is that they are quoted in per-share terms but must be transacted in contracts that rep- resent control of multiple shares. The number of shares controlled by one contract is called the contract size . In the U.S. market, one standard con- tract represents control over 100 shares. Sometimes the number of shares controlled by a single contract differs (in the case of a company that was acquired through the exchange of shares), but these are not usually avail- able to be traded. In general, one is safe remembering that the contract size is 100 shares. Y ou cannot break a contract into smaller pieces or buy just part of a contract—transacting in options means you must do so with indivisible contracts, with each contract controlling 100 shares. Period. As such, every price you see on the preceding screenshot, if you were to transact in one of those options, would cost you 100 times the amount shown. For example, the last price for the $31-strike option was $1.65. The investor who bought that contract paid $165 for it (plus fees, taxes, and commissions, which are not included in the posted price). In the rest of this book, when I make calculations regarding money spent on a certain transaction, you will al- ways see me multiply by 100. Change This is the change from the previous day’s closing price. My broker shows change only for contracts that were actively traded that day. It looks like ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:164 SCORE: 42.00 ================================================================================ Finding Mispriced Options    • 147 the near at-the-money (ATM) strikes were the most active because of the two far OTM options that traded; one’s price didn’t change at all, and the other went up by 1 cent. On a day in which the underlying stock fell, these calls theoretically should have fallen in price as well (because the K/S ratio, the ratio of strike price to stock price, was getting slightly larger). This just shows that sometimes there is a disconnect between theory and practice when it comes to options. To understand what is probably happening, we should understand something about market makers. Market makers are employees at bro- ker-dealers who are responsible for ensuring a liquid, orderly securi- ties market. In return for agreeing to provide a minimum liquidity of 10 contracts per strike price, market makers get the opportunity to earn the bid-ask spread every time a trade is made (I will talk about bid-ask spreads later). However, once a market maker posts a given price, he or she is guaranteeing a trade at that price. If, in this case (because we’re dealing with OTM call options), some unexpected positive news comes out that will create a huge rise in the stock price once it filters into the market and an observant, quick investor sees it before the market maker realizes it, the investor can get a really good price on those far OTM call options (i.e., the investor could buy a far OTM call option for 1 cent and sell it for 50 cents when the market maker realizes what has happened. To provide a little slack that prevents the market maker from losing too much money if this happens, market makers usually post prices for far OTM options or options on relatively illiquid stocks that are a bit unrea- sonable—at a level where a smart investor would not trade with him or her at that price. If someone trades at that price, fine—the market maker has committed to provide liquidity, but the agreement does not stipulate that the liquidity must be provided at a reasonable price. For this reason, frequently you will see prices on far OTM options that do not follow the theoretical “rules” of options. Bid-Ask For a stock investor, the difference between a bid price and an ask price is inconsequential. For option investors, though, it is a factor that must be taken into consideration for reasons that I will detail in subsequent ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:165 SCORE: 76.00 ================================================================================ 148  •   The Intelligent Option Investor paragraphs. The easiest way to think of the bid-ask spread is to think in terms of buying a new car. If you buy a new car, you pay, let’s say, $20,000. This is the ask price. Y ou grab the keys, drive around the block, and return to the showroom offering to sell the car back to the dealership. The dealership buys it for $18,000. This is the bid price. The bid-ask spread is $2,000 in this example. Bid-ask spreads are proportionally much larger for options than they are for stocks. For example, the options I’ve highlighted here are on a very large, important, and very liquid stock. The bid-ask spread on the $32-strike call option (which you will learn in the next section is exactly ATM) is $0.02 on a midprice of $1.09. This works out to a percentage bid- ask spread of 1.8 percent. Compare this with the bid-ask spread on Ora- cle’s stock itself, which was $0.01 on a midprice of $31.855—a percentage spread of 0.03 percent. For smaller, less-liquid stocks, the percentage bid-ask spread is even larger. For instance, here is the option chain for Mueller Water (MW A): 2.5 5 7.5 10 Last C5.30 C2.80 0.55 C0.00 Change Bid AskI mpl. Bid Vol. Impl. Ask Vol. Impl. Bid Vol. Impl. Ask Vol.Delta 2.5 5 7.5 10 2.5 5 7.5 10 12.5 DescriptionCall Last Change BidA sk Delta Put C0.00 C0.00 C0.25 C2.25 C0.00 C0.00 C0.55 C2.35 C0.00 C0.10 C0.85 C2.55 C4.80 5.20 5.50 N/A 340.099% 0.9978 0.9978 0.7330 0.1316 0.9347 0.8524 0.6103 0.1516 0.9933 0.9190 0.6070 0.2566 0.1024 142.171% 46.039% 76.652% N/A N/A 2.95 0.55 0.10 0.20 0.10 N/A N/A N/A 0.10 0.30 2.35 40.733% N/A N/A N/A N/A 36.550% 38.181% 35.520% 35.509% 35.664% 2.10 0.50 0.05 0.10 0.60 2.402.30 0.05 0.15 0.15 0.85 2.60 4.90 0.70 2.45 4.60 2.70 0.500.00 5.20 5.50 3.00 0.90 0.20 2.80 0.80 0.10 5.505.10 3.102.85 1.151.05 0.400.30 0.200.05 39.708% N/A N/A 36.722% N/A 38.754% 38.318% 39.127% 36.347% 36.336% 292.169% 0.0000 -0.0000 -0.2778 -0.8663 -0.0616 -0.1447 -0.3886 -0.8447 -0.0018 -0.0787 -0.3890 -0.7375 -0.8913 128.711% 53.108% 88.008% 117.369% 60.675% 42.433% 44.802% 110.810% 50.757% 42.074% 43.947% 49.401% 163.282% 75.219% 42.610% 45.215% 122.894% 64.543% 42.697% 44.728% 50.218% C5.30 C2.80 C0.85 C0.10 C5.30 C1.10 C0.35 C0.10 3.00 +0.15 AUG 16 ´13 NOV 15 ´13 FEB 21 ´14 Looking at the closest to ATM call options for the November expiration— the ones struck at $7.50 and circled in the screenshot—you can see that the bid-ask spread is $0.10 on a midprice of $0.85. This works out to 11.8 percent. Because the bid-ask spread is so very large on option contracts, round-tripping 1 an option contract creates a large hurdle that the returns of the security must get over before the investor makes any money. In the case of Mueller Water, the options one buys would have to change in price by 11.8 percent before the investor starts making any money at all. It is for this reason that I consider day trading in options and/or using complex ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:166 SCORE: 19.00 ================================================================================ Finding Mispriced Options    • 149 strategies involving the simultaneous purchase and sale of multiple con- tracts to be a poor investment strategy. Implied Bid Volatility/Implied Ask Volatility Because the price is so different between the bid and the ask, the range of fu- ture stock prices implied by the option prices can be thought of as different depending on whether you are buying or selling contracts. Employing the graphic conventions we used earlier in this book, this effect is represented as follows: Implied price range implied by ask price volatility of 23.4% Implied price range implied by bid price volatility of 21.4% 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20131/12/2012 Oracle (ORCL) Price per Share 60 50 40 30 20 10 - Because Oracle is such a big, liquid company, the difference between the stock prices implied by the different bid-ask implied volatilities is not large, but it can be substantial for smaller, less liquid companies. Looking at the ask implied volatility column, you will notice the huge difference between the far ITM options’ implied volatilities and those for ATM and OTM options. The data in the preceding diagram are incomplete, but if you were to graph all the implied volatility data, you would get the following: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:167 SCORE: 28.00 ================================================================================ 150  •   The Intelligent Option Investor 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Strike Price Oracle (ORCL) Implied Volatility Implied Volatility (Percent) 160 180 140 100 120 80 40 60 20 0 Thinking about what volatility means with regard to future stock prices—namely, that it is a prediction of a range of likely values—it does not make sense that options struck at different prices would predict such radi- cally different stock price ranges. What the market is saying, in effect, is that it expects different things about the likely future range of stock prices depending on what option is selected. Clearly, this does not make much sense. This “nonsensical” effect is actually proof that practitioners understand that the Black-Scholes-Merton model’s (BSM’s) assumptions are not correct and specifically that sudden downward jumps in a stock price can and do occur more often than would be predicted if returns fol- lowed a normal distribution. This effect does occur and even has a name— the volatility smile . Although this effect is extremely noticeable when graphed in this way, it is not particularly important for the intelligent op- tion investing strategies about which I will speak. Probably the most im- portant thing to realize is that the pricing on far OTM and far ITM options is a little more informal and approximate than for ATM options, so if you are thinking about transacting in OTM or ITM options, it is worth looking for the best deal available. For example, notice that in the preceding dia- gram, the $21-strike implied volatility is actually notably higher than the ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:168 SCORE: 89.00 ================================================================================ Finding Mispriced Options    • 151 $20-strike volatility. If you were interested in buying an ITM call option, you would pay less time value for the $20-strike than for the $21-strike op- tions—essentially the same investment. I will talk more about the volatility smile in the next section when discussing delta. In a similar way, sometimes the implied volatility for puts is different from the implied volatility for calls struck at the same price. Again, this is one of the market frictions that arises in option markets. This effect also has investing implications that I will discuss in the chapters detailing dif- ferent option investing strategies. The last column in this price display is delta , a measure that is so important that it deserves its own section—to which we turn now. Delta: The Most Useful of the Greeks Someone attempting to find out something about options will almost certainly hear about how the Greeks are so important. In fact, I think that they are so unimportant that I will barely discuss them in this book. If you understand how options are priced—and after reading Part I, you do—the Greeks are mostly common sense. Delta, though, is important enough for intelligent option investors to understand with a bit more detail. Delta is the one number that gives the probability of a stock being above (for calls) or below (for puts) a given strike price at a specific point in time. Deltas for calls always carry a positive sign, whereas deltas for puts are always negative, so, for instance, a call option on a given stock whose delta is exactly 0.50 will have a put delta of −0.50. The call delta of 0.50 means that there is a 50 percent chance that the stock will expire above that strike, and the put delta of −0.50 means that there is a 50 percent chance that the stock will expire below that strike. In fact, this strike demonstrates the technical definition of ATM—it is the most likely future price of the stock according to the BSM. The reason that delta is so important is that it allows you one way of creating the BSM probability cones that you will need to find option investment opportunities. Recall that the straight dotted line in our BSM cone diagrams meant the statistically most likely future price for the stock. The statistically most likely future price for a stock—assuming that stocks ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:169 SCORE: 15.00 ================================================================================ 152  •   The Intelligent Option Investor move randomly, which the BSM does—is the price level at which there is an equal chance of the actual future stock price to be above or below. In other words, the 50-delta mark represents the forward price of a stock in our BSM cones. Recall now also that each line demarcating the cone represents roughly a 16 percent probability of the stock reaching that price at a particular time in the future. This means that if we find the call strike prices that have deltas closest to 0.16 and 0.84 (= 1.00 − 0.16) or the put strike prices that have deltas closest to −0.84 and −0.16 for each expiration, we can sketch out the BSM cone at points in the future (the data I used to derive this graph are listed in tabular format at the end of this section). 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012 Date Oracle (ORCL) Price per Share 45 40 35 30 25 20 5 10 15 - Obviously, the bottom range looks completely distended compared with the nice, smooth BSM cone shown in earlier chapters. This dis- tension is simply another way of viewing the volatility smile. Like the volatility smile, the distended BSM cone represents an attempt by partici- pants in the options market to make the BSM more usable in real situa- tions, where stocks really can and do fall heavily even though the efficient market hypothesis (EMH) says that they should not. The shape is saying, ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:170 SCORE: 12.00 ================================================================================ Finding Mispriced Options    • 153 “We think that these prices far below the current price are much more likely than they would be assuming normal percentage returns. ” (Or, in a phrase, “We’re scared!”) If we compare the delta-derived “cone” with a theoretically derived BSM cone, here is what we would see: Oracle (ORCL) Date Price per Share 60 50 40 30 20 10 - 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012 Of course, we did not need the BSM cone to tell us that the points associated with the downside strikes look too low. But it is interesting to see that the upside and most likely values are fairly close to what the BSM projects. Note also that the downside point on the farthest expiration is nearly fairly priced according to the BSM, contrary to the shorter-tenor options. This effect could be because no one is trading the far ITM call long-term equity anticipation securities (LEAPS), so the market maker has simply posted his or her bid and ask prices using the BSM as a base. In the market, this is what usually happens—participants start out with a mechanically generated price (i.e., using the BSM or some other computational option pricing model) and make adjustments based on what feels right, what arbitrage opportunities are available, and so on. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:171 SCORE: 37.00 ================================================================================ 154  •   The Intelligent Option Investor One important thing to note is that although we are using the delta figure to get an idea of the probability that the market is assigning to a certain stock price outcome, we are also using deltas for options that nearly no one ever trades. Most option volume is centered around the 50-delta mark and a 10 to 20 percentage point band around it (i.e., from 30- to 40-delta to 60- to 70-delta). It is doubtful to me that these thinly traded options contain much real information about market projections of future stock prices. Another problem with using the deltas to get an idea about market projections is that we are limited in the length of time we can project out to only the number of strikes available. For this example, I chose an impor- tant tech company with a very liquid stock, so it has plenty of expirations and many strikes available so that we can get a granular look at deltas. However, what if we were looking at Mueller Water’s option chain and try- ing to figure out what the market is saying? 2.5 5 7.5 10 Last C5.30 C2.80 0.55 C0.00 Change Bid Ask Impl. Bid Vol. Impl. Ask Vol. Delta AUG 16 ´13 2.5 5 7.5 10 NOV 15 ´13 2.5 5 7.5 10 12.5 FEB 21 ´14 DescriptionCall 5.20 5.50 N/A 340.099% 0.9978 0.9978 0.7330 0.1316 0.9347 0.8524 0.6103 0.1516 0.9933 0.9190 0.6070 0.2566 0.1024 142.171% 46.039% 76.652% N/A N/A 2.95 0.55 0.10 2.70 0.500.00 5.20 5.50 3.00 0.90 0.20 2.80 0.80 0.10 5.505.10 3.102.85 1.151.05 0.400.30 0.200.05 39.708% N/A N/A 36.722% N/A 38.754% 38.318% 39.127% 36.347% 36.336% 163.282% 75.219% 42.610% 45.215% 122.894% 64.543% 42.697% 44.728% 50.218% C5.30 C2.80 C0.85 C0.10 C5.30 C1.10 C0.35 C0.10 3.00 +0.15 Here you can see that we only have three expirations: 26, 117, and 215 days from when these data were taken. In addition, there are hardly any strikes that are reasonably close to our crucial 84-delta, 50-delta, and 16-delta strikes, which means that we have to do a lot of extrapolation to try to figure out where the market’s idea of the BSM cone lies. To get a better picture of what the market is saying, I recommend looking at options that are the most heavily traded and assuming that the implied volatility on these strikes gives true information about the mar - ket’s assumptions about the future price range of a stock. Using the im- plied volatility on heavily traded contracts as the true forward volatility expected by the market allows us to create a theoretical BSM cone that we ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:172 SCORE: 17.00 ================================================================================ Finding Mispriced Options    • 155 can extend indefinitely into the future and that is probably a lot closer to representing actual market expectations for the forward volatility (and, by extension, the range of future prices for a stock). Once we have this BSM cone—with its high-low ranges spelled out for us—we can compare it with the best- and worst-case valuations we derived as part of the company analysis process. Let’s look at this process in the next section, where I spell out, step by step, how to compare an intelligent valuation range with that implied by the option market. Note: Data used for Oracle graphing example: Expiration Date Lower Middle Upper 7/25/2013 29.10 31.86 32.75 8/16/2013 22.00 32.00 33.50 9/20/2013 19.00 32.00 35.00 12/20/2013 20.00 32.50 37.00 1/17/2014 19.00 32.50 37.20 1/16/2015 23.00 32.30 42.00 Here I have eyeballed (and sometimes done a quick extrapolation) to try to get the price that is closest to the 84-delta, 50-delta, and 16-delta marks, respectively. Of course, you could calculate these more carefully and get exact numbers, but the point of this is to get a general idea of how likely the market thinks a particular future stock price is going to be. Comparing an Intelligent Valuation Range with a BSM Range The point of this book is to teach you how to be an intelligent option investor and not how to do stochastic calculus or how to program a computer to calculate the BSM. As such, I’m not going to explain how to mathematically derive the BSM cone. Instead, on my website I have an application that will allow you to plug in a few numbers and create a graphic representation of a BSM cone and carry out the comparison process described in this section. The only thing you need to know is what numbers to plug into this web application! ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:173 SCORE: 29.00 ================================================================================ 156  •   The Intelligent Option Investor I’ll break the process into three steps: 1. Create a BSM cone. 2. Overlay your rational valuation range on the BSM cone. 3. Look for discrepancies. Create a BSM Cone The heart of a BSM cone is the forward volatility number. As we have seen, as forward volatility increases, the range of future stock prices projected by the BSM (and expected by the market) also increases. However, after hav- ing looked at the market pricing of options, we also know that a multitude of volatility numbers is available. Which one should we look at? Each strike price has its own implied volatility number. What strike price’s volatility should we use? There are also multiple tenors. What tenor options should we look at? Should we look at implied volatility at the bid price? At the ask price? Perhaps we should take the “kitchen sink” approach and just average all the implied volatilities listed! The answer is, in fact, easy if you use some simplifying assumptions to pick a single volatility number. I am not an academic, so I don’t neces- sarily care if these simplifying assumptions are congruent with theory. Also, I am not an arbitrageur, so I don’t much care about very precise numbers, and this attitude also lends itself well to the use of simplifying assumptions. All we have to make sure of is that the simplifying as- sumptions don’t distort our perception to the degree that we make bad economic choices. Here are the assumptions that we will make: 1. The implied volatility on a contract one or two months from expi- ration that is ATM or at least within the 40- to 60-delta band and that is the most heavily traded will contain the market’s best idea of the true forward volatility of the stock. 2. If a big announcement is scheduled for the near future, implied volatility numbers may be skewed, so their information might not be reliable. In this case, try to find a heavily traded near ATM strike at an expiry after the announcement will be made. If the announcement will be made in about four months or more, just try ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:174 SCORE: 50.00 ================================================================================ Finding Mispriced Options    • 157 to eyeball the ATM volatility for the one- and two-month contracts. 3. If there is a large bid-ask spread, the relevant forward volatility to use is equal to the implied volatility we want to transact. In other words, use the ask implied volatility if you are thinking about gaining exposure and the bid implied volatility if you are thinking about accepting exposure (the online application shows cones for both the bid implied volatility and the ask implied volatility). Basically, these rules are just saying, “If you want to know what the option market is expecting the future price range of a stock to be, find a nice, liquid near ATM strike’s implied volatility and use that. ” Most op- tion trading is done in a tight band around the present ATM mark and for expirations from zero to three months out. By looking at the most heavily traded implied volatility numbers, we are using the market’s price-discov- ery function to the fullest. Big announcements sometimes can throw off the true volatility picture, which is why we try to avoid gathering infor - mation from options in these cases (e.g., legal decisions, Food and Drug Administration trial decisions, particularly impactful quarterly earnings announcements, and so on). If I was looking at Oracle, I would probably choose the $32-strike options expiring in September. These are the 50-delta options with 61 days to expiration, and there is not much of a difference between calls and puts or between the bid and ask. The August expiration op- tions look a bit suspicious to me considering that their implied volatility is a couple of percentage points below that of the others. It probably doesn’t make a big difference which you use, though. We are trying to find opportunities that are severely mispriced, not trying to split hairs of a couple of percentage points. All things considered, I would prob- ably use a number somewhere around 22 percent for Oracle’s forward volatility. C12.02 11.75 N/A 55.427% 0.9897 C0.00 0.02 N/A 50.831%- 0.01032011.90 C11.03 10.70 N/A 123.903% 0.9869 C0.01 0.03 N/A 48.233%- 0.01312112.35 C10.04 9.50 N/A 64.054% 0.9834 C0.03 0.05 37.572% 46.993%- 0.01660.012210.10 C0.06 0.04 20.455% 21.147% 0.0463 C5.03 5.55 N/A 36.111%- 0.95584.95370.05 1.65 1.65 22.720% 23.311% 0.6325 0.84 +0.07 0.82 22.989% 23.384%- 0.36790.80311.68-0.13 1.06 1.08 22.019% 22.407% 0.4997 1.23 +0.05 1.25 22.284% 22.672%- 0.50081.23321.10-0.12 0.66 0.65 21.378% 21.813% 0.3606 1.88 +0.16 1.82 21.453% 22.106%- 0.64021.79330.67-0.07 0.02 0.01 21.354% 23.409% 0.0155 C6.99 7.55 N/A 44.342%- 0.98716.85390.02+0.01 0.03 0.01 19.050% 22.144% 0.0266 C6.00 6.30 17.134% 30.947%- 0.97576.15380.030.00 SEP 20 ´13 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:175 SCORE: 45.00 ================================================================================ 158  •   The Intelligent Option Investor For Mueller Water, it’s a little trickier: 2.5 5 7.5 10 Last C5.30 C2.80 0.55 C0.00 Change BidA sk Delta AUG 16 ´13 2.5 5 7.5 10 NOV 15 ´13 2.5 5 7.5 10 12.5 FEB 21 ´14 DescriptionCall Last Change BidA sk Impl. Bid Vol. Impl. Ask Vol.Impl. Bid Vol. Impl. Ask Vol. Delta Put C0.00 C0.00 C0.25 C2.25 C0.00 C0.00 C0.55 C2.35 C0.00 C0.10 C0.85 C2.55 C4.80 5.20 5.50N /A 340.099% 0.9978 0.9978 0.7330 0.1316 0.9347 0.8524 0.6103 0.1516 0.9933 0.9190 0.6070 0.2566 0.1024 142.171% 46.039% 76.652% N/A N/A 2.95 0.55 0.10 0.20 0.10 N/A N/A N/A 0.10 0.30 2.35 40.733% N/A N/A N/A N/A 36.550% 38.181% 35.520% 35.509% 35.664% 2.10 0.50 0.05 0.10 0.60 2.402.30 0.05 0.15 0.15 0.85 2.60 4.90 2.70 0.500.00 5.20 5.50 3.00 0.90 0.20 2.80 0.80 0.10 5.505.10 3.102.85 1.151.05 0.400.30 0.200.05 39.708% N/A N/A 36.722% N/A 38.754% 38.318% 39.127% 36.347% 36.336% 292.169% 0.0000 -0.0000 -0.2778 -0.8663 -0.0616 -0.1447 -0.3886 -0.8447 -0.0018 -0.0787 -0.3890 -0.7375 -0.8913 128.711% 53.108% 88.008% 117.369% 60.675% 42.433% 44.802% 110.810% 50.757% 42.074% 43.947% 49.401% 163.282% 75.219% 42.610% 45.215% 122.894% 64.543% 42.697% 44.728% 50.218% C5.30 C2.80 C0.85 C0.10 C5.30 C1.10 C0.35 C0.10 3.00 +0.15 0.70 2.45 4.60 In the end, I would probably end up picking the implied volatility associated with the options struck at $7.50 and expiring in August 2013 (26 days until expiration). I was torn between these and the same strike expiring in November, but the August options are at least being actively traded, and the percentage bid-ask spread on the call side is lower for them than for the November options. Note, though, that the August 2013 put options are so far OTM that the bid-ask spread is very wide. In this case, I would probably look closer at the call options’ implied volatilities. In the end, I would have a bid volatility of around 39 percent and an ask volatility of around 46 percent. Because the bid-ask spread is large, I would probably want to see a cone for both the bid and ask. Plugging in the 22.0/22.5 for Oracle, 2 I would come up with this cone: Date Oracle (ORCL) Price per Share 60 40 50 30 10 20 - 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:176 SCORE: 10.00 ================================================================================ Finding Mispriced Options    • 159 Plugging in the 39/46 for Mueller Water, I would get the following: 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012 Date Mueller Water (MWA) Price per Share 25 20 15 5 10 - Y ou can see with Mueller Water just how big a 7 percentage point dif- ference can be for the bid and ask implied volatilities in terms of projected outcomes. The 39 percent bid implied volatility generates an upper range at just around $15; the 46 percent ask implied volatility generates an upper range that is 20 percent or so higher than that! Overlay an Intelligent Valuation Range on the BSM Cone This is simple and exactly the same for a big company or a small one, so I’ll just keep going with the Oracle example. After having done a full valuation as shown in the exam valuation of Oracle on the IOI website, you’ve got a best-case valuation, a worst-case valuation, and probably an idea about what a likely valuation is. Y ou simply draw those numbers onto a chart like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:178 SCORE: 24.00 ================================================================================ Finding Mispriced Options    • 161 On the upside, we can see that our likely case valuation is $43 per share, whereas the BSM’s most likely value is a bit less than $35—a difference of more than 20 percent. This is the area on the graph labeled “ A. ” The BSM prices options based on the likelihood of the stock hitting a certain price level. The BSM considers the $43 price level to be relatively unlikely, whereas I consider it relatively likely. As such, I believe that options that allow me to gain exposure to the upside potential of Oracle—call options—are underval- ued. In keeping with the age-old rule of investing to buy low, I will want to gain exposure to Oracle’s upside by buying low-priced call options. On the downside, I notice that there is a fairly large discrepancy between my worst-case valuation ($30) and the lower leg of the BSM cone (approximately $24)—this is the region of the graph labeled “B, ” and the separation between the two values is again (just by chance) about 20 percent. The BSM is pricing options granting exposure to the downside—put options—struck at $24 as if they were fairly likely to occur; something that is fairly likely to occur will be priced expensively by the BSM. My analysis, on the other hand, makes me think that the BSM’s valuation outcome is very unlikely. The discrepancy implies that I believe the put options to be overvalued—the BSM sees a $24 valuation as likely, with expensive options, whereas I see it as unlikely, with nearly valueless options. In this case, we should consider the other half of the age-old investing maxim and sell high. In a graphic representation, this strategy might look like this: 6/21/201612/24/20156/27/201512/29/20147/2/20141/3/20147/7/20131/8/20137/12/2012 Date Oracle (ORCL) Price per Share 60 Best Case Likely Case Worst Case 40 50 30 10 20 Downside Upside - $52 $43 $30 GREEN RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:181 SCORE: 10.00 ================================================================================ 164  •   The Intelligent Option Investor because of their lack of appreciation for the fact that the sword of lever - age cuts both ways. Certainly an option investor cannot be considered an intelligent investor without having an understanding and a deep sense of respect for the simultaneous power and danger that leverage conveys. New jargon introduced in this chapter includes the following: Lambda Notional exposure Investment Leverage Commit the following definition to memory: Investment leverage is the boosting of investment returns calcu- lated as a percentage by altering the amount of one’s own capital at risk in a single investment. Investment leverage is inextricably linked to borrowing money—this is what I mean by the phrase “altering the amount of one’s own capital at risk. ” In this way, it is very similar to financial leverage. In fact, in my mind, the difference between financial and investment leverage is that a company uses financial leverage to fund projects that will produce goods or provide services, whereas in the case of investing leverage, it is used not to produce goods or services but to amplify the effects of a speculative position. Frequently people think of investing leverage as simply borrowing money to invest. However, as I mentioned earlier, you can invest in options for a lifetime and never explicitly borrow money in the process. I believe that the preceding definition is broad enough to handle both the case of investment leverage generated through explicit borrowing and the case of leverage generated by options. Let’s take a look at a few example investments—unlevered, levered using debt, and levered using options. Unlevered Investment Let’s say that you buy a stock for exactly $50 per share, expecting that its intrinsic value is closer to $85 per share. Over the next year, the stock increases by $5, or 10 percent in value. Y our unrealized percentage gain on this investment is ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:183 SCORE: 9.00 ================================================================================ 166  •   The Intelligent Option Investor And herein lies the painful lesson learned by many a soul in the financial markets: leverage cuts both ways. The profits happily roll in dur- ing the good times, but the losses inexorably crash down during bad times. Levered Investment Using Options Discussing option-based investing leverage is much easier if we focus on the perspective of gaining exposure. Because most people are more com- fortable thinking about the long side of investing, let’s look at an example of gaining upside exposure on a company. Let’s assume we see a $50 per share stock that we believe is worth $85 (in this example, I am assuming that we only have a point estimate of the intrinsic value of the company so as to simplify the following diagram—normally, it is much more helpful to think about fair value ranges, as explained in Part II of this book and demonstrate in the online example). We are willing to buy the share all the way up to a price of $68 (implying a 25 percent return if bought at $68 and sold at $85) and can get call options struck at $65 per share for only $1.50. Graphically, this prospective investment looks like this: Fair Value Estimate 5/18/2012 5/20/2013 249 499 749 999 - 10 20 30 40 50 60 70 80 90 EBP = $66.50 Date/Day Count Advanced Building Corp. (ABC) Stock Price GREEN ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:184 SCORE: 10.00 ================================================================================ Understanding and Managing Leverage    • 167 In two years, you are obligated to pay your counterparty $65 if you want to hold the stock, but the decision as to whether to take possession of the stock in return for payment is solely at your discretion. In essence, then, you can look at buying a call option as a conditional borrowing of funds sometime in the future. Buying the call option, you are saying, “I may want to borrow $65 two years from now. I will pay you some interest up front now, and if I decide to borrow the $65 in two years, I’ll pay you that principal then. ” In graphic terms, we can think about this transaction like this: 5/18/2012 5/20/2013 249 499 749 999 - 10 20 30 40 50 60 70 80 90 $1.50 “prepaid interest” Contingent loan, the future repayment of principal is made solely at the investor’s own discretion. Fair Value Estimate Advanced Building Corp. (ABC) Date/Day Count Stock Price GREEN If the stock does indeed hit the $85 mark just at the time our option expires, we will have realized a gross profit of $20 (= $85 − $65) on an investment of $1.50, for a percentage return of 1,233 percent! Obviously, the call option works very much like a loan in terms of altering the investor’s capital at risk and boosting subsequent investment returns. However, although the leverage looks very similar, there are two impor - tant differences: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:185 SCORE: 34.00 ================================================================================ 168  •   The Intelligent Option Investor 1. As shown and mentioned earlier, when using an option, payment on the principal amount of $65 in this case is conditional and com- pletely discretionary. For an option, the interest payment is made up front and is a sunk cost. 2. Because repayment is discretionary in the case of an option, you do not have any financial risk over and above the prepayment of interest in the form of an option premium. Repayment of a con- ventional loan is mandatory, so you have a large financial risk if you cannot repay the principal at maturity in this case. Regarding the first difference, not only is the loan conditional and discretionary, the loan also has value and can be transferred to another for a profit. What I mean is this: if the stock rises quickly, the value of that option in the open market will increase, and rather than holding the “loan” to maturity, you can simply sell it with your profits offsetting the original cost of the prepaid interest plus giving you a nice profit. Regarding the second difference, consider this: if you are using bor - rowed money to invest and your stock drops heavily, the broker will make a margin call (i.e., ask you to deposit more capital into the account), and if you cannot make the margin call, the broker will liquidate the position (most brokers shoot first and ask questions later, simply closing out the position and selling other assets to cover the loss at the first sign margin requirements will not be met). If this happens, you can be 100 percent correct on your valuation long term but still fail to benefit economically because the position has been forcibly closed. In the case of options, the underlying stock can lose 20 percent in a single day, and the owner of a call option will never receive a margin call. The flip side of this benefit is that although you are not at risk of losing a position to a margin call, option ownership does not guarantee that you will receive an economic reward either. For example, if the option mentioned in the preceding example ex- pires in two years when the stock is trading at $64.99 and the stock has paid $2.10 in dividends over the previous two years, the option holder ends up with neither the stock nor the dividend check. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:186 SCORE: 33.00 ================================================================================ Understanding and Managing Leverage    • 169 Simple Ways of Measuring Option Investment Leverage There are several single-point, easily calculable numbers to measure option-based investment leverage. There are uses for these simple measures of leverage, but unfortunately, for reasons I will discuss, the simple num- bers are not enough to help an investor intelligently manage a portfolio containing option positions. The two simple measures are lambda and notional exposure. Both are explained in the following sections. Lambda The standard measure investors use to determine the leverage in an option position is one called lambda . Lambda—sometimes known as percent delta—is a derivative of the delta 1 factor we discussed in Chapter 7 and is found using the following equation: = ×Lambda deltas tock price optionprice Let’s look at an actual example. The other day, I bought a deep in- the-money (ITM) long-tenor call option struck at $20 when the stock was trading at $30.50. The delta of the option at that time was 0.8707, and the price was $11. The leverage in my option position was calculated as follows: = × = × =Lambda deltas tock price optionprice 0.87 30.50 11 2.40 What this figure of 2.4 is telling us is that when I bought that option, if the price of the underlying moved by 1 percent, the value of my position would move by about 2.4 percent. This is not a hard and fast number—a change in price of either the stock or the option (as a result of a change in volatility or time value or whatever) will change the delta, and the lambda will change based on those things. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:187 SCORE: 39.00 ================================================================================ 170  •   The Intelligent Option Investor Because investment leverage comes about by changing the amount of your own capital that is at risk vis-à-vis the total size of the investment, you can imagine that moneyness has a large influence on lambda. Let’s take a look at how investment leverage changes for in-the-money (ITM), at-the-money (ATM), and out-of-the-money (OTM) options. The stock underlying the following options was trading at $31.25 when these data were taken, so I’m showing the $29 and $32 strikes as ATM: Strike Price K /S Ratio Call Price Delta Lambda 15.00 0.48 17.30 0.91 1.64 20.00 0.64 11.50 0.92 2.50 ITM 21.00 0.67 11.30 0.86 2.38 22.00 0.70 9.60 0.89 2.90 … … … … … 29.00 0.93 3.40 0.68 6.25 30.00 0.96 2.74 0.61 6.96 ATM 31.00 0.99 2.16 0.54 7.81 … … … … … 39.00 1.25 0.18 0.09 15.63 40.00 1.28 0.13 0.06 14.42 OTM 41.00 1.31 0.09 0.05 17.36 When an option is deep ITM, as in the case of the $20-strike call, we are making a significant expenditure of our own capital compared with the size of the investment. Buying a call option struck at $20, we are— as explained in the preceding section—effectively borrowing an amount equal to the $20 strike price. In addition to this, we are spending $11.50 in premium. Of this amount, $11.25 is intrinsic value, and $0.25 is time value. We can look at the time value portion as the prepaid interest we discussed in the preceding section, and we can even calculate the interest rate im- plied by this price (this option had 189 days left before expiration, implying an annual interest charge of 2.4 percent, for example). This prepaid interest can be offset partially or fully by profit realized on the position, but it can never be recaptured so must be considered a sunk cost. Time value always decays independent of the price changes of the underlying, so although an ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:188 SCORE: 48.00 ================================================================================ Understanding and Managing Leverage    • 171 upward movement in the stock will offset the money spent on time value, the amount spent on time value is never recoverable. The remaining $11.25 of the premium paid for a $20-strike call op- tion is intrinsic value . Buying intrinsic value means that we are exposing our own capital to the risk of an unrealized loss if the stock falls below $31.25. Lambda is directly related to the amount of capital we are exposing to an unrealized loss versus the size of the “loan” from the option, so be- cause we are risking $11.25 of our own capital and borrowing $20 with the option (a high capital-to-loan proportion), our investment leverage meas- ured by lambda is a relatively low 2.50. Now direct your attention to a far OTM call option—the one struck at $39. If we invest in the $39-strike option, we are again effectively taking out a $39 contingent loan to buy the shares. Again, we take the time-value portion of the option’s price—in this case the entire premi- um of $1.28—to be the prepaid interest (an implied annualized rate of 6.3 percent) and note that we are exposing none of our own capital to the risk of an unrealized loss. Because we are subjecting none of our own capital in this investment and taking out a large loan, our invest- ment leverage soars to a very high value of 15.63. This implies that a 1 percentage point move in the underlying stock will boost our invest- ment return by over 15 percent! Obviously, these calculations tell us that our investment returns are going to be much more volatile for small changes in the underlying’s price when buying far OTM options than when buying far ITM options. This is fine information for someone interested in more speculative strategies—if a speculator has the sense that a stock will rise quickly, he or she could, rather than buying the stock, buy OTM options, and if the stock went up fast enough and soon enough offset any drop of implied volatility and time decay, he or she would pocket a nice, highly levered profit. However, there are several factors that limit the usefulness of lambda. First, because delta is not a constant, the leverage factor does not stay put as the stock moves around. For someone who intends to hold a position for a longer time, then, lambda provides little information regarding how the position will perform over their investment horizon. In addition, reading the preceding descriptions of lambda, it is ob- vious that this measure deals exclusively with the percentage change in ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:189 SCORE: 23.00 ================================================================================ 172  •   The Intelligent Option Investor the option’s value. Although everyone (especially fly-by-night investment newsletter editors) likes to tout their percentage returns, we know from our earlier investigations of leverage that percentage returns are only part of the story of successful investing. Let’s see why using the three invest- ments I mentioned earlier—an ITM call struck at $20, an OTM call struck at $39, and a long stock position at $31. I believe that there is a good chance that this stock is worth north of $40—in the $43 range, to be precise (my worst-case valuation was $30, and my best-case valuation was in the mid-$50 range). If I am right, and if this stock hits the $43 mark just as my options expire, 2 what do I stand to gain from each of these investments? Let’s take a look. Spent Gross Profit Net Profit Percent Profit $39-strike call 0.18 4.00 3.82 2,122 $20-strike call 11.50 23.00 11.50 100 Shares 31.25 43.00 11.75 38 This table means that in the case of the $20-strike call, we spent $11.50 to win gross proceeds of $23.00 (= $43 − $20) and a profit net of investment of $11.50. Netting $11.50 on an $11.50 investment generates a percentage profit of 100 percent. Looking at this chart, the first thing you are liable to notice is the “Percent Profit” column. That 2,122 percent return looks like something you might see advertised on an option tout service, doesn’t it? Y es, that percentage return is wonderful, until you realize that the absolute value of your dollar winnings will not allow you to buy a latte at Starbuck’s. Likewise, the 100 percent return on the $20-strike options looks heads and shoulders better than the measly 38 percent on the shares, until you again realize that the latter is still giving you more money by a quarter. Recall the definition of leverage as a way of “boosting investment re- turns calculated as a percentage, ” and recall that in my previous discussion of financial leverage, I mentioned that the absolute dollar value is always highest in the unlevered case. The fact is that many people get excited about stratospheric percentage returns, but stratospheric percentage returns only ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:190 SCORE: 26.00 ================================================================================ Understanding and Managing Leverage    • 173 matter if a significant chunk of your portfolio is exposed to those returns! Lambda is a good measure to show how sensitive percentage returns are to a move in the stock price, but it is useless when trying to understand what the portfolio effects of those returns will be on an absolute basis. Notional Exposure Look back at the preceding table. Let’s say that we wanted to make lambda more useful in understanding portfolio effects by seeing how many contracts we would need to buy to match the absolute return of the underlying stock. Because our expected dollar return of one of the $39-strike calls only makes up about a third of the absolute return of the straight stock investment ($3.82 / $11.75 = 32.5% ≈ 1/3), it follows that if we wanted to make the same dollar return by investing in these call options that we expect to make by buying the shares, we would have to buy three of the call options for every share we wanted to buy. Recalling that op- tions are transacted in contract sizes of 100 shares, we know that if we were willing to buy 100 shares of Oracle’s stock, we would have to buy options implying control over 300 shares to generate the same absolute profit for our portfolio. I call this implied control figure notional exposure. Continuing with the $39-strike example, we can see that the measure of our leverage on the basis of notional exposure is 3:1. The value of the notional exposure is cal- culated by multiplying it by the strike; in this case, the notional exposure of 300 shares multiplied by the strike price of $39 gives a notional value for the contracts of $11,700. This value is called the notional amount of the option position. Some people calculate a leverage figure by dividing the notional amount by the total cost of the options. In our example, we would pay $18 per con- tract for three contracts, so leverage measured in this way would work out to be 217 (= $11,700 ÷ $54). I actually do not believe this last measure of lever- age to be very helpful, but notional control will become important when we talk about the leverage of short-call spreads later in this chapter. These simple methods of measuring leverage have their place in ana- lyzing option investment strategies, but in order to really master leverage, you must understand leverage in the context of portfolio management. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:191 SCORE: 8.00 ================================================================================ 174  •   The Intelligent Option Investor Understanding Leverage’s Effects on a Portfolio Looking at leverage from a lambda or notional control perspective gives some limited information about leverage, but I believe that the best way to think about option-based investment leverage is to think about the ef- fect of leverage on an actual portfolio allocation basis. This gives a richer, more nuanced view of how leverage stands to help or hurt our portfolio and allows us more insight into how we can intelligently structure a mixed option-stock portfolio. Let’s start our discussion of leverage in a portfolio context by thinking about how to select investments into a portfolio. We will assume that we have $100 in cash and want to use some or all of that cash to invest in risky securities. Cash is riskless (other than inflation risk, but let’s ignore that for a moment), so the risk we take on in the portfolio will be dampened by keeping cash, and the returns we will win from the portfolio will be similarly dampened. We have a limited amount of capital and want to allocate that capital to risky investments in proportion to two factors: 1. The amount we think we can gain from the investment 2. Our conviction in the investment, which is a measure of our per - ception of the riskiness of the investment We might see a potential investment that would allow us to reap a profit of $9 for every $1 invested (i.e., we would gain a great deal), but if our conviction in that investment is low (i.e., we think the chance of winning $9 for every $1 invested is very low), we would likely not allocate much of our portfolio to it. In constructing a portfolio, most people set a limit on the proportion of their portfolio they want to allocate to any one investment. I personally favor more concentrated positions, but let’s say that you paid better atten- tion to your finance professor in school than I did and figure that you want to limit your risk exposure to any one security to a maximum of $5 of your $100 portfolio. An unlevered portfolio means that each $5 allocation would be made by spending $5 of your own capital. Y ou would know that if the value of the underlying security decreases by $2.50, the value of the allocation will ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:192 SCORE: 14.00 ================================================================================ Understanding and Managing Leverage    • 175 also fall to $2.50. If, instead, the value of the underlying security increases by $2.50, the value of that allocation will rise to $7.50. In a levered portfolio, each $5 allocation uses some proportion of capital that is not yours—borrowed in the case of a margin loan and con- tingently borrowed in the case of an option. This means that for every $1 increase or decrease in the value of the underlying security, the lev- ered allocation increases or decreases by more than $1. Leverage, in this context, represents the rate at which the value of the allocation increases or decreases for every one-unit change in the value of the underlying security. When thinking about the risk of leverage, we must treat different types of losses differently. A realized loss represents a permanent loss of capital—a sunk cost for which future returns can offset but never undo. An unrealized loss may affect your psychology but not your wealth (unless you need to realize the loss to generate cash flow for something else—I talk about this in Chapter 11 when I address hedging). For this reason, when we measure how much leverage we have when the underlying security declines, we will measure it on the basis of how close we are to suffering a realized loss rather than on the basis of the unrealized value of the loss. Leverage on the profit side will be handled the same way: we will treat our fair value estimate as the price at which we will realize a gain. Because the current market price of a security may not sit exactly between our fair value estimate and the point at which we suffer a realized loss, our upside and downside leverage may be different. Let’s see how this comes together with an actual example. For this ex- ample, I looked at the price of Intel’s (INTC) shares and options when the former were trading at $22.99. Let’s say that we want to commit 5 percent of our portfolio value to an investment in Intel, which we believe is worth $30 per share. For every $100,000 in our portfolio, this would mean buying 217 shares. This purchase would cost us $4,988.83 (neglecting taxes and fees, of course) and would leave us with $11.17 of cash in reserve. After we made the buy, the stock price would fluctuate, and depending on what its price was at the end of 540 days [I’m using as an investment horizon the days to expiration of the longest-tenor long-term equity anticipation secu- rities (LEAPS)], the allocation’s profit and loss profile would be represented graphically like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:193 SCORE: 18.00 ================================================================================ 176  •   The Intelligent Option Investor 02468 10 12 14 16 18 20 22 24 Stock Price Unlevered Investment (Full Allocation) Gain (Loss) on Allocation 26 28 30 32 34 36 38 40 42 44 46 48 50(6,000) (4,000) (2,000) - 2,000 4,000 6,000 8,000 Unrealized Gain Unrealized Loss Cash Value Net Gain (Loss) - Unlevered Realized Loss Here the future stock price is listed from 0 to 50 on the horizontal axis, and the net profit or loss to this position is listed on the vertical axis. Obvious- ly, any gain or loss would be unrealized unless Intel’s stock price went to zero, at which point the total position would only be worth whatever spare cash we had. The black profit and loss line is straight—the position will lose or gain on a one-for-one basis with the price of the stock, so our leverage is 1.0. Now that we have a sense of what the graph for a straight stock position looks like, let’s take a look at a few different option positions. When I drew the data for this example, the following 540-day expiration call options were available: Strike Price Ask Price Delta 15 8.00 0.79 22 2.63 0.52 25 1.43 0.35 Let’s start with the ITM option and construct a simple-minded posi- tion that attempts to buy as many of these option contracts as possible with the $5,000 we have reserved for this investment. We will pay $8 per share ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:194 SCORE: 28.00 ================================================================================ Understanding and Managing Leverage    • 177 or $800 per contract, which would allow us to buy six contracts in all for $4,800. There is only $0.01 worth of time value (= $15.00 + $8.00 − $22.99) on these options because they are so far ITM. This means that we are pay- ing $1 per contract worth of time value that is never recoverable, so we shall treat it as a realized loss. If we were to graph our potential profit and loss profile using this option, assuming that we are analyzing the position just as the 540-day options expire, we would get the following 3: Net Gain (Loss) - Levered 0246810 12 14 16 18 20 22 24 Stock Price Levered Strategy Overview Gain (Loss) on Allocation 26 28 30 32 34 36 38 40 42 44 46 48 50(10,000) (5,000) - 5,000 10,000 Unrealized Gain Unrealized Loss Cash Value Realized Loss 15,000 20,000 The most obvious differences from the diagram of the unlevered po- sition are (1) that the net gain/loss line is kinked at the strike price and (2) that we will realize a total loss of invested capital—$4,800 in all—if Intel’s stock price closes at $15 or below. The kinked line demonstrates the meaning of the first point made earlier regarding option-based investment leverage—an asymmetrical return profile for profits and losses. Note that this kinked line is just the hockey-stick representation of option profit and loss at expiration that one sees in every book about options except this one. Although I don’t believe that hockey-stick diagrams are terribly useful for understanding individual option transactions, at a portfolio level, they do represent the effect of leverage very well. This black line represents a ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:196 SCORE: 10.00 ================================================================================ Understanding and Managing Leverage    • 179 In this example, we suffer a realized loss of 96 percent (= $4,800 ÷ $5,000) if the stock falls 35 percent, so the equation becomes = − =− ×Lossleverage 96% 35% 2.8 (By convention, I’ll always write the loss leverage as a negative.) This equation just means that it takes a drop of 35 percent to realize a loss on 96 percent of the allocation. The profit leverage is simply a ratio of the levered portfolio’s net profit to the unlevered portfolio’s net profit at the fair value estimate. For this example, we have == ×Profitleverage $4,200 $1,472 3.0 Let’s do the same exercise for the ATM and OTM options and see what fully levered portfolios with each of these options would look like from a risk-return perspective. If we bought as many $22-strike options as a $5,000 position size would allow (19 contracts in all), our profit and loss graph and table would look like this: 02468 10 12 14 16 18 20 22 24 Stock Price Levered Strategy Overview Gain (Loss) on Allocation 26 28 30 32 34 36 38 40 42 44 46 48 50(20,000) - 40,000 60,000 80,000 100,000 20,000 Unrealized Gain Unrealized Loss Cash Value Net Gain (Loss) - Levered Realized Loss ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:197 SCORE: 23.00 ================================================================================ 180  •   The Intelligent Option Investor Instrument Maximum-Loss Price Net Profit at Fair Value Estimate Stock $0 $1,472 Option $22 (23.2 × stock loss) $10,203 (6.9 × stock profit) This is quite a handsome potential profit—6.9 times higher than we could earn using a straight stock position—but at an enormous risk. Each $1 drop in the stock price equates to a $23.20 drop in the value of the posi- tion. Note that the realized loss shows a step up from $22 to $23. This just shows that above the strike price, our only realized loss is the money we spent on time value. The last example is that of the fully levered OTM call options. Here is the table illustrating this case: Instrument Maximum-Loss Price Net Profit at Fair Value Estimate Stock $0 $1,472 Option $25 (IRL 5 percent) $12,495 (8.5 × stock profit) There is no intrinsic value to this option, so the entire cost of the option is treated as an immediate realized loss (IRL) from inception. The “IRL 5 percent” notation means that there is an immediate realized loss of 5 percent of the total portfolio. The maximum net loss is again at the strike price of $25. The leverage factor at our fair value estimate price is 8.5, but again this leverage comes at the price of having to realize a 5 percent loss on your portfolio—500 basis points of performance—and there is no certainty that you will have enough or any profits to offset this realized loss. Of course, investing choices are not as black and white as what I have presented here. If you want to commit 5 percent of your portfolio to a straight stock idea, you have to spend 5 percent of your portfolio value on stock, but this is not true for options. For example, I might choose to spend 2.5 percent of my portfolio’s worth on ATM calls (nine contracts in this ex- ample), considering the position in terms of a 5 percent stock investment, and then leave the rest as cash reserve. Here is what this investment would look like from a leverage perspective: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:198 SCORE: 10.00 ================================================================================ Understanding and Managing Leverage    • 181 02468 10 12 14 16 18 20 22 24 Stock Price Levered Strategy Overview Gain (Loss) on Allocation 26 28 30 32 34 36 38 40 42 44 46 48 50(5,000) - 15,000 10,000 20,000 25,000 30,000 5,000 Unrealized Gain Unrealized Loss Cash Value Net Gain (Loss) - Levered Realized Loss Instrument Maximum-Loss Price Net Profit at Fair Value Estimate Stock $0 $1,472 Option $22 (11 × stock loss) $4,833 (5.1 × stock profit) The 11 times loss figure was calculated in the following way: there is a total of 47.3 percent of my allocation to this investment that is lost if the price of the stock goes down by 4.3 percent, so −47.3 percent/4.3 percent = −11.0. Obviously, this policy of keeping some cash in reserve represents a sensible ap- proach to portfolio management when leverage is used. An investor in straight stock who makes 20 investments that do not hit his or her expected fair value within the investment horizon might have a few bad years of performance, but an investor who uses maximum option leverage and allocates 5 percent to 20 ideas will end up bankrupt if these don’t work out by expiration time! Similar to setting a cash reserve, you also might decide to make an investment that combines cash, stock, and options. For example, I might buy 100 shares of Intel, three ITM option contracts, and leave the rest of my 5 percent allocation in cash. Here is what that profit and loss profile would look like: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:199 SCORE: 10.00 ================================================================================ 182  •   The Intelligent Option Investor 0 24681 01 21 41 61 82 02 22 4 Stock Price Levered Strategy Overview Gain (Loss) on Allocation 26 28 30 32 34 36 38 40 42 44 46 48 50(6,000) (4,000) (2,000) - 4,000 2,000 6,000 10,000 12,000 8,000 Unrealized Gain Unrealized Loss Cash Value Net Gain (Loss) - Levered Realized Loss Instrument Maximum-Loss Price Net Profit at Fair Value Estimate Stock $0 $1,472 Option $15 (1.8 × stock loss) $3,803 (2.6 × stock profit) Three $800 option contracts represent $2,400 of capital or 48 percent of this allocation’s capital. Thus 48 percent of the capital was lost with a 34.8 per- cent move downward in the stock, generating a −1.4 times value for the options plus we add another −0.4 times value to represent the loss on the small stock allocation; together these generate the −1.8 times figure you see on the loss side. Of course, if the option loss is realized, we still own 100 shares, so the maximum loss will not be felt until the shares hit $0, as shown in the preceding diagram. For the remainder of this book I will describe leverage positions us- ing the two following terms: loss leverage and profit leverage . I will write these in the following way: − X.x Y.y where the first number will be the loss leverage ratio, and the second number will be the profit leverage ratio based on the preceding rules that ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:200 SCORE: 11.00 ================================================================================ Understanding and Managing Leverage    • 183 I’ve used for calculation. All OTM options will be marked with an IRL fol- lowed by the percentage of the total portfolio used in the option purchase (not the percentage of the individual allocation but the total percentage amount of your investment capital). On my website, you’ll find an online leverage tool that allows you to calculate these numbers yourself. Managing Leverage A realized loss is, to me, serious business. There are times when an inves- tor must take a realized loss—specifically when his or her view of the fair value or fair value range of a company changes materially enough that an investment position becomes unattractive. However, if you find yourself taking realized losses because of material changes in valuation too often, you should either figure out where you are going wrong in the valuation process or just put your money into a low-load mutual fund and spend your time doing something more productive. The point is that taking a realized loss is not something you have to do too often if you are a good investor, and hopefully, when those losses are taken, they are small. As such, I believe that there are two ways to successfully manage leverage. First is to use leverage sparingly by investing in combinations of ITM options and stocks. ITM option prices mainly represent intrinsic value, and be- cause the time-value component is that which represents a realized loss right out of the gate, buying ITM options means that you are minimizing realized losses. The second method for managing leverage when you cannot resist taking a higher leverage position is spending as little as possible of your investment capital on it. This means that when you see that there is a com- pany that has a material chance of being worth a lot more or a lot less than it is traded for at present but that material chance is still much less likely than other valuation scenarios, you should invest your capital in the idea sparingly. By making smaller investments with higher leverage, you will not realize a loss on too much of your capital at one time, and if you are right at least some of the time on these low-probability, high-potential- reward bets, you will come out ahead in the end. Of course, you also can use a combination of these two methods. For example, I have found it helpful to take the main part of a position using a ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:201 SCORE: 15.00 ================================================================================ 184  •   The Intelligent Option Investor combination of stock and ITM call options but also perhaps buying a few OTM call options as well. As the investment ages and more data about the company’s operations come in, if this information leads me to be more bullish about the prospects of the stock, I may again increase my leverage using OTM call options—especially when I see implied volatility trading at a particularly low level or if the stock price itself is depressed because of a generally weak market. I used to be of the opinion that if you are confident in your valuation and your valuation implies a big enough unlevered return, it is irrational not to get exposure to that investment with as much leverage as possible. A few large and painful losses of capital have convinced me that where- as levering up on high-conviction investments is theoretically a rational investment regime, practically, it is a sucker’s game that is more likely to deplete your investment capital than it is to allow you to hit home runs. Y ounger investors, who still have a long investing career ahead of them and plenty of time to make up for mistakes early on, probably can feel more comfortable using more leverage, but as you grow closer to the time when you need to use your investments (e.g., paying for retirement, kids’ college expenses, or whatever), using lower leverage is better. Looking back at the preceding tables, one row in one table in particular should stand out to you. This is the last row of the last table, where the leverage is −1.8/2.6. To me, this is a very attractive leverage ratio because of the asymmetry in the risk-reward balance. This position is levered, but the leverage is lopsided in the investor’s favor, so the investor stands to win more than he or she loses. This asymmetry is the key to successful investing—not only from a leverage standpoint but also from an economic standpoint as well. I believe an intelligent, valuation-centric method for investing in companies such as the ones outlined in this book that allow investors an edge up by allowing them to identify cases in which the valuation simply does not line up with the market price. This in itself presents an asymmetrical profit opportunity, and the real job of an intelligent investor is to find as large an asymmetry as possible and courageously invest in that company. If you can also tailor your leverage such that your payout is asymmetrical in your favor as well, this only adds potential for outsized returns, in my opinion. The other reason that the −1.8/2.6 leverage ratio investment interests me is because of the similarity it has to the portfolio of Warren Buffett’s ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:202 SCORE: 12.00 ================================================================================ Understanding and Managing Leverage    • 185 Berkshire Hathaway (BRK.A). In a recent academic paper written by re- searchers at AQR Capital titled, “Buffett’s Alpha, ”4 the researchers found that a significant proportion of Buffett’s legendary returns can be attributed to finding firms that have low valuation risk and investing in them using a leverage ratio of roughly 1.8. The leverage comes from the float from his in- surance companies (the monies paid in premium by clients over and above that required to pay out claims). As individual investors, we do not have a captive insurance company from which we can receive continual float, but by buying options and using leverage prudently, it is possible to invest in a manner similar to a master investor. In this section, we have only discussed leverage considerations when we gain exposure by buying options. There is a good reason to ignore the case where we are accepting exposure by selling options that we will dis- cuss when we talk about margining in Chapter 10. We now continue with chapters on gaining, accepting, and mixing exposure. In these chapters, we will use all of what we have learned about option pricing, valuation, and leverage to discuss practical option investment strategies. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:204 SCORE: 33.00 ================================================================================ 187 Chapter 9 GaininG ExposurE This chapter is designed as an encyclopedic listing of the main strategies for gaining exposure (i.e., buying options) that an intelligent option inves- tor should understand. Gaining exposure seems easy in the beginning be- cause it is straightforward—simply pay your premium up front, then if the stock moves into your option’s range of exposure by expiration time, you win. However, the more you use these strategies in investing exposure, the more nuances arise. What tenor should I choose? What strike price should I choose? Should I exercise early if my option is in the money (ITM)? How much capital should I commit to a given trade? If the stock price goes in the opposite direction from my option’s range of exposure, should I close my option position? All these questions are examples of why gaining exposure by buying options is not as straightforward a process as it may seem at first and are all the types of questions I will cover in the following pages. Gaining exposure means buying options, and the one thing that an option buyer must never lose sight of is that time is always working against him or her. Options expire. If your options expire out of the money (OTM), the capital you spent on premiums on those options is a realized loss. No matter how confident you are about your valuation call, you should al- ways keep this immutable truth of option buying in mind. Indeed, there are ways to reduce the risk of this happening or to manage a portfolio in ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:205 SCORE: 21.00 ================================================================================ 188  •   The Intelligent Option Investor such a way that such a loss of capital becomes just a cost of doing business that will be made up for in another investment down the line. For each of the strategies mentioned in this chapter, I present a stylized graphic representing the Black-Scholes-Merton model (BSM) cone and the option’s range of exposure plus best- and worst- case valuation scenarios. These are two of the required inputs for an intelligent option investing strategy—an intelligently determined valu- ation range and the mechanically determined BSM forecast range. I will also provide a summary of the relative pricing of upside and downside exposure vis-à-vis an intelligent valuation range (e.g., “Upside expo- sure is undervalued”), the steps taken to execute the strategy, and its potential risks and return. After this summary section, I provide textual discussions of tenor se- lection, strike price selection, portfolio management (i.e., rolling, exercise, etc.), and any miscellaneous items of interest to note. Understanding the strategies well and knowing how to use the tools at your disposal to tilt the balance of risk and reward in your favor are the hallmark and pinnacle of intelligent option investing. Intelligent option investors gain exposure when the market underestimates the likelihood of a valuation that the in- vestor believes is a rational outcome. In graphic terms, this means that ei- ther one or both of the investor’s best- and worst-case valuation scenarios lie outside the BSM cone. Simple (one-option) strategies to gain exposure include • Long calls • Long puts Complex (multioption) strategies to gain exposure include • Long strangles • Long straddles Jargon introduced in this chapter includes the following: Roll Ratio(ing) ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:206 SCORE: 22.00 ================================================================================ Gaining Exposure • 189 Long Call GREEN Downside: Fairly priced Upside: Undervalued Execute: Buy a call option Risk: Amount equal to premium paid Reward: Unlimited less amount of premium paid The Gist An investor uses this strategy when he or she believes that there is a material chance that the value of a company is much higher than the present market price. The investor must pay a premium to initiate the position, and the proportion of the premium that represents time value should be recognized as a realized loss because it cannot be recovered. If the stock fails to move into the area of exposure before option expiration, there will be no profit to offset this realized loss. In economic terms, this transaction allows an investor to go long an undervalued company without accepting an uncertain risk of loss if the stock falls. Instead of the uncertain risk of loss, one must pay the fixed pre- mium. This strategy obeys the same rules of leverage as discussed earlier in this book, with in-the-money (ITM) call options offering less leverage but being much more forgiving regarding timing than are at-the-money (ATM) or especially out-of-the-money (OTM) options. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:207 SCORE: 50.00 ================================================================================ 190  •   The Intelligent Option Investor T enor Selection In general, the rule for gaining exposure is to buy as long a tenor as is available. If a stock moves up faster than you expected, the option will still have time value left on it, and you can sell it to recoup the extra money you spent to buy the longer-tenor option. In addition, long-tenor options are usually proportionally less expensive than shorter-tenor ones. Y ou can see this through the following table. These ask prices are for call options on Google (GOOG) struck at whatever price was closest to the 50-delta mark for every tenor available. Days to Expiration Ask Price Marginal Price/Day Delta 3 6.00 2.00 52 10 10.30 0.61 52 17 12.90 0.37 52 24 15.50 0.37 52 31 17.70 0.31 52 59 22.40 0.17 49 87 34.40 0.43 50 150 42.60 0.13 50 178 47.30 0.17 50 241 56.00 0.14 50 542 86.40 0.10 50 The “Marginal Price/Day” column is simply the extra that you pay to get the extra days on the contract. For example, the contract with three days left is $6.00. For seven more days of exposure, you pay a total of $4.30 extra, which works out to a per-day rate of $0.61. We see blips in the marginal price per day field as we go from 59 to 87 to 150 days, but these are just artifacts of data availability; the closest strikes did not have the same delta for each expiration. The preceding chart, it turns out, is just the inverse of the rule we already learned in Chapter 3: “time value slips away fastest as we get closer to expiration. ” If time value slips away more quickly nearer expiration, it must mean that the time value nearer expiration is proportionally worth more than the time value further away from expiration. The preceding table simply illustrates this fact. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:208 SCORE: 43.00 ================================================================================ Gaining Exposure • 191 Value investors generally like bargains and to buy in bulk, so we should also buy our option time value “in bulk” by buying the longest tenor available and getting the lowest per-day price for it. It follows that if long-term equity anticipation securities (LEAPS) are available on a stock, it is usually best to buy one of those. LEAPS are wonderful tools because, aside from the pricing of time value illustrated in the preceding table, if you find a stock that has undervalued upside potential, you can win from two separate effects: 1. The option market prices options as if underlying stocks were ef- ficiently priced when they may not be (e.g., the market thinks that the stock is worth $50 when it’s worth $70). This discrepancy gives rise to the classic value-investor opportunity. 2. As long as interest rates are low, the drift term understates the ac- tual, probable drift of the stock market of around 10 percent per year. This effect tends to work for the benefit of a long-tenor call option whether or not the pricing discrepancy is as profound as originally thought. There are a couple of special cases in which this “buy the longest tenor possible” rule of thumb should not be used. First, if you believe that a company may be acquired, it is best to spend as little on time value as possible. I will discuss this case again when I discuss selecting strike prices, but when a company agrees to be acquired by another (and the market does not think there will be another offer and regulatory approv- als will go through), the time value of an option drops suddenly because the expected life of the stock as an independent entity has been short- ened by the acquiring company. This situation can get complicated for stock-based acquisitions (i.e., those that use stocks as the currency of acquisition either partly or completely) because owners of the acquiree’s options receive a stake in the acquirer’s options with strike price adjusted in proportion to the acquisition terms. In this case, the time value on your acquiree options would not disappear after the acquisition but be transferred to the acquirer’s company’s options. The real point is that it is impossible, as far as I know, to guess whether an acquisition will be made in cash or in shares, so the rule of thumb to buy as little time value as possible still holds. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:209 SCORE: 16.00 ================================================================================ 192  •   The Intelligent Option Investor In general, attempting to profit from potential mergers is dif- ficult using options because you have to get both the timing of the suspected transaction and the acquisition price correct. I will discuss a possible solution to this situation in the next section about picking strike prices. The second case in which it is not necessary to buy as long a tenor as possible is when you are trading in expectation of a particular company announcement. In general, this game of anticipating stock price move- ments is a hard one to win and one that value investors usually steer clear of, but if you are sure that some announcement scheduled for a particular day or week is likely to occur but do not want to make a long-term invest- ment on the company, you can buy a shorter-tenor option that obviously must include the anticipated announcement date. It is probably not a bad idea to build in a little cushion between your expiration and the anticipated date of the announcement because sometimes announcements are pushed back and rescheduled. Strike Price Selection From the discussion regarding leverage in the preceding section, it is clear that selecting strike prices has a lot to do with selecting what level of leverage you have on any given bet. Ultimately, then, strike selec- tion—the management of leverage, in other words—is intimately tied to your own risk profile and the degree to which you are risk averse or risk seeking. My approach, which I will talk more about in the following section on portfolio management, may be too conservative for others, but I put it forward as one alternative among many that I have found over time to be sensible. Any investment has risk to the extent that there is never perfect certainty regarding a company’s valuation. Some companies have a fairly tight valuation range—meaning that the confluence of their revenue stream, profit stream, and investment efficacy does not vary a great deal from best to worst case. Other companies’ valuation ranges are wide, with a few clumps of valuation scenarios far apart or with just one or two outlying valuation scenarios that, although not the most likely, are still materially probable. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:210 SCORE: 9.00 ================================================================================ Gaining Exposure • 193 On the rare occasion in which we find a company that has a valuation range that is far different from the present market price (either tight or wide), I would rather commit more capital to the idea, and for me, committing more capital to a single idea means using less leverage. In other words, I would prefer to buy an ITM call and lever at a reasonable rate (e.g., the −1.8 × /2.6 × level we saw in the Intel example earlier). Graphically, my approach would look like this: Advanced Building Corp. (ABC) 110 100 90 80 70 60 50 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Date/Day Count Stock Price GREEN ORANGE Here I have bought a deep ITM call option LEAPS that gives me lev- erage of about −1.5/2.0. I have maximized my tenor and minimized my leverage ratio with the ITM call. This structure will allow me to profit as long as the stock goes up by the time my option expires, even if the stock price does not hit a certain OTM strike price. In the more common situation, in which we find a company that is probably about fairly valued in most scenarios but that has an outlying valuation scenario or two that doesn’t seem to be priced in properly by the market, I will commit less capital to the idea but use more leverage. Graphically, my approach would look more like this: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:211 SCORE: 14.00 ================================================================================ 194  •   The Intelligent Option Investor Advanced Building Corp. (ABC) 100 90 80 70 60 50 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Date/Day Count Stock Price GREEN Here I have again maximized my tenor by buying LEAPS, but this time I increase my leverage to something like an “IRL/10.0” level in case the stars align and the stock price sales to my outlier valuation. Some people would say that the IIM approach is absolutely the op- posite of a rational one. If you are—the counterargument goes—confident in your valuation range, you should try to get as much leverage on that idea as possible; buying an ITM option is stupid because you are not using the leverage of options to their fullest potential. This counterargument has its point, but I find that there is just too much uncertainty in the markets to be too bold with the use of leverage. Options are time-dependent instruments, and if your option expires worthless, you have realized a loss on whatever time value you original- ly spent on it. Economies, now deeply intertwined all over the globe, are phenomenally complex things, so it is the height of hubris to claim that I can perfectly know what the future value of a firm is and how long it will take for the market price to reflect that value. In addition, I as a human decision maker am analyzing the world and investments through a con- genital filter based on behavioral biases. Retaining my humility in light of the enormous complexity of the marketplace and my ingrained human failings and expressing this humility ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:212 SCORE: 26.00 ================================================================================ Gaining Exposure • 195 by using relatively less leverage when I want to commit a significant amount of capital to an idea constitute, I have found, given my risk tolerance and experience, the best path for me for a general investment. In contrast, we all have special investment loves or wild hares or whatever, and sometimes we must express ourselves with a commitment of capital. For example, “If XYZ really can pull it off and come up with a cure for AIDS, its stock will soar. ” In instances such as these, I would rather commit less capital and express my doubt in the outcome with a smaller but more highly levered bet. If, on average, my investment wild hares come true every once in a while and, when they do, the options I’ve bought on them pay off big enough to more than cover my realized losses on all those that did not, I am net further ahead in the end. These rules of thumb are my own for general investments. In the spe- cial situation of investing in a possible takeover target, there are a few extra considerations. A company is likely to be acquired in one of two situations: (1) it is a sound business with customers, product lines, or geographic exposure that another company wants, or (2) it is a bad business, either because of management incompetence, a secular decline in the business, or something else, but it has some valuable asset(s) such as intellectual prop- erty that a company might want to have. If you think that a company of the first sort may be acquired, I be- lieve that it is best to buy ITM call options to attempt to minimize the time value spent on the investment (you could also sell puts, and I will discuss this approach in Chapter 10). In this case, you want to minimize the time value spent because you know that the time value you buy will drain away when a takeover is announced and accepted. By buying an ITM contract, you are mainly buying intrinsic value, so you lose little time value if and when the takeover goes through. If you think that a company of the second sort (a bad company in decline) may be acquired, I believe that it is best to minimize the time value spent on the investment by not buying a lot of call contracts and by buying them OTM. In this case, you want to minimize the time value spent using OTM options by limiting the number of contracts bought because you do not want to get stuck losing too much capital if and when the bad company’s stock loses value while you are holding the options. Typical buyout premiums are in the 30 percent range, so buy- ing call options 20 percent OTM or so should generate a decent profit if ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:213 SCORE: 24.00 ================================================================================ 196  •   The Intelligent Option Investor the company is taken out. Just keep in mind that the buyout premium is 30 percent over the last price, not 30 percent over the price at which you decided to make your investment. If you buy 20 percent OTM call options and the stock decreases by 10 percent before a 30 percent premium buyout is announced, you will end up with nothing, as shown in the following timeline: $12-Strike Options Bought When the Stock Is Trading for $10 • Stock falls to $9. • Buyout is announced at 30 percent above last price—$11.70. • 12-strike call owner’s profit = $0. However, there is absolutely no assurance that an acguirer will pay some- thing for a prospective acguiree. Depending on how keen the acquirer is to get its hands on the assets of the target, it may actually allow the target company to go bankrupt and then buy its assets at $0.30 on the dollar or whatever. It is precisely this uncertainty that makes it unwise to commit too much capital to an idea involving a bad company—even if you think it may be taken out. Portfolio Management I like to think of intelligent option investing as a meal. In our investment meal, the underlying instrument—the stock—should, in most cases, form the main course. People have different ideas about diversification in a securities portfolio and about the maximum percentage of a portfolio that should be allocated to a specific idea. Clearly, most people are more comfortable allocating a greater percentage of their portfolio to higher-confidence ideas, but this is normal- ly framed in terms of relative levels (i.e., for some people, a high-conviction idea will make up 5 percent of their portfolio and a lower-conviction one 2.5 percent; for others, a high-conviction idea will make up 20 percent of their portfolio and a lower-conviction one 5 percent). Rather than addressing what size of investment meal is best to eat, let’s think about the meal’s composition. Considering the underlying stock as the main course, I consider the leverage as sauces and side dishes. ITM options positions are the main ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:214 SCORE: 14.00 ================================================================================ Gaining Exposure • 197 sauce to make the main course more interesting and flavorful. Y ou can layer ITM options onto the stock to increase leverage to a level with which you feel comfortable. This does not have to be Buffett’s 1.8:1 leverage of course. Levering more lightly will provide less of a kick when a company performs according to your best-case scenario, but also carries less risk of a severe loss if the company’s performance is mediocre or worse. OTM option positions (and “long diagonals” to be discussed in Chapter 11) can be thought of as a spicy side dish to the main meal. They can be added opportunistically (when and if the firm in which you are investing has a bad quarter and its stock price drops for temporary reasons involving sen- timent rather than substance) for extra flavor. OTM options can also be used as a snack to be nibbled on between proper meals. Snack, in this case, means a smaller sized position in firms that have a small but real upside potential but a greater chance that it is fairly valued as is, or in a company in which you don’t have the conviction in its ability to create much value for you, the owner. Another consideration regarding the appropriate level of investment leverage one should apply to a given position is how much operational and financial leverage (both are discussed in detail in Appendix B) a firm has. A firm that is highly levered will have a much wider valuation range and will be much more likely to be affected by macroeconomic considera- tions that are out of the control of the management team and inscrutable to the investor. In these cases, I think the best response is to adjust one’s investment leverage according to the principles of “margin of safety” and contrarianism. By creating a valuation range, rather than thinking only of a single point- estimate for the value of the firm, we have unwittingly allowed ourselves to become very skillful at picking appropriate margins of safety. For example, I recently looked at the value of a company whose stock was trading for around $16 per share. The company had very high operational and financial lever- age, so my valuation range was also very large—from around $6 per share worst case to around $37 per share best case with a most likely value of around $25 per share. The margin of safety is 36 percent (= ($25 − $16)/ $25). While some might think this is a reasonable margin of safety to take a bold, concentrated position, I elected instead to take a small, unlevered one because to me, the $9 margin of safety for this stock is still not wide enough. The best ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:215 SCORE: 8.00 ================================================================================ 198  •   The Intelligent Option Investor time to take a larger position and to use more leverage is when the market is pricing a stock as if it were almost certain that a company will face a worst-case future when you consider this worst-case scenario to be relatively unlikely. In this illustration, if the stock price were to fall by 50 percent—to the $8 per share level—while my assessment of the value of the company remained unchanged (worst, likely, and best case of $6, $25, and $37, respectively), I would think I had the margin of safety necessary to commit a larger proportion of my portfo- lio to the investment and add more investment leverage. With the stock sitting at $8 per share, my risk ($8 − $6 = $2) is low and unlikely to be realized while my potential return is large and much closer to being assured. With the stock’s present price of $16 per share, my risk ($16 − $6 = $10) is large and when bad- case scenarios are factored in along with the worst-case scenario, more likely to occur. Thinking of margins of safety from this perspective, it is obvious that one should not frame them in terms of arbitrary levels (e.g., “I have a rule to only buy stocks that are 30% or lower than my fair value estimate. ”), but rather in terms informed by an intelligent valuation range. In this example, a 36 percent margin of safety is sufficient for me to commit a small proportion of my portfolio to an unlevered investment, but not to go “all in. ” For a concentrated, levered position in this investment, I would need a margin of safety approaching 76 percent (= ($25 − $6)/$25) and at least over 60 percent (= ($25 - $10)/$25). When might such a large margin of safety present itself? Just when the market has lost all hope and is pricing in disaster for the company. This is where the contrarianism comes into play. The best time to make a levered investment in a company with high levels of operational lever - age is when the rest of the market is mainly concerned about the possible negative effects of that operational leverage. For example, during a reces- sion, consumer demand drops and idle time at factories increases. This has a quick and often very negative effect on profitability for companies that own the idle factories, and if conditions are bad enough or look to have no near-term (i.e., within about six months) resolution, the price of those companies’ stocks can plummet. Market prices often fall so low as to imply, from a valuation perspective, that the factories are likely to remain idled forever. In these cases, I believe that not using investment leverage in this case may carry with it more real risk than using investment leverage ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:217 SCORE: 30.00 ================================================================================ 200  •   The Intelligent Option Investor After you enter a position and some time passes, it becomes clearer what valuation scenario the company is tending toward. In some cases, a bit of information will come out that is critical to your valuation of the company on which other market participants may not be focused. Obvi- ously, if a bit of information comes out that has a big, positive or negative impact on your assessment of the company’s value, you should adjust your position size accordingly. If you believe the impact is positive, it makes sense to build to a position by increasing your shares owned and/or by adding “spice” to that meal by adjusting your target leverage level. If the impact is negative, it makes sense to start by reducing leverage (or you can think of it as increasing the proportion of cash supporting a particular position), even if this reduction means realizing a loss. If the impact of the news is so negative that the investment is no longer attractive from a risk- reward perspective, I believe that it should be closed and the lumps taken sooner rather than later. Considering what we know about prospect theory, this is psychologically a difficult thing to do, but in my experience, waiting to close a position in which you no longer have confidence seldom does you any good. Obviously, the risk/reward equation of an investment is also influ- enced by a stock’s market price. If the market price starts scraping against the upper edge of your valuation range, again, it is time to reduce leverage and/or close the position. If your options are in danger of expiring before a stock has reached your fair value estimate, you may roll your position by selling your option position and using the proceeds to buy another option position at a more distant tenor. At this time, you must again think about your target leverage and adjust the strikes of your options accordingly. If the price of the stock has decreased over the life of the option contract, this will mean that you realize a loss, which is not an easy thing to do psychologically, but consid- ering the limitations imposed by time for all option investments, this is an unavoidable situation in this case. One of the reasons I dislike investing in non-LEAPS call options is that rolling means that not only do we have to pay another set of bro- ker and exchange fees, but we also must pay both sides of the bid-ask spread. Keeping in mind how wide the bid-ask spread can be with options and what an enormous drag this can be on returns, you should carefully ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:218 SCORE: 28.00 ================================================================================ Gaining Exposure • 201 consider whether the prospective returns justify entering a long call posi- tion that will likely have to be rolled multiple times before the stock hits your fair value estimate. By the way, it goes without saying that to the extent that an option you want to roll has a significant amount of time value on it, it is better to roll before time decay starts to become extreme. This usually occurs at around three months before expiration. It turns out that option liquidity increases in the last three months before expiration, and rolling is made easier with the greater liquidity. Having discussed gaining bullish exposure with this section about long calls, let’s now turn to gaining bearish exposure in the following sec- tion on long puts. Long Put GREEN Downside: Undervalued Upside: Fairly priced Execute: Buy a put option Risk: Amount of premium paid Reward: Amount equal to strike price—premium The Gist An investor uses this strategy when he or she believes that it is very likely that the value of a company is much lower than the present market price. The investor must pay a premium to initiate the position, and the propor- tion of the premium that represents time value should be recognized as a ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:219 SCORE: 32.00 ================================================================================ 202  •   The Intelligent Option Investor realized loss because it cannot be recovered. If the stock fails to move into the area of exposure before option expiration, there will be no profit to offset this realized loss. In economic terms, this transaction allows an investor to sell short an overvalued company without accepting an uncertain risk of loss if the stock rises. Instead of the uncertain risk of loss, the investor must pay the fixed premium. This strategy obeys the same rules of leverage as discussed earlier in this book, with ITM put options offering less leverage but a great- er cushion before realizing a loss than do ATM or OTM put options. T enor Selection Shorting stocks, which is what you are doing when you buy put op- tions, is hard work, not for the faint of heart. There are a couple of reasons for this: 1. Markets generally go up, and for better or worse, a rising tide usu- ally does lift all boats. 2. Even when a company is overvalued, it is hard to know what cata- lyst will make that fact obvious to the rest of the market and when. In the words of Jim Chanos, head of the largest short-selling hedge fund in the world, the market is a “giant positive reinforcement machine. ” 1 It is psychologically difficult to hold a bearish position when it seems like the whole world disagrees with you. All these difficulties in taking bearish positions are amplified by options because options are levered instruments, and losses feel all the more acute when they occur on a levered position. My rule for gaining bullish exposure is to pick the longest-tenor op- tion possible. I made the point that by buying LEAPS, you can enjoy a likely upward drift that exceeds the drift assumed by option pricing. When buying puts, you are on the opposite side of this drift factor (i.e., the “ris- ing tide lifts all boats” factor), and every day that the stock does not fall is another day of time value that has decayed without you enjoying a profit. On the other hand, if you decide not to spend as much on time value and buy a shorter-tenor put option, unless the market realizes that the stock is ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:220 SCORE: 24.00 ================================================================================ Gaining Exposure • 203 overvalued and it drops before the shorter option expires, you must pay the entire bid-ask spread and the broker and exchange fees again when you roll your put option. The moral of the story is that when selecting tenors for puts, you need to balance the existence of upward market drift (which lends weight to the argument for choosing shorter tenors) with bid-ask spreads and other fees (which lends weight to the argument for longer tenors). If you can iden- tify a catalyst, you can plan the tenor of the option investment based on the expected catalyst. However, it’s unfortunate but mysteriously true that bearish catalysts have a tendency to be ignored by the market’s “happy ma- chine” until the instant when suddenly they are not and the shares collapse. The key for a short seller is to be in the game when the market realizes the stock’s overvaluation. Strike Price Selection When it comes to strike prices, short sellers find themselves fighting drift in much the same way as they did when selecting tenors. A short seller with a position in stocks can be successful if the shares he or she is short go up less than other stocks in the market. The short exposure acts as a hedge to the portfolio as a whole, and if it loses less money than the rest of the port- folio gains, it can be thought of as a successful investment. However, the definition for success is different for buyers of a put option, who must not only see their bearish bets not go up by much but rather must see their bearish bets fall if they are to enjoy a profit. If the investor wanting bearish exposure decides to gain it by buying OTM puts, he or she must—as we learned in the section about leverage—accept a realized loss as soon as the put is purchased. If, on the other hand, the investor wants to minimize the realized loss accepted up front, he or she must accept that he or she is in a levered bearish position so that every 1 percent move to the upside for the stock generates a loss larger than 1 percent for the position. There is another bearish strategy that you can use by accepting exposure that I will discuss in the next section, but for investors who are gaining bearish exposure, there is no way to work around the dilemma of the option-based short seller just mentioned. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:221 SCORE: 10.00 ================================================================================ 204  •   The Intelligent Option Investor Portfolio Management There is certainly no way around the tradeoff between OTM and ITM risk—the rules of leverage are immutable whether in a bullish or a bear - ish investment—but there are some ways of framing the investment that will allow intelligent investors to feel more comfortable with making these types of bearish bets. First, I believe that losses associated with a bearish position are treated differently within our own minds than those associated with bullish positions. The reason for this might be the fact that if you decide to proactively invest in the market, you must buy se- curities, but you need not sell shares short. The fact that you are losing when you are engaged in an act that you perceive as unnecessary just adds to a sense of regret and self-doubt that is necessarily part of the investing process. In addition, investors seem to be able to accept underperform- ing bullish investments in a portfolio context (e.g., “XYZ is losing, but it’s only 5 percent of my holdings, and the rest of my portfolio is up, so it’s okay”) but look at underperforming bearish investments as if they were the only investments they held (e.g., “I’m losing 5 percent on that damned short. Why did I ever short that stock in the first place?”). In gen- eral, people have a hard time looking at investments in a portfolio con- text (I will discuss this more when I talk about hedging in Chapter 11), but this problem seems to be orders of magnitude worse in the case of a bearish position. My solution to this dilemma—perhaps not the best or most rational from a performance standpoint but most manageable to me from a psy- chological one—is to buy OTM puts with much smaller position sizes than I might for bullish bets with the same conviction level. This means that I have smaller, more highly levered positions. The reason this works for me is that once I spend the premium on the put option, I consider the money gone—a sunk cost—and do not even bother to look at the mark-to-market value of the option after that unless there is a large drop in the stock price. Somehow this acknowledgment of a realized loss up front is easier to han- dle psychologically than watching my ITM put position suffer unrealized losses of 1.5 times the rise of the stock every day. This strategy may well be proof that I simply am not a natural-born short seller, and you are encouraged, now that you understand the issues ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:222 SCORE: 20.00 ================================================================================ Gaining Exposure • 205 involved, to devise a method for gaining bearish exposure that fits your own risk profile. Strangle GREEN GREEN Downside: Undervalued Upside: Undervalued Execute: Buy an OTM call option simultaneously with buying an OTM put option Risk: Amount of premium paid Reward: Unlimited on upside, limited to strike less total (two-leg) premium on the downside The Gist The strangle is used when the market is undervaluing the likelihood that a stock’s value is significantly above or below the present market price. It is a more speculative position and, because both legs are OTM, a highly lever- aged one. It can sometimes be useful for companies such as smaller drug companies whose value hinges on the success or failure of a particular drug or for companies that have a material chance of bankruptcy but if they can ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:223 SCORE: 26.00 ================================================================================ 206  •   The Intelligent Option Investor avoid this extreme downside are worth much more than they are presently trading at. The entire premium paid must be treated as a realized loss because it can never be recovered. If the stock fails to move into one of the areas of exposure before option expiration, there will be no profit to offset this realized loss. There is no reason why you have to buy puts and calls in equal num- bers. If you believe that both upside and downside scenarios are materially possible but believe that the downside scenario is more plausible, you can buy more puts than calls. This is called ratioing a position. T enor Selection Because the strangle is a combination of two strategies we have already discussed, the considerations regarding tenor are the same as for each of the components—that is, using the drift advantage in long-term equity an- ticipating securities (LEAPS) and buying them or the longest-tenor calls available and balancing the fight against drift and the cost of rolling and buying perhaps shorter-tenor puts. Strike Price Selection A strangle is slightly different in nature from its two components—long calls and long puts. A strangle is an option investor’s way of expressing the belief that the market in general has underestimated the intrinsic uncertainty in the valuation of a firm. Options are directional instru- ments, but a strangle is a strategy that acknowledges that the investor has no clear idea of which direction a stock will move but only that its future value under different scenarios is different from its present market price. Because both purchased options are OTM ones, this implies, in my mind, a more speculative investment and one that lends itself to taking profit on it before expiration. Nonetheless, my conservatism forces me to select strike prices that would allow a profit on the entire position if the stock price is at one of the two strikes at expiration. Because I am buying exposure to both the upside and the downside, I always like to make sure ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:224 SCORE: 26.00 ================================================================================ Gaining Exposure • 207 that if the option expires when the stock price is at either edge of my valu- ation range, it is far enough in-the-money to pay me back for both legs of the investment (plus an attractive return). Portfolio Management As mentioned earlier, this is naturally a more speculative style of option investment, and it may well be more beneficial to close the successful leg of the strategy before expiration than to hold the position to expiration. Com- pared with the next strategy presented here (the straddle), the strangle ac- tually generates worse returns if held to expiration, so if you are happy with your returns midway through the investment, you should close the posi- tion rather than waiting for expiration. The exception to this rule is that if news comes out that convinces you that the value of the firm is materially higher or lower than what you had originally forecast and uncertainty in the other direction has been removed, you should assess the possibility of making a more substantial investment in the company. One common problem with investors—even experienced and sophis- ticated ones—is that they check the past price history of a stock and decide whether the stock has “more room” to move in a particular direction. The most important two things to know when considering an investment are its value and the uncertainty surrounding that value. Whether the stock was cheaper three years ago or much more expensive does not matter—these are backward-looking measures, and you cannot invest with a rear-view mirror. One final note regarding this strategy is what to do with the unused leg. If the stock moves up strongly and you take profits on the call, what should you do with the put, in other words. Unfortunately, the unused leg is almost always worthless, and often it will cost more than it’s worth to close it. I usually keep this leg open because you never know what may happen, and perhaps before it expires, you will be able to close it at a better price. This is a speculative strategy—a bit of spice or an after-dinner mint in the meal of investing. Don’t expect to get rich using it (if you do get rich using it, it means that you were lucky because you would have had to have used a lot of leverage in the process), but you may be pleasantly surprised with the boost you get from these every once in a while. Let’s now turn briefly to a related strategy—the straddle. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:225 SCORE: 42.00 ================================================================================ 208  •   The Intelligent Option Investor Straddle GREEN Downside: Undervalued Upside: Undervalued Execute: Simultaneously buy an ATM put and an ATM call Risk: Amount of premium paid Reward: Unlimited? The Gist I include the straddle here for completeness sake. I have not included a lot of the fancier multioption strategies in this book because I have found them to be more expensive than they are worth, especially for someone with a definite directional view on a security. However, the straddle is re- ferred to commonly and is deceptively attractive, so I include it here to warn investors against its use, if for no other reason. The straddle shares many similarities with the strangle, of course, but straddles are enormously expensive because you are paying for every pos- sible price the stock will move to over the term of the options. For example, I just looked up option prices for BlackBerry (BBRY), whose stock was trading at $9.00. For the 86 days to expiry, $9-strike calls (delta = 0.56) and $9-strike puts (delta = –0.44) were priced at $1.03 and $1.13, respectively. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:226 SCORE: 23.00 ================================================================================ Gaining Exposure • 209 The total premium of $2.16 represents 24 percent of the stock’s price, which means that if the implied volatility (around 60 percent) remains constant, the stock would have to move 24 percent before an investor even breaks even. It is true that during sudden downward stock price moves, implied volatility usually rises, so it might take a little less of a stock price move- ment to the downside to break even. However, during sudden upside moves, implied volatility often drops, which would make it more difficult to break even to the upside. Despite this expense, a straddle will still give an investor a lower breakeven point than a strangle on the same stock if held to expiration. The key is that a strangle will almost always generate a higher profit than a straddle if it is closed before expiration simply because the initial cost of the strangle is lower and the relative leverage of each of its legs is higher. This is yet another reason to consider closing a strangle early if and when you are pleased with the profits made. If you do not know whether a stock will move up or down, the best you can hope for is to make a speculative bet on the company. When you make speculative bets, it is best to reduce the amount spent on it or you will whittle down all your capital on what amounts to a roulette wheel. Reduc- ing the amount spent on a single bet is the reason an intelligent investor should stay away from straddles. With all the main strategies for gaining exposure covered, let’s now turn to accepting exposure by selling options. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:228 SCORE: 14.00 ================================================================================ 211 Chapter 10 Accepting exposure Brokerages and exchanges treat the acceptance of exposure by counter - parties in a very different way from counterparties who want to gain expo- sure. There is a good reason for this: although an investor gaining exposure has an option to transact in the future, his or her counterparty—an investor accepting exposure—has a commitment to transact in the future at the sole discretion of the option buyer. If the investor accepting exposure does not have the financial wherewithal to carry out the committed transaction, the broker or exchange is on the hook for the liability. 1 For example, an investor selling a put option struck at $50 per share is committing to buy the stock in question for $50 a share at some point in the future—this is the essence of accepting exposure. If, however, the investor does not have enough money to buy the stock at $50 at some point in the future, the investor’s commitment to buy the shares is economically worthless. To guard against this eventuality, brokers require exposure-accepting investors to post a security deposit called margin that will fully cover the fi- nancial obligation to which the investor is committing. In the preceding ex- ample, for instance, the investor would have to keep $5,000 (= $50 per share × 100 shares/contract) in reserve and would not be able to spend those reserved funds for stock or option purchases until the contract has expired worthless. Because of this margin requirement, it turns out that one of our strat- egies for accepting leverage—short puts—always carries with it a loss lev- erage of –1.0—exactly the same as the loss leverage of a stock. Think about it this way: what difference is there between using $50 to buy a stock and ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:229 SCORE: 35.00 ================================================================================ 212  •   The Intelligent Option Investor setting $50 aside in an escrow account you can’t touch and promising that you will buy the stock with the escrow funds in the future if requested to do so? From a risk perspective, “very little” is the answer. Short calls are more complicated, but I will discuss the leverage car - ried by them using elements of the structure I set forth in Chapter 8. In the following overviews, I add one new line item to the tables that details the margin requirements of the positions. Intelligent option investors accept exposure when the market over - estimates the likelihood of a valuation that the investor believes is not a rational outcome. In graphic terms, this means that either one or both of the investor’s best- and worst-case valuation scenarios lie well within the Black-Scholes-Merton model (BSM) cone. Simple (one-option) strategies to accept exposure include 1. Short put 2. Short call (call spread) Complex (multioption) strategies to accept exposure include the following: 1. Short straddle 2. Short strangle Jargon introduced in this chapter includes the following: Margin Put-call parity Early exercise Cover (a position) Writing (an option) Short Put RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:230 SCORE: 35.00 ================================================================================ Accepting Exposure   • 213 Downside: Overvalued Upside: Fairly valued Execute: Sell a put contract Risk: Strike price minus premium received [same as stock inves- tor at the effective buy price (EBP)] Reward: Limited to premium received Margin: Notional amount of position The Gist The market is pricing in a relatively high probability that the stock price will fall. An investor, from a longer investment time frame perspective, believes that the value of the stock is likely worth at least the present mar- ket value and perhaps more. The investor agrees to accept the downside risk perceived by the market and, in return, receives a premium for doing so. The premium cannot be fully realized unless the option expires out- of-the money (OTM). If the option expires in-the-money (ITM), the investor pays an amount equal to the strike price for the stock but can partially offset the cost of the stock by the premium received. The inves- tor thus promises to buy the stock in question at a price of the strike price of the option less the premium received—what I call the effective buy price. I think of the short-put strategy as being very similar to buying cor - porate bonds and believe that the two investment strategies share many similarities. A bond investor is essentially looking to receive a specific monetary return (in the form of interest) in exchange for accepting the risk of the business failing. The only time a bond investor owns a company’s assets is after the value of the firm’s equity drops to zero, and the assets revert to the control of the creditors. Similarly, a short-put in- vestor is looking to receive a specific monetary return (in the form of an option premium) in exchange for accepting the risk that the company’s stock will decrease in value. The only time a short-put investor owns a company’s shares is after the market value of the shares expires below the preagreed strike price. Because the strategies are conceptually similar, I usually think of short- put exposure in similar terms and compare the “yield” I am generating ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:231 SCORE: 29.00 ================================================================================ 214  •   The Intelligent Option Investor from a portfolio of short puts with the yield I might generate from a cor - porate bond portfolio. With this consideration, and keeping in mind that these investments are unlevered, 2 the name of the game is to generate as high a percentage return as possible over the investing time horizon while minimizing the amount of real downside risk you are accepting. T enor Selection To maximize percentage return, in general, it is better to sell options with relatively short-term expirations (usually tenors of from three to nine months before expiration). This is just the other side of the coin of the rule to buy long-tenor options: the longer the time to expiration, the less time value there is on a per-day basis. The rule to sell shorter-tenor options implies that you will make a higher absolute return by chaining together two back-to-back 6-month short puts than you would by selling a single 12-month option at the beginning of the period. During normal market conditions, selling shorter-tenor options is the best tactical choice, but during large market downdrafts, when there is terror in the marketplace and implied volatilities increase enormously for options on all companies, you might be able to make more by sell- ing a longer-tenor option than by chaining together a series of shorter- tenor ones (because, presumably, the implied volatilities of options will drop as the market stabilizes, and this drop means that you will make less money on subsequent put sales). At these times of extreme market stress, there are situations where you can find short-put opportunities on long-tenor options that defy economic logic and should be invested in opportunistically. For example, during the terrible market drops in 2009, I found a company whose slightly ITM put long-term equity anticipation securities (LEAPS) were trading at such a high price that the effective buy price of the stock was less than the amount of cash the firm had on its balance sheet. Obviously, for a firm producing positive cash flows, the stock should not trade at less than the value of cash presently on the balance sheet! I ef- fectively got the chance to buy a firm with $6 of cash on the balance sheet and the near certainty of generating about $2 more over the economic life of the options for $5.50. The opportunity to buy $6–$8 worth of cash for ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:232 SCORE: 51.00 ================================================================================ Accepting Exposure   • 215 $5.50 does not come along very often, so you should take advantage of it when you see it. Of course, the absolute value of premium you will receive by writing (jargon that means selling an option) a short-term put is less than the ab- solute value of the premium you will receive by writing a long-term one. 3 As such, an investor must balance the effective buy price of the stock (the strike price of the option less the amount of premium to be received) in which he or she is investing in the short-put strategy with the percentage return he or she will receive if the put expires OTM. I will talk more about effective buy price in the next section, but keep in mind that we would like to generate the highest percentage return pos- sible and that this usually means choosing shorter-tenor options. Strike Price Selection In general, the best policy is to sell options at as close to the 50-delta [at- the-money (ATM)] mark as one can because that is where time value for any option is at its absolute maximum. Our expectation is that the option’s time value will be worthless at expiration, and if that is indeed the case, we will be selling time value at its maximum and “closing” our time value position at zero—its minimum. In this way, we are obeying (in reverse order) the old investing maxim “Buy low, sell high. ” Selling ATM puts means that our effective buy price will be the strike price at which we sold less the amount of the premium we received. It goes without saying that an intelligent investor would not agree to accept the downside exposure to a stock if he or she were not prepared to buy the stock at the effective buy price. Some people want to sell OTM puts, thereby making the effective buy price much lower than the present market price. This is an understandable impulse, but simply attempting to minimize the effective buy price means that you must ignore the other element of a successful short put strategy: maximizing the return generated. There are times when you might like to sell puts on a company but only at a lower strike price. Rather than accept- ing a lower return for accepting that risk, I find that the best strategy is simply to wait awhile until the markets make a hiccup and knock down the price of the stock to your desired strike price. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:233 SCORE: 8.00 ================================================================================ 216  •   The Intelligent Option Investor Portfolio Management As we have discussed, the best percentage returns on short-put investments come from the sale of short-tenor ATM options. I find that each quarter there are excellent opportunities to find a fairly constant stream of this type of short- term bet that, when strung together in a portfolio, can generate annualized returns in the high-single-digit to low-teens percentage range. This level of returns—twice or more the yield recently found on a high-quality corporate bond portfolio and closer to the bond yield on highly speculative small com- panies with low credit ratings—is possible by investing in strong, high-quality blue chip stocks. In my mind, it is difficult to allocate much money to corpo- rate bonds when this type of alternative is available. Some investors prefer to sell puts on stocks that are not very vola- tile or that have had a significant run-up in price, 4 but if you think about how options are priced, it is clear that finding stocks that the market perceives as more volatile will allow you to generate higher returns. Y ou can confirm this by looking at the diagrams of a short-put investment given two different volatility scenarios. First, a diagram in which implied volatility is low: Advanced Building Corp. (ABC) 80 70 60 50 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Date/Day Count Stock Price RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:234 SCORE: 12.00 ================================================================================ Accepting Exposure   • 217 Now a diagram when implied volatility is higher: RED Advanced Building Corp. (ABC) 80 70 60 50 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Date/Day Count Stock Price Obviously, there is much more of the put option’s range of exposure bounded by the BSM cone in the second, high-volatility scenario, and this means that the price received for accepting the same downside risk will be substantially higher when implied volatility is elevated. The key to setting up a successful allocation of short puts is to find companies that have relatively low downside valuation risk but that also have a significant amount of perceived price risk (as seen by the market)— even if this risk is only temporary in nature. Quarterly earnings seasons are nearly custom made for this purpose. Sell-side analysts (and the market in general) mainly use multiples of reported earnings to generate a target price for a stock. As such, a small shortfall in reported earnings as a result of a transitory and/or nonmaterial accounting technicality can cause sell- side analysts and other market participants to bring down their short-term target price estimates sharply and can cause stock prices to drop sharply as well. 5 These times, when a high-quality company drops sharply as a re- sult of perceived risk by other investors, are a wonderful time to replen- ish a portfolio of short puts. If you time the tenors well, your short-put ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:235 SCORE: 16.00 ================================================================================ 218  •   The Intelligent Option Investor investment will be expiring just about the time another short-put invest- ment is becoming attractive, so you can use the margin that has until re- cently been used to support the first position to support the new one. Obviously, this strategy only works when markets are generally trend- ing upward or at least sideways over the investment horizon of your short puts. If the market is falling, short-put positions expire ITM, so you are left with a position in the underlying stocks. For an option trader (i.e., a short- term speculator), being put a stock is a nightmare because he or she has no concept of the underlying value of the firm. However, for an intelligent option investor, being put a stock simply means the opportunity to receive a dividend and enjoy capital appreciation in a strong stock with very little downside valuation risk. The biggest problem arises when an investor sells a put and then re- vises down his or her lowest-case valuation scenario at a later time. For in- stance, the preceding diagram shows a worst-case scenario of $55 per share. What if new material information became known to you that changed your lower valuation range to $45 per share just as the market price for the stock dropped, as in the following diagram? Advanced Building Corp. (ABC) 80 70 60 50 EBP = $47.50 Overvaluation of downside exposure 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Date/Day Count Stock Price RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:236 SCORE: 13.00 ================================================================================ Accepting Exposure   • 219 Looking at this diagram closely, you should be able to see several things: 1. The investor who is short this put certainly has a notable unrealized loss on his or her position. Y ou can tell this because the put the investor sold is now much more valuable than at the time of the original sale (more of the range of exposure is carved out by the BSM cone now). When you sell something at one price and the value of that thing goes up in the future, you suffer an opportunity loss on your original sale. 2. With the drop in price and the cut in fair value, the downside ex- posure on this stock still looks overvalued. 3. If the company were to perform so that its share price eventually hit the new, reduced best-case valuation mark, the original short- put position would generate a profit—albeit a smaller profit than the one originally envisioned. At this point, there are a couple of choices open to the investor: 1. Convert the unrealized loss on the short-put position to a realized one by buying $50-strike puts to close the position (a.k.a. cover the position). 2. Leave the position open and manage it in the same way that the investor would manage a struggling stock position. It is rarely a sound idea to close a short put immediately after the re- lease of information that drives down the stock price (the first choice above, in other words). At these times, investors are generally panicked, and this panic will cause the price of the option you buy to cover to be more expen- sive than justified. Waiting a few days or weeks for the fear to drain out of the option prices (i.e., for the BSM cone to narrow) and for the stock price to stabilize some will usually allow you to close the option position at a more favorable price. There is one exception to this rule: if your new valuation suggests a fair value at or below the present market price, it is better to close the position immediately and realize those losses. If you do not close the position, you are simply gambling (as opposed to investing) because you no longer have a better than even chance of making money on the investment. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:237 SCORE: 15.00 ================================================================================ 220  •   The Intelligent Option Investor The decision to leave the position open must depend on what other potential investments you are able to make and how the stock position that will likely be put to you at expiration of the option contract stacks up on a relative basis. For instance, let’s assume that you had received a premium of $2.50 for writing the puts struck at $50. This gives you an effective buy price of $47.50. The stock is now trading at $43 per share, so you can think of your position as an unlevered, unrealized loss of $4.50, or a little under 10 percent of your EBP . Y our new worst-case valuation is $55 per share, which implies a gain of about 15 percent on your EBP; your new best-case valuation is $65 per share, which implies a gain of 37 percent. How do these numbers compare with other investments in your port- folio? How much spare capacity does your portfolio have for additional investments? (That is, do you have enough spare cash to increase the size of this investment by selling more puts at the new market price or buying shares of stock? And if so, would your portfolio be weighted too heavily on a single industry or sector?) By answering these questions and understanding how this presently losing investment compares with other existing or poten- tial investments should govern your portfolio management of the position. An investor cannot change the price at which he or she transacted in a security. The best he or she can do is to develop a rational view of the value of a security and judge that security by its relative merit versus other possible investments. Whether you ever make an option transaction, this is a good rule to keep in mind. Let us now take a look at short calls and short-call spreads—the strategy used for accepting upside exposure. Short Call (Call Spread) RED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:238 SCORE: 47.00 ================================================================================ Accepting Exposure   • 221 Downside: Fairly valued Upside: Overvalued Execute: Sell a call contract (short call); sell a call contract while simultaneously buying a call contract at a higher strike price (short-call spread) Risk: Unlimited for short call; difference between strike prices and premium received (short-call spread) Reward: Limited to the amount of premium received Margin: Variable for a short call; dollar amount equal to the differ- ence between strike prices for a short-call spread The Gist The market overestimates the likelihood that the value of a firm is above its pre- sent market price. An investor accepts the overvalued upside exposure in return for a fixed payment of premium. The full amount of the premium will only flow through to the investor if the price of the stock falls and the option expires OTM. There are two variations of this investment—the short call and the short-call spread. This book touches on the former but mainly addresses the latter. A short call opens up the investor to potentially unlimited capital losses (because stocks theoretically do not have an upper bound for their price), and a broker will not allow you to invest using this strategy except for the following conditions: 1. Y ou are a hedge fund manager and have the ability to borrow stocks through your broker and sell them short. 2. Y ou are short calls not on a stock but on a diversified index (such as the Dow Jones Industrial Index or the Standard and Poor’s 500 Index) through an exchange-traded fund (ETF) or a futures con- tract and hold a diversified stock portfolio. For investors fitting the first condition, short calls are margined in the same way as the rest of your short portfolio. That is, you must deposit initial margin on the initiation of the investment, and if the stock price goes up, you must pay in variance margin to support the position. Obviously, as the stock price falls, this margin account is settled in your favor. For investors fitting the second condition, when you originally sell the call option, your broker should ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:239 SCORE: 59.00 ================================================================================ 222  •   The Intelligent Option Investor indicate on your statements that a certain proportion of your account effec- tively will be treated as margin. This means that you stand to receive the eco- nomic benefit from your diversified portfolio of securities but will not be able to liquidate all of it. If the market climbs higher, a larger proportion of your portfolio will be considered as margin; if it falls lower, a smaller proportion of your portfolio will be considered as margin. Basically, a proportion of any gains from your diversified stock portfolio will be reapportioned to serve as collateral for your short call when the market is rising, and a proportion of any losses from your diversified stock portfolio will be offset by a freeing of margin related to your profits on the short call when the market is falling. Most brokers restrict the ability of individual investors to write un- covered calls on individual stocks, so the rest of this discussion will cover the short-call spread strategy for individual stocks. T enor Selection Tenors for short-call spreads should be fairly short under the same reason- ing as that for short puts—one receives more time value per day for short- er-tenor options. Look for calls in the three- to nine-month tenor range. The tenor of the purchased call (at the higher strike price) should be the same as the tenor of the sold calls (at the lower strike price). Theoretically, the bought calls could be longer, but it is hard to think of a valuation justifi- cation for such a structure. By buying a longer-tenor call for the upside leg of the investment, you are expressing an investment opinion that the stock will likely rise over the long term—this exactly contradicts the purpose of this strategy: expressing a bearish investment opinion. Strike Price Selection Theoretically, you can choose any two strike prices, sell the call at the lower price, and buy the call at the higher price and execute this investment. If you sold an ITM call, you would receive premium that consists of both time and intrinsic value. If the stock fell by expiration, you would realize all the wasted time value plus the difference between the intrinsic value at initiation and the intrinsic value at expiration. Despite the theory, however, in practice, the lower strike option is usually sold ATM or OTM because of the threat of assignment. Assignment is the pro- cess the exchange goes through when investors choose to exercise the option ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:240 SCORE: 86.00 ================================================================================ Accepting Exposure   • 223 they own rather than trade them away for a profit. Recall from Chapter 2 that experienced option investors do not do this most of the time; they know that because of the existence of time value, it is usually more beneficial for them to sell their option in the market and use the proceeds to buy the stock if they want to hold the underlying. Inexperienced investors, however, often are not conscious of the time-value nuance and sometimes elect to exercise their option. In this case, the exchange randomly pairs the option holders who wish to exercise with an option seller who has promised to sell at that exercise price. There is one case in which a sophisticated investor might chose to exercise an ITM call option early, related to a principle in option pricing called put-call parity. This rule, which was used to price options before advent of the BSM, simply states that a certain relationship must exist be- tween the price of a put at one strike price, the price of a call at that same strike price, and the market price of the underlying stock. Put-call parity is discussed in Appendix C. In this appendix, you can learn what the exact put-call parity rule is (it is ridiculously simple) and then see how it can be used to determine when it is best to exercise early in case you are long a call and when your short-call (spread) position is in danger of early exercise because of a trading strategy known as dividend arbitrage. The assignment process is random, but obviously, the more contracts you sell, the better the chance is that you will be assigned on some part or all of your sold contracts. Even if you hold until expiration, there is still a chance that you may be assigned to fulfill a contract that was exercised on settlement. Clearly, from the standpoint of option sale efficiency, an ATM call is the most sensible to sell for the same reason that a short put also was most efficient ATM. As such, the discussion that follows assumes that you are selling the ATM strike and buying back a higher strike to cover. In a call-spread strategy, the capital you have at risk is the difference be- tween the two strike prices—this is the amount that must be deposited into margin. Depending on which strike price you use to cover, the net premium received differs because the cost of the covering call is cheaper the further OTM you cover. As the covering call becomes more and more OTM, the ratio of premium received to capital at risk changes. Put in these terms, it seems that the short-call spread is a levered strategy because leverage has to do with altering the capital at risk in order to change the percentage return. This con- trasts with the short-call spread’s mirror strategy on the put side—short puts— in that the short-put strategy is unlevered. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:241 SCORE: 34.00 ================================================================================ 224  •   The Intelligent Option Investor For instance, here are data from ATM and OTM call options on IBM (IBM) expiring in 80 days. I took these data when IBM’s shares were trad- ing at $196.80 per share. Sell a Call at 195 Cover at ($) Net Premium Received ($) Percent Return Capital at Risk ($) 200 2.40 48 5 205 4.26 43 10 210 5.47 36 15 215 6.17 31 20 220 6.51 26 25 225 6.70 22 30 230 6.91 20 35 235 6.90 17 40 240 6.96 15 45 In this table, net premium received was calculated by selling at the $195 strike’s bid price and buying at each of the listed strike price’s ask prices. Percent return is the proportion of net premium received as a percentage of the capital at risk—the width of the spread. This table clearly shows that accepting expo- sure with a call spread is a levered strategy. The potential return on a percent- age basis can be raised simply by lowering the amount of capital at risk. However, although accepting exposure with a call spread is un- deniably levered from this perspective, there is one large difference: un- like the leverage discussed earlier in this book for a purchase of call op- tions—in which your returns were potentially unlimited—the short-call spread investor receives premium up front that represents the maximum return possible on the investment. As such, in the sense of the investor’s potential gains being limited, the short-call spread position appears to be an unlevered investment. Considering the dual nature of a short-call spread, it is most help- ful to think about managing these positions using a two-step process with both tactical and strategic aspects. We will investigate the tactical aspect of leverage in the remainder of this section and the strategic aspect in the portfolio management section. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:242 SCORE: 65.00 ================================================================================ Accepting Exposure   • 225 Tactically, once an investor has decided to accept exposure to a stock’s upside potential using a call spread, he or she has a relatively limited choice of investments. Let’s assume that we sell the ATM strike; in the IBM ex- ample shown earlier, there is a choice of nine strike prices at which we can cover. The highest dollar amount of premium we can receive—what I will call the maximum return—is received by covering at the most distant strike. Every strike between the ATM and the most distant strike will at most generate some percentage of this maximum return. Now let’s look at the risk side. Let’s say that we sell the $195-strike call and cover using the $210-strike call. Now assume that some bit of good news about IBM comes out, and the stock suddenly moves to exactly $210. If the option expires when IBM is trading at $210, we will have lost the entire amount of margin we posted to support this investment—$15 in all. This $15 loss will be offset by the amount of premium we received from selling the call spread—$5.47 in the IBM example—generating a net loss of $9.53 (= $5.47 − $15). Compare this with the loss that we would suffer if we had covered using the most distant call strike. In this case, we would have received $6.96 in premium, so if the option expires when IBM is trading at the same $210 level as earlier, our net loss would be $8.04 (= $6.96 − $15). Because our maximum return is generated with the widest spread, it fol- lows that our minimum loss for the stock going to any intermediate strike price also will be generated with the widest spread. At the same time, if we always select the widest spread, we face an entirely different problem. That is, the widest spread exposes us to the great- est potential loss. If the stock goes only to $210, it is true that the widest spread will generate a smaller loss than the $195–$210 spread. However, in the extreme, if the stock moves up strongly to $240, we would lose the $45 gross amount supporting the margin account and a net amount of $38.04 (= $45 – $6.96). Contrast this with a net loss of $9.53 for the $195–$210 spread. Put simply, if the stock moves up only a bit, we will do better with the wider spread; if it moves up a lot, it is better to choose a narrower spread. In short, when thinking about call spreads, we must balance our amount of total exposure against the exposure we would have for an inter- mediate outcome against the total amount of premium we are receiving. If we are too protective and initiate the smallest spread possible, our chance ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:243 SCORE: 43.00 ================================================================================ 226  •   The Intelligent Option Investor of losing the entire margin amount is higher, but the margin amount lost is smaller. On the other hand, if we attempt to maximize our winnings and initiate the widest spread possible, our total exposure is greatest, even though the chance of losing all of it is lower. Plotting these three variables on a graph, here is what we get: 200 (11%) 0% 20% 40% 60% 80% 106% 102% 94%89% 100% 120% 140% 160% 180% 200% 205 (22%) 210 (33%) 215 (44%) 220 (56%) 225 (67%) 230 (78%) 235 (89%) 240 (100%) Strike (% of Total Exposure) Risk & Return of Call Spreads vs. Maximum Spread Risk Comparison Return Comparison Here, on the horizontal axis, we have the value of the covering strike and the size of the corresponding spread as a percentage of the widest spread. This shows how much proportional capital is at risk (e.g., at the $215-strike, we are risking a total of $20 of margin; $20 is 44 percent of total exposure of $45 if we covered at the $240-strike level). The top line shows how much greater the loss would be if we used that strike to cover rather than the maximum strike and the option expired at that strike price (e.g., if we cover at the $215-strike and the option expires when the stock is trading at $215, our loss would be 6 percent greater than the loss we would suffer if we covered at the $240-strike). The bottom line shows the premium we will realize as income if the stock price declines as a percentage of the total pre- mium possible if we covered at the maximum strike price. Here are the val- ues from the graph in tabular format so that you can see the numbers used: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:244 SCORE: 10.00 ================================================================================ Strike Price Dollar Spread Percent of Maximum Spread (a) Bid Price Ask Price Covering at Strike Covering at Maximum Strike Difference Risk Comparison (%) (b) Return Comparison (%) (c) Potential Gain Worst-Case (Loss) Potential Gain Worst-Case Gain (Loss) 195 — — 7.05 7.10 — — — — — — — 200 5 11 4.55 4.65 2.40 (2.60) 6.96 1.96 (3.55) N.C. 34 205 10 22 2.75 2.79 4.26 (5.74) 6.96 (3.04) 2.29 189 61 210 15 33 1.54 1.58 5.47 (9.53) 6.96 (8.04) 0.87 119 79 215 20 44 0.84 0.88 6.17 (13.83) 6.96 (13.04) 0.53 106 89 220 25 56 0.38 0.54 6.51 (18.49) 6.96 (18.04) 0.39 102 94 225 30 67 0.12 0.35 6.70 (23.30) 6.96 (23.04) 0.30 101 96 230 35 78 0.11 0.14 6.91 (28.09) 6.96 (28.04) 0.25 100 99 235 40 89 0.03 0.15 6.90 (33.10) 6.96 (33.04) 0.21 100 99 240 45 100 0.02 0.09 6.96 (38.04) 6.96 (38.04) 0.18 100 100 227 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:245 SCORE: 15.00 ================================================================================ 228  •   The Intelligent Option Investor With a table like this, you can balance, on the one hand, the degree you are reducing your overall exposure in a worst-case scenario (by look- ing at column a) against how much risk you are taking on for a bad-case (intermediary upward move of the stock) scenario (by looking at column b) against how much less premium you stand to earn if the stock does go down as expected (by looking at column c). There are no hard and fast rules for which is the correct covering strike to select—that will depend on your confidence in the valuation and timing, your risk profile, and the position size—but looking at the table, I tend to be drawn to the $215 and $220 strikes. With both of those strikes, you are reducing your worst-case exposure by about half, increasing your bad-case exposure just marginally, and taking only a small haircut on the premium you are receiving. 6 Now that we have an idea of how to think about the potential risk and return on a per-contract basis, let’s turn to leverage in the strategic sense— figuring out how much capital to commit to a given bearish idea. Portfolio Management When we thought about leverage from a call buyer’s perspective, we thought about how large of an allocation we wanted to make to the idea itself and changed our leverage within that allocation to modify the profits we stood to make. Let’s do this again with IBM—again assuming that we are willing to allocate 5 percent of our portfolio to an investment in the view that this company’s stock price will not go higher. At a price of $196.80, a 5 percent allocation would mean controlling a little more than 25 shares for every $100,000 of portfolio value. 7 Because options have a contract size of 100 shares, an unlevered 5 percent allocation to this investment would require a portfolio size of $400,000. The equation to calculate the leverage ratio on the basis of notional exposure is × =Notional valueo fo ne contract Dollarv alue of allocation number of contractsl everager atio So, for instance, if we had a $100,000 portfolio of which we were willing to commit 5 percent to this short-call spread on IBM, our position would have a leverage ratio of ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:246 SCORE: 29.00 ================================================================================ Accepting Exposure   • 229 ×= ≈$19,500 $5,000 13 .9 4: 1leverage Selling the $195/$220 call spread will generate $651 worth of pre- mium income and put at risk $2,500 worth of capital. Nothing can change these two numbers—in this sense, the short-call spread has no leverage. The 4:1 leverage figure merely means that the percentage return will ap- pear nearly four times as large on a given allocation as a 1:1 allocation would appear. The following table—assuming the sale of one contract of the $195/$220 call spread—shows this in detail: Winning Case Losing Case Premium Received ($) Target Allocation ($) Leverage Stock Move ($) Percent Return on Allocation Stock Move ($) Dollar Return Percent Return on Allocation 651 20,000 1:1 –2 3.3 +25 –1,849 –9.2 651 10,000 2:1 –2 6.5 +25 –1,849 –18.5 651 5,000 4:1 –2 13.0 +25 –1,849 –37.0 Note: The dollar return in the losing case is calculated as the loss of the $2,500 of margin per contract less than the premium received of $651. Notice that the premium received never changes, nor does the worst- case return. Only the perception of the loss changes with the size of our target allocation. Now that we have a sense of how to calculate what strategic leverage we are using, let’s think about how to size the position and about how much risk we are willing to take. When we are selling a call or call spread, we are committing to sell a stock at the strike price. If we were actually selling the stock at that price rather than committing to do so, where would we put our stop loss—in other words, when would we close the position, assuming that our valuation or our timing was not correct? Let’s say that for this stock, if the price rose to $250, you would be willing to admit that you were wrong and would realize a loss of $55 per share, or $5,500 per hundred shares. This figure—the $5,500 per hundred shares you would be willing to lose in an unlevered short stock position—can be used as a guide to select the size of your levered short-call spread. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:247 SCORE: 39.00 ================================================================================ 230  •   The Intelligent Option Investor In this case, you might choose to sell a single $195–$240 call spread, in which case your maximum exposure would be $4,500 [= 1 × (240 – 195) × 100] at the widest spread. This investment would have a leverage ratio of approxi- mately 1:1. Alternatively, you could choose to sell two $195–$220 spreads, in which case your maximum exposure would be $5,000 [= 2 × (220 − 195) × 100], with a leverage ratio of approximately 2:1. Which choice you select will depend on your assessment of the valuation of the stock, your risk tolerance, and the composition of your portfolio (i.e., how much of your portfolio is al- located to the tech sector, in this example of an investment in IBM). Because the monetary returns from a short-call or call-spread strategy are fixed and the potential for losses are rather high, I prefer to execute bearish investments using the long-put strategy discussed in the “Gaining Exposure” section. With this explanation of the short-call spread complete, we have all the building blocks necessary to understand all the other strategies mentioned in this book. Let’s now turn to two nonrecommended complex strategies for accepting exposure—the short straddle and the short strangle—both of which are included not because they are good strategies but rather for the sake of completeness. Short Straddle/Short Strangle Short Straddle RED Downside: Overvalued Upside: Overvalued Execute: Sell an ATM put; simultaneously sell an ATM call spread ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:248 SCORE: 43.00 ================================================================================ Accepting Exposure   • 231 Risk: Amount equal to upper strike price minus premium received Reward: Limited to premium received Margin: Dollar amount equal to upper strike price Short Strangle RED RED Downside: Overvalued Upside: Overvalued Execute: Sell an OTM put; simultaneously sell an OTM call spread Risk: Call-spread leg: Amount equal to difference between strikes and premium received. Put leg: Amount equal to strike price minus premium received. Total exposure is the sum of both legs. Reward: Limited to premium received Margin: Call-spread leg: Amount equal to difference between strikes. Put leg: Amount equal to strike price. Total mar - gin is the sum of both legs. The Gist In my opinion, these are short-term trades rather than investments. Even though a short put uses a short-tenor option, the perspective of the inves- tor is that he or she is buying shares. These strategies are a way to express the belief that the underlying stock price will not move over a short time. In my experience, there is simply no way to develop a rational view of how a single stock will move over a short time frame. In the short term, markets ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:250 SCORE: 18.00 ================================================================================ 233 Chapter 11 Mixing ExposurE Mixing exposure uses combinations of gaining and accepting exposure, employing strategies that we already discussed to create what amounts to sort of a short-term synthetic position in a stock (either long or short). These strategies, nicknamed “diagonals” can be extremely attractive and extremely financially rewarding in cases where stocks are significantly mis- priced (in which case, exposure to one direction is overvalued, whereas the other is extremely undervalued). Frequently, using one of these strategies, an investor can enter a po- sition in a levered out-of-the-money (OTM) option for what, over time, becomes zero cost (or can even net a cash inflow) and zero downside expo- sure. This is possible because the investor uses the sale of one shorter-tenor at-the-money (ATM) option to subsidize the purchase of another longer- tenor OTM one. Once the sold option expires, another can be sold again, and whatever profit is realized from that sale goes to further subsidize the position. This strategy works well because of a couple of rules of option pricing that we have already discussed: 1. ATM options are more expensive than OTM options of the same tenor. 2. Short-tenor options are worth less than long-tenor options, but the value per day is higher for the short-tenor options. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:251 SCORE: 22.00 ================================================================================ 234  •   The Intelligent Option Investor I provide actual market examples of these strategies in this chapter and will point out the effect of both these points in those examples. Because these strategies are a mix of exposures, it makes sense that they are just complex (i.e., multioption) positions. I will discuss the following: 1. Long diagonal 2. Short diagonal Note that the nomenclature I use here is a bit different from what others in the market may use. What I term a diagonal in this book is what others might call a “spit-strike synthetic stock. ” Since Bernie Madoff ’s infamous “split-strike conversion” fraud, this term doesn’t have a very good ring to it. For other market participants, a diagonal means simultaneously buying and selling options of the same type (i.e calls or puts). In this book, it means selling an option of one kind and buying the other kind. I will also talk about what is known in the options world as overlays. One of the most useful things about options is the way that they can be grafted or overlain onto an existing common stock position in a way that alters the port- folio’s overall risk-reward profile. The strategies I will review here are as follows: 1. Covered calls 2. Protective puts 3. Collars These strategies are popular but often misunderstood ways to alter your portfolio’s risk-reward profile. Coming this far in this book, you already have a good understand- ing about how options work, so the concepts presented here will not be difficult, but I will discuss some nuances that will help you to evaluate investment choices and make sound decisions regarding the use of these strategies. I will refer to strike selection and tenor selection in the following pages, but for these, along with “The Gist” section, I’ll include an “Execu- tion” section and a “Common Pitfalls” section. Covered calls are an easy strategy to understand once you understand short puts, so I will discuss those first. Protective puts share a lot of simi- larities with in-the-money (ITM) call options, and I will discuss those next. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:252 SCORE: 24.00 ================================================================================ Mixing Exposure  •  235 Collars are just a combination of the other two overlay strategies and so are easiest left to the end. Long Diagonal GREEN RED Downside: Overvalued Upside: Undervalued Execute: Sell an ATM put option (short put) and simultaneously buy an OTM call option (long call) Risk: Sum of put’s strike price and net premium paid for call Reward: Unlimited Margin: Amount equal to put’s strike price The Gist Other than the blank space in the middle of the diagram and the disparity between the lengths of the tenors, the preceding diagram looks very much like the risk-return profile diagram for a long stock—accepting downside exposure in return for gaining upside exposure. As you can see from the diagram, the range of exposure for the short put lies well within the Black-Scholes-Merton model (BSM) cone, but the range of exposure for the long call is well outside the cone. It is often possible to find short-put–long-call combinations that al- low for an immediate net credit when setting up this investment. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:253 SCORE: 46.00 ================================================================================ 236  •   The Intelligent Option Investor Because we must fully margin a short-put investment, that leg of the long diagonal carries with it a loss leverage ratio of –1.0. However, the OTM call leg represents an immediate realized loss coupled with a very high lambda value for gains. As such, if the put option expires ITM, the long diagonal is simply a levered strategy; if the put option expires OTM, the investment is a very highly levered one because the unlevered put ceases to influence the leverage equation. Another short put may be written after the previous short put expires; this further subsidizes the cost of the calls and so greatly increases the leverage on the strategy. If the stock moves quickly toward the upper valuation range, this structure becomes extremely profitable on an unrealized basis. If the put option expires ITM, the investor is left with a levered long investment in the stock in addition to the long position in the OTM. As in any other complex structure, the investment may be ratioed—for instance, by buying one call for every two puts sold or vice versa. Strike Price Selection The put should be sold ATM or close to ATM in order to maximize the time value sold, as explained earlier in the short-put summary. The call strike may be bought at any level depending on the investor’s appetite for leverage but is usu- ally purchased OTM. The following table shows the net debit or credit associated with the long diagonal between the ATM put ($55 strike price, delta of –0.42, priced at the bid price) with an expiration of 79 days and each call strike (at the ask price) listed, all of which are long-term equity anticipated securities (LEAPS) having expirations in 534 days. The lambda figure for the OTM calls is also given to provide an idea of the comparative leverage of each call option. For this exam- ple, I am using JP Morgan Chase (JPM) when its stock was trading for $56.25. Strike Delta (Debit) Credit Call Lambda (%) 57.50 0.43 (2.52) 5.6 60.00 0.37 (1.57) 6.1 62.50 0.31 (0.76) 6.7 65.00 0.26 (0.25) 7.0 70.00 0.16 0.78 8.4 75.00 0.10 1.28 9.5 80.00 0.06 1.56 10.5 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:254 SCORE: 13.00 ================================================================================ Mixing Exposure  •  237 Here we can see that for a long diagonal using 79-day ATM puts and 594-day LEAPS that are OTM by just over 15 percent, we are paying a net of only $25 per contract for notional control of 100 shares. On a per-contract basis, at the following settlement prices, we would generate the following profits (or losses, in the case of the first row): Settlement Price ($) Dollar Profit per Contract Percentage Return on Original Investment (%) 65 0 –100 66 100 300 67 200 700 68 300 1,100 69 400 1,500 70 500 1,900 71 600 2,300 72 700 2,700 73 800 3,100 74 900 3,500 75 1,000 3,900 If the stock price moves up very quickly, it might be more beneficial to close the position or some portion of the position before expiration. Let’s say that my upper-range estimate for this stock was $75. From the preced- ing table, I can see that my profit per contract if the stock settles at my fair value range is $1,000. If there is enough time value on a contract when the stock is trading in the upper $60 range to generate a realized profit of $1,000, I am likely to take at least some profits at that time rather than wait- ing for the calls to expire. In Chapter 9, I discussed portfolio composition and likened the use of leverage as a side dish to a main course. This is an excellent side dish that can be entered into when we see a chance to supplement the main meal of a long stock–ITM call option position with a bit more spice. Let’s now turn to its bearish mirror—the short diagonal. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:255 SCORE: 34.00 ================================================================================ 238  •   The Intelligent Option Investor Short Diagonal RED GREEN Downside: Undervalued Upside: Overvalued Execute: Sell an ATM call option while buying one to cover at a higher price (short-call spread) and simultaneously buy an OTM put option (long put) Risk: Sum of put’s strike price and net premium paid for call Reward: Amount equal to the put’s strike price minus any net premium paid for it Margin: Amount equal to spread between call options The Gist The diagram for a short diagonal is just the inverse of the long diagonal and, of course, looks very similar to the risk-return profile diagram for a short stock— accepting upside exposure in return for gaining downside exposure. The gist of this strategy is simply the short-exposure equivalent to the long diagonal, so the comments about the long diagonal are applicable to this strategy as well. The one difference is that because you must spend money to cover the short call on the upside, the subsidy that the option sale leg provides to the option purchase leg is less than in the case of the long diagonal. Also, of course, a stock price cannot turn negative, so your profit upside is capped at an amount equal to the effective sell price. This investment also may be ratioed (e.g., by using one short-call spread to subsidize two long puts). ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:256 SCORE: 23.00 ================================================================================ Mixing Exposure  •  239 Strike Price Selection Strike price selection for a short diagonal is more difficult because there are three strikes to price this time. Looking at the current pricing for a call spread with the short call struck at $55, I get the following selection of credits: Upper Call Strike ($) Call Spread Net Credit ($) Percent Total Risk Percent Total Return 57.50 1.27 17 49 60.00 2.14 33 83 62.50 2.44 50 94 65.00 2.51 67 97 70.00 2.59 100 100 Looking at this, let’s say we decide to go with the $55.00/$62.50 call spread. Doing so, we would receive a net credit of $2.44. Now selecting the put to purchase is a matter of figuring out the leverage of the position with which you are comfortable. Strike ($) Delta (Debit) Credit ($) Put Lambda (%) 20.00 –0.02 2.20 –4.5 23.00 –0.02 2.11 –4.6 25.00 –0.03 2.05 –4.6 28.00 –0.04 1.91 –4.8 30.00 –0.05 1.78 –4.8 33.00 –0.07 1.57 –4.8 35.00 –0.09 1.38 –4.8 38.00 –0.12 0.99 –4.8 40.00 –0.15 0.67 –4.7 42.00 –0.17 0.30 –4.7 45.00 –0.23 (0.43) –4.5 47.00 –0.26 (1.01) –4.4 50.00 –0.33 (1.91) –4.4 52.50 –0.39 (3.11) –4.0 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:257 SCORE: 21.00 ================================================================================ 240  •   The Intelligent Option Investor Notice that there is much less leverage on the long-put side than on the long-call side. This is a function of the volatility smile and the abnor - mally high pricing on the far OTM put side. It turns out that the $20-strike puts have an implied volatility of 43.3 percent compared to an ATM im- plied volatility of 22.0 percent. Obviously, the lower level of leverage will make closing before expira- tion less attractive, so it is important to select a put strike price between the present market price and your worst-case fair value estimate. In this way, if the option does expire when the stock is at that level, you will at least be able to realize the profit of the intrinsic value. With these explanations of the primary mixed-exposure strategies, now let’s turn to overlays—where an option position is added to a stock position to alter the risk-return characteristics of the investor’s portfolio. Covered Call Contingent Upside Exposure Contingent Downside Exposure LIGHT GREEN RED LIGHT RED Downside: Overvalued Upside: Fairly valued or undervalued ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:259 SCORE: 24.00 ================================================================================ 242  •   The Intelligent Option Investor We accepted downside exposure when we sold this put, so have no exposure to the upside here. RED The top of the “Covered call” diagram is grayed out because we have sold away the upside exposure to the stock by selling the call option, and we are left only with the acceptance of the stock’s downside exposure. The pictures are slightly different, but the economic impact is the same. The other difference you will notice is that after the option expires, in the case of the covered call, we have represented the graphic as though there is some residual exposure. This is represented in this way because if the option expires ITM, you will have to deliver your stock to the counterparty who bought your call options. As such, your future exposure to the stock is contingent on another investor’s actions and the price movement of the stock. This is an important point to keep in mind, and I will discuss it more in the “Common Pitfalls” section. Execution Because this strategy is identical from a risk-reward perspective to short puts, the execution details should be the same as well. Indeed, covered calls should—like short puts—be executed ATM to get the most time value possible and preferably should be done on a stock that has had a recent fall and whose implied volatility has spiked. However, these theoretical points Short put ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:260 SCORE: 13.00 ================================================================================ Mixing Exposure  •  243 ignore the fact that most people simply want to generate a bit of extra in- come out of the holdings they already have and so are psychologically re- sistant to both selling ATM (because this makes it more likely for their shares to be called away) and selling at a time when the stock price sud- denly drop (because they want to reap the benefit of the shares recovering). Although I understand these sentiments, it is important to realize that options are financial instruments and not magical ones. It would be nice if we could simply find an investment tool that we could bolt onto our present stock holdings that would increase the dividend a nice amount but that wouldn’t put us at risk of having to deliver our beloved stocks to a complete stranger; unfortunately, this is not the case for options. For example, let’s say that you own stock in a company that is paying out a very nice dividend yield of 5 percent at present prices. This is a mature firm that has tons of cash flow but few opportunities for growth, so management has made the welcome choice to return cash to shareholders. The stock is trad- ing at $50 per share, but because the dividend is attractive to you, you are loathe to part with the stock. As such, you would prefer to write the covered call at a $55 or even a $60 strike price. A quick look at the BSM cone tells us why you should not be expecting a big boost in yield from selling the covered calls: 80 Sold call range of exposure 70 60 50 40 30 20 5/18/2012 5/20/2013 249 499 749 999 Cash Flows R Us, Inc. (CASH) Date/Day Count Stock Price GREEN LIGHT GREENGRAY LIGHT REDRED ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:261 SCORE: 28.00 ================================================================================ 244  •   The Intelligent Option Investor Clearly, the range of exposure for the $55-strike call is well above the BSM cone. The BSM cone is pointing downward because the dividend rate is 5 percent—higher than the risk-free rate. This means that BSM drift will be lower. In addition, because this is an old, mature, steady-eddy kind of company, the expected forward volatility is low. Basically, this is a perfect storm for a low option price. My suggestion is to either write calls on stocks you don’t mind de- livering to someone else—stocks for which you are very confident in the valuation range and are now at or above the upper bound—or simply to look for a portfolio of short-put/covered-call investments and treat it like a high-yield bond portfolio, as I described in Chapter 10 when explaining short puts. It goes without saying that if you think that a stock has a lot of unappreciated upside potential, it’s not a good idea to sell that exposure away! One other note about execution: as I have said, short puts and cov- ered calls are the same thing, but a good many investors do not realize this fact or their brokerages prevent them from placing any trade other than a covered call. This leads to a situation in which there is a tremendous sup- ply of calls. Any time there is a lot of supply, the price goes down, and you will indeed find covered calls on some companies paying a lot less than the equivalent short put. Because you will be accepting the same downside exposure, it is better to get paid more for it, so my advice is to write the put rather than the covered call in such situations. To calculate returns for covered calls, I carry out the following steps: 1. Assume that you buy the underlying stock at the market price. 2. Deduct the money you will receive from the call sale as well as any projected dividends—these are the two elements of your cash inflow—from the market price of the stock. The resulting figure is your effective buy price (EBP). 3. Divide your total cash inflow by the EBP . I always include the projected dividend payment as long as I am writ- ing a short-tenor covered call and there are no issues with the company that would prevent it from paying the dividend. Owners of record have a right to receive dividends, even after they have written a covered call on the ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:262 SCORE: 19.00 ================================================================================ Mixing Exposure  •  245 stock, so it makes sense to count the dividend inflow as one element that reduces your EBP . In formula form, this turns out to be −−Coveredc allr eturn= premiumr eceivedf romc all+ projectedd ividends stockp rice premiumf romc allp rojected dividends For a short put, you have no right to receive the dividend, so I find the return using the following formula: −Shortp ut return= premiumr eceivedf roms hort put strikepricep remium from shortp ut Common Pitfalls Taking Profit One mistake I hear people make all the time is saying that they are going to “take profit” using a covered call. Writing a covered call is taking profit in the sense that you no longer enjoy capital gains from the stock’s appre- ciation, but it is certainly not taking profit in the sense of being immune to falls in the market price of the stock. The call premium you receive will cushion a stock price drop, but it will certainly not shield you from it. If you want to take profits on a successful stock trade, hit the “Sell” button. Locking in a Loss A person sent me an e-mail telling me that she had bought a stock at $17, sold covered calls on it when it got to $20 (in order to “take profits”), and now that the stock was trading for $11, she wanted to know how she could “repair” her position using options. Unfortunately, options are not magical tools and cannot make up for a prior decision to buy a stock at $17 and ride it down to $11. If you are in such a position, don’t panic. It will be tempting to write a new call at the lower ATM price ($11 in this example) because the cash inflow from that covered call will be the most. Don’t do it. By writing a covered call at the lower price, you are—if the shares are called away— locking in a realized loss on the position. Y ou can see this clearly if you list each transaction in the example separately. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:263 SCORE: 24.00 ================================================================================ 246  •   The Intelligent Option Investor No. Buy/Sell Instrument Price of Instrument Effective Buy (Sell) Price of Stock Note 1 Buy Stock $17/share $17/share Original purchase 2 Sell Call option $1/share $16/share Selling a covered call to take profits when stock reaches $20/ share leaves the investor with down- side exposure and $1 in premium income. 3 Sell Call option $0.75 ($11.75/ share) Stock falls to $11, and investor sells another covered call to generate income to ameliorate the loss. In transaction 1, the investor buys the shares for $17. In transaction 2, when the stock hits $20 per share, the investor sells a covered call and receives $1 in premium. This reduces the effective buy price to $16 per share and means that the investor will have to deliver the shares if the stock is trad- ing at $20 or above at expiration. When the stock instead falls to $11, the investor—wanting to cushion the pain of the loss—sells another ATM cov- ered call for $0.75. This covered call commits the investor to sell the shares for $11.75. No matter how you look at it, buying at $16 per share and sell- ing at $11.75 per share is not a recipe for investing success. The first step in such a situation as this—when the price of a stock on which you have accepted downside exposure falls—is to look back to your valuation. If the value of the firm has indeed dropped because of some material negative news and the position no longer makes sense from an economic perspective, just sell the shares and take the lumps. If, however, the stock price has dropped but the valuation still makes for a compelling investment, stay in the position; if the investment is ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:264 SCORE: 13.00 ================================================================================ Mixing Exposure  •  247 compelling enough, this is the time to figure out a clever way to get more exposure to it. Y ou can write calls as long as they are at least at the same strike price as your previous purchase price or EBP; this just means that you are buying at $16 and agreeing to sell at at least $16, in other words. Also keep in mind that any dividend payment you receive you can also think of as a reduction of your EBP—that cash inflow is offsetting the cost of the shares. Factoring in dividends and the (very small) cash inflow as- sociated with writing far OTM calls will, as long as you are right about the valuation, eventually reduce your EBP enough so that you can make a profit on the investment. Over-/Underexposure Options are transacted in contract sizes of 100 shares. If you hold a number of shares that is not evenly divisible by 100, you must decide whether you are going to sell the next number down of contracts or the next number up. For example, let’s say that you own 250 shares of ABC. Y ou can either choose to sell two call contracts (in which case you will not be receiving yield on 50 of your shares) or sell three call contracts (in which case you will be effectively shorting 50 shares). My preference is to sell fewer con- tracts controlling fewer shares than I hold, and in fact, your broker may or may not insist that you do so as well. If not, it is an unpleasant feeling to get a call from a broker saying that you have a margin call on a position that you didn’t know you had. Getting Assigned If you write covered calls, you live with the risk that you will have to deliver your beloved shares to a stranger. Y ou can deliver your shares and use the proceeds from that sale (the broker will deposit an amount equal to the strike price times the contract multiplier into your account, and you get to keep the premium you originally received) to buy the shares again, but there is no way around delivering the shares if assigned. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:267 SCORE: 34.00 ================================================================================ 250  •   The Intelligent Option Investor The graphic conventions are a little different, but both diagrams show the acceptance of a narrow band of downside exposure offset by a bound- less gain of upside exposure. The area below the protective put’s strike price shows that economic exposure has been neutralized, and the area below the ITM call shows no economic exposure. The pictures are slightly differ- ent, but the economic impact is the same. The objective of a protective put is obvious—allow yourself the economic benefits from gaining upside exposure while shielding yourself from the economic harm of accepting downside exposure. The problem is that this protection comes at a price. I will provide more infromation about this in the next section. Execution Everyone understands the concept of protective puts—it’s just like the home insurance you buy every year to insure your property against dam- age. If you buy an OTM protective put (let’s say one struck at 90 percent of the current market price of the stock), the exposed amount from the stock price down to the put strike can be thought of as your “deductible” on your home insurance policy. The premium you pay for your put option can be thought of as the “premium” you pay on your home insurance policy. Okay—let’s go shopping for stock insurance. Apple (AAPL) is trad- ing for $452.53 today, so I’ll price both ATM and OTM put insurance for these shares with an expiration of 261 days in the future. I’ll also annualize that rate. Strike ($) “Deductible” ($) “Premium” ($) Premium as Percent of Stock Price Annualized Premium (%) 450 2.53 40.95 9.1 12.9 405 47.53 20.70 4.6 6.5 360 92.53 8.80 1.9 2.7 Now, given these rates and assuming that you are insuring a $500,000 house, the following table shows what equivalent deductibles, annual premiums, and total liability to a home owner would be for deductibles equivalent to the strike prices I’ve picked for Apple: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:268 SCORE: 29.00 ================================================================================ Mixing Exposure  •  251 Equivalent AAPL Strike ($) Deductible ($) Annual Premium ($) Total Liability to Home Owner ($) 450 2,795 64,500 67,295 405 52,516 32,500 85,016 360 102,236 13,500 115,736 I know that I would not be insuring my house at these rates and under those conditions! In light of these prices, the first thing you must consider is whether protecting a particular asset from unrealized price declines is worth the huge realized losses you must take to buy put premium. Buying ATM put protection on AAPL is setting up a 12.9 percent hurdle rate that the stock must surpass in one year just for you to start making a profit on the position, and 13 percent per year is quite a hurdle rate! If there is some reason why you believe that you need to pay for insurance, a better option—cheaper from a realized loss perspective—would be to sell the shares and use part of the proceeds to buy call options as an option-based replacement for the stock position. This approach has a few benefits: 1. The risk-reward profile is exactly the same between the two structures. 2. Any ATM or ITM call will be more lightly levered than any OTM put, meaning a lower realized loss on initiation. 3. For dividend-paying stocks, call owners do not have the right to receive dividends, but the amount of the projected dividend is de- ducted from the premium (as part of the drift calculation shown in the section on covered calls). As such, although not being paid dividends over time, you are getting what amounts to a one-time upfront dividend payment. 4. If you do not like the thought of leverage in your portfolio, you can self-margin the position (i.e., keep enough cash in reserve such that you are not “borrowing” any money through the call purchase). I do not hedge individual positions, but I do like the ITM call op- tion as an alternative for people who feel the need to do so. For hedg- ing of a general portfolio, rather than hedging of a particular holding in a portfolio, options on sector or index exchange-traded funds (ETFs) are more reasonably priced. Here are the ask prices for put options on the SPX ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:269 SCORE: 9.00 ================================================================================ 252  •   The Intelligent Option Investor ETF [tracking the Standard and Poor’s 500 Index (S&P 500), which closed at 1,685.73 when these data were retrieved] expiring in about 10 months: Strike/Stock ($) Ask Price ($) Premium as Percent of Stock Price 0.99 106.60 6.3 0.89 50.90 3.0 0.80 25.80 1.5 This is still a hefty chunk of change to pay for protection on an index but much less than the price of protection on individual stocks. 1 Common Pitfalls Hedge Timing Assume that you had talked to me a year ago and decided to take my ad- vice and avoid buying protective puts on single-name options. Instead, you took a protective put position on the S&P 500. Good for you. Setting aside for a moment how much of your portfolio to hedge, let’s take a look at what happened since you bought the downside protection: S&P 500 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 1,000 8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013 GREEN ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:270 SCORE: 10.00 ================================================================================ Mixing Exposure  •  253 When you bought the protection, the index was trading at 1,375, so you bought one-year puts about 5 percent OTM at $1,300. If the market had fallen heavily or even moderately during the first five months of the contract, your puts would have served you very well. However, now the puts are not 5 percent OTM anymore but 23 percent OTM, and it would take another Lehman shock for the market to make it down to your put strike. Keeping in mind that buying longer-tenor options gives you a better annualized cost than shorter-tenor options, you should be leery of entering into a hedging strategy such as the one pictured here: S&P 500 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 1,000 8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013 GREEN Buying short-tenor puts helps in terms of providing nearer to ATM protection, but the cost is higher, and it gets irritating to keep buying expensive options and never benefiting from them (funny— no one ever says this about home insurance). Although there are no perfect solutions to this quandary, I believe the following approach has merit: ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:271 SCORE: 12.00 ================================================================================ 254  •   The Intelligent Option Investor S&P 500 1,800 1,700 1,600 1,500 1,400 1,300 1,200 1,100 1,000 8/1/20129/1/201210/1/201211/1/201212/1/20121/1/20132/1/20133/1/20134/1/20135/1/20136/1/20137/1/2013 GREEN GREENLIGHT GREEN LIGHT GREEN LIGHT GREEN Here I bought fewer long-term put contracts at the outset and then add- ed put contracts at higher strikes opportunistically as time passed. I have left myself somewhat more exposed at certain times, and my protection doesn’t all pick up at a single strike price, so the insurance coverage is spotty, but I have likely reduced my hedging cost a great deal while still having a potential source of investible cash on hand in the form of options with time value on them. The Unhappy Case of a Successful Hedge Markets are down across the board. Y our brokerage screen is awash in red. The only bright spot is the two or three lines of your screen showing your S&P 500 puts, which are strongly positive. Y ou bought your protection when the market was going up, so it was very cheap to purchase. Now, with the market in a terror, the implied volatilities have shot up, and you are sit- ting on a huge positive unrealized value. Now what? The psychological urge to keep that hedge on will be strong. Such a po- sition is safe after all, and with the rest of the world falling apart, it feels nice to have somewhere safe to go. What should you do with this unrealized profit? ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:275 SCORE: 17.00 ================================================================================ 258  •   The Intelligent Option Investor plan like this in place will allow you to size and time your hedges appropri- ately and will help you to make the most out of whatever temporary crisis might come your way. 2 Now that you have a good understanding of protective puts and hedging, let’s turn to the last overlay strategy—the collar. Collar Contingent Exposure Contingent Exposure Contingent Exposure GREEN LIGHT GREEN LIGHT ORANGE LIGHT RED ORANGE RED Downside: Irrelevant Upside: Undervalued Execute: Sell a call option on a stock or index that you own and on which you have a gain, and use the proceeds from the call sale to buy an OTM put Risk: Flexible, depending on selection of strikes Reward: Limited to level of sold call strike Margin: None because the long position in the hedged security serves as collateral for the sold call option, and the OTM put option is purchased, so it does not require margining ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:276 SCORE: 30.00 ================================================================================ Mixing Exposure  •  259 The Gist This structure is really much simpler and has a much more straightfor - ward investment purpose than it may seem when you look at the preceding diagram. When people talk about “taking profits” using a covered call, the collar is actually the strategy they should be using. Imagine that you bought a stock some time ago and have a nice unrealized gain on it. The stock is about where you think its likely fair value is, but you do not want to sell it for whatever reason (e.g., it is paying a nice dividend or you bought it less than a year ago and do not want to be taxed on short-term capital gains or whatever). Although you do not want to sell it, you would like to protect yourself from downside exposure. Y ou can do this cheaply using a collar. The collar is a covered call, which we have already discussed, whose income subsidizes the purchase of a protective put at some level that will allow you to keep some of the unre- alized gains on your securities position. The band labeled “Orange” on the diagram shows an unrealized gain (or, conversely, a potential unrealized loss). If you buy a put that is within this orange band or above, you will be guaranteed of making at least some realized profit on your original stock or index investment. Depending on how much you receive for the covered call and what strike you select for the protective put, this collar may rep- resent completely “free” downside protection or you might even be able to realize a net credit. Execution The execution of this strategy depends a great deal on personal prefer - ence and on the individual investor’s situation. For example, an investor can sell a short-tenor covered call and use those proceeds to buy a longer- tenor protective put. He or she can sell the covered call ATM and buy a protective put that is close to ATM; this means the maximum and mini- mum potential return on the previous security purchase is in a fairly tight band. Conversely, the investor might sell an OTM covered call and buy a protective put that is also OTM. This would lock in a wider range of guaranteed profits over the life of the option. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:277 SCORE: 33.00 ================================================================================ 260  •   The Intelligent Option Investor I show a couple of examples below that give you the flavor of the possibilities of the collar strategy. With these examples, you can experi- ment yourself with a structure that fits your particular needs. Look on my website for a collar scenario calculator that will allow you to visualize the collar and understand the payoff structure given different conditions. For these examples, I am assuming that I bought Qualcomm stock at $55 per share. Qualcomm is now trading for $64.71—an unrealized gain of 17.7 percent. Collar 1: 169 Days to Expiration Strike Price ($) Bid (Ask) Price ($) Sold call 65.00 3.40 Purchased put 60.00 (2.14) Net credit $1.26 This collar yields the following best- and worst-case effective sell prices (ESPs) and corresponding returns (assuming a $55 buy price): ESP ($) Return (%) Best case 66.26 20.5 Worst case 61.26 11.4 Here we sold the $65-strike calls for $3.40 and used those proceeds to buy the $60-strike put options at $2.14. This gave us a net credit of $1.26, which we simply add to both strike prices to calculate our ESP . We add the net credit to the call strike because if the stock moves above the call strike, we will end up delivering the stock at the strike price while still keeping the net credit. We add the net credit to the put strike because if the stock closes below the put strike, we have the right to sell the shares at the strike price and still keep the net credit. The return numbers are calculated on the basis of a $55 purchase price and the ESPs listed. Thus, by setting up this collar in ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:278 SCORE: 13.00 ================================================================================ Mixing Exposure  •  261 this way, we have locked in a worst possible gain of 11.4 percent and a best possible gain of 20.5 percent for the next five and a half months. Let’s look at another collar with a different profit and loss profile: Collar 2: 78 Days to Expiration Strike Price ($) Bid (Ask) Price ($) Sold call 70 0.52 Purchased put 62.50 (1.55) Net debit (1.03) This collar yields the following best- and worst-case ESPs and corresponding returns (assuming a $55 buy price): ESP ($) Return (%) Best case 68.97 25.4 Worst case 61.47 11.8 This shows a shorter-tenor collar—about two and a half months be- fore expiration—that allows for more room for capital gains. This might be the strategy of a hedge fund manager who is long the stock and uncertain about the next quarterly earnings report. For his or her own business rea- sons, the manager does not want to show an unrealized loss in case Qual- comm’s report is not good, but he or she also doesn’t want to restrict the potential capital gains much either. Calculating the ESPs and the returns in the same way as described here, we get a guaranteed profit range from around 12 to over 25 percent. One thing to note as well is that the protection is provided by a put, and a put option can be sold any time before expiry to generate a cash inflow from time value. Let’s say then that when Qualcomm reports its quarterly earnings, the stock price drops to $61—a mild drop that the hedge fund manager considers a positive sign. Now that the manager is less worried about the downside exposure, he or she can sell the put for a profit. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:280 SCORE: 8.00 ================================================================================ 263 Chapter 12 Risk and the intelligent OptiOn investOR The preceding 11 chapters have given you a great deal of information about the mechanics of option investing and stock valuation. In this last chapter, let’s look at a subject that I have mentioned throughout this book—risk— and see how an intelligent option investor conceives of it. There are many forms of risk—some of which we discussed earlier (e.g., the career risk of an investment business agent, solvency risk of a retiree looking to maintain a good quality of life, and liquidity risk of a parent needing to make a big payment for a child’s wedding). The two risks I discuss here are those that are most applicable to an owner of capital making potentially levered investments in complex, uncertain assets such as stocks. These two risks are market risk and valuation risk. Market Risk Market risk is unavoidable for anyone investing capital. Markets fluctuate, and in the short term, these fluctuations often have little to do with the long-term value of a given stock. Short term, it must be noted, is also relative. In words attributed to John Maynard Keynes, but which is more likely an anonymous aphorism, “The market can remain irrational longer than you can remain sol- vent. ” Indeed, it is this observation and my own painful experience of the truth of it that has brought me to my appreciation for in-the-money (ITM) options as a way to preserve my capital and cushion the blow of timing uncertainty. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:281 SCORE: 10.00 ================================================================================ 264  •   The Intelligent Option Investor Market risk is a factor that investors in levered instruments must always keep in mind. Even an ITM call long-term equity anticipated security (LEAPS) in the summer of 2007 might have become a short-tenor out-of-the-money (OTM) call by the fall of 2008 after the Lehman shock because of the sharp decline in stock prices in the interim. Unexpected things can and do happen. A portfolio constructed oblivious to this fact is a dangerous thing. As long as market fluctuations only cause unrealized losses, market risk is manageable. But if a levered loss must be realized, either because of an option expiration or in order to fund another position, it has the poten- tial to materially reduce your available investment capital. Y ou cannot ma- terially reduce your investment capital too many times before running out. A Lehman shock is a worst-case scenario, and some investors live their entire lives without experiencing such severe and material market risk. In most cases, rather than representing a material threat, market risk represents a wonderful opportunity to an intelligent investor. Most human decision makers in the market are looking at either technical indicators—which are short term by nature—or some sort of multiple value (e.g., price-to-something ratio). These kinds of measures are wonderful for brokers because they encourage brokerage clients to make frequent trades and thus pay the brokerages frequent fees. The reaction of short-term traders is also wonderful for intelligent investors. This is so because a market reaction that might look sensible or rational to someone with an investment time horizon measured in days or months will often look completely ridiculous to an investor with a longer- term perspective. For example, let’s say that a company announces that its earnings will be lower next quarter because of a delay in the release of a new product. Investors who are estimating a short-term value for the stock based on an earnings multiple will sell the stock when they see that earn- ings will likely fall. Technical traders see that the stock has broken through some line of “resistance” or that one moving average has crossed another moving average, so they sell it as well. Perhaps an algorithmic trading engine recognizes the sharp drop and places a series of sell orders that are covered almost as soon as they are filled. In the meantime, someone who has held the stock for a while and has a gain on it gets protective of this gain and decides to buy a put option to protect his or her gains. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:282 SCORE: 15.00 ================================================================================ Risk and the Intelligent Option Investor   • 265 For an intelligent option investor who has a long-term worst-case valuation that is now 20 percent higher than the market price, there is a wonderful opportunity to sell a put and receive a fat premium (with the possibility of owning the stock at an attractive discount to the likely fair value), sell a put and use the proceeds to buy an OTM call LEAPS, or sim- ply buy the stock to open a position. Indeed, this strategy is perfectly in keeping with the dictum, “Be fear- ful when others are greedy and greedy when others are fearful. ” This strat- egy is also perfectly reasonable but obviously rests on the ability of the investor to accurately estimate the actual intrinsic value of a stock. This brings us to the next form of risk—valuation risk. Valuation Risk Although valuation is not a difficult process, it is one that necessarily in- cludes unknowable elements. In our own best- and worst-case valuation methodology, we have allowed for these unknowns by focusing on plausi- ble ranges rather than precise point estimates. Of course, our best- or worst- case estimates might be wrong. This could be due to our misunderstanding of the economic dynamics of the business in which we have invested or may even come about because of the way we originally framed the problem. Thinking back to how we defined our ranges, recall that we were focusing on one-standard-deviation probabilities—in other words, scenarios that might plausibly be expected to materialize two times out of three. Obvi- ously, even if we understand the dynamics of the business very well, one time out of three, our valuation process will generate a fair value range that is, in fact, materially different from the actual intrinsic value of the stock. In contrast to market risk, which most often is a nonmaterial and tem- porary issue, misestimating the fair value of a stock represents a material risk to capital, whether our valuation range is too low or too high. If we esti- mate a valuation range that is too low, we are likely to end up not allocating enough capital to the investment or using inappropriately light leverage. This means that we will have missed the opportunity to generate as much return on this investment as we may have. If we estimate a valuation range that is too high, we are likely to end up allocating too much capital to the ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:284 SCORE: 12.00 ================================================================================ Risk and the Intelligent Option Investor   • 267 Let’s assume that the present market value of the shares is $16 per share. This share price assumes a growth in FCFO of 8 percent per year for the next 5 years and 5 percent per year in perpetuity after that—roughly equal to what we consider our most likely operational performance scenario. We see the possibility of faster growth but realize that this faster growth is unlikely—the valuation layer associated with this faster growth is the $18 to $20 level. We also see the possibility of a slowdown, and the valuation layer associated with this worst-case growth rate is the $11 to $13 level. Now let’s assume that because of some market shock, the price of the shares falls to the $10 range. At the same time, let’s assume that the likely economic scenario, even after the stock price fall, is still the same as before— most likely around $16 per share; the best case is $20 per share, and the worst case is $11 per share. Let’s also say that you can sell a put option, struck at $10, for $1 per share—giving you an effective buy price of $9 per share. In this instance, the valuation risk is indeed small as long as we are correct about the relative levels of our valuation layers. Certainly, in this type of scenario, it is easier to commit capital to your investment idea than it would be, say, to sell puts struck at $16 for $0.75 per share! Thinking of stock prices in this way, it is clear that when the market price of a stock is within a valuation layer that implies unrealistic economic assumptions, you will more than likely be able to use a combination of stocks and options to tilt the balance of risk and reward in your own favor—the very definition of intelligent option investing. Intelligent Option Investing In my experience, most stocks are mostly fairly priced most of the time. There may be scenarios at one tail or the other that might be inappropriately priced by the option market (and, by extension, by the stock market), but by and large, it is difficult to find profoundly mispriced assets—an asset whose market price is significantly different from its most likely valuation layer. Opportunities tend to be most compelling when the short-term pic- ture is the most uncertain. Short-term uncertainties make investing boldly ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:286 SCORE: 9.00 ================================================================================ 269 Appendix A Choose Your Battles WiselY I discuss specific option investment strategies in great detail in Part III of this book. However, after reading Chapters 2 and 3, you should have a good understanding of how options are priced, so it is a good time to see in what circumstances the Black-Scholes-Merton model (BSM) works best and where it works worst. An intelligent investor looks to avoid the condi- tions where the BSM works best like the plague and seek out the conditions where it works worst because those cases offer the best opportunities to tilt the risk-reward balance in the investor’s favor. Jargon introduced in this appendix includes Front month Fungible Idiosyncratic assets Where the BSM Works Best The following are the situations in which the BSM works best and are the conditions you should most avoid: 1. Short investment time horizons 2. Fungible investment assets ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:287 SCORE: 27.00 ================================================================================ 270  •   The Intelligent Option Investor Short Investment Time Horizons When the scholars developing the BSM were researching financial markets for the purpose of developing their model, the longest-tenor options had expirations only a few months distant. Most market partic- ipants tended to trade in the front-month contracts (i.e., the contracts that will expire first), as is still mainly the case. Indeed, thinking back to our preceding discussion about price randomness, over short time horizons, it is very difficult to prove that asset price movements are not random. As such, the BSM is almost custom designed to handle short time horizons well. Perhaps not unsurprisingly, agents 1 are happy to encourage clients to trade options with short tenors because 1. It gives them more opportunities per year to receive fees and com- missions from their clients. 2. They are mainly interested in reliably generating income on the basis of the bid-ask spread, and bid-ask spreads differ on the basis of liquidity, not time to expiration. 3. Shorter time frames offer fewer chances for unexpected price movements in the underlying that the market makers have a hard time hedging. In essence, a good option market maker is akin to a used car sales- man. He knows that he can buy at a low price and sell at a high one, so his main interest is in getting as many customers to transact as possible. With this perspective, the market maker is happy to use the BSM, which seems to give reasonable enough option valuations over the time period about which he most cares. In the case of short-term option valuations, the theory describes reality accurately enough, and structural forces (such as wide bid-ask spreads) make it hard to exploit mispricings if and when they occur. To see an example of this, let’s take a look at what the BSM assumes is a reasonable range of prices for a company with assumed 20 percent volatility over a period of 30 days. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:289 SCORE: 18.00 ================================================================================ 272  •   The Intelligent Option Investor It is important to realize that the fact that options are usually efficiently priced in the short term does not prevent us from transacting in short-tenor options. In fact, some strategies discussed in Part III are actually more attractive when an investor uses shorter-tenor options or combines short- and long-tenor options into a single strategy. Hopefully, the distinction between avoiding short-tenor option strategies and making long-term investments in short-tenor options is clear after reading through Part III. Fungible Underlying Assets Again, returning for a moment to the foundation of the BSM, the scholars built their mathematical models by studying short-term agricultural commodity markets. A commodity is, by definition, a fungible or interchangeable asset; one bushel of corn of a certain quality rating is completely indistinguishable from any other bushel of corn of the same quality rating. Stocks, on the other hand, are idiosyncratic assets. They are intangible markers of value for incredibly complex systems called companies, no two of which is exactly alike (e.g., GM and Ford—the pair that illustrates the idea of “paired” investments in many people’s minds—are both American car companies, but as operating entities, they have some significant differ- ences. For example, GM has a much larger presence in China and has a different capital and governance structure since going bankrupt than Ford, which avoided bankruptcy during the mortgage crisis). The academics who built the BSM were not hesitant to apply a model that would value idiosyncratic assets such as stocks because they had as- sumed from the start that financial markets are efficient—meaning that every idiosyncratic feature for a given stock was already fully “priced in” by the market. This allowed them to overlook the complexity of individual companies and treat them as interchangeable, homogeneous entities. The BSM, then, did not value idiosyncratic, multidimensional companies; rather, it valued single-dimensional entities that the scholars assumed had already been “standardized” or commoditized in some sense by the communal wisdom of the markets. Y ou will see in the next sec- tion that the broad, implicit assumption by option market participants that markets are efficient actually brings about the greatest opportunity ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:293 SCORE: 16.00 ================================================================================ 276  •   The Intelligent Option Investor If someone wanted to make extra income by selling calls to accept expo- sure to the stock’s upside, what price would they likely charge for someone wanting to buy this call option? a. Almost nothing b. A little c. A good bit Obviously, the correct answer to the put option question is c. This option would be pretty expensive because its range of exposure overlaps with so much of the BSM cone. Conversely, the answer to the call option question is a. This option would be really cheap because its range of exposure is well above the BSM cone. Remember, though, that we have our crystal ball, and we know that this stock will likely be somewhere between $70 and $110 per share in a few years. With this confidence, wouldn’t it make sense to take the opposite side of both the preceding trades? Doing so would look like this: 5/18/2012 10 20 30 40 50 60 70 80 90 100 110 120 5/20/2013 249 499 749 999 Date/Day Count Advanced Building Corp. (ABC) Stock Price Best Case, 110 Worst Case, 70 - GREEN RED In this investment, which I explain in detail in Chapter 11, we are receiving a good bit of money by selling an expensive put and paying ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:294 SCORE: 14.00 ================================================================================ Appendix A: Choose Your Battles Wisely   • 277 very little money to buy a cheap call. It may happen that the money we receive for selling the put actually may be greater than the money we pay for the call, so we actually get paid a net fee when we make this transaction! We can sell the put confidently because we know that our worst-case valuation is $70 per share; as long as we are confident in our valuation—a topic covered in Part II of this book—we need not worry about the price declining. We do not mind spending money on the call because we think that the chance is very good that at expiration or before the call will be worth much, much more than we paid for it. Truly, the realization that the BSM is pricing options on inefficiently priced stocks as if they were efficiently priced is the most profound and compelling source of profits for intelligent investors. Furthermore, finding grossly mispriced stocks and exploiting the mispricing using options rep- resents the most compelling method for tilting the risk-reward equation in our direction. The wonderful thing about investing is that it does not require you to swing at all the pitches. Individual investors have a great advantage in that they may swing at only the pitches they know they can hit. The process of intelligent investing is simply one of finding the right pitches, and intel- ligent option investing simply uses an extremely powerful bat to hit that sweet pitch. Bimodal Outcomes Some companies are speculative by nature—for instance, a drug company doing cancer research. The company has nothing but some intangible as- sets (the ideas of the scientists working there) and a great deal of costs (the salaries going to those scientists, the payments going to patent attor - neys, and the considerable costs of paying for clinical trials). If the research proves fruitful, the company’s value is great—let’s say $500 per share. If the clinical trials show low efficacy or dangerous side effects, however, the company’s worth goes to virtually nil. What’s more, it may take years before it is clear which of these alternatives is true. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:295 SCORE: 16.00 ================================================================================ 278  •   The Intelligent Option Investor Given what you know about the BSM, does this seem like the kind of situation conducive to accurate option pricing? This example certainly does not sound like the pricing scenario of a short-term agricultural commodity, after all. If this hypothetical drug company’s stock price was sitting at $50 per share, what is the value of the upper range the option market might be pricing in? Let’s assume that this stock is trading with a forward volatility of 100 percent per year (on the day I am writing this, there are only four stocks with options trading at a price that implies a forward volatility of greater than 100 percent). What price range does this 100 percent per year volatility imply, and can we design an option structure that would allow us to profit from a big move in either direction? Here is a diagram of this situation: 5/18/2012 - 500 50 100 150 200 250 300 350 400 450 5/20/2013 249 499 Date/Day Count Advanced Biotechnology Co. (ABC) Stock Price 749 999 GREEN GREEN Indeed, even boosting volatility assumptions to a very high level, it seems that we can still afford to gain exposure to both the upside and downside of this stock at a very reasonable price. Y ou can see from the pre- ceding diagram that both regions of exposure on the put side and the call side are outside the BSM cone, meaning that they will be relatively cheap. The options market is trying to boost the price of the options enough so that the calls and puts are fairly priced, but for various reasons (including behavioral biases), most of the time it fails miserably. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:297 SCORE: 10.00 ================================================================================ 280  •   The Intelligent Option Investor Clearly, there is not much of a difference between the BSM expected value (shown by the dotted line) and the dot representing a 10 percent upward drift in the stock. However, if we extend this analysis out for three years, look what happens: 5/18/2012 5/20/2013 249 499 Date/Day Count Advanced Building Corp. (ABC) 749 999 20 30 40 50 60 70Stock Price 80 With the longer time horizon, our assumed stock price is significantly higher than what the BSM calculates as its expected price. If we take “assumed future stock price” to mean the price at which we think there is an equal chance that the true stock price will be above or below that mark, we can see that the difference, marked by the double-headed arrow in the preceding diagram, is the advantage we have over the option market. 3 This advantage again means that downside exposure will be overvalued and upside exposure will be undervalued. How, you may ask, can this discrepancy persist? Shouldn’t someone figure out that these options are priced wrong and take advantage of an arbitrage opportunity? The two reasons why these types of opportunities tend to persist are 1. Most people active in the option market are trading on a very short-term basis. Long-term equity anticipated securities (LEAPS)—options with tenors of a year or more—do exist, but ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:298 SCORE: 26.00 ================================================================================ Appendix A: Choose Your Battles Wisely   • 281 generally the volumes are light because the people in the option markets generally are not willing to wait longer than 60 days for their “investment” to work out. Because the time to expiration for most option contracts is so short, the difference between the BSM’s expected price based on a 5 percent risk-free rate and an expected price based on a 10 percent equity return is small, so no one real- izes that it’s there (as seen on the first diagram). 2. The market makers are generally able to hedge out what little ex- posure they have to the price appreciation of LEAPS. They don’t care about the price of the underlying security, only about the size of the bid-ask spread, and they always price the bid-ask spread on LEAPS in as advantageous a way as they can. Also, the career of an equity option trader on the desk of a broker-dealer can change a great deal in a single year. As discussed in Part II, market makers are not incentivized in such a way that they would ever care what happened over the life of a LEAPS. Congratulations. After reading Part I of this book and this appendix, you have a better understanding of the implications of option investing for fundamental investors than most people working on Wall Street. There are many more nuances to options that I discuss in Part III of this book—especially regarding leverage and the sensitivity of options to input changes—but for now, simply understanding how the BSM works puts you at a great advantage over other market participants. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:304 SCORE: 29.00 ================================================================================ 287 Appendix c PUT-cALL PArITy Before the Black-Scholes-Merton model (BSM), there was no way to directly calculate the value of an option, but there was a way to triangulate put and call prices as long as one had three pieces of data: 1. The stock’s price 2. The risk-free rate 3. The price of a call option to figure the fair price of the put, and vice versa In other words, if you know the price of either the put or a call, as long as you know the stock price and the risk-free rate, you can work out the price of the other option. These four prices are all related by a specific rule termed put-call parity. Put-call parity is only applicable to European options, so it is not ter- ribly important to stock option investors most of the time. The one time it becomes useful is when thinking about whether to exercise early in order to receive a stock dividend—and that discussion is a bit more technical. I’ll delve into those technical details in a moment, but first, let’s look at the big picture. Using the intelligent option investor’s graphic format employed in this book, the big picture is laughably trivial. Direct your attention to the following diagrams. What is the differ - ence between the two? ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:305 SCORE: 23.00 ================================================================================ 288  •   The Intelligent Option Investor - 20 5/18/2012 5/20/2013 40 60 80 100 120Stock Price 140 160 180 200 - 20 5/18/2012 5/20/2013 40 60 80 100 120Stock Price 140 160 180 200 GREENGREEN REDRED If you say, “Nothing, ” you are practically right but technically wrong. The image on the left is actually the risk-reward profile of a pur - chased call option struck at $50 paired with a sold put option struck at $50. The image on the right is the risk-reward profile of a stock trading at $50 per share. This simple comparison is the essence of put-call parity. The parity part of put-call parity just means that accepting downside exposure by sell- ing a put while gaining upside exposure by buying a call is basically the same thing as accepting downside exposure and gaining upside exposure by buying a stock. What did I say? It is laughably trivial. Now let’s delve into the details of how the put-call parity relationship can be used to help decide whether to exercise a call option or not (or whether the call option you sold is likely to be exercised or not). Dividend Arbitrage and Put-call Parity Any time you see the word arbitrage , the first thing that should jump to mind is “small differences. ” Arbitrage is the science of observing small dif- ferences between two prices that should be the same (e.g., the price of IBM ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:306 SCORE: 18.00 ================================================================================ Appendix C: Put-Call Parity   • 289 traded on the New Y ork Stock Exchange and the price of IBM traded in Philadelphia) but are not. An arbitrageur, once he or she spots the small difference, sells the more expensive thing and buys the less expensive one and makes a profit without accepting any risk. Because we are going to investigate dividend arbitrage, even a big- picture guy like me has to get down in the weeds because the differences we are going to try to spot are small ones. The weeds into which we are wading are mathematical ones, I’m afraid, but never fear—we’ll use nothing more than a little algebra. We’ll use these variables in our discussion: K = strike price C K = call option struck at K PK = put option struck at K Int = interest on a risk-free instrument Div = dividend payment S = stock price Because we are talking about arbitrage, it makes sense that we are going to look at two things, the value of which should be the same. We are going to take a detailed look at the preceding image, which means that we are going to compare a position composed of options with a position composed of stock. Let’s say that the stock at which we were looking to build a position is trading at $50 per share and that options on this stock expire in exactly one year. Further, let’s say that this stock is expected to yield $0.25 in dividends and that the company will pay these dividends the same day that the op- tions expire. Let’s compare the two positions in the same way as we did in the preceding big-picture image. As we saw in that image, a long call and a short put are the same as a stock. Mathematically, we would express this as follows: C K − PK = SK Although this is simple and we agreed that it’s about right, it is not technically so. The preceding equation is not technically right because we know that a stock is an unlevered instrument and that options are levered ones. In the ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:307 SCORE: 42.00 ================================================================================ 290  •   The Intelligent Option Investor preceding equation, we can see that the left side of the equation is levered (because it contains only options, and options are levered instruments), and the right side is unlevered. Obviously, then, the two cannot be exactly the same. We can fix this problem by delevering the left side of the preceding equation. Any time we sell a put option, we have to place cash in a mar - gin account with our broker. Recall that a short put that is fully margined is an unlevered instrument, so margining the short put should delever the entire option position. Let’s add a margin account to the left side and put $K in it: C K − PK + K = S This equation simply says that if you sell a put struck at K and put $K worth of margin behind it while buying a call option, you’ll have the same risk, return, and leverage profile as if you bought a stock—just as in our big-picture diagram. But this is not quite right if one is dealing with small differences. First, let’s say that you talk your broker into funding the margin ac- count using a risk-free bond fund that will pay some fixed amount of interest over the next year. To fund the margin account, you tell your broker you will buy enough of the bond account that one year from now, when the put expires, the margin account’s value will be exactly the same as the strike price. In this way, even by placing an amount less than the strike price in your margin account originally, you will be able to fulfill the commitment to buy the stock at the strike price if the put expires in the money (ITM). The amount that will be placed in margin originally will be the strike price less the amount of interest you will receive from the risk-free bond. In mathematical terms, the preceding equation becomes C K − PK + (K – Int) = S Now all is right with the world. For a non-dividend-paying stock, this fully expresses the technical definition of put-call parity. However, because we are talking about dividend arbitrage, we have to think about how to adjust our equation to include dividends. We know that a call option on a dividend-paying stock is worth less because the dividend ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:308 SCORE: 49.50 ================================================================================ Appendix C: Put-Call Parity   • 291 acts as a “negative drift” term in the BSM. When a dividend is paid, theory says that the stock price should drop by the amount of the dividend. Be- cause a drop in price is bad for the holder of a call option, the price of a call option is cheaper by the amount of the expected dividend. Thus, for a dividend-paying stock, to establish an option-based position that has exactly the same characteristics as a stock portfolio, we have to keep the expected amount of the dividend in our margin account. 1 This money placed into the option position will make up for the dividend that will be paid to the stock holder. Here is how this would look in our equation: C K − PK + (K − Int) + Div = S With the dividend payment included, our equation is complete. Now it is time for some algebra. Let’s rearrange the preceding equa- tion to see what the call option should be worth: CK = PK + Int − Div + (S − K) Taking a look at this, do you notice last term (S – K )? A stock’s price minus the strike price of a call is the intrinsic value. And we know that the value of a call option consists of intrinsic value and time value. This means that /dncurlybracketleft/dncurlybracketmid/horizcurlybracketext/horizcurlybracketext/dncurlybracketright/horizcurlybracketext/horizcurlybracketext/dncurlybracketleft/dncurlybracketmid/dncurlybracketright=+ −−CP SKKK IntD iv + () Time valueI ntrinsic value So now let’s say that time passes and at the end of the year, the stock is trading at $70—deep ITM for our $50-strike call option. On the day before expiration, the time value will be very close to zero as long as the op- tion is deep ITM. Building on the preceding equation, we can put the rule about the time value of a deep ITM option in the following mathematical equation: P K + Int − Div ≈ 0 If the time value ever falls below 0, the value of the call would trade for less than the intrinsic value. Of course, no one would want to hold an option that has negative time value. In mathematical terms, that scenario would look like this: P K + Int − Div < 0 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:309 SCORE: 30.00 ================================================================================ 292  •   The Intelligent Option Investor From this equation, it follows that if PK + Int < Div your call option has a negative implied time value, and you should sell the option in order to collect the dividend. This is what is meant by dividend arbitrage . But it is hard to get the flavor for this without seeing a real-life example of it. The following table shows the closing prices for Oracle’s stock and options on January 9, 2014, when they closed at $37.72. The options had an expiration of 373 days in the future—as close as I could find to one year—the one-year risk-free rate was 0.14 percent, and the company was expected to pay $0.24 worth of dividends before the options expired. Calls Puts Bid Ask Delta Strike Bid Ask Delta 19.55 19.85 0.94 18 0.08 0.13 −0.02 17.60 17.80 0.94 20 0.13 0.15 −0.03 14.65 14.85 0.92 23 0.25 0.28 −0.05 12.75 12.95 0.91 25 0.36 0.39 −0.07 10.00 10.25 0.86 28 0.66 0.69 −0.12 8.30 8.60 0.81 30 0.97 1.00 −0.17 6.70 6.95 0.76 32 1.40 1.43 −0.23 4.70 4.80 0.65 35 2.33 2.37 −0.34 3.55 3.65 0.56 37 3.15 3.25 −0.43 2.22 2.26 0.42 40 4.80 4.90 −0.57 1.55 1.59 0.33 42 6.15 6.25 −0.65 0.87 0.90 0.22 45 8.25 8.65 −0.75 0.31 0.34 0.10 50 12.65 13.05 −0.87 In the theoretical option portfolio, we are short a put, so its value to us is the amount we would have to pay if we tried to flatten the position by buying it back—the ask price. Conversely, we are long a call, so its value to us is the price we could sell it for—the bid price. Let’s use these data to figure out which calls we might want to exercise early if a dividend payment was coming up. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:310 SCORE: 14.00 ================================================================================ Appendix C: Put-Call Parity   • 293 Strike Call Put (a) Interest2 (b) Put + Interest (a + b) Dividend P + I − D Notes 18 19.55 0.13 0.03 0.16 0.24 (0.08) P + I < D, arbitrage 20 17.60 0.15 0.03 0.18 0.24 (0.06) P + I < D, arbitrage 23 14.65 0.28 0.03 0.31 0.24 0.07 No arbitrage 25 12.75 0.39 0.04 0.43 0.24 0.19 No arbitrage 28 10.00 0.69 0.04 0.73 0.24 0.49 No arbitrage 30 8.30 1.00 0.04 1.04 0.24 0.80 No arbitrage 32 6.70 1.43 0.05 1.48 0.24 1.24 No arbitrage 35 4.70 2.37 0.05 2.42 0.24 2.18 No arbitrage 37 3.55 3.25 0.05 3.30 0.24 3.06 No arbitrage 40 2.22 4.90 0.06 4.96 0.24 4.72 No arbitrage 42 1.55 6.25 0.06 6.31 0.24 6.07 No arbitrage 45 0.87 8.65 0.06 8.71 0.24 8.47 No arbitrage 50 0.31 13.05 0.07 13.12 0.24 12.88 No arbitrage There are only two strikes that might be arbitraged for the dividends—the two furthest ITM call options. In order to realize the arbitrage opportunity, you would wait until the day before the ex-dividend date, exercise the stock option, receive the dividend, and, if you didn’t want to keep holding the stock, sell it and realize the profit. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:312 SCORE: 28.00 ================================================================================ 295 Notes Introduction 1. Options, Futures, and Other Derivatives by John C. Hull (New Y ork: Prentice Hall, Eighth Edition, February 12, 2011), is considered the Bible of the academic study of options. 2. Option Volatility and Pricing by Sheldon Natenberg (New Y ork: McGraw-Hill, Updated and Expanded Edition, August 1, 1994), is considered the Bible of professional option traders. 3. The Greeks are measures of option sensitivity used by traders to man- age risk in portfolios of options. They are named after the Greek symbols used in the Black-Scholes-Merton option pricing model. 4. “To invest successfully over a lifetime does not require a stratospheric IQ, unusual business insights, or inside information. What’s needed is a sound intellectual framework for making decisions and the abil- ity to keep emotions from corroding that framework. ” Preface to The Intelligent Investor by Benjamin Graham (New Y ork: Collins Business, Revised Edition, February 21, 2006). Chapter 1 1. In other words, if all option contracts were specific and customized, every time you wanted to trade an option contract as an individual in- vestor, you would have to first find a counterparty to take the other side of the trade and then do due diligence on the counterparty to make sure that he or she would be able to fulfill his or her side of the bargain. It is hard to imagine small individual investors being very interested in the logistical headaches that this process would entail! ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:313 SCORE: 33.00 ================================================================================ 296 •   N o t e s 2. One more bit of essential but confusing jargon when investing in options is related to exercise. There are actually two styles of exercise; one can be exercised at any time before expiration—these are termed American style—and the other can only be exercised at expiration— termed European style. Confusingly, these styles have nothing to do about the home country of a given stock or even on what exchange they are traded. American-style exercise is normal for all single-stock options, whereas European-style exercise is normal for index futures. Because this book deals almost solely with single-stock options (i.e., options on IBM or GOOG, etc.), I will not make a big deal out of this distinction. There is one case related to dividend-paying stocks where American-style exercise is beneficial. This is discussed in Appendix C. Most times, exercise style is not a terribly important thing. 3. Just like going to Atlantic City, even though the nominal odds for rou- lette are 50:50, you end up losing money in the long run because you have to pay—the house at Atlantic City or the broker on Wall Street— just to play the game. Chapter 3 1. We adjusted and annualized the prices of actual option contracts so that they would correspond to the probability levels we mentioned earlier. It would be almost impossible to find a stock trading at exactly $50 and with the option market predicting exactly the range of future price that we have shown in the diagrams. This table is provided simply to give you an idea of what one might pay for call options of different moneyness in the open market. 2. Eighty-four percent because the bottom line marks the price at which there is only a 16 percent chance that the stock will go any lower. If there is a 16 percent chance that the stock will be lower than $40 in one year’s time, this must mean that there is an 84 percent chance that the stock will be higher than $40 in one year’s time. We write “a little better than 84 percent chance” because you’ll notice that the stock price corresponding to the bottom line of the cone is around $42—a little higher than the strike price. The $40 mark might corre- spond to a chance of, let’s say, 13 percent that the stock will be lower; ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:314 SCORE: 14.00 ================================================================================ Notes  • 297 this would, in turn, imply an 87 percent chance of being higher than $40 in a year. 3. Tenor is just a specialty word used for options and bonds to mean the remaining time before expiration/maturity. We will see later that op- tion tenors usually range from one month to one year and that special long-term options have tenors of several years. 4. We’re not doing any advanced math to figure this out. We’re just eye- balling the area of the exposure range within the cone in this diagram and recalling that the area within the cone of the $60 strike, one-year option was about the same. 5. In other words, in this style of trading, people are anchoring on recent implied volatilities—rather than on recent statistical volatilities—to predict future implied volatilities. 6. Note that even though this option is now ITM, we did not pay for any intrinsic value when we bought the option. As such, we are shading the entire range of exposure in green. Chapter 4 1. The “capital” we have discussed so far is strategic capital. There is an- other form of tactical capital that is vital to companies, termed working capital. Working capital consists of the short-term assets essential for running a business (e.g., inventory and accounts receivables) less the short-term liabilities accrued during the course of running the busi- ness (e.g., accounts payable). Working capital is tactical in the sense that it is needed for day-to-day operation of the business. A company may have the most wonderful productive assets in the world, but if it does not have the money to buy the inventory of raw materials that will allow it to produce its widgets, it will not be able to generate revenues because it will not be able to produce anything. 2. The law of large numbers is actually a law of statistics, but when most people in the investing world use this phrase, it is the colloquial version to which they are referring. 3. Apple Computer, for instance, was a specialized maker of computers mainly used by designers and artists in the late 1990s. Through some ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:317 SCORE: 11.00 ================================================================================ 300 •   N o t e s 4. The original academic paper discussing prospect theory was published in Econometrica, Volume 47, Number 2, in March 1979 under the title: “Prospect Theory: An Analysis of Decision Under Risk. ” 5. Over the years, the paradigm for broker-dealers has changed, so some of what is written here is a bit dated. Broker-dealers have one part of its business dedicated to increasing customer “flow” as is described here. Over the last 20 years or so, however, they have additionally begun to capitalize what amounts to in-house hedge funds, called “proprietary trading desks” or “prop traders. ” While the prop traders are working on behalf of corporations that were historically known as broker-dealers (e.g., Goldman Sachs, Morgan Stanley), they are in fact buy-side institutions. In the interest of clarity in this chapter, I treat broker-dealers as purely sell-side entities even though they in fact have elements of both buy- and sell-sides. Chapter 7 1. Round-tripping means buying a security and selling it later. 2. This bit of shorthand just means a bid volatility of 22.0 and an ask volatility of 22.5. Chapter 8 1. This is one of the reasons why I called delta the most useful of the Greeks. 2. When I pulled these data, I pulled the 189-day options, so my chance of this stock hitting that high a price in this short time period is slim, but the point I am making here about percentage versus absolute re- turns still holds true. 3. A tool to calculate all the downside and upside leverage figures shown in this chapter is available on the intelligent option investor website. 4. “Buffett’s Alpha, ” Andrea Frazzini, David Kabiller, and Lasse H. Ped- ersen, 2012, National Bureau of Economic Research, NBER Working Paper No. 19681. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:320 SCORE: 9.00 ================================================================================ Notes  • 303 Appendix B 1. The idea behind this process is to match the timing of the costs of equipment with revenues from the items produced with that equip- ment. This is a key principle of accountancy called matching. 2. The problem is that troughs, by definition, follow peaks. Usually, just like the timing of large acquisitions, companies decide to spend huge amounts to build new production capacity at just about the same time that economic conditions peak, and the factories come online just as the economy is starting to sputter and fail. Appendix C 1. A penny saved is a penny earned. We can think of the option being cheaper by the amount of the dividend, so we will place the amount that we save on the call option in savings. 2. This is calculated using the following equation: Interest = strike × r × percent of 1 year In the case of the $18 strike, interest = 18 × 0.14% × (373 days/365 days per year) = $0.03. ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:322 SCORE: 12.00 ================================================================================ 305 A Absolute dollar value of returns, 172–173 Accuracy, confidence vs., 119–121 Acquisitions (see Mergers and acquisitions) Activist investors, 110 Against the Gods (Peter Bernstein), 9 Agents: buy-side, 132–136 defined, 131 investment strategies of, 137–138 principals vs., 131–132 sell-side, 136–137 AIG, 301n1 Allocation: and leverage in portfolios, 174–183 and liquidity risk, 256 and portfolio management with short-call spreads, 228–229 Alpha, 134 American-style options, 296n2 (Chapter 1) Analysis paralysis, 120 Anchoring, 60, 97 Announcements: and creating BSM cones, 156, 157 market conditions following, 68–69, 72–73 tenor and trading in expectation of, 192 AOL, 103 Apple Computer, 101, 250–251, 297–298n3 Arbitrage: defined, 288–289 dividend, 223, 288–293 Ask price, 147 Asset allocation, liquidity risk and, 256 Assets: defined, 78–79 fungible, 272–273 in golden rule of valuation, 77 hidden, 110, 111 idiosyncratic, 272 interchangeable, 272–273 mispriced, 274–277 operating, 110 price vs. value of, 79–80 underlying, 33–34, 272–273 Assets under management (AUM), 132 Assignment: with covered calls, 247–248 defined, 222–223 Assumptions: BSM model, 32–33, 40–47, 78, 150 dividend yield, 67 with forward volatility number, 156–157 time-to-expiration, 64–67 volatility, 60–64 At-the-money (ATM) options: BSM cone for, 53 collars, 259 covered calls, 242–243, 245, 246 defined, 13, 16, 17 long calls, 189 long diagonals, 235–237 Index ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:323 SCORE: 47.00 ================================================================================ 306  •   Index At-the-money (ATM) options: (continued) long straddles, 208–209 OTM options vs., 233–234 protective puts, 250–251, 253 short diagonals, 238, 240 short puts, 215, 216 short straddles, 230 short-call spreads, 222–225 AUM (assets under management), 132 B Balance-sheet effects, 92, 108–111 Behavior, efficient market hypothesis as model for, 41–42 Behavioral biases, 114–130 overconfidence, 118–122 pattern recognition, 114–118 perception of risk, 123–130 Behavioral economics, 42, 114 Bentley, 97–98 Berkshire Hathaway, 185 Bernstein, Peter, 9 Biases, behavioral (see Behavioral biases) Bid price, 147 Bid-ask spreads, 147–149 Bimodal outcomes, companies with, 277–278 Black, Fischer, 8–9 BlackBerry, 208–209 Black-Scholes-Merton (BSM) model, 9 assumptions of, 32–33, 40–47, 78, 150 conditions favoring, 269–273 conditions not favoring, 273–281 incorrect facets of, 29 predicting future stock prices from, 32–39 ranges of exposure and price predictions from, 50–56 theory of, 32 (See also BSM cone) Bonds, investing in short puts vs., 213–214 Booms, leverage during, 199 Breakeven line, 25 for call options, 15, 16 for long strangle, 26–27 for put options, 17, 18 (See also Effective buy price [EBP]) Broker-dealers, 137, 299–300n5 Brokers, benefits of short-term trading for, 64 BSM cone: for call options, 50–55 for collars, 258 for covered calls, 240–244 creating, 156–160 defined, 38–39 delta-derived, 151–155 discrepancies between valuation and, 160–162 for ITM options, 57–58 for long calls, 189 for long diagonals, 235 for long puts, 201 for long strangles, 205 overlaying valuation range on, 160 for protective puts, 248, 249 for put options, 54–55 for short diagonals, 238 for short puts, 212, 216, 217 for short straddles, 230 for short strangles, 231 for short-call spreads, 220 with simultaneous changes in variables, 68–74 and time-to-expiration assumptions, 64–67 and volatility assumptions, 60–64 BSM model (see Black-Scholes-Merton (BSM) model) Bubbles, 42–43 Buffett, Warren, xv, 184–185 Buying options (see Exposure-gaining strategies) Buy-side structural impediments, 132–136 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:324 SCORE: 21.00 ================================================================================ Index   • 307 C CAGR (compound annual growth rate), 46 Call options (calls): BSM cone for, 50–55 buying, for growth, 22 covered, 240–248 defined, 11 delta for, 151 dividend arbitrage with, 292–293 leverage with, 167–168 on quotes, 145 short, 14, 221 tailoring exposure with, 24 visual representation of, 12–16 and volatility, 68–74 (See also Covered calls; Long calls; Short-call spreads) Capital: investment, 183–184 strategic vs. working, 297n1 (Chapter 4) Capital asset pricing model (CAPM), 88, 298n4 Capital expense, 80 Career risk, 263 Cash, hedge size and, 257 Cash flows: on behalf of owners, 80–82 expansionary, 82, 104–108 in golden rule of valuation, 77 present value of future, 87–89 summing, from different time periods, 87–89 (See also Free cash flow to owners [FCFO]) “Catalysts, ” 137 CBOE (see Chicago Board Options Exchange) Central counterparties, 8 Change (option quotes), 146–147 Chanos, Jim, 202 Chicago Board Options Exchange (CBOE), 4, 8, 47 Chicago Mercantile Exchange, 8 China, joint ventures in, 84 Cisco Systems, 299n6 (Chapter 5) Closet indexing, 133 Closing prices: change in, 146–147 defined, 146 Collars, 258–262 Commitment, counterparties’ , 211 Commodities, options on, 6–7 Companies: with bimodal outcomes, 277–278 drivers of value for (see Value drivers) economic life of, 82–86, 93–94 economic value of, 137–139 operational details of, xiii–xiv, 110–111 Complex investment strategies, 142 Compound annual growth rate (CAGR), 46 Condors, 27–28 Confidence, accuracy vs., 119–121 Contingent loans, call options as, 167–168 Contract size, 146 Counterparties: central, 8 commitments of, 211 for options contracts, 295n1 (Chapter 1) Counterparty risk, 7–8 Covered calls, 23, 240–248, 301n4 about, 241–242 BSM cone, 240–244 execution of, 242–245 pitfalls with, 245–248 with protective puts, 259–262 Covering positions, 219, 228 Cremers, Martijn, 133 C-system, 115–118 Customer “flow, ” 299n5 (Chapter 6) ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:325 SCORE: 15.00 ================================================================================ 308  •   Index d Debt, investment leverage from, 165–166 Dell, 101 Delta, 151–155, 300n1 (Chapter 8) Demand-side constraints, 84–86 Depreciation, 282–284 Diagonals, 233 long, 235–237 short, 238–240 Directionality of options, 9–20 calls, 12–16 and exposure, 18–20 importance of, 27–28 puts, 16–18 and stock, 10–11 volatility and predications about, 68–74 Discount rate, 87–89, 298n5 Dispersion, 302n1 (Chapter 11) Distribution of returns: fat-tailed, 45 leptokurtic, 45 lognormal, 36–37 normal, 32, 36, 40, 43–45 Dividend arbitrage, 223, 288–293 Dividend yield, 67 Dividend-paying stocks, prices of, 35–36 Dividends, 86 Downturns, short puts during, 214–215 Drift: assumptions about, 32, 35–36 effects of, 67 and long calls, 202–203 and long puts, 191 and long strangles, 206 Drivers of value (see Value drivers) e Early exercise, 223 Earnings before interest, taxes, depreciation, and amortization (EBITDA), 99 Earnings before interest and taxes (EBIT), 99 Earnings per share (EPS), 99 Earnings seasons: and tenor of short puts, 217–218 volatility in, 301n5 EBIT (earnings before interest and taxes), 99 EBITDA (earnings before interest, taxes, depreciation, and amortization), 99 EBP (see Effective buy price) Economic environment, profitability and, 101 Economic life of companies: and golden rule of valuation, 82–86 improving valuations by understanding, 93–94 Economic value of companies, 137–139 Effective buy price (EBP), 24–25, 213, 244 Effective sell price (ESP), 25–26 Efficacy (see Investing level and efficacy) Efficient market hypothesis (EMH), 33, 34, 40–43 Endowments, 135, 136 Enron, 110 EPS (earnings per share), 99 ESP (effective sell price), 25–26 European-style options, 296n2 (Chapter 1) Exchange-traded funds (ETFs), options on, 251–252 Execution of option overlay strategies: collars, 259–262 covered calls, 242–245 protective puts, 250–252 Exercising options, 13, 296n2 (Chapter 1) Expansionary cash flows, 82, 104–108 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:326 SCORE: 42.00 ================================================================================ Index   • 309 Expiration of options, 187 Explicit forecast stage, 93–96 Exposure: accepting, 14, 18–20 canceling out, 18–20 gaining, 13, 18–20 notional, 173 tailoring level of, 24 (See also Ranges of exposure) Exposure-accepting strategies, 211–232 margin requirements for, 211–212 short call, 220–230 short put, 212–220 short straddle, 230–232 short strangle, 231–232 Exposure-gaining strategies, 187–209 and expiration of options, 187 long call, 189–201 long put, 201–205 straddle, 208–209 strangle, 205–207 Exposure-mixing strategies, 233–262 collar, 258–262 covered call, 240–248 long diagonal, 235–237 and OTM vs. ATM options, 233–234 protective put, 248–258 short diagonal, 238–240 Exxon, 299n4 (Chapter 5) F False precision, 93, 96–97 Fama, Eugene, 42 Fat-tailed distribution, 45 FCFO (see Free cash flow to owners) “Fight or flight” response, 118 Financial crises, 302n2 (Chapter 11) Financial leverage: defined, 285–286 investment vs., 164 and level of investment leverage, 197–199 Financial statements, xv Flexibility (with option investing), 20–28 Float, 185 Ford, 103, 272 Forward prices: adding ranges to, 36–39 calculating, 34–36 defined, 35–36 ranges of exposure and, 50–56 Forward volatility: choosing forward volatility number, 156–160 defined, 59–61 and strike–stock price ratio, 67–74 Free cash flow to owners (FCFO): defined, 82 and drivers of value, 111–112 in joint ventures, 84 and supply-side constraints, 83 Front-month contracts, 270 Fungible assets, 272–273 G Gains, levered vs. unlevered, 165 Gaussian distribution (see Normal distribution) GDP (gross domestic product), 104–108 Gillette Razors, 84 GM, 272 Goals, for hedges, 257 “Going long, ” 10, 21 “Going short, ” 21 Golden rule of valuation, 77–89 cash flows generated on behalf of owners in, 80–82 and definition of assets, 78–80 and drivers of value, 91–92 and economic life of company, 82–86 and summing cash flows from different time periods, 87–89 Google, 84, 127–130, 190 “Greeks, ” xiv, 295n3 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:327 SCORE: 19.00 ================================================================================ 310  •   Index Gross domestic product (GDP), 104–108 Growth: buying call options for, 22 nominal GDP , 104–108 revenue, 92, 97–99 structural growth stage, 94, 95 H Hedge funds, 132–134, 136 Hedge funds of funds (HFoF), 134 Hedges: reinvesting profit from, 254–255 size of, 255–258 timing of, 252–254 Hedging: planning for, 255–258 for portfolios, 251–252 Herding, 138, 299n1 HFoF (hedge funds of funds), 134 Historical volatility, 60 Hostile takeovers, 110 The Human Face of Big Data (Rick Smolan), 114 I IBM, 224–230, 299n5 (Chapter 5), 301n6 Idiosyncratic assets, 272 Immediate realized loss (IRL), 180, 183 Implied volatility: bid/ask, 149–151 changing assumptions about, 60–64 and short puts, 216–217 Income, selling put options for, 23 Indexing, closet, 133 Insurance, 5, 250 Insurance companies, 135, 136 Intel, 175 Interchangeable assets, 272–273 Interest: calculating, 303n2 options and payment on, 168 prepaid, 170 Interest rates, 67 In-the-money (ITM) options: calls vs. puts, 27 covered calls, 242 defined, 13, 16, 17 investment leverage for, 170–172 levered strategy with, 176–180 long calls, 189, 193–197 long diagonals, 236 long puts, 204 managing leverage with, 183–184 and market risk, 263–264 pricing of, 56–59, 150 protective puts, 249–251 short puts, 213–215 short-call spread, 222, 223 time decay for, 66–67 Intrinsic value, 56–59, 171 Investing level and efficacy, 92, 103–108 Investment capital, leverage and, 183–184 Investment leverage, 163–185 from debt, 165–166 defined, 164 managing, 183–185 margin of safety for, 197–199 measuring, 169–173 from options, 166–168 and portfolio management, 196–197 in portfolios, 174–183 unlevered investments, 164–165 Investment phase (investment stage), 86, 93–96 Investors: activist, 110 risk-averse, 123, 125–127 risk-neutral, 124–126 risk-seeking, 123, 125–127 IRL (immediate realized loss), 180, 183 ITM (see In-the-money options) ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:328 SCORE: 23.00 ================================================================================ Index   • 311 J Jaguar, 103 Joint ventures (JVs), 84–85 JP Morgan Chase, 236–237 K Kahneman, Daniel, 42, 123, 126 Keen, Steven, 43 Keynes, John Maynard, 263 Kroger, 100 K/S (see Strike–stock price ratio) L Lambda, 169–173 Large numbers, law of, 85, 297n2 (Chapter 4) Last (option quotes), 146 LEAPS (see Long-term equity anticipated securities) Legs (option structure), 27 Lehman Brothers, 264 Lenovo, 299n5 (Chapter 5) Leptokurtic distribution, 45 Leverage, 163, 282–286 financial, 164, 197–199, 285–286 operating (operational), 101, 197–199, 282–284 (See also Investment leverage) Leverage ratio, 228–229 Levered investments, portfolios with, 176–183 Liabilities, hidden, 110–111 Life insurance companies, 135 Liquidity risk, 256, 263 Listed look-alike option market, 6 Literary work, options on, 5–6 Lo, Andrew, 42 Load, 132, 134 Loans, call options as, 167–168 Lognormal curve, 37 Lognormal distribution, 36–37 Long calls, 13, 189–201 about, 189 BSM cone, 189 in long diagonals, 235–237 portfolio management with, 196–201 strike price for, 192–196 tenor for, 190–192 Long diagonals, 235–237 Long puts, 201–205 about, 201–202 BSM cone, 201 portfolio management with, 204–205 in short diagonals, 238–240 strike price for, 203 tenor for, 202–203 Long straddles, 208–209 Long strangles, 26–27, 205–207, 209 Long-term equity anticipated securities (LEAPS), 153, 191, 280–281 Loss leverage: conventions for, 182–183 formula, 178–179 with short puts, 211–212 Losses: with levered vs. unlevered instruments, 165–166 locking in, 245–247 on range of exposure, 15 unrealized, 175–176 (See also Realized losses) M MacKinlay, Craig, 42 Margin calls, 168 Margin of safety, 197–199 Margin requirements, 211–212 Market conditions, 59–74 assumptions about drift and dividend yield, 67 simultaneous changes in, 67–74 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:329 SCORE: 29.00 ================================================================================ 312  •   Index Market conditions (continued) time-to-expiration assumptions, 64–67 and types of volatility, 59–60 volatility assumptions, 60–64 Market efficiency, 32–34, 40–43 Market makers, 147, 281 Market risk, 263–265 Matching, 302n1 (Appendix B) Maximum return, 225 Mergers and acquisitions: strike prices selection and, 195–196 tenor and, 191–192 Merton, Robert, 8–9 Miletus, 6–7 Mispriced assets, 274–277 Mispriced options, 143–162 deltas of, 151–155 reading option quotes, 144–151 and valuation risk, 266 and valuation vs. BSM range, 155–162 Moneyness of options: calls, 13–14 puts, 16–17 Morningstar, 132 Most likely (term), 38 Motorola Mobility Systems, 84 Mueller Water, 148–149, 154, 158–160 Multiples-based valuation, 99–100 Mutual funds, 132–133, 136 n Nominal GDP growth: owners’ cash profit vs., 104–108 as structural constraint, 104 Normal distribution, 32, 36, 40, 43–45 Notional amount of position, 173 Notional exposure, 173 O OCC (Options Clearing Corporation), 8 OCP (see Owners’ cash profit) Operating assets, 110 Operating leverage (operational leverage): defined, 282–284 and level of investment leverage, 197–199 and profitability, 101 Operational details of companies, xiii–xiv, 110–111 Option investing: choices in, 22–24 conditions favoring BSM, 269–273 conditions not favoring BSM, 273–281 flexibility in, 20–28 long-term strategies, 1 misconceptions about, 1 risk in, 268 shortcuts for valuation in, 93–97 stock vs., 21–22 strategies for, 142 (See also specific types of strategies) structural impediments in, 131–139 three-step process, xiv valuation in, 75 Option pricing, 29–47, 49–74 and base assumptions of BSM, 40–47 market conditions in, 59–74 predicting future stock prices from, 32–39 and ranges of exposure, 50–56 theory of, 30–32 time vs. intrinsic value in, 56–59 Option pricing models: base assumptions of, 40–47 history of, 8–9 operational details of companies in, xiii–xiv predicting future stock prices with, 32–39 ranges of exposure and price predictions from, 50–56 (See also Black-Scholes-Merton [BSM] model) Option quotes, 144–151 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:330 SCORE: 21.00 ================================================================================ Index   • 313 Optionality, 4 Options, 3–28 buying (see Exposure-gaining strategies) characteristics of, 4 defined, 4 directionality of, 9–20 examples of, 5–6 expiration of, 187 history of, 6–9 investment leverage from, 166–168 misconceptions about, 1 mispriced, 143–162 (See also specific types) Options Clearing Corporation (OCC), 8 Options contracts: counterparties for, 295n1 (Chapter 1) examples of, 5–6 front-month, 270 private, 6–8 Oracle, 107–108, 144, 146, 148–153, 155, 157, 159–162 Organic revenue growth, 97 Out-of-the-money (OTM) options: ATM options vs., 233–234 call vs. put, 27 collars, 258–262 defined, 13, 16, 17 investment leverage for, 171–172 levered strategy with, 180, 181 long calls, 193, 195–197 long diagonals, 235–237 long puts, 203, 204 long strangles, 205–207 and market makers, 147 pricing of, 150 protective puts, 248, 250–253 realized losses and, 187 rising volatility and, 70–74 short diagonals, 238–240 short puts, 213, 215 short strangles, 231 short-call spreads, 221–224 time decay for, 66–67 unrealized losses, 187 Overconfidence, 118–122 Overexposure, 247 Overlays, 23, 234 Owners: cash flows generated on behalf of, 80–82 free cash flow to (see Free cash flow to owners (FCFO)) Owners’ cash profit (OCP): defined, 82 nominal GDP growth vs., 104–108 profitability as, 99–102 P Parity, 288 Pattern recognition, 114–118 Peaks (business-cycle): operational leverage in, 284 and troughs, 302–303n2 Pension funds, 135, 136 Percent delta, 169–173 Percent profit, 172–173 Percentage return, 229 Portfolio management: for long calls, 196–201 for long puts, 204–205 for long strangles, 207 for short puts, 216–220 for short-call spreads, 228–230 Portfolios: hedging, 251–252 investment leverage in, 174–183 Precision, false, 93, 96–97 Premium, 13 Prepaid interest, 170 Present value of future cash flows, 87–89 Pricing power, 98 Principal (financial), 168 Principals, agents vs., 131–132 Problem solving, X- vs. C-system, 115–118 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:331 SCORE: 21.00 ================================================================================ 314  •   Index Procter & Gamble, 84 Productivity, 102 Profit: from covered calls, 245 from hedging, 254–255 owners’ cash, 82 percent, 172–173 Profit leverage, 179–180, 182–183 Profitability: and financial leverage, 285–286 and operational leverage, 283–284 as value driver, 92, 99–102 Proprietary trading desks (prop traders), 300n5 Prospect theory, 123–127 Protective puts, 248–258 about, 248–250 BSM cone, 248, 249 with covered calls, 259–262 execution of, 250–252 pitfalls with, 252–258 Pure Digital, 299n6 (Chapter 5) Put options (puts): BSM cone for, 54–55 buying, for protection, 23 defined, 11 delta for, 151 on quotes, 145 selling, for income, 23 tailoring exposure with, 24 visual representation of, 16–18 (See also Long puts; Protective puts; Short puts) Put-call parity, 223, 287–293 defined, 287–288 and dividend arbitrage, 288–293 for non-dividend-paying stock, 289–290 Q Qualcomm, 260–262 Quotes, option, 144–151 R Random-walk principal, 41 Ranges of exposure, 3 for call options, 12–13, 15 for ITM options, 58–59 and option pricing, 50–56 Rankine, Graeme, 41–42 Ratioing, 206, 238 Realized losses: and buying puts, 203 immediate, 180, 183 managing leverage to minimize, 183–185 and option buying, 187–188 unrealized vs., 175–176 Recessions, leverage during, 198, 199 Reflective thought processes, 116–118 Reflexive thought processes, 116–118 Return(s): absolute dollar value of, 172–173 for covered calls, 244–245 maximum, 225 percentage, 229 for short puts, 245 (See also Distribution of returns) Revenue growth, 92, 97–99 Risk, 263–268 career, 263 counterparty, 7–8 liquidity, 256, 263 market, 263–265 in option investing, 267–268 perception of, 123–130 and size of hedges, 255–256 solvency, 256, 263 valuation, 265–267 Risk-averse investors, 123, 125–127 Risk-free rate: borrowing at, 32, 40, 46 BSM model assumption about, 32, 35–36, 40, 45–46 Risk-neutral investors, 124–126 Risk-seeking investors, 123, 125–127 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:332 SCORE: 16.00 ================================================================================ Index   • 315 Rolling, 200–201 Round-tripping, 148–149, 300n1 (Chapter 7) S Safeway, 100 Schiller, Robert, 43 Scholes, Myron, 8–9 Secular downturns, 302n2 (Chapter 11) Secular shifts, profitability and, 101–102 Sell-side structural impediments, 136–137 Settlement prices, 146 Shiller, Robert, 42 Short calls, 14, 221 Short diagonal, 238–240 Short puts, 211–220 about, 213–214 BSM cone, 212 covered calls and, 241–244 in long diagonals, 235–237 loss leverage with, 211–212 portfolio management with, 216–220 protective puts vs., 248–250 returns for, 245 strike price for, 215 tenor for, 214–215 Short straddles, 230–232 Short strangles, 231–232 Short-call spreads, 220–230 about, 221–222 BSM cone, 220 portfolio management with, 228–230 in short diagonals, 238–240 strike price for, 222–228 tenor for, 222 Short-term trading strategies: implied volatility in, 63–64 intelligent investing vs., 267–268 and market risk, 264–265 Slovic, Paul, 119 Smolan, Rick, 114 Solvency risk, 256, 263 S&P 500 (see Standard & Poor’s 500 Index) Special-purpose vehicles, 110 Spreads: bid-ask, 147–149 short-call (see Short-call spreads) SPX ETF , 251–252 Standard & Poor’s 500 Index (S&P 500): correlation of hedge funds and, 134 distribution of returns, 44–46 protective puts on, 252–254 Startup stage, 86 Statistical volatility, 60 Stock investing, xiii choices in, 20–22 visual representation of, 10–11 Stock prices: BSM model assumption about, 32, 34–35, 40–47 directional predictions of, 68–74 of dividend-paying stocks, 35–36 predicting, with BSM model, 32–39 (See also Forward prices; strike– stock price ratio [K/S]) Stock-split effect, 42 Stop loss, 229 Straddles: long, 208–209 short, 230–232 Straight-line depreciation, 283 Strangles: long, 26–27, 205–207, 209 short, 231–232 Strategic capital, 297n1 (Chapter 4) Strike prices: and BSM cone, 52–54 defined, 12 long call, 192–196 long diagonal, 236–237 long put, 203 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:333 SCORE: 23.00 ================================================================================ 316  •   Index Strike prices: (continued ) long strangle, 206–207 short diagonal, 239–240 short put, 215 short-call spread, 222–228 Strike–stock price ratio (K/S): and change in closing price, 146–147 defined, 53–54 and forward volatility, 67–74 Structural constraints, 86, 104 Structural downturns, 302n2 (Chapter 11) Structural growth stage, 94, 95 Structural impediments, 131–139 buy-side, 132–136 and investment strategies, 137–139 principals vs. agents, 131–132 sell-side, 136–137 Sun Microsystems, 108 Supply-side constraints, 83 Symmetry, bias associated with, 114–118 T “Taking profit” with covered calls, 245 Taxes, BSM model assumption about, 32, 40, 46 Technical analysis, 115 Tenor, 297n3 (Chapter 3) defined, 59 for long calls, 190–192 for long puts, 202–203 for long strangles, 206 for protective puts, 252–254 for short puts, 214–215 for short-call spreads, 222 Terminal phase, 86 Time decay, 65–67 Time horizons: long, 279–281 short, 270–272 Time value: intrinsic vs., 56–59 of money, 87, 93–95 Time Warner, 103 Time-to-expiration assumptions, 64–67 Toyota, 97 Trading restrictions, 32, 40, 46 Troughs (business-cycle): operational leverage in, 283–284 and peaks, 302–303n2 Tversky, Amos, 123, 126 “2-and-20” arrangements, 134 U Uncertainty, 118–119 Underexposure, 247 Underlying assets: fungible, 272–273 and future stock price, 33–34 University of Chicago, 41 Unlevered investments: levered vs., 164–165 in portfolios, 175–176, 178 Unrealized losses, 175–176 Unrealized profit, 254–255 Unused leg, long strangle, 207 U.S. Treasury bonds, 45–46 Utility curves, 124–126 V Valuation: golden rule of, 77–89 multiples-based, 99–100 shortcuts for, 93–97 value drivers in, 91–97 Valuation range: BSM cone vs., 160–162 creating, 122 and margins of safety, 197–199 overlaying BSM cone with, 160 and strike price selection, 192–194 Valuation risk, 265–267 ================================================================================ SOURCE: eBooks\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options\Erik Kobayashi-Solomon - The Intelligent Option Investor- Applying Value Investing to the World of Options.pdf#page:336 SCORE: 10.00 ================================================================================ ABOUT THE AUTHOR erik Kobayashi-Solomon, a veteran from the investment banking and hedge fund world, is the founder and principal of IOI, LLC a financial consultancy for individual and institutional investors. In addition to publishing an institutional investor-focused subscription product, Erik runs option and investment “boot camps” and consults on risk control, option strategies, and stock valuations for individual and institutional investors. Before starting IOI, Erik worked for Morningstar in its stock research department for over six years. At Morningstar, he first managed a team of semiconductor industry analysts before becoming the coeditor and driv- ing force of Morningstar’s OptionInvestor newsletter and serving as the company’s Market Strategist. In addition to coauthoring a guide to fundamental investing and option strategies used in the Morningstar Investor Training Options Course and popular weekly articles about using options as a tool for in- vestment portfolios, Erik was the host of several popular webinars such as “Covered Calls A to Z” and “Hedging 101. ” His video lecture about avoid- ing behavioral and structural pitfalls called “Making Better Investment Decisions” was so popular that he was invited to be the featured speaker at several investment conferences throughout the United States. In addition, he represented Morningstar on television and radio, was interviewed by magazines and newspapers from Dallas to Tokyo to New Delhi, and was a frequent guest contributor to other Morningstar/Ibbotson publications. Erik started his career in the world of finance at Morgan Stanley Japan, where he ultimately headed Morgan’s listed derivatives operations in Tokyo. After returning to the United States, Erik founded a small hedge ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:15 SCORE: 28.00 ================================================================================ Preface When the listed option market originated in April 1973, a new world of investment strategies was opened to the investing public. The standardization of option terms and the formation of a liquid secondary market created new investment vehicles that, adapted properly, can enhance almost every investment philosophy, from the con­ servative to the speculative. This book is about those option strategies -which ones work in which situations and why they work. Some of these strategies are traditionally considered to be complex, but with the proper knowledge of their underlying principles, most investors can understand them. While this book contains all the basic definitions concerning options, little time or space is spent on the most elementary definitions. For example, the reader should be familiar with what a call option is, what the CBOE is, and how to find and read option quotes in a newspaper. In essence, everything is contained here for the novice to build on, but the bulk of the discussion is above the beginner level. The reader should also be somewhat familiar with technical analysis, understanding at least the terms support and resistance. Certain strategies can be, and have been, the topic of whole books - call buy­ ing, for example. While some of the strategies discussed in this book receive a more thorough treatment than others, this is by no means a book about only one or two strategies. Current literature on stock options generally does not treat covered call writing in a great deal of detail. But because it is one of the most widely used option strategies by the investing public, call writing is the subject of one of the most in­ depth discussions presented here. The material presented herein on call and put buying is not particularly lengthy, although much of it is of an advanced nature - especially the parts regarding buying volatility and should be useful even to sophis­ ticated traders. In discussing each strategy, particular emphasis is placed on showing why one would want to implement the strategy in the first place and on demonstrat- xv ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:16 SCORE: 37.00 ================================================================================ xviii Preface are made for using the computer as a tool in follow-up action, including an example printout of an advanced follow-up analysis. THIRD EDITION There were originally six new chapters in the third edition. There were new chapters on LEAPS, CAPS, and PERCS, since they were new option or option-related prod­ ucts at that time. LEAPS are merely long-term options. However, as such, they require a little different viewpoint than regular short-term options. For example, short-term inter­ est rates have a much more profound influence on a longer-term option than on a short-term one. Strategies are presented for using LEAPS as a substitute for stock ownership, as well as for using LEAPS in standard strategies. PERCS are actually a type of preferred stock, with a redemption feature built in. They also pay significantly larger dividends than the ordinary common stock. The redemption feature makes a PERCS exactly like a covered call option write. As such, several strategies apply to PERCS that would also apply to covered writers. Moreover, suggestions are given for hedging PERCS. Subsequently, the PERCS chapter was enveloped into a larger chapter in the fourth edition. The chapters on futures and other non-equity options that were written for the second edition were deleted and replaced by two entirely new chapters on futures options. Strategists should familiarize themselves with futures options, for many prof­ it opportunities exist in this area. Thus, even though futures trading may be unfamil­ iar to many customers and brokers who are equity traders, it behooves the serious strategist to acquire a knowledge of futures options. A chapter on futures concentrates on definitions, pricing, and strategies that are unique to futures options; another chap­ ter centers on the use of futures options in spreading strategies. These spreading strategies are different from the ones described in the first part of the book, although the calendar spread looks similar, but is really not. Futures traders and strategists spend a great deal of time looking at futures spreads, and the option strategies pre­ sented in this chapter are designed to help make that type of trading more profitable. A new chapter dealing with advanced mathematical concepts was added near the end of the book. As option trading matured and the computer became more of an integral way of life in monitoring and evaluating positions, more advanced tech­ niques were used to monitor risk. This chapter describes the six major measures of risk of an option position or portfolio. The application of these measures to initialize positions that are doubly or triply neutral is discussed. Moreover, the use of the com­ puter to predict the results and "shape" of a position at points in the future is described. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:17 SCORE: 20.00 ================================================================================ Preface xix There were substantial revisions to the chapters on index options as well. Part of the revisions are due to the fact that these were relatively new products at the time of the writing of the second edition; as a result, many changes were made to the prod­ ucts - delisting of some index options and introduction of others. Also, after the crash of 1987, the use of index products changed somewhat (with introduction of circuit breakers, for example). FOURTH EDITION Once again, in the ever-changing world of options and derivatives, some new important products have been introduced and some new concepts in trading have come to the forefront. Meanwhile, others have been delisted or fallen out of favor. There are five new chapters in the fourth edition, four of which deal with the most important approach to option trading today - volatility trading. The chapter on CAPS was deleted, since CAPS were delisted by the option exchanges. Moreover, the chapter on PERCS was incorporated into a much larger and more comprehensive chapter on another relatively new trading vehicle - struc­ tured products. Structured products encompass a fairly wide range of securities - many of which are listed on the major stock exchanges. These versatile products allow for many attractive, derivative-based applications - including index funds that have limited downside risk, for example. Many astute investors buy structured prod­ ucts for their retirements accounts. Volatility trading has become one of the most sophisticated approaches to option trading. The four new chapters actually comprise a new Part 6 - Measuring And Trading Volatility. This new part of the book goes in-depth into why one should trade volatility (it's easier to predict volatility than it is to predict stock prices), how volatility affects common option strategies - sometimes in ways that are not initially obvious to the average option trader, how stock prices are distributed ( which is one of the reasons why volatility trading "works"), and how to construct and monitor a volatility trade. A number of relatively new techniques regarding measuring and pre­ dicting volatility are presented in these chapters. Personally, I think that volatility buying of stock options is the most useful strategy, in general, for traders of all levels - from beginners through experts. If constructed properly, the strategy not only has a high probability of success, but it also requires only a modest amount of work to monitor the position after it has been established. This means that a volatility buyer can have a "life" outside of watching a screen with dancing numbers on it all day. Moreover, most of the previous chapters were expanded to include the latest techniques and developments. For example, in Chapter 1 (Definitions), the entire area of option symbology has been expanded, because of the wild movements of ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:18 SCORE: 42.00 ================================================================================ xx Preface stocks in the past few years. Also, the margin rules were changed in 2000, and those changes are noted throughout the book. Those chapters dealing with the sale of options - particularly naked options - have been expanded to include more discussion of the way that stocks behave and how that presents problems and opportunities for the option writer. For example, in the chapter on Reverse Spreads, the reverse calendar spread is described in detail because - in a high-volatility environment - the strategy becomes much more viable. Another strategy that receives expanded treatment is the "collar" - the purchase of a put and simultaneous sale of a call against an underlying instrument. In fact, a similar strategy can be used - with a slight adjustment - by the outright buyer of an option (see the chapter on Spreads Combining Puts and Calls). I am certain that many readers of this book expect to learn what the "best" option strategy is. While there is a chapter discussing this subject, there is no defin­ itively "best" strategy. The optimum strategy for one investor may not be best for another. Option professionals who have the time to monitor positions closely may be able to utilize an array of strategies that could not possibly be operated diligently by a public customer employed in another full-time occupation. Moreover, one's partic­ ular investment philosophy must play an important part in determining which strat­ egy is best for him. Those willing to accept little or no risk other than that of owning stock may prefer covered call writing. More speculative strategists may feel that low­ cost, high-profit-potential situations suit them best. Every investor must read the Options Clearing Corporation Prospectus before trading in listed options. Options may not be suitable for every investor. There are risks involved in any investment, and certain option strategies may involve large risks. The reader must determine whether his or her financial situation and investment objectives are compatible with the strategies described. The only way an investor can reasonably make a decision on his or her own to trade options is to attemptto acquire a knowledge of the subject. Several years ago, I wrote that "the option market shows every sign of becom­ ing a stronger force in the investment world. Those who understand it will be able to benefit the most." Nothing has happened in the interim to change the truth of that statement, and in fact, it could probably be even more forcefully stated today. For example, the Federal Reserve Board now often makes decisions with an eye to how derivatives will affect the markets. That shows just how important derivatives have become. The purpose of this book is to provide the reader with that understanding of options. I would like to express my appreciation to several people who helped make this book possible: to Ron Dilks and Howard Whitman, who brought me into the bro- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:23 SCORE: 40.00 ================================================================================ CHAPTER 1 Definitions The successful implementation of various investment strategies necessitates a sound working knowledge of the fundamentals of options and option trading. The option strategist must be familiar with a wide range of the basic aspects of stock options how the price of an option behaves under certain conditions or how the markets function. A thorough understanding of the rudiments and of the strategies helps the investor who is not familiar with options to decide not only whether a strategy seems desirable, but also - and more important - whether it is suitable. Determining suit­ ability is nothing new to stock market investors, for stocks themselves are not suitable for every investor. For example, if the investor's primary objectives are income and safety of principal, then bonds, rather than stocks, would be more suitable. The need to assess the suitability of options is especially important: Option buyers can lose their entire investment in a short time, and uncovered option writers may be subjected to large financial risks. Despite follow-up methods designed to limit risk, the individual investor must decide whether option trading is suitable for his or her financial situa­ tion and investment objective. ELEMENTARY DEFINITIONS A stock option is the right to buy or sell a particular stock at a certain price for a lim­ ited period of time. The stock in question is called the underlying security. A call option gives the owner ( or holder) the right to buy the underlying security, while a put option gives the holder the right to sell the underlying security. The price at which the stock may be bought or sold is the exercise price, also called the striking price. (In the listed options market, "exercise price" and "striking price" are synony­ mous.) A stock option affords this right to buy or sell for only a limited period of time; 3 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:24 SCORE: 83.00 ================================================================================ 4 Part I: Basic Properties of Stodc Options thus, each option has an expiration date. Throughout the book, the term "options" is always understood to mean listed options, that is, options traded on national option exchanges where a secondary market exists. Unless specifically mentioned, over-the­ counter options are not included in any discussion. DESCRIBING OPTIONS Four specifications uniquely describe any option contract: 1. the type (put or call), 2. the underlying stock name, 3. the expiration date, and 4. the striking price. As an example, an option referred to as an "XYZ July 50 call" is an option to buy (a call) 100 shares (normally) of the underlying XYZ stock for $50 per share. The option expires in July. The price of a listed option is quo!_ed on a per-share basis, regardless of how many shares of stock can be bought with the option. Thus, if the price of the XYZ July 50 call is quoted at $5, buying the option would ordinarily cost $500 ($5 x 100 shares), plus commissions. THE VALUE OF OPTIONS An option is a "wasting" asset; that is, it has only an initial value that declines (or "wastes" away) as time passes. It may even expire worthless, or the holder may have to exercise it in order to recover some value before expiration. Of course, the holder may sell the option in the listed option market before expiration. An option is also a security by itself, but it is a derivative security. The option is irrevocably linked to the underlying stock; its price fluctuates as the price of the underlying stock rises or falls. Splits and stock dividends in the underlying stock affect the terms of listed options, although cash dividends do not. The holder of a call does not receive any cash dividends paid by the underlying stock. STANDARDIZATION The listed option exchanges have standardized the terms of option contracts. The terms of an option constitute the collective name that includes all of the four descrip­ tive specifications. While the type (put or call) and the underlying stock are self-evi­ dent and essentially standardized, the striking price and expiration date require more explanation. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:25 SCORE: 46.00 ================================================================================ Chapter 1: Definitions s Striking Price. Striking prices are generally spaced 5 points apart for stocks, although for more expensive stocks, the striking prices may be 10 points apart. A $35 stock might, for example, have options with striking prices, or "strikes," of 30, 35, and 40, while a $255 stock might have one at 250 and one at 260. Moreover, some stocks have striking prices that are 2½ points apart - generally those selling for less than $35 per share. That is, a $17 stock might have strikes at 15, 17½, and 20. These striking price guidelines are not ironclad, however. Exchange officials may alter the intervals to improve depth and liquidity, perhaps spacing the strikes 5 points apart on a nonvolatile stock even if it is selling for more than $100. For exam­ ple, if a $155 stock were very active, and possibly not volatile, then there might well be a strike at 155, in addition to those at 150 and 160. Expiration Dates. Options have expiration dates in one of three fixed cycles: L the January/April/July/October cycle, 2. the February/May/August/November cycle, or 3. the March/June/September/December cycle. In addition, the two nearest months have listed options as well. However, at any given time, the longest-term expiration dates are normally no farther away than 9 months. Longer-term options, called LEAPS, are available on some stocks (see Chapter 25). Hence, in any cycle, options may expire in 3 of the 4 major months (series) plus the near-term months. For example, on February 1 of any year, XYZ options may expire in February, March, April, July, and October - not in January. The February option ( the closest series) is the short- or near-term option; and the October, the far- or long­ term option. If there were LEAPS options on this stock, they would expire in January of the following year and in January of the year after that. The exact date of expiration is fixed within each month. The last trading day for an option is the third Friday in the expiration month. Although the option actually does not expire until the following day (the Saturday following), a public customer must invoke the right to buy or sell stock by notifying his broker by 5:30 P.M., New York time, on the last day of trading. THE OPTION ITSELF: OTHER DEFINITIONS Classes and Series. A class of options refers to all put and call contracts on the same underlying security. For instance, all IBM options - all the puts and calls at various strikes and expiration months - form one class. A series, a subset of a class, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:26 SCORE: 72.00 ================================================================================ 6 Part I: Basic Properties of Stock Options consists of all contracts of the same class (IBM, for example) having the same expi­ ration date and striking price. Opening and Closing Transactions. An opening transaction is the ini­ tial transaction, either a buy or a sell. For example, an opening buy transaction creates or increases a long position in the customer's account. A closing trans­ action reduces the customer's position. Opening buys are often followed by clos­ ing sales; correspondingly, opening sells often precede closing buy trades. Open Interest. The option exchanges keep track of the number of opening and closing transactions in each option series. This is called the open interest. Each opening transaction adds to the open interest and each closing transaction decreases the open interest. The open interest is expressed in number of option contracts, so that one order to buy 5 calls opening would increase the open interest by 5. Note that the open interest does not differentiate between buyers and sellers - there is no way to tell if there is a preponderance of either one. While the magnitude of the open interest is not an extremely important piece of data for the investor, it is useful in determining the liquidity of the option in question. If there is a large open interest, then there should be little problem in making fairly large trades. However, if the open interest is small - only a few hundred contracts outstanding - then there might not be a reasonable second­ ary market in that option series. The Holder and Writer. Anyone who buys an option as the initial transac­ tion - that is, buys opening - is called the holder. On the other hand, the investor who sells an option as the initial transaction - an opening sale - is called the writer of the option. Commonly, the writer ( or seller) of an option is referred to as being short the option contract. The term "writer" dates back to the over­ the-counter days, when a direct link existed between buyers and sellers of options; at that time, the seller was the writer of a new contract to buy stock. In the listed option market, however, the issuer of all options is the Options Clearing Corporation, and contracts are standardized. This important difference makes it possible to break the direct link between the buyer and seller, paving the way for the formation of the secondary markets that now exist. Exercise and Assignment. An option owner ( or holder) who invokes the right to buy or sell is said to exercise the option. Call option holders exercise to buy stock; put holders exercise to sell. The holder of most stock options may exercise the option at any time after taking possession of it, up until 8:00 P.M. on ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:27 SCORE: 110.00 ================================================================================ O,apter 1: Definitions 7 the last trading day; the holder does not have to wait until the expiration date itself before exercising. (Note: Some options, called "European" exercise options, can be exercised only on their expiration date and not before - but they are generally not stock options.) These exercise notices are irrevocable; once generated, they cannot be recalled. In practical terms, they are processed only once a day, after the market closes. Whenever a holder exercises an option, somewhere a writer is assigned the obligation to fulfill the terms of the option contract: Thus, if a call holder exercises the right to buy, a call writer is assigned the obligation to sell; conversely, if a put holder exercises the right to sell, a put writer is assigned the obligation to buy. A more detailed description of the exer­ cise and assignment of call options follows later in this chapter; put option exer­ cise and assignment are discussed later in the book. RELATIONSHIP OF THE OPTION PRICE AND STOCK PRICE In- and Out-of-the-Money. Certain terms describe the relationship between the stock price and the option's striking price. A call option is said to be out-of-the­ money if the stock is selling below the striking price of the option. A call option is in­ the-money if the stock price is above the striking price of the option. (Put options work in a converse manner, which is described later.) Example: XYZ stock is trading at $47 per share. The XYZ July 50 call option is out­ of-the-money, just like the XYZ October 50 call and the XYZ July 60 call. However, the XYZ July 45 call, XYZ October 40, and XYZ January 35 are in-the-money. The intrinsic value of an in-the-money call is the amount by which the stock price exceeds the striking price. If the call is out-of-the-money, its intrinsic value is zero. The price that an option sells for is commonly referred to as the premium. The premium is distinctly different from the time value premium ( called time premium, for short), which is the amount by which the option premium itself exceeds its intrin­ sic value. The time value premium is quickly computed by the following formula for an in-the-money call option: Call time value premium = Call option price + Striking price - Stock price Example: XYZ is trading at 48, and XYZ July 45 call is at 4. The premium - the total price - of the option is 4. With XYZ at 48 and the striking price of the option at 45, the in-the-money amount (or intrinsic value) is 3 points (48-45), and the time value isl(4-3). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:28 SCORE: 74.00 ================================================================================ 8 Part I: Basic Properties ol Stoclc Options If the call is out-of-the-money, then the premium and the time value premium are the same. Example: With XYZ at 48 and an XYZ July 50 call selling at 2, both the premium and the time value premium of the call are 2 points. The call has no intrinsic value by itself with the stock price below the striking price. An option normally has the largest amount of time value premium when the stock price is equal to the striking price. As an option becomes deeply in- or out-of­ the-money, the time value premium shrinks substantially. Table 1-1 illustrates this effect. Note that the time value premium increases as the stock nears the striking price (50) and then decreases as it draws away from 50. Parity. An option is said to be trading at parity with the underlying security if it is trading for its intrinsic value. Thus, if XYZ is 48 and the xyz July 45 call is selling for 3, the call is at parity. A common practice of particular interest to option writers ( as shall be seen later) is to refer to the price of an option by relat­ ing how close it is to parity with the common stock. Thus, the XY2 July 45 call is said to be a half-point over parity in any of the cases shown in Table 1-2. TABLE 1-1. Changes in time value premium. XYZ Stock XYZ Jul 50 Intrinsic Time Value Price Call Price Value Premium 40 1/2 0 ¼ 43 1 0 1 35 2 0 2 47 4 0 3 ➔50 5 0 5 53 7 3 4 55 8 5 3 57 9 7 2 60 101/2 10 ¼ 70 191/2 20 -1/20 asimplistically, a deeply in-the-money call may actually trade at a discount from intrinsic value, because call buyers are more interested in less expensive calls that might return better percentage profits on an upward move in the stock. This phenomenon is discussed in more detail when arbitrage techniques are examined. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:29 SCORE: 38.00 ================================================================================ Cl,apter 1: Definitions 9 TABLE 1-2. Comparison of XYZ stock and call prices. XYZ July 45 XYZ Stock Over Striking Price + Coll Price Price Parity (45 + 45 1/2) 1/2 (45 + 21/2 47 ) 1/2 (45 + 51/2 50 ) ½ (45 + 151/2 60 ) 1/2 FACTORS INFLUENCING THE PRICE OF AN OPTION An option's price is the result of properties of both the underlying stock and the terms of the option. The major quantifiable factors influencing the price of an option are the: 1.. price of the underlying stock, 2. striking price of the option itself, 3. time remaining until expiration of the option, 4. volatility of the underlying stock, 5. current risk-free interest rate (such as for 90-day Treasury bills), and 6. dividend rate of the underlying stock. The first four items are the major determinants of an option's price, while the latter two are generally less important, although the dividend rate can be influential in the case of high-yield stock. THE FOUR MAJOR DETERMINANTS Probably the most important influence on the option's price is the stock price, because if the stock price is far above or far below the striking price, the other fac­ tors have little influence. Its dominance is obvious on the day that an option expires. On that day, only the stock price and the striking price of the option determine the option's value; the other four factors have no bearing at all. At this time, an option is worth only its intrinsic value. Example: On the expiration day in July, with no time remaining, an XYZ July 50 call has the value shown in Table 1-3; each value depends on the stock price at the time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:30 SCORE: 36.00 ================================================================================ 10 Part I: Basic Properties of Stock Options TABLE 1-3. XYZ option's values on the expiration day. XYZ July 50 Coll (Intrinsic) Value XYZ Stock Price ot Expiration 40 45 48 50 52 55 60 0 0 0 0 2 5 10 The Call Option Price Curve. The call option price curve is a curve that plots the prices of an option against various stock prices. Figure 1-1 shows the axes needed to graph such a curve. The vertical axis is called Option Price. The horizontal axis is for Stock Price. This figure is a graph of the intrinsic value. When the option is either out-of-the-money or equal to the stock price, the intrinsic value is zero. Once the stock price passes the striking price, it reflects the increase of intrinsic value as the stock price goes up. Since a call is usually worth at least its intrinsic value at any time, the graph thus represents the min­ imum price that a call may be worth. FIGURE 1-1. The value of an option at expiration, its intrinsic value. ~ it C: .Q 15.. 0 The intrinsic value line bends at the st~iking ~ pnce. ~ Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:31 SCORE: 65.00 ================================================================================ Chapter 1: Definitions 11 When a call has time remaining to its expiration date, its total price consists of its intrinsic value plus its time value premium. The resultant call option price curve takes the form of an inverted arch that stretches along the stock price axis. If one plots the data from Table 1-4 on the grid supplied in Figure 1-2, the curve assumes two characteristics: 1. The time value premium ( the shaded area) is greatest when the stock price and the striking price are the same. 2. When the stock price is far above or far below the striking price (near the ends of the curve), the option sells for nearly its intrinsic value. As a result, the curve nearly touches the intrinsic value line at either end. [Figure 1-2 thus shows both the intrinsic value and the option price curve.] This curve, however, shows only how one might expect the XYZ July 50 call prices to behave with 6 months remaining until expiration. As the time to expiration grows shorter, the arched line drops lower and lower, until, on the final day in the life of the option, it merges completely with the intrinsic value line. In other words, the call is worth only its intrinsic value at expiration. Examine Figure 1-3, which depicts three separate XYZ calls. At any given stock price (a fixed point on the stock price scale), the longest-term call sells for the highest price and the nearest-term call sells for the lowest price. At the striking price, the actual differences in the three option prices are the greatest. Near either end of the scale, the three curves are much clos­ er together, indicating that the actual price differences from one option to another are small. For a given stock price, therefore, option prices decrease as the expiration date approaches. TABLE 1-4. The prices of a hypothetical July 50 call with 6 months of time remaining, plotted in Figure 1-2. XYZ Stock Price (Horizontal Axis) 40 45 48 ➔SO 52 55 60 XYZ July 50 Call Price (Vertical Axis) 2 3 4 5 61/2 11 Intrinsic Value 0 0 0 0 2 5 10 Time Value Premium (Shading) 2 3 4 3 11/2 1 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:32 SCORE: 25.00 ================================================================================ 12 Part I: Basic Properties of Stock Options Example: On January 1st, XYZ is selling at 48. An XYZ July 50 call will sell for more than an April 50 call, which in turn will sell for more than a January 50 call. FIGURE 1-2. Six-month July call option (see Table 1 ·4). .g a. C 0 a 11 10 9 8 7 6 5 Greatest Value for Time Value Premium 0 4 ---------------------- 3 2 0 FIGURE 1-3. 40 45 represents the option's time value premium. --------L---------50\ 55 60 Stock Price Intrinsic value remains at zero until striking price is passed. Price Curves for the 3-, 6·, and 9-month call options. / Intrinsic Value 9-Month Curve Striking Price Stock Price As expiration date draws closer, the lower curve merges with the intrinsic value line. The option price then equals its intrinsic value. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:33 SCORE: 46.00 ================================================================================ Chapter 1: Definitions 13 This statement is true no matter what the stock price is. The only reservation is that with the stock deeply in- or out-of-the-money, the actual difference between the January, April, and July calls will be smaller than with XYZ stock selling at the strik­ ing price of 50. Time Value Premium Decay. In Figure 1-3, notice that the price of the 9- month call is not three times that of the 3-month call. Note next that the curve in Figure 1-4 for the decay of time value premium is not straight; that is, the rate of decay of an option is not linear. An option's time value premium decays much more rapidly in the last few weeks of its life ( that is, in the weeks immediately preceding expiration) than it does in the first few weeks of its existence. The rate of decay is actually related to the square root of the time remaining. Thus, a 3- month option decays (loses time value premium) at twice the rate of a 9-month option, since the square root of 9 is 3. Similarly, a 2-month option decays at twice the rate of a 4-month option (-..f4 = 2). This graphic simplification should not lead one to believe that a 9-month option necessarily sells for twice the price of a 3-month option, because the other factors also influence the actual price relationship between the two calls. Of those other fac­ tors, the volatility of the underlying stock is particularly influential. More volatile underlying stocks have higher option prices. This relationship is logical, because if a FIGURE 1-4. Time value premium decay, assuming the stock price remains con­ stant. 9 4 Time Remaining Until Expiration (Months) 0 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:34 SCORE: 36.00 ================================================================================ 14 Part I: Basic Properties ol Stodc Options stock has the ability to move a relatively large distance upward, buyers of the calls are willing to pay higher prices for the calls - and sellers demand them as well. For exam­ ple, if AT&T and Xerox sell for the same price (as they have been known to do), the Xerox calls would be more highly priced than the AT&T calls because Xerox is a more volatile stock than AT&T. The interplay of the four major variables - stock price, striking price, time, and volatility can be quite complex. While a rising stock price (for example) is directing the price of a call upward, decreasing time may be simultaneously driving the price in the opposite direction. Thus, the purchaser of an out-of-the-money call may wind up with a loss even after a rise in price by the underlying stock, because time has eroded the call value. THE TWO MINOR DETERMINANTS The Risk-Free Interest Rate. This rate is generally construed as the current rate of 90-day Treasury bills. Higher interest rates imply slightly higher option pre­ miums, while lower rates imply lower premiums. Although members of the financial community disagree as to the extent that interest rates actually affect option price, they remain a factor in most mathematical models used for pricing options. (These models are covered much later in this book.) The Cash Dividend Rate of the Underlying Stock. Though not clas­ sified as a major determinant in option prices, this rate can be especially impor­ tant to the writer (seller) of an option. If the underlying stock pays no dividends at all, then a call option's worth is strictly a function of the other five items. Dividends, however, tend to lower call option premiums: The larger the dividend of the underlying common stock, the lower the price of its call options. One of the most influential factors in keeping option premiums low on high-yielding stock is the yield itself. Example: XYZ is a relatively low-priced stock with low volatility selling for $25 per share. It pays a large annual dividend of $2 per share in four quarterly payments of $.50 each. What is a fair price of an XYZ call with striking price 25? A prospective buyer of XYZ options is determined to figure out a fair price. In six months XYZ will pay $1 per share in dividends, and the stock price will thus be reduced by $1 per share when it goes ex-dividend over that time period. In that case, if XYZ's price remains unchanged except for the ex-dividend reductions, it will then be $24. Moreover, since XYZ is a nonvolatile stock, it may not readily climb back to 25 after the ex-dividend reductions. Therefore, the call buyer makes a low bid - even ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:35 SCORE: 59.00 ================================================================================ Chapter I: Definitions 15 for a 6-month call - because the underlying stock's price will be reduced by the ex­ dividend reduction, and the call holder does not receive the cash dividends. This particular call buyer calculated the value of the XYZ July 25 call in terms of what it was worth with the stock discounted to 24 - not at 25. He knew for certain that the stock was going to lose 1 point of value over the next 6 months, provided the dividend rate of XYZ stock did not change. In actual practice, option buyers tend to discount the upcoming dividends of the stock when they bid for the calls. However, not all dividends are discounted fully; usually the nearest dividend is discounted more heavily than are dividends to be paid at a later date. The less-volatile stocks with the higher dividend payout rates have lower call prices than volatile stocks with low payouts. In fact, in certain cases, an impending large dividend payment can substan­ tially increase the probability of an exercise of the call in advance of expiration. (This phenomenon is discussed more fully in the following section.) In any case, to one degree or another, dividends exert an important influence on the price of some calls. OTHER INFLUENCES These six factors, major and minor, are only the quantifiable influences on the price of an option. In practice, nonquantitative market dynamics - investor sentiment - can play various roles as well. In a bullish market, call premiums often expand because of increased demand. In bearish markets, call premiums may shrink due to increased supply or diminished demand. These influences, however, are normally short-lived and generally come into play only in dynamic market periods when emo­ tions are running high. EXERCISE AND ASSIGNMENT: THE MECHANICS The holder of an option can exercise his right at any time during the life of an option: Call option holders exercise to buy stock, while put option holders exercise to sell stock. In the event that an option is exercised, the writer of an option with the same terms is assigned an obligation to fulfill the terms of the option contract. EXERCISING THE OPTION The actual mechanics of exercise and assignment are fairly simple, due to the role of the Options Clearing Corporation (OCC). As the issuer of all listed option contracts, it controls all listed option exercises and assignments. Its activities are best explained by an example. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:36 SCORE: 45.00 ================================================================================ 16 Part I: Bask Properties ol Stock Options Example: The holder of an XYZ January 45 call option wishes to exercise his right to buy XYZ stock at $45 per share. He instructs his broker to do so. The broker then notifies the administrative section of the brokerage firm that handles such matters. The firm then notifies the OCC that they wish to exercise one contract of the XYZ January 45 call series. Now the OCC takes over the handling. OCC records indicate which member (brokerage) firms are short or which have written and not yet covered XYZ Jan 45 calls. The OCC selects, at random, a member firm that is short at least one XYZ Jan 45 call, and it notifies the short firm that it has been assigned. That firm must then deliver 100 shares of XYZ at $45 per share to the firm that exercised the option. The assigned firm, in tum, selects one of its customers who is short the XYZ January 45 call. This selection for the assignment may be either: 1. at random, 2. on a first-in/first-out basis, or 3. on any other basis that is fair, equitable, and approved by the appropriate exchange. The selection of the customer who is short the XYZ January 45 completes the exercise/assignment process. (If one is an option writer, he should obviously deter­ mine exactly how his brokerage firm assigns its option contracts.) HONORING THE ASSIGNMENT The assigned customer must deliver the stock - he has no other choice. It is too late to try buying the option back in the option market. He must, without fail, deliver 100 shares of XYZ stock at $45 per share. The assigned writer does, however, have a choice as to how to fulfill the assignment. If he happens to be already long 100 shares of XYZ in his account, he merely delivers that 100 shares as fulfillment of the assign­ ment notice. Alternatively, he can go into the stock market and buy XYZ at the cur­ rent market price - presumably something higher than $45 - and then deliver the newly purchased stock as fulfillment. A third alternative is merely to notify his bro­ kerage firm that he wishes to go short XYZ stock and to ask them to deliver the 100 shares of XYZ at 45 out of his short account. At times, borrowing stock to go short may not be possible, so this third alternative is not always available on every stock. Margin Requirements. If the assigned writer purchases stock to fulfill a contract, reduced margin requirements generally apply to the transaction, so that he would not have to fully margin the purchased stock merely for the pur­ pose of delivery. Generally, the customer only has to pay a day-trade margin of ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:37 SCORE: 40.00 ================================================================================ Oapter 1: Definitions 17 the difference between the current price of XYZ and the delivery price of $45 per share. If he goes short to honor the assignment, then he has to fully margin the short sale at the current rate for stock sold short on a margin basis. AFTER EXERCISING THE OPTION The OCC and the customer exercising the option are not concerned with the actual method in which the delivery is handled by the assigned customer. They want only to ensure that the 100 shares of XYZ at 45 are, in fact, delivered. The holder who exer­ cised the call can keep the stock in his account if he wants to, but he has to margin it fully or pay cash in a cash account. On the other hand, he may want to sell the stock immediately in the open market, presumably at a higher price than 45. If he has an established margin account, he may sell right away without putting out any money. If he exercises in a cash account, however, the stock must be paid for in full - even if it is subsequently sold on the same day. Alternatively, he may use the delivered stock to cover a short sale in his own account if he happens to be short XYZ stock. COMMISSIONS Both the buyer of the stock via the exercise and the seller of the stock via the assign­ ment are charged a full stock commission on 100 shares, unless a special agreement exists between the customer and the brokerage firm. Generally, option holders incur higher commission costs through assignment than they do selling the option in the secondary market. So the public customer who holds an option is better off selling the option in the secondary market than exercising the call. Example: XYZ is $55 per share. A public customer owns the XYZ January 45 call option. He realizes that exercising the call, buying XYZ at 45, and then immediately selling it at 55 in the stock market would net a profit of 10 points - or $1,000. However, the combined stock commissions on both the purchase at 45 and the sale at 55 might easily exceed $100. The net gain would actually be only $900. On the other hand, the XYZ January 45 call is worth (and it would normally sell for) at least 10 points in the listed options market. The commission for selling one call at a price of 10 is roughly $30. The customer therefore decides to sell his XYZ January 45 call in the option market. He receives $1,000 (10 points) for the call and pays only $30 in commissions - for a net of $970. The benefit of his decision is obvi­ ous. Of course, sometimes a customer wants to own XYZ stock at $45 per share, despite the stock commissions. Perhaps the stock is an attractive addition that will ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:38 SCORE: 81.00 ================================================================================ 18 Part I: Basic Properties of Stock Options bring greater potential to a portfolio. Or if the customer is already short the XYZ stock, he is going to have to buy 100 shares and pay the commissions sooner or later in any case; so exercising the call at the lower stock price of 45 may be more desir­ able than buying at the current price of 55. ANTICIPATING ASSIGNMENT The writer of a call often prefers to buy the option back in the secondary market, rather than fulfill the obligation via a stock transaction. It should be strJssed again that once the writer receives an assignment notice, it is too late to attempt to buy back (cover) the call. The writer must buy before assignment, or live up to the terms upon assignment. The writer who is aware of the circumstances that generally cause the holders to exercise can anticipate assignment with a fair amount of certainty. In antic­ ipation of the assignment, the writer can then close the contract in the secondary mar­ ket. As long as the writer covers the position at any time during a trading day, he can­ not be assigned on that option. Assignment notices are determined on open positions as of the close of trading each day. The crucial question then becomes, "How can the writer anticipate assignment?" Several circumstances signal assignments: 1. a call that is in-the-money at expiration, 2. an option trading at a discount prior to expiration, or 3. the underlying stock paying a large dividend and about to go ex-dividend. Automatic Exercise. Assignment is all but certain if the option is in-the­ money at expiration. Should the stock close even a half-point above the striking price on the last day of trading, the holder will exercise to take advantage of the half-point rather than let the option expire. Assignment is nearly inevitable even if a call is only a few cents in-the-money at expiration. In fact, even if the call trades in-the-money at any time during the last trading day, assignment may be forthcoming. Even if a holder forgets that he owns an option and fails to exer­ cise, the OCC automatically exercises any call that is ¾-point in-the-money at expiration, unless the individual brokerage firm whose customer is long the call gives specific instructions not to exercise. This automatic exercise mechanism ensures that no investor throws away money through carelessness. Example: XYZ closes at 51 on the third Friday of January (the last day of trading for the January option series). Since options don't expire until Saturday, the next day, the OCC and all brokerage firms have the opportunity to review their records to issue assignments and exercises and to see if any options could have been profitably exer- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:39 SCORE: 81.00 ================================================================================ Gapter 1: Definitions 19 cised but were not. If XYZ closed at 51 and a customer who owned a January 45 call option failed to either sell or exercise it, it is automatically exercised. Since it is worth $600, this customer stands to receive a substantial amount of money back, even after stock commissions. In the case of an XYZ January 50 call option, the automatic exercise procedure is not as clear-cut with the stock at 51. Though the OCC wants to exercise the call automatically, it cannot identify a specific owner. It knows only that one or more XYZ January calls are still open on the long side. When the OCC checks with the broker­ age firm, it may find that the firm does not wish to have the XYZ January 50 call exer­ cised automatically, because the customer would lose money on the exercise after incurring stock commissions. Yet the OCC must attempt to automatically exercise any in-the-money calls, because the holder may have overlooked a long position. When the public customer sells a call in the secondary market on the last day of trading, the buyer on the other side of the trade is very likely a market-maker. Thus, when trading stops, much of the open interest in in-the-money calls held long belongs to market-makers. Since they can profitably exercise even for an eighth of a point, they do so. Hence, the writer may receive an assignment notice even if the stock has been only slightly above the strike price on the last trading day before expi­ ration. Any writer who wishes to avoid an assignment notice should always buy back ( or cover) the option if it appears the stock will be above the strike at expiration. The probabilities of assignment are extremely high if the option expires in-the-money. Early Exercise Due to Discount. When options are exercised prior to expiration, this is called early, or premature, exercise. The writer can usually expect an early exercise when the call is trading at or below parity. A parity or discount situation in advance of expiration may mean that an early exercise is forthcoming, even if the discount is slight. A writer who does not want to deliv­ er stock should buy back the option prior to expiration if the option is apparently going to trade at a discount to parity. The reason is that arbitrageurs (floor traders or member firm traders who pay only minimal commissions) can take advantage of discount situations. (Arbitrage is discussed in more detail later in the text; it is mentioned here to show why early exercise often occurs in a dis­ count situation.) Example: XYZ is bid at $50 per share, and an XYZ January 40 call option is offered at a discount price of 9.80. The call is actually "worth" 10 points. The arbitrageur can take advantage of this situation through the following actions, all on the same day: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:40 SCORE: 44.00 ================================================================================ 20 Part I: Basic Properties ol Stoclc Options 1. Buy the January 40 call at 9.80. 2. Sell short XYZ common stock at 50. 3. Exercise the call to buy XYZ at 40. The arbitrageur makes 10 points from the short sale of XYZ (steps 2 and 3), from which he deducts the 9.80 points he paid for the call. Thus, his total gain is 20 cents - the amount of the discount. Since he pays only a minimal commission, this trans- action results in a net profit. ' Also, if the writer can expect assignment when the option has no time value pre­ mium left in it, then conversely the option will usually not be called if time premium is left in it. Example: Prior to the expiration date, XYZ is trading at 50½, and the January 50 call is trading at 1. The call is not necessarily in imminent danger of being called, since it still has half a point of time premium left. Time value Call Striking Stock = + premium price price price = 1 + 50 50½ = ½ Early Exercise Due to Dividends on the Underlying Stock. Some­ times the market conditions create a discount situation, and sometimes a large dividend gives rise to a discount. Since the stock price is almost invariably reduced by the amount of the dividend, the option price is also most likely reduced after the ex-dividend. Since the holder of a listed option does not receive the dividend, he may decide to sell the option in the secondary market before the ex-date in anticipation of the drop in price. If enough calls are sold because of the impending ex-dividend reduction, the option may come to parity or even to a discount. Once again, the arbitrageurs may move in to take advantage of the sit­ uation by buying these calls and exercising them. If assigned prior to the ex-date, the writer does not receive the dividend for he no longer owns the stock on the ex-date. Furthermore, if he receives an assignment notice on the ex-date, he must deliver the stock with the dividend. It is therefore very important for the writer to watch for discount situations on the day prior to the ex­ date. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:41 SCORE: 49.00 ================================================================================ 0.,,,,, I: Definitions 21 A word of caution: Do not conclude from this discussion that a call will be exer­ cised for the dividend if the dividend is larger than the remaining time premium. It won't. An example will show why. Emmple: XYZ stock, at 50, is going to pay a $1 dividend with the ex-date set for the next day. An XYZ January 40 call is selling at 10¼; it has a quarter-point of time pre­ mium. (TVP = 10¼ + 40 - 50 = ¼). The same type of arbitrage will not work Suppose that the arbitrageur buys the call at 10¼ and exercises it: He now owns the stock for the ex-date, and he plans to sell the stock immediately at the opening on the ex-date, the next day. On the ex-date, XYZ opens at 49, because it goes ex-dividend by $1. The arbitrageur's transactions thus consist of: 1. Buy the XYZ January 40 call at 10¼. 2. Exercise the call the same day to buy XYZ at 40. 3. On the ex-date, sell XYZ at 49 and collect the $1 dividend. He makes 9 points on the stock (steps 2 and 3), and he receives a 1-point dividend, for a total cash inflow of 10 points. However, he loses 10¼ points paying for the call. The overall transaction is a loser and the arbitrageur would thus not attempt it. A dividend payment that exceeds the time premium in the call, therefore, does not imply that the writer will be assigned. More of a possibility, but a much less certain one, is that the arbitrageur may attempt a "risk arbitrage" in such a situation. Risk arbitrage is arbitrage in which the arbitrageur runs the risk of a loss in order to try for a profit. The arbitrageur may sus­ pect that the stock will not be discounted the full ex-dividend amount or that the call's time premium will increase after the ex-date. In either case (or both), he might make a profit: If the stock opens down only 60 cents or if the option premium expands by 40 cents, the arbitrageur could profit on the opening. In general, howev­ er, arbitrageurs do not like to take risks and therefore avoid this type of situation. So the probability of assignment as the result of a dividend payment on the underlying stock is small, unless the call trades at parity or at a discount. Of course, the anticipation of an early exercise assumes rational behavior on the part of the call holder. If time premium is left in the call, the holder is always better off financially to sell that call in the secondary market rather than to exercise it. However, the terms of the call contract give a call holder the right to go ahead and exercise it anyway - even if exercise is not the profitable thing to do. In such a case, a writer would receive an assignment notice quite unexpectedly. Financially unsound early exercises do happen, though not often, and an option writer must realize that, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:42 SCORE: 24.00 ================================================================================ 22 Part I: Basic Properties of Stock Options in a very small percentage of cases, he could be assigned under very illogical cir­ cumstances. THE OPTION MARKETS The trader of stocks does not have to become very familiar with the details of the way the stock market works in order to make money. Stocks don't expire, nor Cal} an investor be pulled out of his investment unexpectedly. However, the option trader is required to do more homework regarding the operation of the option markets. In fact, the option strategist who does not know the details of the working of the option markets will likely find that he or she eventually loses some money due to ignorance. MARKET-MAKERS In at least one respect, stock and listed option markets are similar. Stock markets use specialists to do two things: First, they are required to make a market in a stock by buying and selling from their own inventory, when public orders to buy or sell the stock are absent. Second, they keep the public book of orders, consisting of limit orders to buy and sell, as well as stop orders placed by the public. When listed option trading began, the Chicago Board Options Exchange (CBOE) introduced a similar method of trading, the market-maker and the board broker system. The CBOE assigns several market-makers to each optionable stock to provide bids and offers to buy and sell options in the absence of public orders. Market-makers cannot handle public orders; they buy and sell for their own accounts only. A separate person, the board broker, keeps the book of limit orders. The board broker, who cannot do any trading, opens the book for traders to see how many orders to buy and sell are placed nearest to the current market (consisting of the highest bid and lowest offer). (The specialist on the stock exchange keeps a more closed book; he is not required to for­ mally disclose the sizes and prices of the public orders.) In theory, the CBOE system is more efficient than the stock exchange system. With several market-makers competing to create the market in a particular security, the market should be a more efficient one than a single specialist can provide. Also, the somewhat open book of public orders should provide a more orderly market. In practice, whether the CBOE has a more efficient market is usually a subject for heat­ ed discussion. The strategist need not be concerned with the question. The American Stock Exchange uses specialists for its option trading, but it also has floor traders who function similarly to market-makers. The regional option exchanges use combinations of the two systems; some use market-makers, while oth­ ers use specialists. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:43 SCORE: 54.00 ================================================================================ Cl,apter 1: Definitions 23 OPTION SYMBOLOGY It is probably a good idea for an option trader to understand how option symbols are created and used, for it may prove to be useful information. If one has a sophisticat­ ed option quoting and pricing system, the quote vendor will usually provide the translation between option symbols and their meanings. The free option quote sec­ tion on the CBOE's Web site, www.cboe.com, can be useful for that purpose as well. Even with those aids, it is important that an option trader understand the concepts surrounding option symbology. THE OPTION BASE SYMBOL The basic option symbol consists of three parts: Option symbol = Base symbol + Expiration month code + Striking price code The base symbol is never more than three characters in length. In its simplest form, the base symbol is the same as the stock symbol. That works well for stocks with three or fewer letters in their symbol, such as General Electric (GE) or IBM (IBM), but what about NASDAQ stocks? For NASDAQ stocks, the OCC makes up a three-let­ ter symbol that is used to denote options on the stock. A few examples are: Stock Cisco Microsoft Qualcomm Stock Symbol csco MSFT QCOM Option Base Symbol CYQ MSQ QAQ In the three examples, there is a letter "Q" in each of the option base symbols. However, that is not always the case. The option base symbol assigned by the OCC for a NASDAQ stock may contain any three letters (or, rarely, only two letters). THE EXPIRATION MONTH CODE The next part of an option symbol is the expiration month code, which is a one-char­ acter symbol. The symbology that has been created actually uses the expiration month code for two purposes: (1) to identify the expiration month of the option, and (2) to designate whether the option is a call or a put. The concept is generally rather simple. For call options, the letter A stands for January, B for February, and so forth, up through L for December. For put options, the letter M stands for January, N for February, and so forth, up through X for December. The letters Y and Z are not used for expiration month codes. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:44 SCORE: 37.00 ================================================================================ 24 Part I: Basic Properties ol Stock Options THE STRIKING PRICE CODE This is also a one-character symbol, designed to identify the striking price of the option. Things can get ve:iy complicated where striking price codes are concerned, but simplistically the designations are that the letter A stands for 5, B stands for 10, on up to S for 95 and T for 100. If the stock being quoted is more expensive - say, trading at $150 per share - then it is possible that A will stand for 105, B for 110, S for 195 and T for 200 (although, as will be shown later, a more complicated approach might have to be used in cases such as these). It should be noted that the exchanges - who designate the striking price codes and their numerical meaning - do not have • to adhere to any of the generalized conventions described here. They usually adhere to as many of them as they can, in order to keep things somewhat standardized, but they can use the letters in any way they want. Typically, they would only use any strik­ ing price code letter outside of its conventional designation after a stock has split or perhaps paid a special dividend of some sort. Before getting into the more complicated option symbol constructions, let's look at a few simple, straightforward examples: Stock Stock Symbol Description Option Symbol IBM IBM IBM July 125 call IBMGE Cisco csco Cisco April 75 put CYQPO Ford Motor F Ford March 40 call FCH General Motors GM GM December 65 put GMXM In each option symbol, the last two characters are the expiration month code and the striking price code. Preceding them is the option base symbol. For the IBM July 125, the option symbol is quite straightforward. IBM is the option base symbol (as well as the stock symbol), G stands for July, and E for 125, in this case. For the Cisco April 75 put, the option base symbol is CYQ (this was given in the previous table, but if one didn't know what the base symbol was, you would have to look it up on the Internet or call a broker). The expiration month code in this case is P, because P stands for an April put option. Finally, the striking price code is 0, which stands for 75. The Ford March 40 call and the GM December 65 put are similar to the oth­ ers, except that the stock symbols only require one and two characters, respectively, so the option symbol is thus a shorter symbol as well - first using the stock symbol, then the standard character for the expiration month, followed by the standard char­ acter for the striking price. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:45 SCORE: 17.00 ================================================================================ Chapter 1: Definitions 25 MORE STRIKING PRICE CODES The letters A through T cannot handle all of the possible striking price codes. Recall that many stocks, especially lower-priced ones, have striking prices that are spaced 2½ points apart. In those cases, a special letter designation is usually used for the striking price codes: Striking Price Code u V w X y z Possible Meanings 7.5 or 37.5 or 67.5 or 97.5 or even 127.5! 12.5 or 42.5 or 72.5 or 102.5 or 132.5 17.5 or 47.5 or 77.5 or 107.5 or 137.5 22.5 or 52.5 or 82.5 or 112.5 or 142.5 27.5 or 57.5 or 87.5 or 117.5 or 147.5 32.5 or 62.5 or 92.5 or 122.5 or 152.5 Typically, only the first or second meaning is used for these letters. The higher-priced ones only occur after a very expensive stock splits 2-for-l (say, a stock that had a strike price of 155 and split 2-for-l, creating a strike. price of 155 divided by 2, or 77.50). WRAPS Note that any striking price code can have only one meaning. Thus, if the letter A is being used to designate a strike price of 5, and the underlying stock has a tremen­ dous rally to over $100 per share, then the letter A cannot also be used to designate the strike price of 105. Something else must be done. In the early years of option trading, there was no need for wrap symbols, but in recent - more volatile - times, stocks have risen 100 points during the life of an option. For example, if XYZ was originally trading at 10, there might be a 9-month, XYZ December 10 call. Its symbol would be XYZLB. If, in the course of the next few months, XYZ traded up to nearly 110 while the December 10 call was still in exis­ tence, the exchange would want to trade an XYZ December 110 call. But a new let­ ter would have to be designated for any new strikes (A already stands for 5, so it can­ not stand for 105; B already stands for 10, so it cannot stand for 110, etc.). There aren't enough letters in the alphabet to handle this, so the exchange creates an addi­ tional option base symbol, called a wrap symbol. In this case, the exchange might say that the option base symbol XYA is now going to be used to designate strike prices of 105 and higher ( up to 200) for the com­ mon stock whose symbol is XYZ. Having done that, the letter A can be used for 105, B for 110, etc. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:46 SCORE: 45.00 ================================================================================ 26 Option XYZ December 10 call XYZ December 110 call Part I: Basic Properties ol Stock Options Symbol XYZLB XYALB (wrap symbol is XYA) Note that the wrap symbol now allows the usage of Bin its standard interpretati<,n once again. This process can be extended. Suppose that, by some miracle, this stock rose to 205 prior to the December expiration. Things like this happened to Yahoo (YHOO), Amazon (AMZN), Qualcomm (QCOM), and others during the 1990s. If that hap­ pened, the exchange would now create another wrap symbol and use it to designate strike prices from 205 to 300. Suppose XYZ traded up to 210, and the exchange then said that YYA would now be the wrap symbol for the higher strikes. In that case, these symbols would exist: Option XYZ December 10 call XYZ December 110 call XYZ December 210 call Symbol XYZLB XYALB (wrap symbol is XYA) YYALB (wrap symbol is YYA) Note that there doesn't have to be any particular relationship between the wrap sym­ bols and the stock itself; any three-character designation could be used. LEAPS SYMBOLS A LEAPS option is one that is very long-term, expiring one or more years hence. Consequently, the expiration month codes encounter a problem with LEAPS similar to the one seen for striking price codes where wraps are concerned. The letter A stands for January as an expiration month code. However, if there is a LEAPS option on this same stock, and that LEAPS option expires in January of the next year, the letter A cannot be used to designate the expiration month of the LEAPS option, since it is already being used for the "standard" option. Consequently, LEAPS options have a different base option symbol than the "standard" base option symbol. Example: The current year is 2001. The OCC might have designated that, for IBM, LEAPS options expiring in the year 2002 will have the option base symbol VBM, and those expiring in the year 2003 will have the option base symbol WBM. Thus, the fol­ lowing symbols would be used to describe the designated options: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:47 SCORE: 40.00 ================================================================================ Chapter 1: Definitions Option Description IBM January 125 call (expiring in 2001) IBM January 125 call (expiring in 2002) IBM January 125 call (expiring in 2003) IBM January 125 put (expiring in 2003) 27 Option Symbol IBMAE VBMAE WBMAE WBMME Note that the last line shows a LEAPS put option symbol. The letter M stands for a January put option - the standard usage for the expiration month code. STOCK SPLITS Stock splits often wreak havoc on option symbols, as the exchanges are forced to use the standard characters in nonstandard ways in order to accommodate all the addi­ tional strikes that are created when a stock splits. The actual discussion of stock splits and the resultant option symbology is deferred to the next section. SYMBOLOGY SUMMARY The exchanges do a good job of making symbol information available. Each exchange has a Web site where memos detailing the changes required by LEAPS, wraps, and splits are available for viewing. The OCC and the exchanges have been forced to create multiple option base symbols for a single stock in order to accommodate the various strike price and expi­ ration month situations - to avoid duplication of the standardized character used for the strike or expiration month. This is unwieldy and confusing for option traders and for data vendors as well. In some rare cases, mistakes are made, and there can briefly be two designations for the same option symbol. The only way to eliminate this con­ fusion would be to use a longer, more descriptive option symbol that included the expiration year and the striking price as numerical values, much as is done with futures options. It is the member firms themselves and some of the quote vendors who object to the transformation to this less confusing system, because they would have to recode their software and alter their databases. DETAILS OF OPTION TRADING The facts that the strategist should be concerned with are included in this section. They are not presented in any particular order of importance, and this list is not nec­ essarily complete. Many more details are given in the discussion of specific strategies throughout this text. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:48 SCORE: 57.00 ================================================================================ 28 Part I: Basic Properties of Stock Options 1. Options expire on the Saturday following the third Friday of the expiration rrwnth, although the third Friday is the last day of trading. In general, however, waiting past 3:30 P.M. on the last day to place orders to buy or sell the expiring options is not advisable. In the "crush" of orders during the final minutes of trad- • ing, even a market order may not have enough time to be executed. 2. Option trades have a one-day settlement cycle. The trade settles on the next busi­ ness day after the trade. Purchases must be paid for in full, and the credits from sales "hit" the account on the settlement day. Some brokerage firms require set­ tlement on the same day as the trade, when the trade occurs on the last trading day of an expiration series. 3. Options are opened for trading in rotation. When the underlying stock opens for trading on any exchange, regional or national, the options on that stock then go into opening rotation on the corresponding option exchange. The rotation system also applies if the underlying stock halts trading and then reopens during a trad­ ing day; options on that stock .reopen via a rotation. In the rotation itself, interested parties make bids and offers for each particular option series one at a time - the XYZ January 45 call, the XYZ January 50 call, and so on - until all the puts and calls at various expiration dates and striking prices have been opened. Trades do not necessarily have to take place in each series, just bids and offers. Orders such as spreads, which involve more than one option, are not executed during a rotation. While the rotation is taking place, it is possible that the underlying stock could make a substantial move. This can result in option prices that seem unrealistic when viewed from the perspective of each option's opening. Consequently, the opening price of an option can be a somewhat suspicious statistic, since none of them open at exactly the same time. Also, it should be noted that most option traders do not trade during rotation, so a market order may receive a very poor price. Hence, if one is considering trad­ ing during rotation, a limit order should be used. ( Order entry is discussed in more detail in a later section of this chapter.) 4. When the underlying stock splits or pays a stock dividend, the terms of its options are adjusted. Such an adjustment may result in fractional striking prices and in options for other than 100 shares per contract. No adjustments in terms are made for cash dividends. The actual details of splits, stock dividends, and rights offer­ ings, along with their effects on the option terms, are always published by the option exchange that trades those options. Notices are sent to all member firms, who then make that information available to their brokers for distribution to clients. In actual practice, the option strategist should ascertain from the broker ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:49 SCORE: 57.00 ================================================================================ 28 Part I: Bask Properties of Stock Options l. Options expire on the Saturday following the third Friday of the expiration rrwnth, although the third Friday is the last day of trading. In general, however, waiting past 3:30 P.M. on the last day to place orders to buy or sell the expiring options is not advisable. In the "crush" of orders during the final minutes of trad- , ing, even a market order may not have enough time to be executed. 2. Option trades have a one-day settlement cycle. The trade settles on the next busi­ ness day after the trade. Purchases must be paid for in full, and the credits from sales "hit" the account on the settlement day. Some brokerage firms require set­ tlement on the same day as the trade, when the trade occurs on the last trading day of an expiration series. 3. Options are opened for trading in rotation. When the underlying stock opens for trading on any exchange, regional or national, the options on that stock then go into opening rotation on the corresponding option exchange. The rotation system also applies if the underlying stock halts trading and then reopens during a trad­ ing day; options on that stock reopen via a rotation. In the rotation itself, interested parties make bids and offers for each particular option series one at a time - the XYZ January 45 call, the XYZ January 50 call, and so on - until all the puts and calls at various expiration dates and striking prices have been opened. Trades do not necessarily have to take place in each series, just bids and offers. Orders such as spreads, which involve more than one option, are not executed during a rotation. While the rotation is taking place, it is possible that the underlying stock could make a substantial move. This can result in option prices that seem unrealistic when viewed from the perspective of each option's opening. Consequently, the opening price of an option can be a somewhat suspicious statistic, since none of them open at exactly the same time. Also, it should be noted that most option traders do not trade during rotation, so a market order may receive a very poor price. Hence, if one is considering trad­ ing during rotation, a limit order should be used. ( Order entry is discussed in more detail in a later section of this chapter.) 4. When the underlying stock splits or pays a stock dividend, the terms of its options are adjusted. Such an adjustment may result in fractional striking prices and in options for other than 100 shares per contract. No adjustments in terms are made for cash dividends. The actual details of splits, stock dividends, and rights offer­ ings, along with their effects on the option terms, are always published by the option exchange that trades those options. Notices are sent to all member firms, who then make that information available to their brokers for distribution to clients. In actual practice, the option strategist should ascertain from the broker ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:50 SCORE: 57.00 ================================================================================ 28 Part I: Basic Properties ol Stock Options 1. Options expire on the Saturday following the third Friday of the expiration month, although the third Friday is the last day of trading. In general, however, waiting past 3:30 P.M. on the last day to place orders to buy or sell the expiring options is not advisable. In the "crush" of orders during the final minutes of trad- , ing, even a market order may not have enough time to be executed. 2. Option trades have a one-day settlement cycle. The trade settles on the next busi­ ness day after the trade. Purchases must be paid for in full, and the credits from sales "hit" the account on the settlement day. Some brokerage firms require set­ tlement on the same day as the trade, when the trade occurs on the last trading day of an expiration series. 3. Options are opened for trading in rotation. When the underlying stock opens for trading on any exchange, regional or national, the options on that stock then go into opening rotation on the corresponding option exchange. The rotation system also applies if the underlying stock halts trading and then reopens during a trad­ ing day; options on that stock reopen via a rotation. In the rotation itself, interested parties make bids and offers for each particular option series one at a time - the XYZ January 45 call, the XYZ January 50 call, and so on - until all the puts and calls at various expiration dates and striking prices have been opened. Trades do not necessarily have to take place in each series, just bids and offers. Orders such as spreads, which involve more than one option, are not executed during a rotation. While the rotation is taking place, it is possible that the underlying stock could make a substantial move. This can result in option prices that seem unrealistic when viewed from the perspective of each option's opening. Consequently, the opening price of an option can be a somewhat suspicious statistic, since none of them open at exactly the same time. Also, it should be noted that most option traders do not trade during rotation, so a market order may receive a very poor price. Hence, if one is considering trad­ ing during rotation, a limit order should be used. ( Order entry is discussed in more detail in a later section of this chapter.) 4. When the underlying stock splits or pays a stock dividend, the terms of its options are adjusted. Such an adjustment may result in fractional striking prices and in options for other than 100 shares per contract. No adjustments in terms are made for cash dividends. The actual details of splits, stock dividends, and rights offer­ ings, along with their effects on the option terms, are always published by the option exchange that trades those options. Notices are sent to all member firms, who then make that information available to their brokers for distribution to clients. In actual practice, the option strategist should ascertain from the broker ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:51 SCORE: 46.00 ================================================================================ a.,,., 1: Definitions 29 the specific terms of the new option series, in case the broker has overlooked the information sent. E«ample 1: XYZ is a $50 stock with option striking prices of 45, 50, and 60 for the January, April, and July series. It declares a 2-for-l stock split. Usually, in a 2-for-l split situation, the number of outstanding option contracts is doubled and the strik­ ing prices are halved. The owner of 5 XYZ January 60 calls becomes the owner of 10 XYZ January 30 calls. Each call is still for 100 shares of the underlying stock. If fractional striking prices arise, the exchange also publishes the quote symbol that is to be used to find the price of the new option. The XYZ July 45 call has a sym­ bol ofXYZGI: G stands for July and I is for 45. After the 2-for-l split, one July 45 call becomes 2 July 22½ calls. The strike of 22½ is assigned a letter. The exchanges usu­ ally attempt to stay with the standard symbols as much as possible, meaning that X would be designated for 22½. Hence, the symbol for the XYZ July 22½ call would be XYZGX. After the split, XYZ has options with strikes of 22½, 25, and 30. In some cases, the option exchange officials may introduce another strike if they feel such a strike is necessary; in this example, they might introduce a striking price of 20. E«ample 2: UVW Corp. is now trading at 40 with strikes of 35, 40, and 45 for the January, April, and July series. UVW declares a 2½ percent stock dividend. The con­ tractually standardized 100 shares is adjusted up to 102, and the striking prices are reduced by 2 percent (rounded to the nearest eighth). Thus, the "old" 35 strike becomes a "new" strike of 343/s: 1.02 divided into 35 equals 34.314, which is 343/s when rounded to the nearest eighth. The "old" 40 strike becomes a "new" strike of 39¼, and the "old" 45 strike becomes 441/s. Since these new strikes are all fraction­ al, they are given special symbols - probably U, V, and W. Thus, the "old" symbol UVWDH (UVW April 40) becomes the "new" symbol UVWDV (UVW April 39¼). After the split, the exchange usually opens for trading new strikes of 35, 40, and 45 - each for 100 shares of the underlying stock. For a while, there are six striking prices for UVW options. As time passes, the fractional strikes are eliminated as they expire. Since they are not reintroduced, they eventually disappear as long as UVW does not issue further stock dividends. Example 3: WWW Corp. (symbol WWW) is trading at $120 per share, with strike prices of ll0, ll5, 120, 125, and 130. WWW declares a 3-for-l split. In this case, the strike prices would be divided by 3 (and rounded to the nearest eighth); the number of contracts in every account would be tripled; and each option would still be an option on 100 shares of WWW stock. The general rule of thumb is that when a split results in round lots (2-for-l, 3-for-l, 4-for-l, etc.), the number of option contracts is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:52 SCORE: 56.00 ================================================================================ 30 Part I: Basic Properties ol Stock Options increased and the strike price is decreased, and each option still represents 100 shares of the underlying stock. In this case, the strikes listed above (110 through 130) would be adjusted to• become new strikes: 36.625, 38.375, 40, 41.625, and 43.375. The 40 strike would be assigned the standard strike price symbol of the letter H. However, the others would need to be designated by the exchange, so U might stand for 38.375, V for 41.625, and so forth. Example 4: When a split does not result in a round lot, a different adjustment must be used for the options. Suppose that AAA Corp. (symbol: AAA) is trading at $60 per share and declares a 3-for-2 split. In this case, each option's strike will be multiplied by two-thirds (to reflect the 3-for-2 split), but the number of contracts held in an account will remain the same and each option will be an option on 150 shares of AAA stock. Suppose that there were strikes of 55, 60, and 65 preceding this split. After the split, AAA common itself would be trading at $40 per share, reflecting the post-split 3-for-2 adjustment from its previous price of 60. There would be new options with strikes of 36.625, 40, and 43.375 (these had been the pre-split strikes of 55, 60, and 65). Since each of these options would be for 150 shares of the underlying stock, the exchange creates a new option base symbol for these options, because they no longer represent 100 shares of AAA common. Suppose the exchange says that the post-split, 150-share option contracts will henceforth use the option symbol AAX. After the split, the exchange will then list "normal" 100-share options on AAA, perhaps with strike prices of 35, 40, and 45. This creates a situation that can some­ times be confusing for traders and can lead to problems. There will actually be two options with striking prices of 40 - one for 100 shares and the other for 150 shares. Suppose the July contract is being considered. The option with symbol AAAGH is a July 40 option on 100 shares of AAA Corp., while the option with symbol AAXGH is a July 40 option on 150 shares of AAA Corp. Since option prices are quoted on a per­ share basis, they will have nearly identical price quotes on any quote system (see item 5). If one is not careful, you might trade the wrong one, thereby incurring a risk that you did not intend to take. For example, suppose that you sell, as an opening transaction, the AAXGH July 40 call at a price of 3. Furthermore, suppose that you did not realize that you were selling the 150-share option; this was a mistake, but you don't yet realize it. A couple of days later, you see that this option is now selling at 13 - a loss of 10 points. You might think that you had just lost $1,000, but upon examining your brokerage state­ ment (or confirms, or day trading sheet), you suddenly see that the loss is $1,500 on ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:53 SCORE: 44.00 ================================================================================ 0.,,,, 1: Definitions 31 that contract! Quite a difference, especially if multiple contracts are involved. This could come as a shock if you thought you were hedged (perhaps you bought 100 shares of AAA common when you sold this call), only to find out later that you didn't have a correctly hedged position in place after all. Even more severe problems can arise if this stock splits again during the life of this option. Sometimes the options will be adjusted so that they represent a non­ standard number of shares, such as the 150-share options involved here; and after multiple splits, the exchange may even apply a multiplier to the option, rather than adjusting its strike price repeatedly. This type of thing wouldn't happen on the first stock split, but it might occur on subsequent stock splits, spaced closely together over the life of an option. In such a case, the dollar value of the option moves much faster than one would expect from looking at a quote of the contract. So you must be sure that you are trading the exact contract you intend to, and not relying on the fact that the striking price is correct and the option price quote seems to be in line. One must verify that the option being bought or sold is exactly the one intended. In general, it is a good idea, after a split or similar adjustment, to establish opening positions solely with the standard contracts and to leave the split­ adjusted contracts alone. 5. All options are quoted on a per-share basis, regardless of how many shares of stock the option involves. Normally the quote assumes 100 shares of the under­ lying stock. However, in a case like the UVW options just described, a quote of 3 for the UVW April 39¼ means a dollar price of $306 ($3 x 102). 6. Changes in the price of the underlying stock can also bring about new striking prices. XYZ is a $47 stock with striking prices of 45 and 50. If the price of XYZ stock falls to $40, the striking prices of 45 and 50 do not give option traders enough opportunities in XYZ. So the exchange might introduce a new striking price of 40. In practice, a new series is generally opened when the stock trades at the lowest (or highest) existing strike in any series. For example, if XYZ is falling, as soon as it traded at or below 45, the striking price of 40 may be intro­ duced. The officials of the option exchange that trades XYZ options make the decision as to the exact day when the strike begins trading. POSITION LIMIT AND EXERCISE LIMIT 1. An investor or a group of investors cannot be long or short more than a set limit of contracts in one stock on the same side of the market. The actual limit varies according to the trading activity in the underlying stock. The most heavily trad­ ed stocks with a large number of shares outstanding have position limits of 75,000 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:54 SCORE: 24.00 ================================================================================ 32 Part I: Basic Properties ol Stock Options contracts. Smaller stocks have position limits of 60,000, 31,000, 22,500, or 13,500 contracts. These limits can be expected to increase over time, if stocks' capital­ izations continue to increase. The exchange on which the option is listed makes available a list of the position limits on each of its optionable stocks. So, if one were long the limit of XYZ call options, he cannot at the same time be short any XYZ put options. Long calls and short puts are on the same side of the market; that is, both are bullish positions. Similarly, long puts and short calls are both on the bearish side of the market. While these position limits generally exceed by far any position that an individual investor normally attains, the limits apply to "relat­ ed" accounts. For instance, a money manager or investment advisor who is man­ aging many accounts cannot exceed the limit when all the accounts' positions are combined. 8. The numher of contracts that can be exercised in a particular period of time ( usu­ ally 5 business days) is also limited to the same arrwunt as the position limit. This exercise limit prevents an investor or group from "cornering" a stock by repeat­ edly buying calls one day and exercising them the next, day after day. Option exchanges set exact limits, which are subject to change. ORDER ENTRY Order Information Of the various types of orders, each specifies: 1. whether the transaction is a buy or sell, 2. the option to be bought or sold, 3. whether the trade is opening or closing a position, 4. whether the transaction is a spread (discussed later), and 5. the desired price. TYPES OF ORDERS Many types of orders are acceptable for trading options, but not all are acceptable on all exchanges that trade options. Since regulations change, information regarding which order is valid for a given exchange is best supplied by the broker to the cus­ tomer. The following orders are acceptable on all option exchanges: Market Order. This is a simple order to buy or sell the option at the best pos­ sible price as soon as the order gets to the exchange floor. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:55 SCORE: 8.00 ================================================================================ Cl,apter 1: Definitions 33 Market Not Held Order. The customer who uses this type of order is giv­ ing the floor broker discretion in executing the order. The floor broker is not held responsible for the final outcome. For example, if a floor broker has a "mar­ ket not held" order to buy, and he feels that the stock will "downtick" (decline in price) or that there is a surplus of sellers in the crowd, he may often hold off on the execution of the buy order, figuring that the price will decline shortly and that the order can then be executed at a more favorable price. In essence, the customer is giving the floor broker the right to use some judgment regarding the execution of the order. If the floor broker has an opinion and that opinion is cor­ rect, the customer will probably receive a better price than if he had used a reg­ ular market order. If the broker's opinion is wrong, however, the price of the execution may be worse than a regular market order. Limit Order. The limit order is an order to buy or to sell at a specified price - the limit. It may be executed at a better price than the limit - a lower one for buyers and a higher one for sellers. However, if the limit is never reached, the order may never be executed. Sometimes a limit order may specify a discretionary margin for the floor broker. In other words, the order may read "Buy at 5 with dime discretion." This instruction enables the floor broker to execute the order at 5.10 if he feels that the market will never reach 5. Under no circumstances, however, can the order be executed at a price higher than 5.10. Other orders may or may not be accepted·on some option exchanges. Stop Order. This order is not always valid on all option exchanges. A stop order becomes a market order when the security trades at or through the price specified on the order. Buy stop orders are placed above the current market price, and sell stop orders are entered below the current market price. Such orders are used to either limit loss or protect a profit. For example, if a holder's option is selling for 3, a sell stop order for 2 is activated if the market drops down below the 2 level, whereupon the floor broker would execute the order as soon as possible. The customer, however, is not guaranteed that the trade will be exactly at 2. Stop-Limit Order. This order becomes a limit order when the specified price is reached. Whereas the stop order has to be executed as soon as the stop price is reached, the stop-limit may or may not be filled, depending on market behav­ ior. For instance, if the option is trading at 3 while a stop-limit order is placed at a price of 2, the floor broker may not be able to get a trade exactly at 2. If the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:56 SCORE: 29.00 ================================================================================ 34 Part I: Basic Properties of Stock Options option continues to decline through 2 - 1.90, 1.80, 1.70, and so on - without ~ ever regaining the 2 level, then the broker's hands are tied. He may not execute what is now a limit order unless the call trades at 2. Good-Until-Canceled Order. A limit, stop, or stop-limit order may be des­ ignated "good until canceled." If the conditions for the order execution do not occur, the order remains valid for 6 months without renewal by the customer. Customers using an on-line broker will not be able to enter "market not held" orders, and may not be able to use stop orders or good-until-canceled orders either, depending on the brokerage firm. PROFITS AND PROFIT GRAPHS A visual presentation of the profit potential of any position is important to the over­ all understanding and evaluation of it. In option trading, the many multi-security positions especially warrant strict analysis: stock versus options (as in covered or ratio writing) or options versus options (as in spreads). Some strategists prefer a table list­ ing the outcomes of a particular strategy for the stock at various prices; others think the strategy is more clearly demonstrated by a graph. In the rest of the text, both a table and a graph will be presented for each new strategy discussed. Example: A customer wishes to evaluate the purchase of a call option. The potential profits or losses of a purchase of an XYZ July 50 call at 4 can be arrayed in either a table or a graph of outcomes at expiration. Both Table 1-5 and Figure 1-5 depict the same information; the graph is merely the line representing the column marked "Profit or Loss" in the table. The vertical axis represents dollars of profit or loss, and the horizontal axis shows the stock price at expiration. In this case, the dollars of prof­ it and the stock price are at the expiration date. Often, the strategist wants to deter­ mine what the potential profits and losses will be before expiration, rather than at the expiration date itself. Tables and graphs lend themselves well to the necessary analy­ sis, as will be seen in detail in various places later on. In practice, such an example is too simple to require a table or a graph - cer­ tainly not both - to evaluate the potential profits and losses of a simple call purchase held to expiration. However, as more complex strategies are discussed, these tools become ever more useful for quickly determining such things as when a position makes money and when it loses, or how fast one's risk increases at certain stock prices. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:61 SCORE: 45.00 ================================================================================ CHAPl'ER 2 Covered Call Writing Covered call writing is the name given to the strategy by which one sells a call option while simultaneously owning the obligated number of shares of underlying stock. The writer should be mildly bullish, or at least neutral, toward the underlying stock. By writing a call option against stock, one always decreases the risk of owning the stock. It may even be possible to profit from a covered write if the stock declines somewhat. However, the covered call writer does limit his profit potential and there­ fore may not fully participate in a strong upward move in the price of the underlying stock. Use of this strategy is becoming so common that the strategist must under­ stand it thoroughly. It is therefore discussed at length. THE IMPORTANCE OF COVERED CALL WRITING COVERED CALL WRITING FOR DOWNSIDE PROTECTION Example: An investor owns 100 shares of XYZ common stock, which is currently sell­ ing at $48 per share. If this investor sells an XYZ July 50 call option while still hold­ ing his stock, he establishes a covered write. Suppose the investor receives $300 from the sale of the July 50 call. If XYZ is below 50 at July expiration, the call option that was sold expires worthless and the investor earns the $300 that he originally received for writing the call. Thus, he receives $300, or 3 points, of downside protection. That is, he can afford to have the XYZ stock drop by 3 points and still break even on the total transaction. At that time he can write another call option if he so desires. Note that if the underlying stock should fall by more than 3 points, there will be a loss on the overall position. Thus, the risk in the covered writing strategy material­ izes if the stock falls by a distance greater than the call option premium that was orig­ inally taken in. 39 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:62 SCORE: 38.00 ================================================================================ 40 Part II: Call Option Strategies THE BENEFITS OF AN INCREASE IN STOCK PRICE If XYZ increases in price moderately, the trader may be able to have the best of both worlds. Example: If XYZ is at or just below 50 at July expiration, the call still expires worth­ less, and the investor makes the $300 from the option in addition to having a small profit from his stock purchase. Again, he still owns the stock. Should XYZ increase in price by expiration to levels above 50, the covered writer has a choice of alternatives. As one alternative, he could do nothing, in which case the option would be assigned and his stock would be called away at the striking price of 50. In that case, his profits would be equal to the $300 received from selling the call plus the profit on the increase of his stock from the purchase price of 48 to the sale price of 50. In this case, however, he would no longer own the stock. If as another alternative he desires to retain his stock ownership, he can elect to buy back ( or cover) the written call in the open market. This decision might involve taking a loss on the option part of the covered writing transaction, but he would have a cor­ respondingly larger profit, albeit unrealized, from his stock purchase. Using some specific numbers, one can see how this second alternative works out. Example: XYZ rises to a price of 60 by July expiration. The call option then sells near its intrinsic value of 10. If the investor covers the call at 10, he loses $700 on the option portion of his covered write. (Recall that he originally received $300 from the sale of the option, and now he is buying it back for $1,000.) However, he relieves the obligation to sell his stock at 50 ( the striking price) by buying back the call, so he has an unrealized gain of 12 points in the stock, which was purchased at 48. His total profit, including both realized and unrealized gains, is $500. This profit is exactly the same as he would have made if he had let his stock be called from him. If called, he would keep the $300 from the sale of the call, and he would make 2 points ( $200) from buying the stock at 48 and selling it, via exercise, at 50. This profit, again, is a total of $500. The major difference between the two cases is that the investor no longer owns his stock after letting it be called away, whereas he retains stock ownership if he buys back the written call. Which of the two alter­ natives is the better one in a given situation is not always clear. No matter how high the stock climbs in price, the profit from a covered write is limited because the writer has obligated himself to sell stock at the striking price. The covered writer still profits when the stock climbs, but possibly not by as much as he might have had he not written the call. On the other hand, he is receiving $300 of immediate cash inflow, because the writer may take the premium immediately and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:63 SCORE: 29.00 ================================================================================ Gapter 2: Covered Call Writing 41 do with it as he pleases. That income can represent a substantial increase in the income currently provided by the dividends on the underlying stock, or it can act to offset part of the loss in case the stock declines. For readers who prefer formulae, the profit potential and break-even point of a covered write can be summarized as follows: Maximum profit potential = Strike price Stock price + Call price Downside break-even point = Stock price - Call price QUANTIFICATION OF THE COVERED WRITE Table 2-1 and Figure 2-1 depict the profit graph for the example involving the XYZ covered write of the July 50 call. The table makes the assumption that the call is bought back at parity. If the stock is called away, the same total profit of $500 results; but the price involved on the stock sale is always 50, and the option profit is always $300. Several conclusions can be drawn. The break-even point is 45 (zero total prof­ it) with risk below 45; the maximum profit attainable is $500 if the position is held until expiration; and the profit if the stock price is unchanged is $300, that is, the cov­ ered writer makes $300 even if his stock goes absolutely nowhere. The profit graph for a covered write always has the shape shown in Figure 2-1. Note that the maximum profit always occurs at all stock prices equal to or greater than the striking price, if the position is held until expiration. However, there is downside risk. If the stock declines in price by too great an amount, the option pre­ mium cannot possibly compensate for the entire loss. Downside protective strategies, which are discussed later, attempt to deal with the limitation of this downside risk. TABLE 2-1. The XYZ July 50 call. XYZ Price Stock July 50 Call Call Total at Expiration Profit at Expiration Profit Profit 40 -$ 800 0 +$300 -$500 45 - 300 0 + 300 0 48 0 0 + 300 + 300 50 + 200 0 + 300 + 500 55 + 700 5 - 200 + 500 60 + 1,200 10 - 700 + 500 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:64 SCORE: 21.00 ================================================================================ 42 FIGURE 2-1. XYZ covered write. C +$500 0 e ·a. i.ti cii en $0 en 0 ...J 0 ~ a. Part II: Call Option Strategies Maximum Profit Range 50 55 60 "-. Downside Risk Stock Price at Expiration COVERED WRITING PHILOSOPHY The primary objective of covered writing, for most investors, is increased income through stock ownership. An ever-increasing number of private and institutional investors are writing call options against the stocks that they own. The facts that the option premium acts as a partial compensation for a decline in price by the underly­ ing stock, and that the premium represents an increase in income to the stockhold­ er, are evident. The strategy of owning the stock and writing the call will outperform outright stock ownership if the stock falls, remains the same, or even rises slightly. In fact, the only time that the outright owner of the stock will outperform a covered writer is if the stock increases in price by a relatively substantial amount during the life of the call. Moreover, if one consistently writes call options against his stock, his portfolio will show less variability of results from quarter to quarter. The total posi­ tion - long stock and short option - has less volatility than the stock alone, so on a quarter-by-quarter basis, results will be closer to average than they would be with normal stock ownership. This is an attractive feature, especially for portfolio man­ agers. However, one should not assume that covered writing will outperform stock ownership. Stocks sometimes tend to make most of their gains in large spurts. A cov­ ered writer will not participate in moves such as that. The long-term gains that are quoted for holding stocks include periods of large gains and sometimes periods of large losses as well. The covered writer will not participate in the largest of those gains, since his profit potential is limited. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:65 SCORE: 26.00 ================================================================================ Chapter 2: Covered Call Writing 43 PHYSICAL LOCATION Of THE STOCK Before getting more involved in the details of covered writing strategy, it may be use­ ful to review exactly what stock holdings may be written against. Recall that this dis­ cussion applies to listed options. If one has deposited stock with his broker in either a cash or a margin account, he may write an option for each 100 shares that he owns without any additional requirement. However, it is possible to write covered options without actually depositing stock with a brokerage firm. There are several ways in which to do this, all involving the deposit of stock with a bank. Once the stock is deposited with the bank, the investor may have the bank issue an escrow receipt or letter of guarantee to the brokerage firm at which the investor does his option business. The bank must be an "approved" bank in order for the bro­ kerage firm to accept a letter of guarantee, and not all firms accept letters of guaran­ tee. These items cost money, and as a new receipt or letter is required for each new option written, the costs may become prohibitive to the customer if only 100 or 200 shares of stock are involved. The cost of an escrow receipt can range from as low as $15 to upward of $40, depending on the bank involved. There is another alternative open to the customer who wishes to write options without depositing his stock at the brokerage firin. He may deposit his stock with a bank that is a member of the Depository Trust Corporation (DTC). The DTC guar­ antees the Options Clearing Corporation that it will, in fact, deliver stock should an assignment notice be given to the call writer. This is the most convenient method for the investor to use, and is the one used by most of the institutional covered writing investors. There is usually no additional charge for this service by the bank to insti­ tutional accounts. However, since only a limited number of banks are members of DTC, and these banks are generally the larger banks located in metropolitan centers, it may be somewhat difficult for many individual investors to take advantage of the DTC opportunity. TYPES Of COVERED WRITES While all covered writes involve selling a call against stock that is owned, different terms are used to describe various categories of covered writing. The two broadest terms, under which all covered writes can be classified, are the out-of the-rrwney cov­ ered write and the in-the-rrwney covered write. These refer, obviously, to whether the option itself was in-the-money or out-of-the-money when the write was first estab­ lished. Sometimes one may see covered writes classified by the nature of the stock involved (low-priced covered write, high-yield covered write, etc;), but these are only subcases of the two broad categories. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:66 SCORE: 18.00 ================================================================================ 44 Part II: Call Option Strategies. In general, out-of-the-money covered writes offer higher potential rewards but have less risk protection than do in-the-money covered writes. One can establish an aggressive or defensive covered writing position, depending on how far the call option is in- or out-of-the-money when the write is established. In-the-money writes are more defensive covered writing positions. Some examples may help to illustrate how one covered write can be consider­ ably more conservative, from a strategy viewpoint, than another. Example: XYZ common stock is selling at 45 and two options are being considered for writing: an XYZ July 40 selling for 8, and an XYZ July 50 selling for 1. Table 2-2 depicts the profitability of utilizing the July 40 or the July 50 for the covered writing. The in-the-money covered write of the July 40 affords 8 points, or nearly 18% pro­ tection down to a price of 37 (the break-even point) at expiration. The out-of-the­ money covered write of the July 50 offers only 1 point of downside protection at expi­ ration. Hence, the in-the-rrwney covered write offers greater downside protection than does the out-of-the-rrwney covered write. This statement is true in general - not merely for this example. In the balance of the financial world, it is normally true that investment posi­ tions offering less risk also have lower reward potential. The covered writing exam­ ple just given is no exception. The in-the-money covered write of the July 40 has a maximum potential profit of $300 at any point above 40 at the time of expiration. However, the out-of-the-money covered write of the July 50 has a maximum poten­ tial profit of $600 at any point above 50 at expiration. The maximum potential profit of an out-of-the-rrwney covered write is generally greater than that of an in-the­ rrwney write. TABLE 2-2. Profit or loss of the July 40 and July 50 calls. In-the-Money Write Out-of-the-Money Write of July 40 of July SO Stock of Total Stock at Total Expiration Profit Expiration Profit 35 -$200 35 -$900 37 0 40 - 400 40 + 300 44 0 45 + 300 45 + 100 50 + 300 50 + 600 60 + 300 60 + 600 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:67 SCORE: 37.00 ================================================================================ Cl,apter 2: Covered Call Writing 45 To make a true comparison between the two covered writes, one must look at what happens with the stock between 40 and 50 at expiration. The in-the-money write attains its maximum profit anywhere within that range. Even a 5-point decline by the underlying stock at expiration would still leave the in-the-money writer with his maximum profit. However, realizing the maximum profit potential with an out-of the-money covered write always requires a rise in price by the underlying stock. This further illustrates the more conservative nature of the in-the-money write. It should be noted that in-the-money writes, although having a smaller profit potential, can still be attractive on a percentage return basis, especially if the write is done in a margin account. One can construct a more aggressive position by writing an out-of-the-money call. One's outlook for the underlying stock should be bullish in that case. If one is neutral or moderately bearish on the stock, an in-the-money covered write is more appropriate. If one is truly bearish on a stock he owns, he should sell the stock instead of establishing a covered write. THE TOTAL RETURN CONCEPT OF COVERED WRITING When one writes an out-of-the-money option, the overall position tends to reflect more of the result of the stock price movement and less of the benefits of writing the call. Since the premium on an out-of-the-money call is relatively small, the total posi­ tion will be quite susceptible to loss if the stock declines. If the stock rises, the posi­ tion will make money regardless of the result in the option at expiration. On the other hand, an in-the-money write is more of a "total" position - taking advantage of the benefit of the relatively large option premium. If the stock declines, the position can still make a profit; in fact, it can even make the maximum profit. Of course, an in­ the-money write will also make money if the stock rises in price, but the profit is not generally as great in percentage terms as is that of an out-of-the-money write. Those who believe in the total return concept of covered writing consider both downside protection and maximum potential return as important factors and are willing to have the stock called away, if necessary, to meet their objectives. When premiums are moderate or small, only in-the-money writes satisfy the total return philosophy. Some covered writers prefer never to lose their stock through exercise, and as a result will often write options quite far out-of-the-money to minimize the chances of being called by expiration. These writers receive little downside protection and, to make money, must depend almost entirely on the results of the stock itself. Such a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:68 SCORE: 25.00 ================================================================================ 46 Part II: Call Option Strategies philosophy is more like being a stockholder and trading options against one's stock position than actually operating a covered writing strategy. In fact, some covered writers will attempt to buy back written options for quick profits if such profits mate­ rialize during the life of the covered write. This, too, is a stock ownership philosophy, not a covered writing strategy. The total return concept represents the true strategy in covered writing, whereby one views the entire position as a single entity and is not predominantly concerned with the results of his stock ownership. THE CONSERVATIVE COVERED WRITE Covered writing is generally accepted to be a conservative strategy. This is because the covered writer always has less risk than a stockholder, provided that he holds the covered write until expiration of the written call. If the underlying stock declines, the covered writer will always offset part of his loss by the amount of the option premi­ um received, no matter how small. As was demonstrated in previous sections, however, some covered writes are clearly more conservative than others. Not all option writers agree on what is meant by a conservative covered write. Some believe that it involves writing an option (probably out-of-the-money) on a conservative stock, generally one with high yield and low volatility. It is true that the stock itself in such a position is conservative, but the position is more aptly termed a covered write on a conservative stock. This is dis­ tinctly different from a conservative covered write. A true conservative covered write is one in which the total position is conserva­ tive - offering reduced risk and a good probability of making a profit. An in-the-money wiite, even on a stock that itself is not conservative, can become a conservative total position when the option itself is properly chosen. Clearly, an investor cannot write calls that are too deeply in-the-money. If he did, he would get large amounts of down­ side protection, but his returns would be severely limited. If all that one desired was maximum protection of his money at a nominal rate of profit, he could leave the money in a bank. Instead, the conservative covered writer strives to make a potential­ ly acceptable return while still receiving an above-average amount of protection. Example: Again assume XYZ common stock is selling at 45 and an XYZ July 40 call is selling at 8. A covered write of the XYZ July 40 would require, in a cash account, an investment of $3,700 - $4,500 to purchase 100 shares of XYZ, less the $800 received in option premiums. The write has a maximum profit potential of $300. The potential return from this position is therefore $300/$3, 700, just over 8% for the peri­ od during which the write must be held. Since it is most likely that the option has 9 months of life or less, this return would be well in excess of 10% on a per annum ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:69 SCORE: 26.00 ================================================================================ Chapter 2: Covered Call Writing 47 basis. If the write were done in a margin account, the return would be considerably higher. Note that we have ignored dividends paid by the underlying stock and commis­ sion charges, factors that are discussed in detail in the next section. Also, one should be aware that if he is looking at an annualized return from a covered write, there is no guarantee that such a return could actually be obtained. All that is certain is that the writer could make 8% in 9 months. There is no guarantee that 9 months from now, when the call expires, there will be an equivalent position to establish that will extend the same return for the remainder of the annualization period. Annual returns should be used only for comparative purposes between covered writes. The writer has a position that has an annualized return (for comparative pur­ poses) of over 10% and 8 points of downside protection. Thus, the total position is an investment that will not lose money unless XYZ common stock falls by more than 8 points, or about 18%; and is an investment that could return the equivalent of 10% annually should XYZ common stock rise, remain the same, or fall by 5 points (to 40). This is a conservative position. Even if XYZ itself is not a conservative stock, the action of writing this option has made the total position a conservative one. The only factor that might detract from the conservative nature of the total position would be if XYZ were so volatile that it could easily fall more than 8 points in 9 months. In a strategic sense, the total position described above is better and more con­ servative than one in which a writer buys a conservative stock -yielding perhaps 6 or 7% - and writes an out-of-the-money call for a minimal premium. If this conserva­ tive stock were to fall in price, the writer would be in danger of being in a loss situa­ tion, because here the option is not providing anything more than the most minimal downside protection. As was described earlier, a high-yielding, low-volatility stock will not have much time premium in its in-the-money options, so that one cannot effectively establish an in-the-money write on such a "conservative" stock. COMPUTING RETURN ON INVESTMENT Now that the reader has some general feeling for covered call writing, it is time to discuss the specifics of computing return on investment. One should always know exactly what his potential returns are, including all costs, when he establishes a cov­ ered writing position. Once the procedure for computing returns is clear, one can more logically decide which covered writes are the most attractive. There are three basic elements of a covered write that should be computed before entering into the position. The first is the return if exercised. This is the return on investment that one would achieve if the stock were called away. For an out-of-the- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:70 SCORE: 26.00 ================================================================================ 48 Part II: Call Option Strategies money covered write, it is necessary for the stock to rise in price in order for the return if exercised to be achieved. However, for an in-the-money covered write, the return if exercised would be attained even if the stock were unchanged in price at option expi­ ration. Thus, it is often advantageous to compute the return if unchanged - that is, the return that would be realized if the underlying stock were unchanged when the option expired. One can more fairly compare out-of-the-money and in-the-money covered writes by using the return if unchanged, since no assumption is made concerning stock price movement. The third important statistic that the covered writer should consid­ er is the exact downside break-even point after all costs are included. Once this down­ side break-even point is known, one can readily compute the percentage of downside protection that he would receive from selling the call. Example 1: An investor is considering the following covered write of a 6-month call: Buy 500 XYZ common at 43, sell 5 XYZ July 45 calls at 3. One must first compute the net investment required (Table 2-3). In a cash account, this investment consists of paying for the stock in full, less the net proceeds from the sale of the options. Note that this net investment figure includes all commissions necessary to establish the position. (The commissions used here are approximations, as they vary from firm to firm.) Of course, if the investor withdraws the option premium, as he is free to do, his net investment will consist of the stock cost plus commissions. Once the neces­ sary investment is known, the writer can compute the return if exercised. Table 2-4 illustrates the computation. One first computes the profit if exercised and then divides that quantity by the net investment to obtain the return if exercised. Note that dividends are included in this computation; it is assumed that XYZ stock will pay $500 in dividends on the 500 shares during the life of the call. Moreover, all com­ missions are included as well - the net investment includes the original stock pur­ chase and option sale commissions, and the stock sale commission is explicitly listed. For the return computed here to be realized, XYZ stock would have to rise in price from its current price of 43 to any price above 45 by expiration. As noted ear­ lier, it may be more useful to know what return could be made by the writer if the stock did not move anywhere at all. Table 2-5 illustrates the method of computing the TABLE 2-3. Net investment required-cash account. Stock cost (500 shares at 43) Plus stock purchase commissions Less option premiums received Plus option sale commissions Net cash investment + $21,500 320 1,500 + 60 $20,380 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:71 SCORE: 15.00 ================================================================================ Oapter 2: Covered Call Writing TABLE 2-4. Return if exercised-cash account. Stock sale proceeds (500 shares at 45) Less stock sale commissions Plus dividends earned until expiration Less net investment Net profit if exercised Return if exercised $2,290 = 11 2o/c $20,380 . 0 TABLE 2-5. Return if unchanged-cash account. Unchanged stock value (500 shares at 43) Plus dividends Less net investment Profit if unchanged Return if unchanged $1,620 = 7.9'¼ $20,380 ° + $22,500 330 500 - 20,380 $ 2,290 $21,500 + 500 - 20,380 $ 1,620 49 return if unchanged - also called the static return and sometimes incorrectly referred to as the "expected return." Again, one first calculates the profit and then calculates the return by dividing the profit by the net investment. An important point should be made here: There is no stock sale commission included in Table 2-5. This is the most common way of calculating the return if unchanged; it is done this way because in a majority of cases, one would continue to hold the stock if it were unchanged and would write another call option against the same stock. Recall again, though, that if the written call is in-the-rrwney, the return if unchanged is the same as the return if exercised. Stock sale commissions must therefore be included in that case. Once the necessary returns have been computed and the writer has a feeling for how much money he could make in the covered write, he next computes the exact downside break-even point to determine what kind of downside protection the writ­ ten call provides (Table 2-6). The total return concept of covered writing necessitates viewing both potential income and downside protection as important criteria for selecting a writing position. If the stock were held to expiration and the $500 in div­ idends received, the writer would break even at a price of 39.8. Again, a stock sale commission is not generally included in the break-even point computation, because ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:72 SCORE: 14.00 ================================================================================ 50 Part II: Call Option Strategies the written call would expire totally worthless and the writer might then write anoth­ er call on the same stock. Later, we discuss the subject of continuing to write against stocks already owned. It will be seen that in many cases, it is advantageous to con­ tinue to hold a stock and write against it again, rather than to sell it and establish a covered write in a new stock. TABLE 2-6. Downside break-even point-cash account. Net investment Less dividends Total stock cost to expiration Divide by shares held Break-even price $20,380 500 $19,880 + 500 39.8 Next, we translate the break-even price into percent downside protection (Table 2-7), which is a convenient way of comparing the levels of downside protec­ tion among variously priced stocks. We will see later that it is actually better to com­ pare the downside protection with the volatility of the underlying stock. However, since percent downside protection is a common and widely accepted method that is more readily calculated, it is necessary to be familiar with it as well. Before moving on to discuss what kinds of returns one should attempt to strive for in which situati_ons, the same example will be worked through again for a covered write in a margin account. The use of margin will provide higher potential returns, since the net investment will be smaller. However, the margin interest charge incurred on the debit balance (the amount of money borrowed from the brokerage firm) will cause the break-even point to be higher, thus slightly reducing the amount of downside protection available from writing the call. Again, all commissions to establish the position are included in the net investment computation. TABLE 2-7. Percent downside protection-cash account. Initial stock price Less break-even price Points of protection Divide by original stock price Equals percent downside protection 43 -39.8 3.2 +43 7.4% ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:73 SCORE: 34.00 ================================================================================ Clrapter 2: Covered Call Writing 51 Example 2: Recall that the net investment for the cash write was $20,380. A margin covered write requires less than half of the investment of a cash write when the margin rate (set by the Federal Reserve) is 50%. In a margin account, if one desires to remove the premium from the account, he may do so immediately provid­ ed that he has enough reserve equity in the account to cover the purchase of the stock. If he does so, his net investment would be equal to the debit balance calcula­ tion shown on the right in Table 2-8. TABLE 2-8. Net investment required-margin account. Stock cost $21,500 Plus stock commissions + 320 Debit balance calculation: Net stock cost $21,820 Net stock cost $21,820 Times margin rate X 50% Less equity - 10,910 Equity required $10,910 Debit balance $10,910 Less premiums received 1,500 (at 50% margin) Plus option commissions + 60 Net margin investment $ 9,470 Tables 2-9 to 2-12 illustrate the computation of returns from writing on margin. If one has already computed the cash returns, he can use method 2 most easily. Method 1 involves no prior profit calculations. TABLE 2-9. Return if exercised-margin account. Method 1 Method 2 Stock sale proceeds Less stock commission Plus dividends $22,500 Net profit if exercised-cash $2,290 + Less margin interest charges 330 500 (10% on $10,910 for 6 months) - 545 Less debit balance Less net margin investment Net profit-margin - 10,910 - 9 470 $ 1,745 Less margin interest charges - Net profit if exercised­ margin $1,745 Return if exercised = $9 ,470 = 18.4% 545 $1,745 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:74 SCORE: 35.00 ================================================================================ 52 TABLE 2-10. Return if unchanged-margin account. Method 1 Unchanged stock value (500 shares at 43) Plus dividends Less margin interest charges (10% on $10,910 debit for 6 months) Less debit balance Less net investment (margin) Net profit if unchanged­ margin $21,500 + 500 545 10,910 - 9 470 $ 1,075 Part II: Call Option Strategies Method 2 Profit if unchanged-cash Less margin interest charges - Net profit if unchanged­ margin $1,620 545 $1,075 Return if unchanged = $ l ,075 = 11 .4% $9,470 TABLE 2-11. Break-even point-margin write. Net margin investment Plus debit balance Less dividends Plus margin interest charges Total stock cost to expiration Divide by shares held Break-even point-margin TABLE 2-12. Percent downside protection-margin write. Initial stock price Less break-even price-margin Points of protection Divide by original stock price Equals percent downside protection-margin $ 9,470 + 10,910 500 + 545 $20,425 + 500 40.9 43 -40.9 2.1 +43 4.9% The return if exercised is 18.4% for the covered write using margin. In Example 1 the return if exercised for a cash write was computed as 11.2%. Thus, the return if exercised from a margin write is considerably higher. In fact, unless a fairly deep in­ the-money write is being considered, the return on margin will always be higher than ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:75 SCORE: 63.00 ================================================================================ Cl,apter 2: Covered Call Writing 53 the return from cash. The farther out-of-the-money that the written call is, the big­ ger the discrepancy between cash and margin returns will be when the return if exer­ cised is computed. As with the computation for return if exercised for a write on margin, the return if unchanged calculation is similar for cash and margin also. The only difference is the subtraction of the margin interest charges from the profit. The return if unchanged is also higher for a margin write, provided that there is enough option premium to com­ pensate for the margin interest charges. The return if unchanged in the cash example was 7.9% versus 11.4% for the margin write. In general, the farther from the strike in either direction - out-of-the-money or in-the-money - the less the return if unchanged on margin will exceed the cash return if unchanged. In fact, for deeply out­ of-the-money or deeply in-the-money calls, the return if unchanged will be higher on cash than on margin. Table 2-11 shows that the break-even point on margin, 40.9, is higher than the break-even point from a cash write, 39.8, because of the margin inter­ est charges. Again, the percent downside protection can be computed as shown in Table 2-12. Obviously, since the break-even point on margin is higher than that on cash, there is less percent downside protection in a margin covered write. One other point should be made regarding a covered write on margin: The bro­ kerage firm will loan you only half of the strike price amount as a maximum. Thus, it is not possible, for example, to buy a stock at 20, sell a deeply in-the-money call struck at 10 points, and trade for free. In that case, the brokerage firm would loan you only 5 - half the amount of the strike. Even so, it is still possible to create a covered call write on margin that has little or even zero margin .requirement. For example, suppose a stock is selling at 38 and that a long-term LEAPS option struck at 40 is selling for 19. Then the margin requirement is zero! This does not mean you're getting something for free, however. True, your invest­ ment is zero, but your risk is still 19 points. Also, your broker would ask for some sort of minimum margin to begin with and would of course ask for maintenance margin if the underlying stock should fall in price. Moreover, you would be paying margin interest all during the life of this long-term LEAPS option position. Leverage can be a good thing or a bad thing, and this strategy has a great deal of leverage. So be careful if you utilize it. COMPOUND INTEREST The astute reader will have noticed that our computations of margin interest have been overly simplistic; the compounding effect of interest rates has been ignored. That is, since interest charges are normally applied to an account monthly, the investor will be paying interest in the later stages of a covered writing position not only on the original debit, but on all previous monthly interest charges. This effect is described in detail in a later chapter on arbitrage techniques. Briefly stated, rather ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:76 SCORE: 20.00 ================================================================================ 54 Part II: Call Option Strategies than computing the interest charge as the debit times the interest rate multiplied by the time to expiration, one should technically use: Margin interest charges = Debit [(l + r/ -1] where r is the interest rate per month and t the number of months to expiration. (It would be incorrect to use days to expiration, since brokerage firms compute interest monthly, not daily.) In Example 2 of the preceding section, the debit was $10,910, the time was 6 months, and the annual interest rate was 10%. Using this more complex formula, the margin interest charges would be $557, as opposed to the $545 charge computed with the simpler formula. Thus, the difference is usually small, in terms of percent­ age, and it is therefore comrrwn practice to use the simpler method. SIZE OF THE POSITION So far it has been assumed that the writer was purchasing 500 shares of XYZ and sell­ ing 5 calls. This requires a relatively considerable investment for one position for the individual investor. However, one should be aware that buying too few shares for cov­ ered writing purposes can lower returns considerably. Example: If an investor were to buy 100 shares of XYZ at 43 and sell l July 45 call for 3, his return if exercised would drop from the 11.2% return (cash) that was com­ puted earlier to a return of9.9% in a cash account. Table 2-13 verifies this statement. Since commissions are less, on a per-share basis, when one buys more stock and sells more calls, the returns will naturally be higher with a 500- or 1,000-share posi­ tion than with a 100- or 200-share position. This difference can be rather dramatic, as Tables 2-14 and 2-15 point out. Several interesting and worthwhile conclusions can be drawn from these tables. The first and most obvious conclusion is that the rrwre shares TABLE 2-13. Cash investment vs. return. Net Investment-Cash ( l 00 shares) Stock cost $4,300 Plus commissions + 85 Less option premium 300 Plus option commissions + 25 Net investment $4,110 Return If Exercised-Cash ( l 00 shares) Stock sale price Stock commissions Plus dividend Less net investment Net profit if exercised $4,500 85 + 100 - 4 110 $ 405 Return if exercised = $4 05 = 9. 9% $4,110 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:77 SCORE: 24.00 ================================================================================ Cl,apter 2: Covered Call Writing 55 one writes against, the higher his returns and the lower his break-even point will be. This is true for both cash and margin and is a direct result of the way commissions are figured: Larger trades involve smaller percentage commission charges. While the per­ centage returns increase as the number of shares increases for both cash and margin covered writing, the increase is much more dramatic in the case of margin. Note that in Table 2-14, which depicts cash transactions, the return from writing against 100 shares is 9.9% and increases to 12. 7% if 2,000 shares are written against. This is an increase, but not a particularly dramatic one. However, in Table 2-15, the return if exercised more than doubles (21.6 vs. 10.4) and the return if unchanged nearly triples (13.0 vs. 4.4) when the 100-share write is compared to the 2,000-share write. This effect is more dramatic for margin writes due to two factors - the lower investment required and the more burdensome effect of margin interest charges on the profits of smaller positions. This effect is so dramatic that a 100-share write in a cash account in our example actually offers a higher return if unchanged than does the margin write - 7.1 % vs. 4.4%. This implies that one should carefully compute his potential returns if he is writing against a small number of shares on margin. TABLE 2-14. Cash covered writes (costs included). Shares Written Against 100 200 300 400 500 1,000 2,000 Return if exercised (%) 9.9 10.0 10.4 10.8 11.2 12.1 12.7 Re~rn if unchanged(%) 7.1 7.2 7.5 7.7 7.9 8.4 8.7 Break-even point 40.1 40.0 39.9 39.9 39.8 39.6 39.5 TABLE 2-15. Margin covered writes (costs included). Shares Written Against 100 200 300 400 500 1,000 2,000 Return if exercised (%) 10.4 15.8 16.6 17.4 18.4 20.4 21.6 Return if unchanged (%) 4.4 9.8 10.3 10.8 11.4 12.3 13.0 Break-even point 41.2 41.1 41.0 41.0 40.9 40.7 40.6 WHAT A DIFFERENCE A DIME MAKES Another aspect of covered writing that can be important as far as potential returns are concerned is, of course, the prices of the stock and option involved in the write. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:78 SCORE: 37.00 ================================================================================ 56 Part II: Call Option Strategies It may seem insignificant that one has to pay an extra few cents for the stock or pos­ sibly receives a dime or 20 cents less for the call, but even a relatively small fraction can alter the potential returns by a surprising amount. This is especially true for in­ the-money writes, although any write will be affected. Let us use the previous 500- share covered writing example, again including all costs. As before, the results are more dramatic for the margin write than for the cash write. In neither case does the break-even point change by much. However, the potential returns are altered significantly. Notice that if one pays an extra dime for the stock and receives a dime less for the call - the far right-hand column in Table 2-16 - he may greatly negate the effect of writing against a larger number of shares. From Table 2-16, one can see that writing against 300 shares at those prices (43 for the stock and 3 for the call) is approximately the same return as writing against 500 shares if the stock costs 431/s and the option brings in 27/s. Table 2-16 should clearly demonstrate that entering a covered writing order at the market may not be a prudent thing to do, especially if one's calculations for the potential returns are based on last sales or on closing prices in the newspaper. In the next section, we discuss in depth the proper procedure for entering a covered writ­ ing order. TABLE 2-16. Effect of stock and option prices on writing returns. Buy Stock at 43 Buy Stock at 43.10 Sell Call at 3 Sell Call at 3 Return if exercised 11.2% cash 10.9% cash 18.4% margin 17.7% margin Return if unchanged 7.9% cash 7.6% cash 11 .4% margin 10.7% margin Break-even point 39.8 cash 39.9 cash 40.9 margin 41.0 margin EXECUTION OF THE COVERED WRITE ORDER Buy Stock at 43. I 0 Sell Call at 2.90 10.6% cash 16. 9% margin 7.3% cash 9.9% margin 40.0 cash 41.1 margin When establishing a covered writing position, the question often arises: Which should be done first - buy the stock or sell the option? The correct answer is that nei­ ther should be done first! In fact, a simultaneous transaction of buying the stock and selling the option is the only way of assuring that both sides of the covered write are established at desired price levels. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:79 SCORE: 24.00 ================================================================================ Cl,apter 2: Covered Call Writing 57 If one "legs" into the position - that is, buys the stock first and then attempts to sell the option, or vice versa - he is subjecting himself to a risk. Example: An investor wants to buy XYZ at 43 and sell the July 45 call at 3. Ifhe first sells the option at 3 and then tries to buy the stock, he may find that he has to pay more than 43 for the stock. On the other hand, if he tries to buy the stock first and then sell the option, he may find that the option price has moved down. In either case the writer will be accepting a lower return on his covered write. Table 2-16 demon­ strated how one's returns might be affected ifhe has to give up an eighth by "legging" into the position. ESTABLISHING A NET POSITION What the covered writer really wants to do is ensure that his net price is obtained. If he wants to buy stock at 43 and sell an option at 3, he is attempting to establish the position at 40 net. He normally would not mind paying 43.10 for the stock if he can sell the call at 3.10, thereby still obtaining 40 net. A "net" covered writing order must be placed with a brokerage firm because it is essential for the person actually executing the order to have full access to both the stock exchange and the option exchange. This is also referred to as a contingent order. Most major brokerage firms offer this service to their clients, although some place a minimum number of shares on the order. That is, one must write against at least 500 or 1,000 shares in order to avail himself of the service. There are, however, brokerage firms that will take net orders even for 100-share covered writes. Since the chances of giving away a dime are relatively great if one attempts to execute his own order by placing separate orders on two exchanges - stock and option - he should avail himself of the broker's service. Moreover, if his orders are for a small number of shares, he should deal with a broker who will take net orders for small positions. The reader must understand that there is no guarantee that a net order will be filled. The net order is always a "not held" order, meaning that the customer is not guaranteed an execution even if it appears that the order could be filled at prevailing market bids and offers. Of course, the broker will attempt to fill the order if it can reasonably be accomplished, since that is his livelihood. However, if the net order is slightly away from current market prices, the broker may have to "leg" into the posi­ tion to fill the order. The risk in this is the broker's responsibility, not the customer's. Therefore, the broker may elect not to take the risk and to report "nothing done" - the order is not filled. If one buys stock at 43 and sells the call at 3, is the return really the same as buy­ ing the stock at 43.10 and selling the call at 3.10? The answer is, yes, the returns are ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:80 SCORE: 12.00 ================================================================================ 58 Part II: Call Option Strategies very similar when the prices differ by small amounts. This can be seen without the use of a table. If one pays a dime more for the stock, his investment increases by $10 per 100 shares, or $50 total on a 500-share transaction. However, the fact that he has received an extra dime for the call means that the investment is reduced by $62.50. Thus, there is no effect on the net investment except for commissions. The commis­ sion on 500 shares at 43.10 may be slightly higher than the commission for 500 shares at 43. Similarly, the commission on 5 calls at 3.10 may be slightly higher than that on 5 calls at 3. Even so, the increase in commissions would be so small that it would not affect the return by more than one-tenth of 1 %. To carry this concept to extremes may prove somewhat misleading. If one were to buy stock at 40½ and sell the call at ½, he would still be receiving 40 net, but sev­ eral aspects would have changed considerably. The return if exercised remains amaz­ ingly constant, but the return if unchanged and the percentage downside protection are reduced dramatically. If one were to buy stock at 48 and sell the call at 8 - again for 40 net - he would improve the return if unchanged and the percentage downside protection. In reality, when one places a "net" order with a brokerage firm, he nor­ mally gets an execution with prices quite close to the ones at the time the order was first entered. It would be a rare case, indeed, when either upside or downside extremes such as those mentioned here would occur in the same trading day. SELECTING A COVERED WRITING POSITION The preceding sections, in describing types of covered writes and how to compute returns and break-even points, have laid the groundwork for the ultimate decision that every covered writer must make: choosing which stock to buy and which option to write. This is not necessarily an easy task, because there are large numbers of stocks, striking prices, and expiration dates to choose from. Since the primary objective of covered writing for most investors is increased income through stock ownership, the return on investment is an important consider­ ation in determining which write to choose. However, the decision must not be made on the basis of return alone. More volatile stocks will offer higher returns, but they may also involve more risk because of their ability to fall in price quickly. Thus, the amount of downside protection is the other important objective of covered writing. Finally, the quality and technical or fundamental outlook of the underlying stock itself are of importance as well. The following section will help to quantify how these factors should be viewed by the covered writer. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:81 SCORE: 16.00 ================================================================================ Chapter 2: Covered Call Writing PROJECTED RETURNS 59 The return that one strives for is somewhat a matter of personal preference. In gen­ eral, the annualized return if unchanged should be used as the comparative measure between various covered writes. In using this return as the measuring criterion, one does not make any assumptions about the stock moving up in price in order to attain the potential return. A general rule used in deciding what is a minimally acceptable return is to consider a covered writing position only when the return if unchanged is at least 1 % per month. That is, a 3-month write would have to offer a return of at least 3% and a 6-month write would have to have a return if unchanged of at least 6%. During periods of expanded option premiums, there may be so many writes that satisfy this criterion that one would want to raise his sights somewhat, say to 1 ½% or 2% per month. Also, one must feel personally comfortable that his minimum return criterion - whether it be 1 % per month or 2% per month - is large enough to com­ pensate for the risks he is taking. That is, the downside risk of owning stock, should it fall far enough to outdistance the premium received, should be adequately com­ pensated for by the potential return. It should be pointed out that 1 % per month is not a return to be taken lightly, especially if there is a reasonable assurance that it can be attained. However, if less risky investments, such as bonds, were yielding 12% annually, the covered writer must set his sights higher. Normally, the returns from various covered writing situations are compared by annualizing the returns. One should not, however, be deluded into believing that he can always attain the projected annual return. A 6-month write that offers a 6% return annualizes to 12%. But if one establishes such a position, all that he can achieve is 6% in 6 months. One does not really know for sure that 6 months from now there will be another position available that will provide 6% over the next 6 months. The deeper that the written option is in-the-money, the higher the probability that the return if unchanged will actually be attained. In an in-the-money situation, recall that the return if unchanged is the same as the return if exercised. Both would be attained unless the stock fell below the striking price by expiration. Thus, for an in­ the-money write, the projected return is attained if the stock rises, remains unchanged, or even falls slightly by the time the option expires. Higher potential returns are avail­ able for out-of-the-money writes if the stock rises. However, should the stock remain the same or decline in price, the out-of-the-money write will generally underperform the in-the-money write. This is why the return if unchanged is a good comparison. DOWNSIDE PROTECTION Downside protection is more difficult to quantify than projected returns are. As men­ tioned earlier, the percentage of downside protection is often used as a measure. This ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:82 SCORE: 13.00 ================================================================================ 60 Part II: Call Option Strategies is somewhat misleading, however, since the more volatile stocks will always offer a large percentage of downside protection (their premiums are higher). The difficulty arises in trying to decide if 10% protection on a volatile stock is better than or worse than, say, 6% protection on a less volatile stock. There are mathematical ways to quantify this, but because of the relatively advanced nature of the computations involved, they are not discussed until later in the text, in Chapter 28 on mathemati­ cal applications. Rather than go into involved mathematical calculations, many covered writers use the percentage of downside protection and will only consider writes that offer a certain minimum level of protection, say 10%. Although this is not exact, it does strive to ensure that one has minimal downside protection in a covered write, as well as an acceptable return. A standard figure that is often used is the 10% level of pro­ tection. Alternatively, one may also require that the write be a certain percent in-the­ money, say 5%. This is just another way of arriving at the same concept. THE IMPORTANCE OF STRATEGY In a conservative option writing strategy, one should be looking for minimum returns if unchanged of 1 % per month, with downside protection of at least 10%, as general guidelines. Employing such criteria automatically forces one to write in-the-money options in line with the total return concept. The overall position constructed by using such guidelines as these will be a relatively conservative position - regardless of the volatility of the underlying stock - since the levels of protection will be large but a reasonable return can still be attained. There is a danger, however, in using fixed guidelines, because market conditions change. In the early days of listed options, premiums were so large that virtually every at- or in-the-money covered write satisfied the foregoing criteria. However, now one should work with a ranked list of covered writing positions, or perhaps two lists. A daily computer ranking of either or both of the following categories would help establish the most attractive types of conservative covered writes. One list would rank, by annualized return, the writes that afford, as a minimum, the desired downside protection level, say 10%. The other list would rank, by percentage downside protection, all the writes that meet at least the minimum acceptable return if unchanged, say 12%. If premium lev­ els shrink and the lists become quite small on a daily basis, one might consider expanding the criteria to view more potential situations. On the other hand, if pre­ miums expand dramatically, one might consider using more restrictive criteria, to reduce the number of potential writing candidates. A different group of covered writers may favor a more aggressive strategy of out­ of-the-money writes. There is some mathematical basis to believe, in the long rnn, that ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:83 SCORE: 20.00 ================================================================================ Chapter 2: Covered Call Writing 61 rrwderately out-of the-rrwney covered writes will peiform better than in-the-rrwney writes. In falling or static markets, any covered writer, even the more aggressive one, will outperform the stockowner who does not write calls. The out-of-the-money cov­ ered writer has more risk in such a market than the in-the-money writer does. But in a rising market, the out-of-the-money covered writer will not limit his returns as much as the in-the-money writer will. As stated earlier, the out-of-the-money writer's per­ formance will more closely follow the performance of the underlying stock; that is, it will be more volatile on a quarter-by-quarter basis. There is merit in either philosophy. The in-the-money writes appeal to those investors looking to earn a relatively consistent, moderate rate of return. This is the total return concept. These investors are generally concerned with preservation of capital, thus striving for the greater levels of downside protection available from in­ the-money writes. On the other hand, some investors prefer to strive for higher potential returns through writing out-of-the-money calls. These more aggressive investors are willing to accept more downside risk in their covered writing positions in exchange for the possibility of higher returns should the underlying stock rise in price. These investors often rely on a bullish research opinion on a stock in order to select out-of-the-money writes. Although the type of covered writing strategy pursued is a matter of personal philosophy, it would seem that the benefits of in-the-money strategy- more consis­ tent returns and lessened risk than stock ownership will normally provide - would lead the portfolio manager or less aggressive investor toward this strategy. If the investor is interested in achieving higher returns, some of the strategies to be pre­ sented later in the book may be able to provide higher returns with less risk than can out-of-the-money covered writing. The final important consideration in selecting a covered write is the underlying stock itself. One does not necessarily have to be bullish on the underlying stock to take a covered writing position. As long as one does not foresee a potential decline in the underlying stock, he can feel free to establish the covered writing position. It is generally best if one is neutral or slightly bullish on the underlying stock. If one is bearish, he should not take a covered writing position on that stock, regardless of the levels of protection that can be obtained. An even broader statement is that one should not establish a covered write on a stock that he does not want to own. Some individual investors may have qualms about buying stock they feel is too volatile for them. Impartially, if the return and protection are adequate, the characteristics of the total position are different from those of the underlying stock. However, it is still true that one should not invest in positions that he considers too risky for his portfolio, nor should one establish a covered write just because he likes a particular stock. If the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:85 SCORE: 16.00 ================================================================================ Chapter 2: Covered Call Writing Return if exercised - margin Downside break-even point cash Downside break-even point - margin XYZ 7.9% 46.3 47.6 63 AAA 16.2% 44.9 46.1 Seeing these calculations, the XYZ stockholder may feel that it is not advisable to write against his stock, or he may even be tempted to sell XYZ and buy AAA in order to establish a covered write. Either of these actions could be a mistake. First, he should compute what his returns would be, at current prices, from writing against the XYZ he already owns. Since the stock is already held, no stock buy commissions would be involved. This would reduce the net investment shown below by the stock purchase commissions, or $345, giving a total net investment (cash) of $23,077. In theory, the stockholder does not really make an investment per se; after all, he already owns the stock. However, for the purposes of computing returns, an investment figure is necessary. This reduction in the net investment will increase his profit by the same amount - $345 - thus, bringing the profit up to $1,828. Consequently, the return if exercised (cash) wpuld be 7.9% on XYZ stock already held. On margin, the return would increase to 11.3% after eliminating purchase com­ missions. This return, assumed to be for a 6-month period, is well in excess of 1 % per TABLE 2-17. Summary of covered writing returns, XYZ and AAA. XYZ AAA Buy 500 shares at 50 $25,000 $25,000 Plus stock commissions + 345 + 345 Less option premiums received - 2,000 - 3,000 Plus option sale commissions + 77 + 91 Net investment-cash $23,422 $22,436 Sell 500 shares at 50 $25,000 $25,000 Less stock sale commissions 345 345 Dividend received + 250 0 Less net investment - 23,422 - 22,436 Net profit $ 1,483 $ 2,219 Return if exercised-cash 6.3% 9.9% ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:86 SCORE: 13.00 ================================================================================ ' 64 Part II: Call Option Strategies month, the level nominally used for acceptable covered writes. Thus, the investor who already owns stock may inadvertently be overlooking a potentially attractive cov­ ered write because he has not computed the returns excluding the stock purchase commission on his current stock holding. It could conceivably be an even more extreme oversight for the investor to switch from XYZ to AAA for writing purposes. The investor may consider making this switch because he thinks that he could substantially increase his return, from 6.3% to 9.9% for the 6-month period, as shown in Table 2-17 comparing the two writes. However, the returns are not truly comparable because the investor already owns XYZ. To make the switch, he would first have to spend $345 in stock commis­ sions to sell his XYZ, thereby reducing his profits on AAA by $345. Referring again to the preceding detailed breakdown of the return if exercised, the profit on AAA would then decline to $1,874 on the investment of $22,436, a return if exercised (cash) of 8.4%. On margin, the comparable return from switching stocks would drop to 14.8%. The real comparison in returns from writing against these two stocks should be made in the following manner. The return from writing against XYZ that is already held should be compared with the return from writing against AAA after switching fromXYZ: Return if exercised - cash Return if exercised - margin XYZ Already Held 7.9% 11.3% Switch from XYZ to AAA 8.4% 14.8% Each investor must decide for himself whether it is worth this much smaller increase in return to switch to a more volatile stock that pays a smaller dividend. He can, of course, only make this decision by making the true comparison shown imme­ diately above as opposed to the first comparison, which assumed that both stocks had to be purchased in order to establish the covered write. The same logic applies in situations in which an investor has been doing cov­ ered writing. If he owns stock on which an option has expired, he will have to decide whether to write against the same stock again or to sell the stock and buy a new stock for covered writing purposes. Generally, the investor should write against the stock already held. This justifies the method of computation of return if unchanged for out­ of-the-money writes and also the computation of downside break-even points in which a stock sale commission was not charged. That is, the writer would not nor­ mally sell his stock after an option has expired worthless, but would instead write another option against the same stock. It is thus acceptable to make these computa­ tions without including a stock sales commission. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:87 SCORE: 35.00 ================================================================================ Chapter 2: Covered Call Writing A WORD OF CAUTION 65 The stockholder who owns stock from a previous purchase and later contemplates writing calls against that stock must be aware of his situation. He must realize and accept the fact that he might lose his stock via assignment. If he is determined to retain ownership of the stock, he may have to buy back the written option at a loss should the underlying stock increase in price. In essence, he is limiting the stock's upside potential. If a stockholder is going to be frustrated and disappointed when he is not fully participating during a rally in his stock, he should not write a call in the first place. Perhaps he could utilize the incremental return concept of covered writ­ ing, a topic covered later in this chapter. As stressed earlier, a covered writing strategy involves viewing the stock and option as a total position. It is not a strategy wherein the investor is a stockholder who also trades options against his stock position. If the stockholder is selling the calls because he thinks the stock is going to decline in price and the call trade itself will be profitable, he may be putting himself in a tenuous position. Thinking this way, he will probably be satisfied only if he makes a profit on the call trade, regardless of the unrealized result in the underlying stock. This sort of philosophy is contrary to a cov­ ered writing strategy philosophy. Such an investor - he is really becoming a trader should carefully review his motives for writing the call and anticipate his reaction if the stock rises substantially in price after the call has been written. In essence, writing calls against stock that you have no intention of selling is tantamount to writing naked calls! If one is going to be extremely frustrated, perhaps even experiencing sleepless nights, if his stock rises above the strike price of the call that he has written, then he is experiencing trials and tribulations much as the writer of a naked call would if the same stock move occurred. This is an unacceptable level of emotional worry for a true covered writing strategist. Think about it. If you have some very low-cost-basis stock that you don't really want to sell, and then you sell covered calls against that stock, what do you wish will happen? Most certainly you wish that the options will expire worthless (i.e., that the stock won't get called away) - exactly what a naked writer wishes for. The problems can be compounded if the stock rises, and one then decides to roll these calls. Rather than spend a small debit to close out a losing position, an investor may attempt to roll to more distant expiration months and higher strike prices in order to keep bringing in credits. Eventually, he runs out of room as the lower strikes disappear, and he has to either sell some stock or pay a big debit to buy back the written calls. So, if the underlying stock continues to run higher, the writer suffers emotional devastation as he attempts to "fight the market." There have been some classic cases of Murphy's law whereby people have covered the calls at a big ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:88 SCORE: 10.00 ================================================================================ 66 Part II: Call Option Strategies debit rather than let their "untouchable" stock be called away, just before the stock itself or the stock market collapsed. One should be very cautious about writing covered calls against stocks that he doesn't intend to sell. If one feels that he cannot sell his stock, for whatever reason - tax considerations, emotional ties, etc. - he really should not sell covered calls against it. Perhaps buying a protective put ( discussed in a later chapter) would be a better strategy for such a stockholder. DIVERSIFYING RETURN AND PROTECTION IN A COVERED WRITE FUNDAMENTAL DIVERSIFICATION TECHNIQUES Quite clearly, the covered writing strategist would like to have as much of a combina­ tion of high potential returns and adequate downside protection as he can obtain. Writing an out-of-the-money call will offer higher returns if exercised, but it usually affords only a modest amount of downside protection. On the other hand, writing an in-the-money call will provide more downside cushion but offers a lower return if exercised. For some strategists, this diversification is realized in practice by writing out-of-the-money calls on some stocks and in-the-moneys on other stocks. There is no guarantee that writing in this manner on a list of diversified stocks will produce supe­ rior results. One is still forced to pick the stocks that he expects will perform better (for out-of-the-money writing), and that is difficult to do. Moreover, the individual investor may not have enough funds available to diversify into many such situations. There is, however, another alternative to obtaining diversification of both returns and downside protection in a covered writing situation. The writer may often do best by writing half of his position against in-the-rrwn­ eys and half against out-of the-rrwneys on the same stock. This is especially attractive for a stock whose out-of-the-money calls do not appear to provide enough downside protection, and at the same time, whose in-the-money calls do not provide quite enough return. By writing both options, the writer may be able to acquire the return and protection diversification that he is seeking. Example: The following prices exist for 6-month calls: XYZ common stock, 42; XYZ April 40 call, 4; and XYZ April 45 call, 2. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:89 SCORE: 12.00 ================================================================================ Chapter 2: Covered Call Writing 67 The writer wishing to establish a covered write against XYZ common stock may like the protection afforded by the April 40 call, but may not find the return particularly attractive. He may be able to improve his return by writing April 45's against part of his position. Assume the writer is considering buying 1,000 shares of XYZ. Table 2-18 compares the attributes of writing the out-of-the-money (April 45) only, or of writing only the in-the-money (April 40), or of writing 5 of each. The table is based on a cash covered write, but returns and protection would be similar for a margin write. Commissions are included in the figures. It is easily seen that the "combined" write - half of the position against the April 40's and the other half against the April 45's - offers the best balance of return and protection. The in-the-money call, by itself, provides over 10% downside protection, but the 5% return if exercised is less than 1 % per month. Thus, one might not want to write April 40's against his entire position, because the potential return is small. At the same time, the April 45's, if written against the entire stock position, would pro­ vide for an attractive return if exercised (over 2% per month) but offer only 5% down­ side protection. The combined write, which has the better features of both options, offers over 8% return if exercised (11h% per month) and affords over 8% downside protection. By writing both calls, the writer has potentially solved the problems inher­ ent in writing entirely out-of-the-moneys or entirely in-the-moneys. The "combined" write frees the covered writer from having to initially take a bearish (in-the-money write) or bullish (out-of-the-money write) posture on the stock ifhe does not want to. This is often necessary on a low-volatility stock trading between striking prices. TABLE 2-18. Attributes of various writes. Buy 1,000 XYZ and sell Return if exercised Re~rn if unchanged Percent protection In-the-Money Write 10 April 40's 5.1% 5.1% 10.5% Out-of-the-Money Write l O April 45's 12.2% 6.0% 5.7% Write Both Calls 5 April 40's and 5 April 45's 8.4% 5.4% 8.1% For those who prefer a graphic representation, the profit graph shown in Figure 2-2 compares the combined write of both calls with either the in-the-money write or the out-of-the-money write (dashed lines). It can be observed that all three choices are equal if XYZ is near 42 at expiration; all three lines intersect there. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:90 SCORE: 13.00 ================================================================================ 68 Part II: Call Option Strategies FIGURE 2-2. Comparison: combined write vs. in-the-money write and out-of-the­ money write. Out-of-the-Money Write , .-------► ,,, Combined Write , / In-the-Money Write -----------➔ Stock Price at Expiration Since this technique can be useful in providing diversification between protec­ tion and return, not only for an individual position but for a large part of a portfolio, it may be useful to see exactly how to compute the potential returns and break-even points. Tables 2-19 and 2-20 calculate the return if exercised and the return if unchanged using the prices from the previous example. Assume XYZ will pay $1 per share in dividends before April expiration. Note that the profit calculations are similar to those described in earlier sec­ tions, except that now there are two prices for stock sales since there are two options involved. In the "return if exercised" section, half of the stock is sold at 45 and half is sold at 40. The "return if unchanged" calculation is somewhat more complicated now, TABLE 2-19. Net investment-cash account. Buy 1,000 XYZ at 42 Plus stock commissions Less options premiums: Sell 5 April 40's at 4 Sell 5 April 45's at 2 Plus total option commissions Net investment + $42,000 460 - 2,000 1,000 + 140 $39,600 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:91 SCORE: 8.00 ================================================================================ Chapter 2: Covered Call Writing TABLE 2-20. Net return-cash account. Return If Exercised Sell 500 XYZ at 45 $22,500 Sell 500 XYZ at 40 20,000 Less total stock sale commissions 560 Plus dividends ($1 /share) + 1,000 Less net investment - 39,600 Net profit if exercised $ 3,340 Return if exercised = 3,340 = 8_4% (cash) 39,600 69 Return If Unchanged Unchanged stock value (500 shares at 42) $21,000 Sell 500 at 40 + 20,000 Commissions on sale at 40 280 Plus dividends ($1 /share) . + 1,000 Less net investment - 39,600 Net profit if unchanged $ 2, 120 Return if unchanged = 2, 120 = 5 _4% (cash) 39,600 because half of the stock will be called away if it remains unchanged (the in-the­ money portion) whereas the other half will not. This is consistent with the method of calculating the return if unchanged that was introduced previously. The break-even point is calculated as before. The "total stock cost to expiration" would be the net investment of $39,600 less the $1,000 received in dividends. This is a total of $38,600. On a per-share basis, then, the break-even point of 38.6 is 8.1 % below the current stock price of 42. Thus, the amount of percentage downside pro­ tection is 8.1 %. The foregoing calculations clearly demonstrate that the returns on the "com­ bined" write are not exactly the averages of the in-the-money and out-of-the-money returns, because of the different commission calculations at various stock prices. However, if one is working with a computer-generated list and does not want to both­ er to calculate exactly the return on the combined write, he can arrive at a relatively close approximation by averaging the returns for the in-the-money write and the out­ of-the-money write. OTHER DIVERSIFICATION TECHNIQUES Holders of large positions in a particular stock may want even more diversification than can be provided by writing against two different striking prices. Institutions, pension funds, and large individual stockholders may fall into this category. It is often advisable for such large stockholders to diversify their writing over time as well as over at least two striking prices. By diversifying over time - for example, writing one- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:92 SCORE: 30.00 ================================================================================ 70 Part II: Call Option Strategies third of the position against near-term calls, one-third against middle-term calls, and the remaining third against long-term calls - one can gain several benefits. First, all of one's positions need not be adjusted at the same time. This includes either having the stock called away or buying back one written call and selling another. Moreover, one is not subject only to the level of option premiums that exist at the time one series of calls expires. For example, if one writes only 9-month calls and then rolls them over when they expire, he may unnecessarily be subjecting himself to the potential of lower returns. If option premium levels happen to be low when it is time for this 9-month call writer to sell more calls, he will be establishing a less-than-opti­ mum write for up to 9 months. By spreading his writing out over time, he would, at worst, be subjecting only one-third of his holding to the low-premium write. Hopefully, premiums would expand before the next eXpiration 3 months later, and he would then be getting a relatively better premium on the next third of his portfolio. There is an important aside here: The individual or relatively small investor who owns only enough stock to write one series of options should generally not write the longest-term calls for this very reason. He may not be obtaining a particularly attrac­ tive level of premiums, but may feel he is forced to retain the position until expira­ tion. Thus, he could be in a relatively poor write for as long as 9 months. Finally, this type of diversification may also lead to having calls at various striking prices as· the market fluctuates cyclically. All of one's stock is not necessarily committed at one price if this diversification technique is employed. This concludes the discussion of how to establish a covered writing position against stock. Covered writes against other types of securities are described later. FOLLOW-UP ACTION Establishing a covered write, or any option position for that matter, is only part of the strategist's job. Once the position has been taken, it must be monitored closely so that adjustments may be made should the stock drop too far in price. Moreover, even if the stock remains relatively unchanged, adjustments will need to be made as the writ­ ten call approaches expiration. Some writers take no follow-up action at all, preferring to let a stock be called away if it rises above the striking price at the expiration of the option, or preferring to let the original expire worthless if the stock is below the strike. These are not always optimum actions; there may be much more decision making involved. Follow-up action can be divided into three general categories: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:93 SCORE: 44.00 ================================================================================ Chapter 2: Covered Call Writing 71 1. protective action to take if the stock drops, 2. aggressive action to take when the stock rises, or 3. action to avoid assignment if the time premium disappears from an in-the-money call. There may be times when one decides to close the entire position before expiration or to let the stock be called away. These cases are discussed as well. PROTECTIVE ACTION IF THE UNDERLYING STOCK DECLINES IN PRICE The covered writer who does not take protective action in the face of a relatively sub­ stantial drop in price by the underlying stock may be risking the possibility of large losses. Since covered writing is a strategy with limited profit potential, one should also take care to limit losses. Otherwise, one losing position can negate several win­ ning positions. The simplest form of follow-up action in a decline is to merely close out the position. This might be done if the stock declines by a certain percentage, or if the stock falls below a technical support level. Unfortunately, this method of defen­ sive action may prove to be an inferior one. The investor will often do better to con­ tinue to sell more time value in the form of additional option premiums. Follow-up action is generally taken by buying back the call that was originally written and then writing another call, with a different striking price and/or expiration date, in its place. Any adjustment of this sort is referred to as a rolling action. When the underlying stock drops in price, one generally buys back the original call - pre­ sumably at a profit since the underlying stock has declined - and then sells a call with a lower striking price. This is known as rolling down, since the new option has a lower striking price. Example: The covered writing position described as "buy XYZ at 51, sell the XYZ January 50 call at 6" would have a maximum profit potential at expiration of 5 points. Downside protection is 6 points down to a stock price of 45 at expiration. These fig­ ures do not include commissions, but for the purposes of an elementary example, the commissions will be ignored. If the stock begins to decline in price, taking perhaps two months to fall to 45, the following option prices might exist: XYZ common, 45; XYZ January 50 call, l; and XYZ January 45 call, 4. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:94 SCORE: 21.00 ================================================================================ 72 Part II: Call Option Strategies • The covered writer of the January 50 would, at this time, have a small unrealized loss of one point in his overall position: His loss on the common stock is 6 points, but he has a 5-point gain in the January 50 call. (This demonstrates that prior to expiration, a loss occurs at the "break-even" point.) If the stock should continue to fall from these levels, he could have a larger loss at expiration. The call, selling for one point, only affords one more point of downside protection. If a further stock price drop is anticipated, additional downside protection can be obtained by rolling down. In this example, if one were to buy back the January 50 call at 1 and sell the January 45 at 4, he would be rolling down. This would increase his protection by another three points - the credit generated by buying the 50 call at 1 and selling the 45 call at 4. Hence, his downside break-even point would be 42 after rolling down. Moreover, if the stock were to remain unchanged - that is, if XYZ were exactly 45 at January expiration - the writer would make an additional $300. If he had not rolled down, the most additional income that he could make, if XYZ remained unchanged, would be the remaining $100 from the January 50 call. So rolling down gives more downside protection against a further drop in stock price and may also produce additional income if the stock price stabilizes. In order to more exactly evaluate the overall effect that was obtained by rolling down in this example, one can either compute a profit table (Table 2-21) or draw a net profit graph (Figure 2-3) that compares the original covered write with the rolled-down position. Note that the rolled-down position has a smaller maximum profit potential than the original position did. This is because, by rolling down to a January 45 call, the writer limits his profits anywhere above 45 at expiration. He has committed himself to sell stock 5 points lower than the original position, which utilized a January 50 call and thus had limited profits above 50. Rolling down generally reduces the maximum TABLE 2·21. Profit table. XYZ Price at Profit from Profit from Expiration January 50 Write Rolled Position 40 -$500 -200 42 - 300 0 45 0 +300 48 + 300 +300 50 + 500 +300 60 + 500 +300 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:95 SCORE: 16.00 ================================================================================ Chapter 2: Covered Call Writing FIGURE 2-3. Comparison: original covered write vs. rolled-down write. +$500 c: +$300 0 ~ ]- iii en en 0 ...J 5 -e a. $0 Original Write Rolled-Down Write 50 Stock Price at Expiration 73 profit potential of the covered write. Limiting the maximum profit may be a second­ ary consideration, however, when a stock is breaking downward. Additional downside protection is often a more pressing criterion in that case. Anywhere below 45 at expiration, the rolled-down position does $300 better than the original position, because of the $300 credit generated from rolling down. In fact, the rolled-down position will outperform the original position even if the stock rallies back to, but not above, a price of 48. At 48 at expiration, the two posi­ tions are equal, both producing a $300 profit. If the stock should reverse direction and rally back above 48 by expiration, the writer would have been better off not to have rolled down. All these facts are clear from Table 2-21 and Figure 2-3. Consequently, the only case in which it does not pay to roll down is the one in which the stock experiences a reversal - a rise in price after the initial drop. The selection of where to roll down is important, because rolling down too early or at an inappropriate price could limit the returns. Technical support levels of the stock are often useful in selecting prices at which to roll down. If one rolls down after techni­ cal support has been broken, the chances of being caught in a stock-price-reversal situation would normally be reduced. The above example is rather simplistic; in actual practice, more complicated sit­ uations may arise, such as a sudden and fairly steep decline in price by the underly­ ing stock. This may present the writer with what is called a locked-in loss. This means, simply, that there is no option to which the writer can roll down that will provide him ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:96 SCORE: 16.00 ================================================================================ 74 Part II: Call Option Strategies with enough premium to realize any profit if the stock were then called away at expi­ ration. These situations arise more commonly on lower-priced stocks, where the striking prices are relatively far apart in percentage terms. Out-of-the-money writes are more susceptible to this problem than are in-the-money writes. Although it is not emotionally satisfying to be in an investment position that cannot produce a profit - at least for a limited period of time - it may still be beneficial to roll down to protect as much of the stock price decline as possible. Example: For the covered write described as "buy XYZ at 20, sell the January 20 call at 2," the stock unexpectedly drops very quickly to 16, and the following prices exist: XYZ common, 16; XYZ January 20 call,½; and XYZ January 15 call, 2½. The covered writer is faced with a difficult choice. He currently has an unrealized loss of 2½ points - a 4-point losson the stock which is partially offset by a 1 ½-point gain on the January 20 call. This represents a fairly substantial percentage loss on his investment in a short period of time. He could do nothing, hoping for the stock to recover its loss. Unfortunately, this may prove to be wishful thinking. If he considers rolling down, he will not be excited by what he sees. Suppose that the writer wants to roll down from the January 20 to the January 15. He would thus buy the January 20 at ½ and sell the January 15 at 2½, for a net credit of 2 points. By rolling down, he is obligating himself to sell his stock at 15, the striking price of the January 15 call. Suppose XYZ were above 15 in January and were called away. How would the writer do? He would lose 5 points on his stock, since he origi­ nally bought it at 20 and is selling it at 15. This 5-point loss is substantially offset by his option profits, which amount to 4 points: 1 ½ points of profit on the January 20, sold at 2 and bought back at ½, plus the 2½ points received from the sale of the January 15. However, his net result is a 1-point loss, since he lost 5 points on the stock and made only 4 points on the options. Moreover, this 1-point loss is the best that he can hope for! This is true because, as has been demonstrated several times, a covered writing position makes its maximum profit anywhere above the striking price. Thus, by rolling down to the 15 strike, he has limited the position severely, to the extent of "locking in a loss." Even considering what has been shown about this loss, it is still correct for this writer to roll down to the January 15. Once the stock has fallen to 16, there is noth­ ing anybody can do about the unrealized losses. However, if the writer rolls down, he can prevent the losses from accumulating at a faster rate. In fact, he will do better by ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:97 SCORE: 12.00 ================================================================================ Chapter 2: Covered Call Writing 75 rolling down if the stock drops further, remains unchanged, or even rises slightly. Table 2-22 and Figure 2-4 compare the original write with the rolled-down position. It is clear from the figure that the rolled-down position is locked into a loss. However, the rolled-down position still outperforms the original position unless the stock ral­ lies back above 17 by expiration. Thus, if the stock continues to fall, if it remains unchanged, or even if it rallies less than 1 point, the rolled-down position actually outperforms the original write. It is for this reason that the writer is taking the most logical action by rolling down, even though to do so locks in a loss. TABLE 2-22. Profits of original write and rolled position. Stock Price at Profit from Expiration January 20 Write 10 -$800 15 - 300 18 0 20 + 200 25 + 200 FIGURE 2-4. Comparison: original write vs. 11 locked-in loss." c: +$200 Original Write ~ t «i ~ o -$100 ~ a.. 15 20 Stock Price at Expiration Profit from Rolled Position -$600 - 100 - 100 - 100 - 100 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:98 SCORE: 8.00 ================================================================================ 76 Part II: Call Option Strategies Technical analysis may be able to provide a little help for the writer faced with the dilemma of rolling down to lock in a loss or else holding onto a position that has no further downside protection. IfXYZ has broken a support level or important trend line, it is added evidence for rolling down. In our example, it is difficult to imagine the case in which a $20 stocksuddenly drops to become a $16 stock without sub­ stantial harm to its technical picture. Nevertheless, if the charts should show that there is support at 15½ or 16, it may be worth the writer's while to wait and see if that support level can hold before rolling down. Perhaps the best way to avoid having to lock in losses would be to establish posi­ tions that are less likely to become such a problem. In-the-money covered writes on higher-priced stocks that have a moderate amount of volatility will rarely force the writer to lock in a loss by rolling down. Of course, any stock, should it fall far enough and fast enough, could force the writer to lock in a loss if he has to roll down two or thr..ee times in a fairly short time span. However, the higher-priced stock has striking prices that are much closer together (in percentages); it thus presents the writer with the opportunity to utilize a new option with a lower striking price much sooner in the decline of the stock. Also, higher volatility should help in generating large enough premiums that substantial portions of the stock's decline can be hedged by rolling down. Conversely, low-priced stocks, especially nonvolatile ones, often present the most severe problems for the covered writer when they decline in price. A related point concerning order entry can be inserted here. When one simul­ taneously buys one call and sells another, he is executing a spread. Spreads in gener­ al are discussed at length later. However, the covered writer should be aware that whenever he rolls his position, the order can be placed as a spread order. This will normally help the writer to obtain a better price execution. AN ALTERNATIVE METHOD OF ROLLING DOWN There is another alternative that the covered writer can use to attempt to gain some additional downside protection without necessarily having to lock in a loss. Basically, the writer rolls down only part of his covered writing position. Example: One thousand shares of XYZ were bought at 20 and 10 January 20 calls were sold at 2 points each. As before, the stock falls to 16, with the following prices: XYZ January 20 call, ½; and XYZ January 15 call, 2½. As was demonstrated in the last section, if the writer were to roll all 10 calls down from the January 20 to the January 15, he would be locking in a loss. Although there may be some justification for this action, the writer would naturally rather not have to place himself in such a position. One can attempt to achieve some balance between added downside protection and upward profit potential by rolling down only part of the calls. In this example, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:99 SCORE: 20.00 ================================================================================ Chapter 2: Covered Call Writing 77 the writer would buy back only 5 of the January 20's and sell 5 January 15 calls. He would then have this position: long 1,000 XYZ at 20; short 5 XYZ January 20's at 2; short 5 XYZ January 15's at 2½; and realized gain, $750 from 5 January 20's. This strategy is generally referred to a partial roll-down, in which only a portion of the original calls is rolled, as opposed to the more conventional complete roll-down. Analyzing the partially rolled position makes it clear that the writer no longer locks in a loss. IfXYZ rallies back above 20, the writer would, at expiration, sell 500 XYZ at 20 (breaking even) and 500 at 15 (losing $2,500 on this portion). He would make $1,000 from the five January 20's held until expiration, plus $1,250 from the five January 15's, plus the $750 of realized gain from the January 20's that were rolled down. This amounts to $3,000 worth of option profits and $2,500 worth of stock losses, or an overall net gain of $500, less commissions. Thus, the partial roll-down offers the writer a chance to make some profit if the stock rebounds. Obviously, the partial roll­ down will not provide as much downside protection as the complete roll-down does, but it does give more protection than not rolling down at all. To see this, compare the results given in Table 2-23 if XYZ is at 15 at expiration. TABLE 2-23. Stock at 15 at expiration. Strategy Original position Partial roll-down Complete roll-down Stock Loss -$5,000 - 5,000 - 5,000 Option Profit Total Loss +$2,000 -$3,000 + 3,000 - 2,000 + 4,000 - 1,000 In summary, the covered writer who would like to roll down, but who does not want to lock in a loss or who feels the stock may rebound somewhat before expira­ tion, should consider rolling down only part of his position. If the stock should con­ tinue to drop, making it evident that there is little hope of a strong rebound back to the original strike, the rest of the position can then be rolled down as well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:100 SCORE: 37.00 ================================================================================ 78 Part II: Call Option Strategies UTILIZING DIFFERENT EXPIRATION SERIES WHEN ROLLING DOWN In the examples thus far, the same expiration month has been used whenever rolling­ down action was taken. In actual practice, the writer may often want to use a more distant expiration month when rolling down and, in some cases, he may even want to use a nearer expiration month. The advantage of rolling down into a more distant expiration series is that more actual points of protection are received. This is a common action to take when the underlying stock has become somewhat worrisome on a technical or fundamental basis. However, since rolling down reduces the maximum profit potential - a fact that has been demonstrated several times - every roll-down should not be made to a more distant expiration series. By utilizing a longer-term call when rolling down, one is reducing his maximum profit potential for a longer period of time. Thus, the longer­ term·call should be used only if the writer has grown concerned over the stock's capa­ bility to hold current price levels. The partial roll-down strategy is particularly amenable to rolling down to a longer-term call since, by rolling down only part of the position, one has already left the door open for profits if the stock should rebound. Therefore, he can feel free to avail himself of the maximum protection possible in the part of his position that is rolled down. The writer who must roll down to lock in a loss, possibly because of circum­ stances beyond his control, such as a sudden fall in the price of the underlying stock, may actually want to roll down to a near-term option. This allows him to make back the available time premium in the short-term call in the least time possible. Example: A writer buys XYZ at 19 and sells a 6-month call for 2 points. Shortly there­ after, however, bad news appears concerning the common stock and XYZ falls quick­ ly to 14. At that time, the following prices exist for the calls with the striking price 15: XYZ common, 14: near-term call, l; middle-term call, 1 ½; and far-term call, 2. If the writer rolls down into any of these three calls, he will be locking in a loss. Therefore, the best strategy may be to roll down into the near-term call, planning to capture one point of time premium in 3 months. In this way, he will be beginning to work himself out of the loss situation by availing himself of the most potential time premium decay in the shortest period of time. When the near-term call expires 3 months from now, he can reassess the situation to decide if he wants to write ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:101 SCORE: 24.00 ================================================================================ Chapter 2: Covered Call Writing 79 another near-term call to continue taking in short-term premiums, or perhaps write a long-term call at that time. When rolling down into the near-term call, one is attempting to return to a potentially profitable situation in the shortest period of time. By writing short-term calls one or two times, the writer will eventually be able to reduce his stock cost near­ er to 15 in the shortest time period. Once his stock cost approaches 15, he can then write a long-term call with striking price 15 and return again to a potentially prof­ itable situation. He will no longer be locked into a loss. ACTION TO TAKE IF THE STOCK RISES A more pleasant situation for the covered writer to encounter is the one in which the underlying stock rises in price after the covered writing position has been estab­ lished. There are generally several choices available if this happens. The writer may decide to do nothing and to let his stock be called away, thereby making the return that he had hoped for when he established the position. On the other hand, if the underlying stock rises fairly quickly and the written call comes to parity, the writer may either close the position early or roll the call up. Each case is discussed. Example: Someone establishes a covered writing position by buying a stock at 50 and selling a 6-month call for 6 points. His maximum profit potential is 6 points anywhere above 50 at expiration, and his downside break-even point is 44. Furthermore, sup­ pose that the stock experiences a substantial rally and that it climbs to a price of 60 in a short period of time. With the stock at 60, the July 50 might be selling for 11 points and a July 60 might sell for as much as 7 points. Thus, the writer may consid­ er buying back the call that was originally written and rolling up to the call with a higher striking price. Table 2-24 summarizes the situation. TABLE 2·24. Comparison of original and current prices. Original Position Current Prices Buy XYZ at 50 XYZ common 60 Sell XYZ July 50 call at 6 XYZ July 50 11 XYZ Jul 60 7 If the writer were to roll-up - that is, buy back the July 50 and sell the July 60 - he would be increasing his profit potential. If XYZ were above 60 in July and were called away, he would make his option credits - 6 points from the July 50 plus 7 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:102 SCORE: 21.00 ================================================================================ 80 Part II: Call Option Strategies points from the July 60 - less the 11 points he paid to buy back the July 50. Thus, his option profits would amount to 2 points, which, added to the stock profit of 10 points, increases his maximum profit potential to 12 points anywhere above 60 at July expi­ ration. To increase his profit potential by such a large amount, the covered writer has given up some of his downside protection. The downside break-even point is always raised by the anwunt of the debit required to roll up. The debit required to roll up in this example is 4 points - buy the July 50 at 11 and sell the July 60 at 7. Thus, the break-even point is increased from the original 44 level to 48 after rolling up. There is another method of calculating the new profit potential and break-even point. In essence, the writer has raised his net stock cost to 55 by taking the realized 5-point loss on the July 50 call. Hence, he is essentially in a covered write whereby he has bought stock at 55 and has sold a July 60 call for 7. When expressed in this manner, it may be easier to see that the break-even point is 48 and the maximum profit poten­ tial, above 60, is 12 points. Note that when one rolls up, there is a debit incurred. That is, the investor must deposit additional cash into the covered writing position. This was not the case in rolling down, because credits were generated. Debits are considered by many investors to be a seriously negative aspect of rolling up, and they therefore prefer never to roll up for debits. Although the debit required to roll up may not be a neg­ ative aspect to every investor, it does translate directly into the fact that the break­ even point is raised and the writer is subjecting himself to a potential loss if the stock should pull back. It is often advantageous to roll to a more distant expiration when rolling up. This will reduce the debit required. The rolled-up position has a break-even point of 48. Thus, if XYZ falls back to 48, the writer who rolled up will be left with no profit. However, if he had not rolled up, he would have made 4 points with XYZ at 48 at expiration in the original position. A further comparison can be made between the original position and the rolled-up position. The two are equal at July expiration at a stock price of 54; both have a prof­ it of 6 points with XYZ at 54 at July expiration. Thus, although it may appear attrac­ tive to roll up, one should determine the point at which the rolled-up position and the original position will be equal at expiration. If the writer believes XYZ could be subject to a 10% correction by expiration from 60 to 54 - certainly not out of the question for any stock - he should stay with his original position. Figure 2-5 compares the original position with the rolled-up position. Note that the break-even point has moved up from 44 to 48; the maximum profit potential has increased from 6 points to 12 points; and at expiration the two writes are equal, at 54. In summary, it can be said that rolling up increases one's profit potential but also exposes one to risk of loss if a stock price reversal should occur. Therefore, an ele- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:103 SCORE: 13.00 ================================================================================ Chapter 2: Covered Call Writing FIGURE 2-5. Comparison: original write vs. rolled-up position. +$1,200 Rolled-Up Write +$600 Original Write 54 60 Stock Price at Expiration 81 ment of risk is introduced as well as the possibility of increased rewards. Generally, it is not advisable to roll up if at least a 10% correction in the stock price cannot be withstood. One's initial goals for the covered write were set when the position was established. If the stock advances and these goals are being met, the writer should be very cautious about risking that profit. A SERIOUS BUT ALL-TOO-COMMON MISTAKE When an investor is overly intent on keeping his stock from being called away (per­ haps he is writing calls against stock that he really has no intention of selling), then he will normally roll up and/or forward to a more distant expiration month whenev­ er the stock rises to the strike of the written call. Most of these rolls incur a debit. If the stock is particularly strong, or if there is a strong bull market, these rolls for deb­ its begin to weigh heavily on the psychology of the covered writer. Eventually, he wears down emotionally and makes a mistake. He typically takes one of two roads: (1) He buys back all of the calls for a (large) debit, leaving the entire stock holding exposed to downside movements after it has risen dramatically in price and after he ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:104 SCORE: 34.00 ================================================================================ 82 Part II: Call Option Strategies has amassed a fairly large series of debits from previous rolls; or (2) he begins to sell some out-of-the-money naked puts to bring in credits to reduce the cost of continu­ ally rolling the calls up for debits. This latter action is even worse, because the entire position is now leveraged tremendously, and a sharp drop in the stock price may cause horrendous losses - perhaps enough to wipe out the entire account. As fate would have it, these mistakes are usually made when the stock is near a top in price. Any price decline after such a dramatic rise is usually a sharp and painful one. The best way to avoid this type of potentially serious mistake is to allow the stock to be called away at some point. Then, using the funds that are released, either establish a new position in another stock or perhaps even utilize another strategy for a while. If that is not feasible, at least avoid making a radical change in strategy after the stock has had a particularly strong rise. Leveraging the position through naked put sales on top of rolling the calls up for debits should expressly be avoided. The discussion to this point has been directed at rolling up before expiration. At or near expiration, when the time value premium has disappeared from the written call, one may have no choice but to write the next-higher striking price if he wants to retain his stock. This is discussed when we analyze action to take at or near expiration. If the underlying stock rises, one's choices are not necessarily limited to rolling up or doing nothing. As the stock increases in price, the written call will lose its time premium and may begin to trade near parity. The writer may decide to close the posi­ tion himself - perhaps well in advance of expiration - by buying back the written call and selling the stock out, hopefully near parity. Example: A customer originally bought XYZ at 25 and sold the 6-month July 25 for 3 points - a net of 22. Now, three months later, XYZ has risen to 33 and the call is trading at 8 (parity) because it is so deeply in-the-money. At this point, the writer may want to sell the stock at 33 and buy back the call at 8, thereby realizing an effective net of 25 for the covered write, which is his maximum profit potential. This is cer­ tainly preferable to remaining in the position for three more months with no more profit potential available. The advantage of closing a parity covered write early is that one is realizing the maximum return in a shorter period than anticipated. He is there­ by increasing his annualized return on the position. Although it is generally to the cash writer's advantage (margin writers read on) to take such action, there are a few additional costs involved that he would not experience if he held the position until the call expired. First, the commission for the option purchase (buy-back) is an addi­ tional expense. Second, he will be selling his stock at a higher price than the striking price, so he may pay a slightly higher commission on that trade as well. If there is a dividend left until expiration, he will not be receiving that dividend if he closes the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:105 SCORE: 54.00 ================================================================================ Chapter 2: Covered Call Writing 83 write early. Of course, if the trade was done in a margin account, the writer will be reducing the margin interest that he had planned to pay in the position, because the debit will be erased earlier. In most cases, the increased commissions are very small and the lost dividend is not significant compared to the increase in annualized return that one can achieve by closing the position early. However, this is not always true, and one should be aware of exactly what his costs are for closing the position early. Obviously, getting out of a covered writing position can be as difficult as estab­ lishing it. Therefore, one should place the order to close the position with his bro­ kerage firm's option desk, to be executed as a "net" order. The same traders who facil­ itate establishing covered writing positions at net prices will also facilitate getting out of the positions. One would normally place the order by saying that he wanted to sell his stock and buy the option "at parity" or, in the example, at "25 net." Just as it is often necessary to be in contact with both the option and stock exchanges to estab­ lish a position, so is it necessary to maintain the same contacts to renwve a position at parity. ACTION TO TAKE AT OR NEAR EXPIRATION As expiration nears and the time value premium disappears from a written call, the covered writer may often want to roll forward, that is, buy back the currently written call and sell a longer-term call with the same striking price. For an in-the-money call, the optimum time to roll forward is generally when the time value premium has com­ pletely disappeared from the call. For an out-of-the-money call, the correct time to move into the more distant option series is when the return offered by the near-term option is less than the return offered by the longer-term call. The in-the-money case is quite simple to analyze. As long as there is time pre­ mium left in the call, there is little risk of assignment, and therefore the writer is earning time premium by remaining with the original call. However, when the option begins to trade at parity or a discount, there arises a significant probability of exer­ cise by arbitrageurs. It is at this time that the writer should roll the in-the-money call forward. For example, if XYZ were offered at 51 and the July 50 call were bid at 1, the writer should be rolling forward into the October 50 or January 50 call. The out-of-the-money case is a little more difficult to handle, but a relatively straightforward analysis can be applied to facilitate the writer's decision. One can compute the return per day remaining in the written call and compare it to the net return per day from the longer-term call. If the longer-term call has a higher return, one should roll forward. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:106 SCORE: 32.00 ================================================================================ 84 Part II: Call Option Strategies Example: An investor previously entered a covered writing situation in which he wrote five January 30 calls against 500 XYZ common. The following prices exist cur­ rently, l month before expiration: XYZ common, 29¼; January 30 call,¼; and April 30 call, 2¼. The writer can only make ¼ a point more of time premium on this covered write for the time remaining until expiration. It is possible that his money could be put to bet­ ter use by rolling forward to the April 30 call. Commissions for rolling forward must be subtracted from the April 30's premium to present a true comparison. By remaining in the January 30, the writer could make, at most, $250 for the 30 days remaining until January expiration. This is a return of $8.33 per day. The com­ missions for rolling forward would be approximately $100, including both the buy­ back and the new sale. Since the current time premium in the April 30 call is $250 per option, this would mean that the writer would stand to make 5 times $250 less the $100 in commissions during the 120-day period until April expiration; $1,150 divided by 120 days is $9.58 per day. Thus, the per-day return is higher from the April 30 than from the January 30, after commissions are included. The writer should roll forward to the April 30 at this time. Rolling forward, since it involves a positive cash flow ( that is, it is a credit trans­ action) simultaneously increases the writer's maximum profit potential and lowers the break-even point. In the example above, the credit for rolling forward is 2 points, so the break-even point will be lowered by 2 points and the maximum profit potential is also increased by the 2-point credit. A simple calculator can provide one with the return-per-day calculation neces­ sary to make the decision concerning rolling forward. The preceding analysis is only directly applicable to rolling forward at the same striking price. Rolling-up or rolling­ down decisions at expiration, since they involve different striking prices, cannot be based solely on the differential returns in time premium values offered by the options in question. In the earlier discussion concerning rolling up, it was mentioned that at or near expiration, one may have no choice but to write the next higher striking price if he wants to retain his stock. This does not necessarily involve a debit transaction, how­ ever. If the stock is volatile enough, one might even be able to roll up for even money or a slight credit at expiration. Should this occur, it would be a desirable situation and should always be taken advantage of. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:107 SCORE: 31.00 ================================================================================ Cbapter 2: Covered Ca# Writing Example: The following prices exist at January expiration: XYZ, 50; XYZ January 45 call, 5; and XYZ July 50 call, 7. 85 In this case, if one had originally written the January 45 call, he could now roll up to the July 50 at expiration for a credit of 2 points. This action is quite prudent, since the break-even point and the maximum profit potential are enhanced. The break­ even point is lowered by the 2 points of credit received from rolling up. The maxi­ mum profit potential is increased substantially - by 7 points - since the striking price is raised by 5 points and an additional 2 points of credit are taken in from the roll up. Consequently, whenever one can roll up for a credit, a situation that would normally arise only on more volatile stocks, he should do so. Another choice that may occur at or near expiration is that of rolling down. The case may arise whereby one has allowed a written call to expire worthless with the stock more than a small distance below the striking price. The writer is then faced with the decision of either writing a small-premium out-of-the-money call or a larg­ er-premium in-the-money call. Again, an example may prove to be useful. Example: Just after the January 25 call has expired worthless, XYZ is at 22, XYZ July 25 call at ¾, and XYZ July 20 call at 3½. If the investor were now to write the July 25 call, he would be receiving only¾ of a point of downside protection. However, his maximum profit potential would be quite large if XYZ could rally to 25 by expiration. On the other hand, the July 20 at 3½ is an attractive write that affords substantial downside protection, and its 1 ½ points of time value premium are twice that offered by the July 25 call. In a purely analytic sense, one should not base his decision on what his performance has been to date, but that is a difficult axiom to apply in practice. If this investor owns XYZ at a high­ er price, he will almost surely opt for the July 25 call. If, however, he owns XYZ at approximately the same price, he will have no qualms about writing the July 20 call. There is no absolute rule that can be applied to all such situations, but one is usual­ ly better off writing the call that provides the best balance between return and down­ side protection at all times. Only if one is bullish on the underlying stock should he write the July 25 call. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:108 SCORE: 43.00 ================================================================================ 86 Part II: Call Option Strategies AVOIDING THE UNCOVERED POSITION There is a margin rule that the covered writer must be aware of if he is considering taking any sort of follow-up action on the day that the written call ceases trading. If another call is sold on that day, even though the written call is obviously going to expire worthless, the writer will be considered uncovered for margin purposes over the weekend and will be obligated to put forth the collateral for an uncovered option. This is usually not what the writer intends to do; being aware of this rule will elimi­ nate unwanted margin calls. Furthermore, uncovered options may be considered unsuitable for many covered writers. Example: A customer owns XYZ and has January 20 calls outstanding on the last day of trading of the January series (the third Friday of January; the calls actually do not expire until the following day, Saturday). IfXYZ is at 15 on the last day of trading, the January 20 call will almost certainly expire worthless. However, should the writer decide to sell a longer-term call on that day without buying back the January 20, he will be considered uncovered over the weekend. Thus, if one plans to wait for an option to expire totally worthless before writing another call, he must wait until the Monday after expiration before writing again, assuming that he wants to remain cov­ ered. The writer should also realize that it is possible for some sort of news item to be announced between the end of trading in an option series and the actual expira­ tion of the series. Thus, call holders might exercise because they believe the stock will jump sufficiently in price to make the exercise profitable. This has happened in the past, two of the most notable cases being IBM in January 1975 and Carrier Corp. in September 1978. WHEN TO LET STOCK BE CALLED AWAY Another alternative that is open to the writer as the written call approaches expira­ tion is to let the stock be called away if it is above the striking price. In many cases, it is to the advantage of the writer to keep rolling options forward for credits, there­ by retaining his stock ownership. However, in certain cases, it may be advisable to allow the stock to be called away. It should be emphasized that the writer often has a definite choice in this matter, since he can generally tell when the call is about to be exercised - when the time value premium disappears. The reason that it is normally desirable to roll forward is that, over time, the covered writer will realize a higher return by rolling instead of being called. The option commissions for rolling forward every three or six months are smaller than the commissions for buying and selling the underlying stock every three or six months, and therefore the eventual return will be higher. However, if an inferior return has ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:109 SCORE: 23.00 ================================================================================ Cl,opter 2: Covered Call Writing 87 to be accepted or the break-even point will be raised significantly by rolling forward, one must consider the alternative of letting the stock be called away. Example: A covered write is established by buying XYZ at 49 and selling an April 50 call for 3 points. The original break-even point was thus 46. Near expiration, suppose XYZ has risen to 56 and the April 50 is trading at 6. If the investor wants to roll for­ ward, now is the time to do so, because the call is at parity. However, he notes that the choices are somewhat limited. Suppose the following prices exist with XYZ at 56: XYZ October 50 call, 7; and XYZ October 60 call, 2. It seems apparent that the pre­ mium levels have declined since the original writing position was established, but that is an occurrence beyond the control of the writer, who must work in the current market environment. If the writer attempts to roll forward to the October 50, he could make at most 1 additional point of profit until October (the time premium in the call). This repre­ sents an extremely low rate of return, and the writer should reject this alternative since there are surely better returns available in covered writes on other securities. On the other hand, if the writer tries to roll up and forward, it will cost 4 points to do so - 6 points to buy back the April 50 less 2 points received for the October 60. This debit transaction means that his break-even point would move up from the orig­ inal level of 46 to a new level of 50. If the common declines below 54, he would be eating into profits already at hand, since the October 60 provides only 2 points of pro­ tection from the current stock price of 56. If the writer is not confidently bullish on the outlook for XYZ, he should not roll up and forward. At this point, the writer has exhausted his alternatives for rolling. His remaining choice is to let the stock be called away and to use the proceeds to establish a cov­ ered write in a new stock, one that offers a more attractive rate of return with rea­ sonable downside protection. This choice of allowing the stock to be called away is generally the wisest strategy if both of the following criteria are met: 1. Rolling forward offers only a minimal return. 2. Rolling up and forward significantly raises the break-even point and leaves the position relatively unprotected should the stock drop in price. SPECIAL WRITING SITUATIONS Our discussions have pertained directly to writing against common stock. However, one may also write covered call options against convertible securities, warrants, or LEAPS. In addition, a different type of covered writing strategy - the incremental ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:110 SCORE: 13.00 ================================================================================ 88 Part II: Call Option Strategies return concept - is described that has great appeal to large stockholders, both indi­ viduals and institutions. COVERED WRITING AGAINST A CONVERTIBLE SECURITY It may be more advantageous to buy a security that is convertible into common stock than to buy the stock itself, for covered call writing purposes. Convertible bonds and convertible preferred stocks are securities commonly used for this purpose. One advantage of using the convertible security is that it often has a higher yield than does the common stock itself. Before describing the covered write, it may be beneficial to review the basics of convertible securities. Suppose XYZ common stock has an XYZ convertible Preferred A stock that is convertible into 1.5 shares of common. The number of shares of com­ mon that the convertible security converts into is an important piece of information that the writer must know. It can be found in a Standard & Poor's Stock Guide (or Bond Guide, in the case of convertible bonds). The writer also needs to determine how many shares of the convertible securi­ ty must be owned in order to equal 100 shares of the common stock. This is quickly determined by dividing 100 by the conversion ratio - 1.5 in our XYZ example. Since 100 divided by 1.5 equals 66.666, one must own 67 shares of XYZ cv Pfd A to cover the sale of one XYZ option for 100 shares of common. Note that neither the market prices of XYZ common nor the convertible security are necessary for this computa­ tion. When using a convertible bond, the conversion information is usually stated in a form such as, "converts into 50 shares at a price of 20." The price is irrelevant. What is important is the number of shares that the bond converts into - 50 in this case. Thus, if one were using these bonds for covered writing of one call, he would need two (2,000) bonds to own the equivalent of 100 shares of stock. Once one knows how much of the convertible security must be purchased, he can use the actual prices of the securities, and their yields, to determine whether a covered write against the common or the convertible is more attractive. Example: The following information is known: XYZ common, 50; XYZ CV Pfd A, 80; XYZ July 50 call, 5; XYZ dividend, 1.00 per share annually; and XYZ cv Pfd A dividend, 5.00 per share annually. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:111 SCORE: 28.00 ================================================================================ Chapter 2: Covered CaH Writing 89 Note that, in either case, the same call - the July 50 -would be written. The use of the convertible as the underlying security does not alter the choice of which option to use. To make the comparison of returns easier, commissions are ignored in the cal­ culations given in Table 2-25. In reality, the commissions for the stock purchase, either common or preferred, would be very similar. Thus, from a numerical point of view, it appears to be more advantageous to write against the convertible than against the common. TABLE 2-25. Comparison of common and convertible writes. Write against Common Write against Convertible Buy underlying security $5,000(100 XYZ) $5,360 (67 XYZ CV Pfd A) Sell one July 50 call 500 - 500 Net cash investment $4,500 $4,860 Premium collected $ 500 $ 500 Dividends until July 50 250 Maximum profit potential $ 550 $ 750 Return (profit divided by investment) 12.2% 15.4% When writing against a convertible security, additional considerations should be looked at. The first is the premium of the convertible security. In the example, with XYZ selling at 50, the XYZ cv Pfd A has a true value of 1.5 times 50, or $75 per share. However, it is selling at 80, which represents a premium of 5 points above its com­ puted value of 75. Normally, one would not want to buy a convertible security if the premium is too large. In this example, the premium appears quite reasonable. Any convertible premium greater than 15% above computed value might be considered to be too large. Another consideration when writing against convertible securities is the han­ dling of assignment. If the writer is assigned, he may either (1) convert his preferred stock into common and deliver that, or (2) sell the preferred in the market and use the proceeds to buy 100 shares of common stock in the market for delivery against the assignment notice. The second choice is usually preferable if the convertible security has any premium at all, since converting the preferred into common causes the loss of any premium in the convertible, as well as the loss of accrued interest in the case of a convertible bond. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:112 SCORE: 29.00 ================================================================================ 90 Part II: Call Option Strategies The writer should also be aware of whether or not the convertible is catlable and, if so, what the exact terms are. Once the convertible has been called by the com­ pany, it will no longer trade in relation to the underlying stock, but will instead trade at the call price. Thus, if the stock should climb sharply, the writer could be incur­ ring losses on his written option without any corresponding benefit from his con­ vertible security. Consequently, if the convertible is called, the entire position should normally be closed immediately by selling the convertible and buying the option back. Other aspects of covered writing, such as rolling down or forward, do not change even if the option is written against a convertible security. One would take action based on the relationship of the option price and the common stock price, as usual. WRITING AGAINST WARRANTS It is also possible to write covered call options against warrants. Again, one must own enough warrants to convert into 100 shares of the underlying stock; generally, this would be 100 warrants. The transaction must be a cash transaction, the warrants must be paid for in full, and they have no loan value. Technically, listed warrants may be marginable, but many brokerage houses still require payment in full. There may be an additional investment requirement. Warrants also have an exercise price. If the exercise price of the warrant is higher than the striking price of the call, the covered writer must also deposit the difference between the two as part of his investment. The advantage of using warrants is that, if they are deeply in-the-money, they may provide the cash covered writer with a higher return, since less of an investment is involved. Example: XYZ is at 50 and there are XYZ warrants to buy the common at 25. Since the warrant is so deeply in-the-money, it will be selling for approximately $25 per warrant. XYZ pays no dividend. Thus, if the writer were considering a covered write of the XYZ July 50, he might choose to use the warrant instead of the common, since his investment, per 100 shares of common, would only be $2,500 instead of the $5,000 required to buy 100 XYZ. The potential profit would be the same in either case because no dividend is involved. Even if the stock does pay a dividend (warrants themselves have no dividend), the writer may still be able to earn a higher return by writing against the warrant than against the common because of the smaller investment involved. This would depend, of course, on the exact size of the dividend and on how deeply the warrant is in-the­ money. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:113 SCORE: 37.00 ================================================================================ Cbapter 2: Covered Call Writing 91 Covered writing against warrants is not a frequent practice because of the small number of warrants on optionable stocks and the problems inherent in checking available returns. However, in certain circumstances, the writer may actually gain a decided advantage by writing against a deep in-the-money warrant. It is often not advisable to write against a warrant that is at- or out-of-the-money, since it can decline by a large percentage if the underlying stock drops in price, producing a high­ risk position. Also, the writer's investment may increase in this case if he rolls down to an option with a striking price lower than the warrant's exercise price. WRITING AGAINST LEAPS A form of covered call writing can be constructed by buying LEAPS call options and selling shorter-term out-of-the-money calls against them. This strategy is much like writing calls against warrants. This strategy is discussed in more detail in Chapter 25 on LEAPS, under the subject of diagonal spreads. PERCS The PERCS (Preferred Equity Redemption Cumulative Stock) is a form of covered writing. It is discussed in Chapter 32. THE INCREMENTAL RETURN CONCEPT OF COVERED WRITING The incremental return concept of covered call writing is a way in which the covered writer can earn the full value of stock appreciation between todays stock price and a target sale price, which may be substantially higher. At the same time, the writer can earn an incremental, positive return from writing options. Many institutional investors are somewhat apprehensive about covered call writing because of the upside limit that is placed on profit potential. If a call is writ­ ten against a stock that subsequently declines in price, most institutional managers would not view this as an unfavorable situation, since they would be outperforming all managers who owned the stock and who did not write a call. However, if the stock rises substantially after the call is written, many institutional managers do not like having their profits limited by the written call. This strategy is not only for institu­ tional money managers, although one should have a relatively substantial holding in an underlying stock to attempt the strategy - at least 500 shares and preferably 1,000 shares or more. The incremental return concept can be used by anyone who is plan­ ning to hold his stock, even if it should temporarily decline in price, until it reaches a predetermined, higher price at which he is willing to sell the stock. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:114 SCORE: 32.00 ================================================================================ 92 Part II: Call Option Strategies The basic strategy involves, as an initial step, selecting the target price at which the writer is willing to sell his stock. Example: A customer owns 1,000 shares of XYZ, which is currently at 60, and is will­ ing to sell the stock at 80. In the meantime, he would like to realize a positive cash flow from writing options against his stock. This positive cash flow does not neces­ sarily result in a realized option gain until the stock is called away. Most likely, with the stock at 60, there would not be options available with a striking price of 80, so one could not write 10 July 80's, for example. This would not be an optimum strategy even if the July 80's existed, for the investor would be receiving so little in option pre­ miums - perhaps 10 cents per call - that writing might not be worthwhile. The incre­ mental return strategy allows this investor to achieve his objectives regardless of the existence of options with a higher striking price. The foundation of the incremental return strategy is to write against only a part of the entire stock holding initially, and to write these calls at the striking price near­ est the current stock price. Then, should the stock move up to the next higher strik­ ing price, one rolls up for a credit by adding to the number of calls written. Rolling for a credit is mandatory and is the key to the strategy. Eventually, the stock reaches the target price and the stock is called away, the investor sells all his stock at the tar­ get price, and in addition earns the total credits from all the option transactions. Example: XYZ is 60, the investor owns 1,000 shares, and his target price is 80. One might begin by selling three of the longest-term calls at 60 for 7 points apiece. Table 2-26 shows how a poor case - one in which the stock climbs directly to the target price - might work. As Table 2-26 shows, if XYZ rose to 70 in one month, the three original calls would be bought back and enough calls at 70 would be sold to produce a credit - 5 XYZ October 70's. If the stock continued upward to 80 in another month, the 5 calls would be bought back and the entire position - 10 calls - would be writ­ ten against the target price. If XYZ remains above 80, the stock will be called away and all 1,000 shares will be sold at the target price of 80. In addition, the investor will earn all the option cred­ its generated along the way. These amount to $2,800. Thus, the writer obtained the full appreciation of his stock to the target price plus an incremental, positive return from option writing. In a flat market, the strategy is relatively easy to monitor. If a written call loses its time value premium and therefore might be subject to assignment, the writer can roll forward to a more distant expiration series, keeping the quantity of written calls constant. This transaction would generate additional credits as well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:115 SCORE: 29.00 ================================================================================ C1,,,pter 2: Covered Call Writing TABLE 2-26. Two months of incremental return strategy. Day 1 : XYZ = 60 Sell 3 XYZ October 60's at 7 One month later: XYZ = 70 Buy back the 3 XYZ Oct 60's at 11 and sell 5 XYZ Oct 70's at 7 Two months later: XYZ = 80 Buy back the 5 Oct 70's at 11 and sell 10 XYZ Oct 80's at 6 COVERED CALL WRITING SUMMARY 93 +$2, 100 credit -$3,300 debit +$3,500 credit -$5 ,500 debit +$6.000 credit +$2,800 credit This concludes the chapter on covered call writing. The strategy will be referred to later, when compared with other strategies. Here is a brief summary of the more important points that were discussed. Covered call writing is a viable strategy because it reduces the risk of stock own­ ership and will make one's portfolio less volatile to short-term market movements. It should be understood, however, that covered call writing may underperform stock ownership in general because of the fact that stocks can rise great distances, while a covered write has limited upside profit potential. The choice of which call to write can make for a more aggressive or more conservative write. Writing in-the-money calls is strategically more conservative than writing out-of-the-money calls, because of the larger amount of downside protection received. The total return concept of covered call writing attempts to achieve the maximum balance between income from all sources - option premiums, stock ownership, and dividend income - and down­ side protection. This balance is usually realized by writing calls when the stock is near the striking price, either slightly in- or slightly out-of-the-money. The writer should compute various returns before entering into the position: the return if exercised, the return if the stock is unchanged at expiration, and the break-even point. To truly compare various writes, returns should be annualized, and all commissions and dividends should be included in the calculations. Returns will be increased by taking larger positions in the underlying stock - 500 or 1,000 shares. Also, by utilizing a brokerage firm's capability to produce "net" executions, buying the stock and selling the call at a specified net price differential, one will receive better executions and realize higher returns in the long run. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:116 SCORE: 32.00 ================================================================================ 92 Part II: Call Option Strategies The basic strategy involves, as an initial step, selecting the target price at which the writer is willing to sell his stock Example: A customer owns 1,000 shares ofXYZ, which is currently at 60, and is will­ ing to sell the stock at 80. In the meantime, he would like to realize a positive cash flow from writing options against his stock This positive cash flow does not neces­ sarily result in a realized option gain until the stock is called away. Most likely, with the stock at 60, there would not be options available with a striking price of 80, so one could not write 10 July 80's, for example. This would not be an optimum strategy even if the July 80's existed, for the investor would be receiving so little in option pre­ miums - perhaps 10 cents per call - that writing might not be worthwhile. The incre­ mental return strategy allows this investor to achieve his objectives regardless of the existence of options with a higher striking price. The foundation of the incremental return strategy is to write against only a part of the entire stock holding initially, and to write these calls at the striking price near­ est the current stock price. Then, should the stock move up to the next higher strik­ ing price, one rolls up for a credit by adding to the number of calls written. Rolling for a credit is mandatory and is the key to the strategy. Eventually, the stock reaches the target price and the stock is called away, the investor sells all his stock at the tar­ get price, and in addition earns the total credits from all the option transactions. Example: XYZ is 60, the investor owns 1,000 shares, and his target price is 80. One might begin by selling three of the longest-term calls at 60 for 7 points apiece. Table 2-26 shows how a poor case - one in which the stock climbs directly to the target price - might work. As Table 2-26 shows, if XYZ rose to 70 in one month, the three original calls would be bought back and enough calls at 70 would be sold to produce a credit - 5 XYZ October 70's. If the stock continued upward to 80 in another month, the 5 calls would be bought back and the entire position - 10 calls - would be writ­ ten against the target price. IfXYZ remains above 80, the stock will be called away and all 1,000 shares will be sold at the target price of 80. In addition, the investor will earn all the option cred­ its generated along the way. These amount to $2,800. Thus, the writer obtained the full appreciation of his stock to the target price plus an incremental, positive return from option writing. In a flat market, the strategy is relatively easy to monitor. If a written call loses its time value premium and therefore might be subject to assignment, the writer can roll f01ward to a more distant expiration series, keeping the quantity of written calls constant. This transaction would generate additional credits as well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:117 SCORE: 29.00 ================================================================================ O.,,er 2: Covered Call Writing TABLE 2-26. Two months of incremental return strategy. Doy 1 : XYZ = 60 Sell 3 XYZ October 60's at 7 One month later: XYZ = 70 Buy back the 3 XYZ Oct 60's at 11 and sell 5 XYZ Oct 70's at 7 Twa months later: XYZ = 80 Buy back the 5 Oct 70's at 11 and sell 10 XYZ Oct 80's at 6 COVERED CALL WRITING SUMMARY 93 +$2, 100 credit -$3 ,300 debit +$3,500 credit -$5 ,500 debit +$6,000 credit +$2,800 credit This concludes the chapter on covered call writing. The strategy will be referred to later, when compared with other strategies. Here is a brief summary of the more important points that were discussed. Covered call writing is a viable strategy because it reduces the risk of stock own­ ership and will make one's portfolio less volatile to short-term market movements. It should be understood, however, that covered call writing may underperform stock ownership in general because of the fact that stocks can rise great distances, while a covered write has limited upside profit potential. The choice of which call to write can make for a more aggressive or more conservative write. Writing in-the-money calls is strategically more conservative than writing out-of-the-money calls, because of the larger amount of downside protection received. The total return concept of covered call writing attempts to achieve the maximum balance between income from all sources - option premiums, stock ownership, and dividend income - and down­ side protection. This balance is usually realized by writing calls when the stock is near the striking price, either slightly in- or slightly out-of-the-money. The writer should compute various returns before entering into the position: the return if exercised, the return if the stock is unchanged at expiration, and the break-even point. To truly compare various writes, returns should be annualized, and all commissions and dividends should be included in the calculations. Returns will be increased by taking larger positions in the underlying stock - 500 or 1,000 shares. Also, by utilizing a brokerage firm's capability to produce "net" executions, buying the stock and selling the call at a specified net price differential, one will receive better executions and realize higher returns in the long run. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:118 SCORE: 23.00 ================================================================================ 94 Part II: Call Option Strategies The selection of which call to write should be made on a comparison of avail­ able returns and downside protection. One can sometimes write part of his position out-of-the-money and the other part in-the-money to force a balance between return and protection that might not otherwise exist. Finally, one should not write against an underlying stock if he is bearish on the stock. The writer should be slightly bullish, or at least neutral, on the underlying stock. Follow-up action can be as important as the selection of the initial position itself. By rolling down if the underlying stock drops, the investor can add downside protection and current income. If one is unwilling to limit his upside potential too severely, he may consider rolling down only part of his call writing position. As the written call expires, the writer should roll forward into a more distant expiration month if the stock is relatively close to the original striking price. Higher consistent returns are achieved in this manner, because one is not spending additional stock commissions by letting the stock be called away. An aggressive follow-up action can also be taken when the underlying stock rises in price: The writer can roll up to a higher striking price. This action increases the maximum profit potential but also exposes the position to loss if the stock should subsequently decline. One would want to take no follow-up action and let his stock be called if it is above the striking price and if there are better returns available elsewhere in other securities. Covered call writing can also be done against convertible securities - bonds or preferred stocks. These convertibles sometimes offer higher dividend yields and therefore increase the overall return from covered writing. Also, the use of warrants or LEAPS in place of the underlying stock may be advantageous in certain circum­ stances, because the net investment is lowered while the profit potential remains the same. Therefore, the overall return could be higher. Finally, the larger individual stockholder or institutional investor who wants to achieve a certain price for his stock holdings should operate his covered writing strat­ egy under the incremental return concept. This will allow him to realize the full prof­ it potential of his underlying stock, up to the target sale price, and to earn additional positive income from option writing. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:119 SCORE: 20.00 ================================================================================ Call Buying The success of a call buying strategy depends primarily on one's ability to select stocks that will go up and to time the selection reasonably well. Thus, call buying is not a strategy in the same sense of the word as most of the other strategies discussed in this text. Most other strategies are designed to remove some of the exactness of stock picking, allowing one to be neutral or at least to have some room for error and still make a profit. Techniques of call buying are important, though, because it is nec­ essary to understand the long side of calls in order to understand more complex strategies correctly. Call buying is the simplest form of option investment, and therefore is the most frequently used option "strategy" by the public investor. The following section out­ lines the basic facts that one needs to know to implement an intelligent call buying program. WHY BUY? The main attraction in buying calls is that they provide the speculator with a great deal of leverage. One could potentially realize large percentage profits from only a modest rise in price by the underlying stock. Moreover, even though they may be large percentagewise, the risks cannot exceed a fixed dollar amount - the price orig­ inally paid for the call. Calls must be paid for in full; they have no margin value and do not constitute equity for margin purposes. Note: The preceding statements regarding payment for an option in full do not necessarily apply to LEAPS options, which were declared marginable in 1999. The following simple example illustrates how a call purchase might work. 95 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:120 SCORE: 22.00 ================================================================================ 96 Part II: Call Option Strategies Example: Assume that XYZ is at 48 and the 6-month call, the July 50, is selling for 3. Thus, with an investment of $300, the call buyer may participate, for 6 months, in a move upward in the price ofXYZ common. IfXYZ should rise in price by 10 points (just over 20%), the July 50 call will be worth at least $800 and the call buyer would have a 167% profit on a move in the stock of just over 20%. This is the leverage that attracts speculators to call buying. At expiration, if XYZ is below 50, the buyer's loss is total, but is limited to his initial $300 investment, even if XYZ declines in price sub­ stantially. Although this risk is equal to 100% of his initial investment, it is still small dollarwise. One should nornwlly not invest more than 15% of his risk capital in call buying, because of the relatively large percentage risks involved. Some investors participate in call buying on a limited basis to add some upside potential to their portfolios while keeping the risk to a fixed amount. For example, if an investor normally only purchased low-volatility, conservative stocks because he wanted to limit his downside risk, he might consider putting a small percentage of his cash into calls on more volatile stocks. In this manner, he could "trade" higher-risk stocks than he might normally do. If these volatile stocks increase in price, the investor will profit handsomely. However, if they decline substantially - as well they might, being volatile - the investor has limited his dollar risk by owning the calls rather than the stock. Another reason some investors buy calls is to be able to buy stock at a reason­ able price without missing a market. Example: With XYZ at 75, this investor might buy a call on XYZ at 80. He would like to own XYZ at 80 if it can prove itself capable of rallying and be in-the-money at expi­ ration. He would exercise the call in that case. On the other hand, if XYZ declines in price instead, he has not tied up money in the stock and can lose only an amount equal to the call premium that he paid, an amount that is generally much less than the price of the stock itself. Another approach to call buying is sometimes utilized, also by an investor who does not want to "miss the market." Suppose an investor knows that, in the near future, he will have an amount of money large enough to purchase a particular stock; perhaps he is closing the sale of his house or a certificate of deposit is maturing. However, he would like to buy the stock now, for he feels a rally is imminent. He might buy calls at the present time if he had a small amount of cash available. The call purchases would require an investment much smaller than the stock purchase. Then, when he receives the cash that he knew was forthcoming, he could exercise the calls and buy the stock. In this way, he might have participated in a rally by the stock before he actually had the money available to pay for the stock in full. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:121 SCORE: 35.00 ================================================================================ Cl,opter 3: Call Buying 97 RISK AND REWARD FOR THE CALL BUYER The most important fact for the call buyer to realize is that he will normally win only if the stock rises in price. All the worthwhile analysis in the world spent in selecting which call to buy will not produce profits if the underlying stock declines. However, this fact should not dissuade one from making reasonable analyses in his call buying selections. Too often, the call buyer feels that a stock will move up, and is correct in that part of his projection, but still loses money on his call purchase because he failed to analyze the risk and rewards involved with the various calls available for purchase at the time. He bought the wrong call on the right stock. Since the best ally that the call buyer has is upward movement in the underly­ ing stock, the selection of the underlying stock is the most important choice the call buyer has to make. Since timing is so important when buying calls, the technical fac­ tors of stock selection probably outweigh the fundamentals; even if positive funda­ mentals do exist, one does not know how long it will take in order for them to be reflected in the price of the stock. One must be bullish on the underlying stock in order to consider buying calls on that stock. Once the stock selection has been made, only then can the call buyer begin to consider other factors, such as which striking price to use and which expiration to buy. The call buyer may have another ally, but not one that he can normally predict: If the stock on which he owns a call becomes more volatile, the call's price will rise to reflect that change. The purchase of an out-of-the-money call generally offers both larger potential risk and larger potential reward than does the purchase of an in-the-money call. Many call buyers tend to select the out-of-the-money call merely because it is cheap­ er in price. Absolute dollar price should in no way be a deciding factor for the call buyer. If one's funds are so limited that he can only afford to buy the cheapest calls, he should not be speculating in this strategy. If the underlying stock increases in price substantially, the out-of-the-money call will naturally provide the largest rewards. However, if the stock advances only moderately in price, the in-the-money call may actually perform better. Example: XYZ is at 65 and the July 60 sells for 7 while the July 70 sells for 3. If the stock moves up to 68 relatively slowly, the buyer of the July 70 - the out-of-the­ money call - may actually experience a loss, even if the call has not yet expired. However, the holder of the in-the-money July 60 will definitely have a profit because the call will sell for at least 8 points, its intrinsic value. The point is that, percentage­ wise, an in-the-rrwney call will offer better rewards for a rrwdest stock gain, and an out-ofthe-rrwney call is better for larger stock gains. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:122 SCORE: 36.00 ================================================================================ 98 Part II: Call Option Strategies When risk is considered, the in-the-money call clearly has less probability of risk. In the prior example, the in-the-money call buyer would not lose his entire investment unless XYZ fell by at least 5 points. However, the buyer of the out-of-the­ money July 70 would lose all of his investment unless the stock advanced by more than 5 points by expiration. Obviously, the probability that the in-the-money call will expire worthless is much smaller than that for the out-of-the-money call. The time remaining to expiration is also relevant to the call buyer. If the stock is fairly close to the striking price, the near-term call will most closely follow the price movement of the underlying stock, so it has the greatest rewards and also the great­ est risks. The far-term call, because it has a large amount of time remaining, offers the least risk and least percentage reward. The intermediate-temi call offers a mod­ erate amount of each, and is therefore often the most attractive one to buy. Many times an investor will buy the longer-term call because it only costs a point or a point and a half more than the intermediate-term call. He feels that the extra price is a bar­ gain to pay for three extra months of time. This line of thought may prove somewhat misleading, however, because most call buyers don't hold calls for more than 60 or 90 days. Thus, even though it looks attractive to pay the extra point for the long-term call, it may prove to be an unnecessary expense if, as is usually the case, one will be selling the call in two or three months. CERTAINTY OF TIMING The certainty with which one expects the underlying stock to advance may also help to play a part in his selection of which call to buy. If one is fairly sure that the under­ lying stock is about to rise immediately, he should strive for more reward and not be as concerned about risk. This would mean buying short-term, slightly out-of-the­ money calls. Of course, this is only a general rule; one would not normally buy an out­ of-the-money call that has only one week remaining until expiration, in any case. At the opposite end of the spectrum, if one is very uncertain about his timing, he should buy the longest-term call, to moderate his risk in case his timing is wrong by a wide margin. This situation could easily result, for example, if one feels that a positive fun­ damental aspect concerning the company will assert itself and cause the stock to increase in price at an unknown time in the future. Since the buyer does not know whether this positive fundamental will come to light in the next month or six months from now, he should buy the longer-term call to allow room for error in timing. In many cases, one is not intending to hold the purchased call for any signifi­ cant period of time; he is just looking to capitalize on a quick, short-term movement by the underlying stock. In this case, he would want to buy a relatively short-term in­ the-money call. Although such a call may be more ex-pensive than an out-of-the- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:123 SCORE: 65.00 ================================================================================ Cl,apter 3: Call Buying 99 money call on the same underlying stock, it will most surely move up on any increase in price by the underlying stock. Thus, the short-term trader would profit. THE DELTA The reader should by now be familiar with basic facts concerning call options: The time premium is highest when the stock is at the striking price of the call; it is lowest deep in- or out-of-the-money; option prices do not decay at a linear rate -the time pre­ mium disappears more rapidly as the option approaches expiration. As a further means of review, the option pricing curve introduced in Chapter 1 is reprinted here. Notice that all the facts listed above can be observed from Figure 3-1. The curves are much nearer the "intrinsic value" line at the ends than they are in the middle, implying that the time value premium is greatest when the stock is at the strike, and is least when the stock moves away from the strike either into- or out-of-the-money. Furthermore, the fact that the curve for the 3-month option lies only about halfway between the intrinsic value line and the curve of the 9-month option implies that the rate of decay of an at- or near-the-money option is not linear. The reader may also want to refer back to the graph of time value premium decay in Chapter 1 (Figure 1-4). There is another property of call options that the buyer should be familiar with, the delta of the option (also called the hedge ratio). Simply stated, the delta of an option is the arrwunt by which the call will increase or decrease in price if the under­ lying stock moves by 1 point. FIGURE 3-1. Option pricing curve; 3-, 6-, and 9-month calls. Q) 0 ~ C: 0 a 0 9-Month Curve 6-Month Curve 3-Month Curve / Intrinsic Value Striking Price Stock Price As expiration date draws closer, the lower curve merges with the intrinsic value line. The option price then equals its intrinsic value. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:124 SCORE: 99.00 ================================================================================ 100 Part II: Call Option Strategies Example: The delta of a call option is close to 1 when the underlying stock is well above the striking price of the call. If XYZ were 60 and the XYZ July 50 call were 101/s, the call would change in price by nearly 1 point ifXYZ moved by 1 point, either up or down. A deeply out-of-the-money call has a delta of nearly zero. If XYZ were 40, the July 50 call might be selling at¼ of a point. The call would change very little in price if XYZ moved by one point, to either 41 or 39. When the stock is at the strik­ ing price, the delta is usually between one-half of a point and five-eighths of a point. Very long-term calls may have even larger at-the-money deltas. Thus, if XYZ were 50 and the XYZ July 50 call were 5, the call might increase to 5½ if XYZ rose to 51 or decrease to 4½ if XYZ dropped to 49. Actually, the delta changes each time the underlying stock changes even frac­ tionally in price; it is an exact mathematical derivation that is presented in a later chapter. This is most easily seen by the fact that a deep in-the-money option has a delta of 1. However, if the stock should undergo a series of I-point drops down to the striking price, the delta will be more like½, certainly not 1 any longer. In reality, the delta changed instantaneously all during the price decline by the stock. For those who are geometrically inclined, the preceding option price curve is useful in deter­ mining a graphic representation of the delta. The delta is the slope of the tangent line to the price curve. Notice that a deeply in-the-money option lies to the upper right side of the curve, very nearly on the intrinsic value line, which has a slope of 1 above the strike. Similarly, a deeply out-of-the-money call lies to the left on the price curve, again near the intrinsic value line, which has a slope of zero below the strike. Since it is more common to relate the option's price change to a full point change in the underlying stock (rather than to deal in "instantaneous" price changes), the concepts of up delta and down delta arise. That is, if the underlying stock moves up by 1 full point, a call with a delta of .50 might increase by 5/s. However, should the stock fall by one full point, the call might decrease by only 3/s. There is a different net price change in the call when the stock moves up by 1 full point as opposed to when it falls by a point. The up delta is observed to be 5/s while the down delta is 3/s. In the true mathematical sense, there is only one delta and it measures "instantaneous" price change. The concepts of up delta and down delta are practical, rather than the­ oretical, concepts that merely illustrate the fact that the true delta changes whenev­ er the stock price changes, even by as little as 1 point. In the following examples and in later chapters, only one delta is referred to. The delta is an important piece of information for the call buyer because it can tell him how much of an increase or decrease he can expect for short-term moves by the underlying stock. This piece of information may help the buyer decide which call to buy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:125 SCORE: 29.00 ================================================================================ Chapter 3: Call Buying 101 Example: If XYZ is 4 7½ and the call buyer expects a quick, but possibly limited, rise in price in the underlying stock, should he buy the 45 call or the 50 call? The delta may help him decide. He has the following information: XYZ: 471/2 XYZ July 45 call: price = 31/2, XYZ July 50 call: price = 1, delta = 5/a delta = 1/4 It will make matters easier to make a slightly incorrect, but simplifying, assumption that the deltas remain constant over the short term. Which call is the better buy if the buyer expects the stock to quickly rise to 49? This would represent a 1 ½-point increase in XYZ, which would translate into a 15/16 increase in the July 45 (l½ times 5/s) or a 3/s increase in the July 50 (1 ½ times ¼). Consequently, the July 45, if it increased in price by 15/16, would appreciate by 27%. The July 50, if it increased by 3/a, would appreciate by over 37%. Thus, the July 50 appears to be the better buy in this simple example. Commissions should, of course, be included when making an analysis for actual investment. The investor does not have to bother with computing deltas for himself. Any good call-buying data service will supply the information, and some brokerage hous­ es provide this information free of charge. More advanced applications of deltas are described in many of the succeeding chapters, as they apply to a variety of strategies. WHICH OPTION TO BUY? There are various trading strategies, some short-term, some long-term (even buy and hold). If one decides to use an option to implement a trading strategy, the time hori­ zon of the strategy itself often dictates the general category of option that should be bought - in-the-money versus out-of-the-money, near-term versus long-term, etc. This statement is true whether one is referring to stock, index, or futures options. The general rule is this: The shorter-term the strategy, the higher the delta should be of the instrument being used to trade the strategy. DAY TRADING For example, day trading has become a popular endeavor. Statistics have been pro­ duced that indicate that most day traders lose money. In fact, there are profitable day traders; it simply requires more and harder work than many are willing to invest. Many day traders have attempted to use options in their strategies. These day traders ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:126 SCORE: 80.00 ================================================================================ 102 Part II: Call Option Strategies apparently are attracted by the leverage available from options, but they often lose money via option trading as well. What many of these option-oriented day traders fail to realize is that, for day­ trading purposes, the instrument with the highest possible delta should be used. That instrument is the underlying, for it has a delta of 1.0. Day trading is hard enough without complicating it by trying to use options. So of you're day trading Microsoft (MSFT), trade the stock, not an option. What makes options difficult in such a short-term situation is their relatively wide bid-asked spread, as compared to that of the underlying instrument itself. Also, a day trader is looking to capture only a small part of the underlying's daily move; an at-the-money or out-of-the-money option just won't respond well enough to those movements. That is, if the delta is too low, there just isn't enough room for the option day trader to make money. If a day trader insists on using options, a short-term, in-the-money should be bought, for it has the largest delta available - preferably something approaching .90 or higher. This option will respond quickly to small movements by the underlying. SHORT-TERM TRADING Suppose one employs a strategy whereby he expects to hold the underlying for approximately a week or two. In this case, just as with day trading, a high delta is desirable. However, now that the holding period is more than a day, it may be appro­ priate to buy an option as opposed to merely trading the underlying, because the option lessens the risk of a surprisingly large downside move. Still, it is the short­ term, in-the-money option that should be bought, for it has the largest delta, and will thus respond most closely to the movement in the underlying stock. Such an option has a very high delta, usually in excess of .80. Part of the reason that the high-delta options make sense in such situations is that one is fairly certain of the timing of day trading or very short-term trading systems. When the system being used for selection of which stock to trade has a high degree of timing accuracy, then the high-delta option is called for. INTERMEDIATE-TERM TRADING As the time horizon of one's trading strategy lengthens, it is appropriate to use an option with a lesser delta. This generally means that the timing of the selection process is less exact. One might be using a trading system based, for ernmple, on sen­ timent, which is generally not an exact timing indicator, but rather one that indicates a general trend change at major turning points. The timing of the forthcoming move ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:127 SCORE: 38.00 ================================================================================ Gapter 3: Call Buying 103 is not exact, because it often takes time for an extreme change in sentiment to reflect itself in a change of direction by the underlying. Hence, for a strategy such as this, one would want to use an option with a small­ er delta. The investor would limit his risk by using such an option, knowing that large moves are possible since the position is going to be held for several weeks or perhaps even a couple of months or more. Therefore, an at-the-money option can be used in such situations. I.ONG-TERM TRADING If one's strategy is even longer-term, an option with a lower delta can be considered. Such strategies would generally have only vague timing qualities, such as selecting a stock to buy based on the general fundamental outlook for the company. In the extreme, it would even apply to "buy and hold" strategies. Generally, buying out-of-the-money options is not recommended; but for very long-term strategies, one might consider something slightly out-of-the-money, or at least a fairly long-term at-the-money option. In either case, that option will have a lower delta as compared to the options that have been recommended for the other strategies mentioned above. Alternatively, LEAPS options might be appropriate for stock strategies of this type. ADVANCED SELECTION CRITERIA The criteria presented previously represented elementary techniques for selecting which call to buy. In actual practice, one is not usually bullish on just one stock at a time. In fact, the investor would like to have a list of the "best" calls to buy at any given time. Then, using some method of stock selection, either technical or funda­ mental, he can select three or four calls that appear to offer the best rewards. This list should be ranked in order of the best potential rewards available, but the con­ struction of the list itself is important. Call option rankings for buying purposes must be based on the volatilities of the underlying stocks. This is not easy to do mathematically, and as a result many pub­ lished rankings of calls are based strictly on percentage change in the underlying stock. Such a list is quite misleading and can lead one to the wrong conclusions. Example: There are two stocks with listed calls: NVS, which is not volatile, and VVS, which is quite volatile. Since a call on the volatile stock will be higher-priced than a call on the nonvolatile stock, the following prices might exist: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:128 SCORE: 30.00 ================================================================================ 104 Part II: Call Option Strategies NVS: 40 VVS: 40 NVS July 40 call: 2 VVS July 40 call: 4 If these two calls are ranked for buying purposes, based strictly on a percentage change in the underlying stock, the NVS call will appear to be the better buy. For example, one might see a list such as "best call buys if the underlying stock advances by 10%." In this example, if each stock advanced 10% by expiration, both NVS and WS would be at 44. Thus, the NVS July 40 would be worth 4, having doubled in price, for a 100% potential profit. Meanwhile, the WS July 40 would be worth 4 also, for a 0% profit to the call buyer. This analysis would lead one to believe that the NVS July 40 is the better buy. Such a conclusion may be wrong, because an incorrect assumption was made in the ranking of the potentials of the two stocks. It is not right to assume that both stocks have the same probability of moving 10% by expiration. Certainly, the volatile stock has a much better chance of advancing by 10% ( or more) than the nonvolatile stock does. Any ranking based on equal percentage changes in the underlying stock, without regard for their volatilities, is useless and should be avoided. The correct method of comparing these two July 40 calls is to utilize the actual volatilities of the underlying stocks. Suppose that it is known that the volatile stock, WS, could expect to move 15% in the time to July expiration. The nonvolatile stock, NVS, however, could only expect a move of 5% in the same period. Using this infor­ mation, the call buyer can arrive at the conclusion that WS July 40 is the better call to buy: Stock Price in July VVS: 46 (up 15%) NVS: 42 (up 5%) Coll Price VVS July 40: 6 (up 50%) NVS July 40: 2 (unchanged) By assuming that each stock can rise in accordance with its volatility, we can see that the WS July 40 has the better reward potential, despite the fact that it was twice as expensive to begin with. This method of analysis is much more realistic. One more refinement needs to be made in this ranking process. Since most call purchases are made for holding periods of from 30 to 90 days, it is not correct to assume that the calls will be held to expiration. That is, even if one buys a 6-month call, he will normally liquidate it, to take profits or cut losses, in 1 to 3 months. The call buyer's list should thus be based on how the call will peiform if held for a realis­ tic time period, such as 90 days. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:129 SCORE: 27.00 ================================================================================ Chapter 3: Call Buying 105 Suppose the volatile stock in our example, WS, has the potential to rise by 12% in 90 days, while the less volatile stock, NVS, has the potential of rising only 4% in 90 days. In 90 days, the July 40 calls will not be at parity, because there will be some time remaining until July expiration. Thus, it is necessary to attempt to predict what their prices will be at the end of the 90-day holding period. Assume that the following prices are accurate estimates of what the July 40 calls will be selling for in 90 days, if the underlying stocks advance in relation to their volatilities: Stock Price in 90 Days VVS: 44.8 (up 12%) NVS: 41 .6 (up 4%) Coll Price VVS July 40: 6 (up 50%) NVS July 40: 21/2 (up 25%) With some time remaining in the calls, they would both have time value premium at the end of 90 days. The bigger time premium would be in the WS call, since the underlying stock is more volatile. Under this method of analysis, the WS call is still the better one to buy. The correct method of ranking potential reward situations for call buyers is as follows: 1. Assume each underlying stock can advance in accordance with its volatility over a fixed period (30, 60, or 90 days). 2. Estimate the call prices after the advance. 3. Rank all potential call purchases by highest percentage reward opportunity for aggressive purchases. 4. Assume each stock can decline in accordance with its volatility. 5. Estimate the call prices after the decline. 6. Rank all purchases by reward/risk ratio ( the percentage gain from item 2 divided by the percentage loss from item 5). The list from item 3 will generate more aggressive purchases because it incorporates potential rewards only. The list from item 6 would be a less speculative one. This method of analysis automatically incorporates the criteria set forth earlier, such as buying short-term out-of-the-money calls for aggressive purchases and buying longer-term in-the-money calls for a more conservative purchase. The delta is also a function of the volatility and is essentially incorporated by steps 1 and 4. It is virtually impossible to perform this sort of analysis without a computer. The call buyer can generally obtain such a list from a brokerage firm or from a data serv­ ice. For those individuals who have access to a computer and would like to generate ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:130 SCORE: 38.00 ================================================================================ 106 Part II: Call Option Strategies such an analysis for themselves, the details of computing a stock's volatility and pre­ dicting the call prices are provided in Chapter 28 on mathematical techniques. OVERPRICED OR UNDERPRICED CALLS Formulae exist that are capable of predicting what a call should be selling for, based on the relationship of the stock price and the striking price, the time remaining to expiration, and the volatility of the underlying stock. These are useful, for example, in performing the second step in the foregoing analysis, estimating the call price after an advance in the underlying stock. In reality, a call's actual price may deviate some­ what from the price computed by the formula. If the call is actually selling for more than the "fair" ( computed) price, the call is said to be overvalued. An undervalued call is one that is actually trading at a price that is less than the "fair" price. If the calls are truly overpriced, there may be a strategy that can help reduce their cost while still preserving upside profit potential. This strategy, however, requires the addition of a put spread to the call purchase, so it is beyond the scope of the subject matter at the current time. It is described in Chapter 23 on spreads combining calls and puts. Generally, the amount by which a call is overvalued or undervalued may be only a small fraction of a point, such as 10 or 20 cents. In theory, the call buyer who pur­ chases an undervalued call has gained a slight advantage in that the call should return to its "fair" value. However, in practice, this information is most useful only to mar­ ket-makers or firm traders who pay little or no commissions for trading options. The general public cannot benefit directly from the knowledge that such a small discrep­ ancy exists, because of commission costs. One should not base his call buying decisions merely on the fact that a call is underpriced. It is small solace to the call buyer to find that he bought a "cheap" call that subsequently declined in price. The method of ranking calls for purchase that has been described does, in fact, give some slight benefit to underpriced calls. However, under the recommended method of analysis, a call will not automatically appear as an attractive purchase just because it is slightly undervalued. TIME VALUE PREMIUM IS A MISNOMER This is a topic that will be mentioned several times throughout the book, most notably in conjunction with volatility trading. It is introduced here because even the inexperienced option trader must understand that the portion of an option's price that is not intrinsic value - the part that we routinely call "time value premium" - is really composed of much more than just time value. Yes, time will eventually wear ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:131 SCORE: 53.00 ================================================================================ Chpter 3: Call Buying 107 away that portion of the option's price as expiration approaches. However, when an option has a considerable amount of time remaining until its expiration, the more important component of the option value is really volatility. If traders expect the underlying stock to be volatile, the option will be expensive; if they expect the oppo­ site, the option will be cheap. This expensiveness and cheapness is reflected in the portion of the option that is not intrinsic value. For example, a six-month option will not decay much in one day's time, but a quick change in volatility expectations by option traders can heavily affect the price of the option, especially one with a good deal of time remaining. So an option buyer should carefully assess his purchases, not just view them as something that will waste away. With careful analysis, option buy­ ers can do very well, if they consider what can happen during the life of the option, and not merely what will happen at expiration. CALL BUYERS' FRUSTRATIONS Despite one's best efforts, it may often seem that one does not make much money when a fairly volatile stock makes a quick move of 3 or 4 points. The reasons for this are somewhat more complex than can be addressed at this time, although they relate strongly to delta, time decay, and the volatility of the underlying stock. They are dis­ cussed in Chapter 36, 'The Basics of Volatility Trading." If one plans to conduct a serious call buying strategy, he should read that chapter before embarking on a pro­ gram of extensive call buying. FOLLOW-UP ACTION The simplest follow-up action that the call buyer can implement when the underly­ ing stock drops is to sell his call and cut his losses. There is often a natural tendency to hold out hope that the stock can rally back to or above the striking price. Most of the time, the buyer does best by cutting his losses in situations in which the stock is performing poorly. He might use a "mental" stop price or could actually place a sell stop order, depending on the rules of the exchange where the call is traded. In gen­ eral, stop orders for options result in poor executions, so using a "mental" stop is bet­ ter. That is, one should base his exit point on the technical pattern of the underlying stock itself. If it should break down below support, for example, then the option holder should place a market (not held) order to sell his call option. If the stock should rise, the buyer should be willing to take profits as well. Most buyers will quite readily take a profit if, for example, a call that was bought for 5 points had advanced to be worth 10 points. However, the same investor is often ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:132 SCORE: 28.00 ================================================================================ 108 Part II: Call Option Strategies reluctant to sell a call at 2 that he had previously bought for 1 point, because "I've only made a point." The similarity is clear - both cases resulted in approximately a 100% profit - and the investor should be as willing to accept the one as he is the other. This is not to imply that all calls that are bought at 1 should be sold when and if they get to 2, but the same factors that induce one to sell the 10-point call after doubling his money should apply to the 2-point call as well. In fact, taking partial profits after a call holding has increased in value is often a wise plan. For example, if someone bought a number of calls at a price of 3, and they later were worth 5, it might behoove the call holder to sell one-third to one-half of his position at 5, thereby taking a partial profit. Having done that, it is often easi­ er to let the profits run on the balance, and letting profits run is generally one of the keys to successful trading. It is rarely to the call buyer's benefit to exercise the call if he has to pay com­ missions. When one exercises a call, he pays a stock commission to buy the stock at the striking price. Then when the stock is sold, a stock sale commission must also be paid. Since option commissions are much smaller, dollarwise, than stock commis­ sions, the call holder will usually realize more net dollars by selling the call in the option market than by exercising it. LOCKING IN PROFITS When the call buyer is fortunate enough to see the underlying stock advance rela­ tively quickly, he can implement a number of strategies to enhance his position. These strategies are often useful to the call buyer who has an unrealized profit but is torn between taking the profit or holding on in an attempt to generate more profits if the underlying stock should continue to rise. Example: A call buyer bought an XYZ October 50 call for 3 points when the stock was at 48. Then the stock rises to 58. The buyer might consider selling his October 50 (which would probably be worth about 9 points) or possibly taking one of several actions, some of which might involve the October 60 call, which may be selling for 3 points. Table 3-1 summarizes the situation. At this point, the call buyer might take one of four basic actions: 1. Liquidate the position by selling the long call for a profit. 2. Sell the October 50 that he is currently long and use part of the proceeds to pur­ chase October 60's. 3. Create a spread by selling the October 60 call against his long October 50. 4. Do nothing and remain long the October 50 call. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:133 SCORE: 24.00 ================================================================================ Gapter 3: Call Buying TABLE 3-1. Present situation on XYZ October calls. Original Trade XYZ common: 48 Bought XYZ October 50 at 3 109 Current Prices XYZ Common: 58 XYZ October 50: 9 XYZ October 60: 3 Each of these actions would produce different levels of risk and reward from this point forward. If the holder sells the October 50 call, he makes a 6-point profit, less commissions, and terminates the position. He can realize no further appreciation from the call, nor can he lose any of his current profits; he has realized a 6-point gain. This is the least aggressive tactic of the four: If the underlying stock continues to advance and rises above 63, any of the other three strategies will outperform the complete liquidation of the call. However, if the underlying stock should instead decline below 50 by expiration, this action would have provided the most profit of the four strategies. The other simple tactic, the fourth one listed, is to do nothing. If the call is then held to expiration, this tactic would be the riskiest of the four: It is the only one that could produce a loss at expiration if XYZ fell back below 50. However, if the under­ lying stock continues to rise in price, more profits would accrue on the call. Every call buyer realizes the ramifications of these two tactics - liquidating or doing nothing and is generally looking for an alternative that might allow him to reduce some of his risk without cutting off his profit potential completely. The remaining two tactics are geared to this purpose: limiting the total risk while providing the opportunity for fur­ ther profits of an amount greater than those that could be realized by liquidating. The strategy in which the holder sells the call that he is currently holding, the October 50, and uses part of the proceeds to buy the call at the next higher strike is called rolling up. In this example, he could sell the October 50 at 9, pocket his initial 3-point investment, and use the remaining proceeds to buy two October 60 calls at 3 points each. Thus, it is sometimes possible for the speculator to recoup his entire original investment and still increase the number of calls outstanding by rolling up. Once this has been done, the October 60 calls will represent pure profits, whatever their price. The buyer who "rolls up" in this rrwnner is essentially speculating with someone else's money. He has put his own money back in his pocket and is using accrued profits to attempt to realize further gains. At expiration, this tactic would perform best if XYZ increased by a substantial amount. This tactic turns out to be the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:134 SCORE: 48.00 ================================================================================ 110 Part II: Call Option Strategies worst of the four at expiration if XYZ remains near its current price, staying above 53 but not rising above 63 in this example. The other alternative, the third one listed, is to continue to hold the October 50 call but to sell the October 60 call against it. This would create what is known as a bull spread, and the tactic can be used only by traders who have a margin account and can meet their firm's minimum equity requirement for spreading (generally $2,000). This spread position has no risk, for the long side of the spread - the October 50 cost 3 points, and the short side of the spread - the October 60 - brought in 3 points via its sale. Even if the underlying stock drops below 50 by expiration and all the calls expire worthless, the trader cannot lose anything except commissions. On the other hand, the maximum potential of this spread is 10 points, the difference between the striking prices of 50 and 60. This maximum potential would be realized if XYZ were anywhere above 60 at expiration, for at that time the October 50 call would be worth 10 points more than the October 60 call, regardless of how far above 60 the underlying stock had risen. This strategy will be the best peiformer of the four if XYZ remains relative­ ly unchanged, above the lower strike but not much above the higher strike by expira­ tion. It is interesting to note that this tactic is never the worst peiforrner of the four tactics, no matter where the stock is at expiration. For example, if XYZ drops below 50, this strategy has no risk and is therefore better than the "do nothing" strategy. If XYZ rises substantially, this spread produces a profit of 10 points, which is better than the 6 points of profit offered by the "liquidate" strategy. There is no definite answer as to which of the four tactics is the best one to apply in a given situation. However, if a call can be sold against the currently long call to produce a bull spread that has little or no risk, it may often be an attractive thing to do. It can never tum out to be the worst decision, and it would produce the largest profits if XYZ does not rise substantially or fall substantially from its current levels. Tables 3-2 and 3-3 summarize the four alternative tactics, when a call holder has an unrealized profit. The four tactics, again, are: 1. "Do nothing" - continue to hold the currently long call. 2. "Liquidate" - sell the long call to take profits and do not reinvest. 3. "Roll up" - sell the long call, pocket the original investment, and use the remain­ ing proceeds to purchase as many out-of-the-money calls as possible. 4. "Spread" - create a bull spread by selling the out-of-the-money call against the currently profitable long call, preferably taking in at least the original cost of the long call. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:135 SCORE: 20.00 ================================================================================ Cl,apter 3: Call Buying 111 TABLE 3-2. Comparison of the four alternative strategies. If the underlying stock then. . . The best tactic was. . . And the worst tactic was ... continues to rise dramatic­ ally ... "roll up" rises moderately above the do nothing next strike ... remains relatively unchanged . .. spread falls back below the original liquidate strike ... TABLE 3-3. Results at expiration. XYZ Price at "Roll-up" "Do Nothing" Expiration Profit Profit 50 or below $ 0 -$ 300(W) 53 0(W) 0(W) 56 0(W) + 300 60 0(W) + 700 63 + 600(W) + 1,000(B) 67 + 1,400(B) + 1,400(B) 70 + 2,000(B) + 1,700 liquidate liquidate or "roll up" "roll up" do nothing "Spread" Profit $ 0 + 300 + 600(B) + 1,000(B) + 1,000(B) + 1,000 + 1,000 Liquidating Profit +$600(B) + 600(B) + 600(B) + 600 + 600(W) + 600(W) + 600(W) Note that each of the four tactics proves to be the best tactic in one case or another, but that the spread tactic is never the worst one. Tables 3-2 and 3-3 represent the results from holding until expiration. For those who prefer to see the actual numbers involved in making these comparisons between the four tactics, Table 3-3 summa­ rizes the potential profits and losses of each of the four tactics using the prices from the example above. 'W" indicates that the tactic is the worst one at that price, and "B" indicates that it is the best one. There are, of course, modifications that an investor might make to any of these tactics. For example, he might decide to sell out half of his long call position, recov­ ering a major part of his original cost, and continue to hold the remainder of the long calls. This still leaves room for further appreciation. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:136 SCORE: 37.00 ================================================================================ 112 Part II: Call Option Strategies DEFENSIVE ACTION Two follow-up strategies are sometimes employed by the call buyer when the under­ lying stock declines in price. Both involve spread strategies; that is, being long and short two different calls on the same underlying stock simultaneously. Spreads are discussed in detail in later chapters. This discussion of spreads applies only to their use by the call buyer. ·"Rolling Down." If an option holder owns an option at a currently unreal­ ized loss, it may be possible to greatly increase the chances of making a limited profit on a relatively small rebound in the stock price. In certain cases, the investor may be able to implement such a strategy at little or no increase in risk. Many call buyers have encountered a situation such as this: An XYZ October 35 call was originally bought for 3 points in hopes of a quick rise in the stock price. However, because of downward movements in the stock- to 32, say- the call is now at 1 ½ with October expiration nearer. If the call buyer still expects a mild rally in the stock before expiration, he might either hold the call or possibly "average down" (buy more calls at I½). In either case he will need a rally to nearly 38 by expiration in order to break even. Since this would necessitate at least a 15% upward move by the stock before expiration, it cannot be considered very likely. Instead, the buyer should consider implementing the following strategy, which will be explained through the use of an example. Example: The investor is long the October 35 call at this time: XYZ, 32; XYZ October 35 call, 1 ½; and XYZ October 30 call, 3. One could sell two October 35's and, at the same time, buy one October 30 for no additional investment before commissions. That is, the sale of 2 October 35's at $150 each would bring in $300, exactly the cost, before commissions, of buying the October 30 call. This is the key to implementing the roll-down strategy: that one be able to buy the lower strike call and sell two of the higher strike calls for nearly even money. Note that the investor is now short the call that he previously owned, the October 35. Where he previously owned one October 35, he has now sold two of them. He is also now long one October 30 call. Thus, his position is: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:137 SCORE: 36.00 ================================================================================ 0.,,., 3: Call Buying long 1 XYZ October 30 call, 1hort 1 XYZ October 35 call. 113 This is technically known as a bull spread, but the terminology is not important. Table 3-4 summarizes the transactions that the buyer has made to acquire this spread. The trader now "owns" the spread at a cost of $300, plus commissions. By making this trade, he has lowered his break-even point significantly without increas­ ing his risk. However, the maximum profit potential has also been limited; he can no longer capitalize on a strong rebound by the underlying stock. In order to see that the break-even point has been lowered, consider what the results are~ is at 33 at October expiration. The October 30 call would be worth 3 points and the October 35 would expire worthless with XYZ at 33. Thus, the October 30 call could be sold to bring in $300 at that time, and there would not be any expense to buy back the October 35. Consequently, the spread could be liqui­ dated for $300, exactly the amount for which it was "bought." The spread then breaks even at 33 at expiration. If the call buyer had not rolled down, his break-even point would be 38 at expiration, for he paid 3 points for the original October 35 call and he would thus need XYZ to be at 38 in order to be able to liquidate the call for 3 points. Clearly, the stock has a better chance of recovering to 33 than to 38. Thus, the call buyer significantly lowers his break-even point by utilizing this strategy. Lowering the break-even point is not the investor's only concern. He must also be aware of what has happened to his profit and loss opportunities. The risk remains essentially the same the $300 in debits, plus commissions, that has been paid out. The risk has actually increased slightly, by the amount of the commissions spent in "rolling down." However, the stock price at which this maximum loss would be real­ ized has been lowered. With the original long call, the October 35, the buyer would lose the entire $300 investment anywhere below 35 at October expiration. The TABLE 3-4. Transactions in bull spread. Original trade Later trade Net position Trade Buy 1 October 35 call at 3 Sell 2 October 35 calls at 1 1/2 Buy 1 October 30 call at 3 Long 1 October 30 call Short 1 October 35 call Cost before Commissions $300 debit $300 credit $300 debit $300 debit ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:138 SCORE: 39.00 ================================================================================ 114 Part II: Call Option Strategies spread strategy, however, would result in a total loss of $300 only if XYZ were below 30 at October expiration. With XYZ above 30 in October, the long side of the spread could be liquidated for some value, thereby avoiding a total loss. The investor has reduced the chance of realizing the maximum loss, since the stock price at which that loss would occur has been lowered by 5 points. As with most investments, the improvement of risk exposure - lowering the break-even point and lowering the maximum loss price - necessitates that some potential reward be sacrificed. In the original long call position (the October 35), the maximum profit potential was unlimited. In the new position, the potential profit is limited to 2 points if XYZ should rally back to, or anywhere above, 35 by October expiration. To see this, assume XYZ is 35 at expiration. Then the long October 30 call would be worth 5 points, while the October 35 would expire worthless. Thus, the spread could be liquidated for 5 points, a 2-point profit over the 3 points paid for the spread. This is the limit of profit for the spread, however, since if XYZ is above 35 at expiration, any further profits in the long October 30 call would be offset by a corre­ sponding loss on the short October 35 call. Thus, if XYZ were to rally heavily by expi­ ration, the "rolled down" position would not realize as large a profit as the original long call position would have realized. Table 3-5 and Figure 3-2 summarize the original and new positions. Note that the new position is better for stock prices between 30 and 40. Below 30, the two posi­ tions are equal, except for the additional commissions spent. If the stock should rally back above 40, the original position would have worked out better. The new position is an improvement, provided that XYZ does not rally back above 40 by expiration. The chances that XYZ could rally 8 points, or 25%, from 32 to 40 would have to be considered relatively remote. Rolling the long call down into the spread would thus appear to be the correct thing to do in this case. This example is particularly attractive, because no additional money was required to establish the spread. In many cases, however, one may find that the long call cannot be rolled into the spread at even money. Some debit may be required. This fact should not necessarily preclude making the change, since a small addition­ al investment may still significantly increase the chance of breaking even or making a profit on a rebound. Example: The following prices now exist, rather than the ones used earlier. Only the October 30 call price has been altered: XYZ, 32; XYZ October 35 call, 1 ½; and XYZ October 30 call, 4. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:139 SCORE: 17.00 ================================================================================ O.,ter 3: Call Buying TABLE 3-5. Original and spread positions compared. Stock Price Long Call at Expiration Result 25 -$300 30 - 300 33 - 300 35 - 300 38 0 40 + 200 45 + 700 FIGURE 3-2. Companion: original call purchase vs. spread. § ~ +$200 ·5.. ~ al tJ) .3 0 :1: e c.. -$300 Stock Price at Expiration Spread Result -$300 - 300 0 + 200 + 200 + 200 + 200 115 With these prices, a 1-point debit would be required to roll down. That is, selling 2 October 35 calls would bring in $300 ($150 each), but the cost of buying the October 30 call is $400. Thus, the transaction would have to be done at a cost of $100, plus commissions. With these prices, the break-even point after rolling down would be 34, still well below the original break-even price of 38. The risk has now been increased by the additional 1 point spent to roll down. If XYZ should drop below 30 at October expiration, the investor would have a total loss of 4 points plus commissions. The maximum loss with the original long October 35 call was limited to 3 points plus a smaller amount of commissions. Finally, the maximum amount of money that the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:140 SCORE: 48.00 ================================================================================ 116 Part II: Call Option Strategies spread could make is now $100, less commissions. The alternative in this example is not nearly as attractive as the previous one, but it might still be worthwhile for the call buyer to invoke such a spread if he feels that XYZ has limited rally potential up to October expiration. One should not automatically discard the use of this strategy merely because a debit is required to convert the long call to a spread. Note that to "average down" by buying an additional October 35 call at 1 ½ would require an additional investment of $150. This is more than the $100 required to convert into the spread position in the immediately preceding example. The break-even point on the position that was "averaged down" would be over 37 at expiration, whereas the break-even point on the spread is 34. Admittedly, the averaged-down position has much more profit potential than the spread does, but the conversion to the spread is less expensive than "aver­ aging down" and also provides a lower break-even price. In summary, then, if the call buyer finds himself with an unrealized loss because the stock has declined, and yet is unwilling to sell, he may be able to improve his chances of breaking even by "rolling down" into a spread. That is, he would sell 2 of the calls that he is currently long - the one that he owns plus another one - and simultaneously buy one call at the next lower striking price. If this transaction of sell­ ing 2 calls and buying 1 call can be done for approximately even money, it could def­ initely be to the buyer's benefit to implement this strategy, because the break-even point would be lowered considerably and the buyer would have a much better chance of getting out even or making a small profit should the underlying stock have a small rebound. Creating a Calendar Spread. A different type of defensive spread strategy is sometimes used by the call buyer who finds that the underlying stock has declined. In this strategy, the holder of an intermediate- or long-term call sells a near-term call, with the same striking price as the call he already owns. This creates what is known as a calendar spread. The idea behind doing this is that if the short-term call expires worthless, the overall cost of the long call will be reduced to the buyer. Then, if the stock should rally, the call buyer has a better chance of making a profit. Example: Suppose that an investor bought an XYZ October 35 call for 3 points some­ time in April. By June the stock has fallen to 32, and it appears that the stock might remain depressed for a while longer. The holder of the October 35 call might con­ sider selling a July 35 call, perhaps for a price of 1 point. Should XYZ remain below 35 until July expiration, the short call would expire worthless, earning a small, 1-point profit. The investor would still own the October 35 call and would then hope for a rally by XYZ before October in order to make profits on that call. Even if XYZ does ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:141 SCORE: 26.00 ================================================================================ Chpter 3: Call Buying 117 not rally by October, he has decreased his overall loss by the amount received for the sale of the July 35 call. This strategy is not as attractive to use as the previous one. If XYZ should rally before July expiration, the investor might find himself with two losing positions. For example, suppose that XYZ rallied back to 36 in the next week. His short call that he sold for 1 point would be selling for something more than that, so he would have an unrealized loss on the short July 35. In addition, the October 35 would probably not have appreciated back to its original price of 3, and he would therefore have an unre­ alized loss on that side of the spread as well. Consequently, this strategy should be used with great caution, for if the under­ lying stock rallies quickly before the near-term expiration, the spread could be at a loss on both sides. Note that in the former spread strategy, this could not happen. Even if XYZ rallied quickly, some profit would be made on the rebound. A FURTHER COMMENT ON SPREADS Anyone not familiar with the margin requirements for spreads, under both the exchange margin rules and the rules of the brokerage firm he is dealing with, should not attempt to utilize a spread transaction. Later chapters on spreads outline the more common requirements for spread transactions. In general, one must have a margin account to establish a spread and must have a minimum amount of equity in the account. Thus, the call buyer who operates in a cash account cannot necessarily use these spread strategies. To do so might incur a margin call and possible restric­ tion of one's trading account. Therefore, check on specific requirements before uti­ lizing a spread strategy. Do not assume that a long call can automatically be "rolled" into any sort of spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:142 SCORE: 20.00 ================================================================================ Other Call Buying Strategies In this chapter, two additional strategies that utilize the purchase of call options are described. Both of these strategies involve buying calls against the short sale of the underlying stock. When listed puts are traded on the underlying stock, these strate­ gies are often less effective than when they are implemented with the use of put options. However, the concept is important, and sometimes these strategies are more viable in markets where calls are ve:iy liquid but puts are not. These strategies are generally known as "synthetic" strategies. THE PROTECTED SHORT SALE (OR SYNTHETIC PUT) Purchasing a call at the same time that one is short the underlying stock is a means of limiting the risk of the short sale to a fixed amount. Since the risk is theoretically unlimited in a short sale, many investors are reluctant to use the strategy. Even for those investors who do sell stock short, it can be rather upsetting if the stock rises in price. One may be forced into an emotional - and perhaps incorrect - decision to cover the short sale in order to relieve the psychological pressure. By owning a call at the same time he is short, the investor limits the risk to a fixed and generally small amount. Example: An investor sells XYZ short at 40 and simultaneously purchases an XYZ July 40 call for 3 points. If XYZ falls in price, the short seller will make his profit on the short sale, less the 3 points paid for the call, which will expire worthless. Thus, by buying the call for protection, a small amount of profit potential is sacrificed. However, the advantage of owning the call is demonstrated when the results are examined for a stock rise. IfXYZ should rise to any price above 40 by July expiration, 118 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:143 SCORE: 28.00 ================================================================================ Cl,apter 4: Other Call Buying Strategies 119 the short seller can cover his short by exercising the long call and buying stock at 40. Thus, the maximum risk that the short seller can incur in this example is the 3 points paid for the call. Table 4-1 and Figure 4-1 depict the results at expiration from uti­ lizing this strategy. Commissions are not included. Note that the break-even point is 37 in this example. That is, if the stock drops 3 points, the protected short sale posi­ tion will break even because of the 3-point loss on the call. The short seller who did not spend the extra money for the long call would, of course, have a 3-point profit at 37. To the upside, however, the protected short sale outperforms a regular short sale if the stock climbs anywhere above 43. At 43, both types of short sales have $300 loss­ es. But above that level, the loss would continue to grow for a regular short sale, while it is fixed for the short seller who also bought a call. In either case, the short seller's risk is increased slightly by the fact that he is obligated to pay out the dividends on the underlying stock, if any are declared. A simple formula is available for determining the maximum amount of risk when one protects a short sale by buying a call option: Risk = Striking price of purchased call + Call price - Stock price Depending on how much risk the short seller is willing to absorb, he might want to buy an out-of-the-money call as protection rather than an at-the-money call, as was shown in the example above. A smaller dollar amount is spent for the protection when one buys an out-of-the-money call, so that the short seller does not give away as much of his profit potential. However, his risk is larger because the call does not start its protective qualities until the stock goes above the striking price. Example: With XYZ at 40, the short seller of XYZ buys the July 45 call at ½ for pro­ tection. His maximum possible loss, if XYZ is above 45 at July expiration, would be TABLE 4-1. Results at expiration-protected short sale. XYZ Price at Profit Call Price at Profit Total Expiration on XYZ Expiration on Call Profit 20 +$2,000 0 -$ 300 +$1,700 30 + 1,000 0 - 300 + 700 37 + 300 0 - 300 0 40 0 0 - 300 300 50 - 1,000 10 + 700 300 60 - 2,000 20 + 1,700 300 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:144 SCORE: 13.00 ================================================================================ 120 FIGURE 4-1. Protected short sale. C: 0 .:; ~ 'a.. X UJ 1o +$0 en en 0 ...J 0 -e 0.-$300 40' ', Stock Price at Expiration ' Part II: Call Option Strategies 43 ', ', ' ', ' ', Short ', ' Sale 'll 5½ points - the five points between the current stock price of 40 and the striking price of 45, plus the amount paid for the call. On the other hand, if XYZ declines, the protected short seller will make nearly as much as the short seller who did not pro­ tect, since he only spent ½ point for the long call. If one buys an in-the-nwney call as protection for the short sale, his risk will be quite minimal. However, his profit potential will be severely limited. As an example, with XYZ at 40, if one had purchased a July 35 call at 5½, his risk would be limited to½ point anywhere above 35 at July expiration. Unfortunately, he would not realize any profit on the position until the stock went below 34½, a drop of 5½ points. This is too much protection, for it limits the profit so severely that there is only a small hope of making a profit. Generally, it is best to buy a call that is at-the-nwney or only slightly out-of the­ money as the protection for the short sale. It is not of much use to buy a deeply out­ of-the-money call as protection, since it does very little to moderate risk unless the stock climbs quite dramatically. Normally, one would cover a short sale before it went heavily against him. Thus, the money spent for such a deeply out-of-the-money call is wasted. However, if one wants to give a short sale plenty of room to "work" and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:145 SCORE: 42.00 ================================================================================ Cl,opter 4: Other Call Buying Strategies 121 feels ve:ry certain that his bearish view of the stock is the correct view, he might then buy a fairly deep out-of-the-money call just as disaster protection, in case the stock suddenly bolted upward in price (if it received a takeover bid, for example). MARGIN REQUIREMENTS The newest margin rules now allow one to receive favorable margin treatment when a short sale of stock is protected by a long call option. The margin required is the lower of (1) 10% of the call's striking price plus any out-of-the-money amount, or (2) 30% of the current short stock's market value. The position will be marked to market daily, and most brokers will require that the short sale be margined at "normal" rates if the stock is below the strike price. Example: Suppose the following prices exist: XYZ Common stock: 47 Oct 40 call: 8 Oct 50 call: 3 Oct 60 call: 1 Suppose that one is considering a short sale of 100 shares of XYZ at 47 and the purchase of one of the calls as protection. Here are the margin requirements for the various strike prices. (Note that the option price, per se, is not part of the margin requirement, but all options must be paid for in full, initially). Position Short XYZ, long Oct 40 call Short XYZ, long Oct 50 call Short XYZ, long Oct 60 call l 0% strike + out-of-the-money 400 + 0 = 400* 500 + 300 = 800* 600 + 1,300 = 1,900 30% stock price 1,410 1,410 1,41 0* *Since the margin requirement is the lower of the two figures, the items marked with an asterisk in this table are the margin requirements. Again, remember that the long call would have to be paid for in full, and that most brokers impose a maintenance requirement of at least the value of the short sale itself as long as the stock is below the strike price of the long call, in addition to the above requirements. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:146 SCORE: 38.00 ================================================================================ 122 Part II: Call Option Strategies FOLLOW-UP ACTION There is little that the protected short seller needs to perform in the way of follow­ up action in this strategy, other than closing out the position. If the underlying stock moves down quickly and it appears that it might rebound, the short sale could be cov­ ered without selling the long call. In this manner, one could potentially profit on the call side as well if the stock came back above the original striking price. If the under­ lying stock rises in price, a similar strategy of taking off only the profitable call side of the transaction is not recommended. That is, if XYZ climbed from 40 to 50 and the July 40 call also rose from 3 to 10, it is not advisable to take the 7-point profit in the call, hoping for a drop in the stock price. The reason for this is that one is entering into a highly risk-oriented situation by removing his protection when the call is in­ the-money. Thus, when the stock drops, it is all right - perhaps even desirable - to take the profit, because there is little or no additional risk if the stock continues to drop. However, when the stock rises, it is not an equivalent situation. In that case, if the short seller sells his call for a profit and the stock subsequently rises even further, large losses could result. It may often be advisable to close the position if the call is at or near parity, in-the-money, by exercising the call. In most strategies, the option holder has no advantage in exercising the call because of the large dollar difference between stock commissions and option commissions. However, in the protected short sale strategy, the short seller is eventually going to have to cover the short stock in any case and incur the stock commission by so doing. It may be to his advantage to exercise the call and buy his stock at the striking price, thereby buying stock at a lower price and perhaps paying a slightly lower commission amount. Example: XYZ rises to 50 from the original short sale price of 40, and the XYZ July 40 call is selling at 10 somewhere close to expiration. The position could be liquidat­ ed by either (1) buying the stock back at 50 and selling the call at 10, or (2) exercis­ ing the call to buy stock at 40. In the first case, one would pay a stock commission at a price of $50 per share plus an option commission on a $10 option. In the second case, the only commission would be a stock commission at the price of $40 per share. Since both actions accomplish the same end result - closing the position entirely for 40 points plus commissions - clearly the second choice is less costly and therefore more desirable. Of course, if the call has time value premium in it of an amount greater than the commission savings, the first alternative should be used. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:147 SCORE: 37.00 ================================================================================ Orapter 4: Other Call Buying Strategies 123 THE REVERSE HEDGE (SIMULATED STRADDLE) There is another strategy involving the purchase of long calls against the short sale of stock. In this strategy, one purchases calls on more shares than he has sold short. The strategist can profit if the underlying stock rises far enough or falls far enough dur­ ing the life of the calls. This strategy is generally referred to as a reverse hedge or sim­ ulated straddle. On stocks for which listed puts are traded, this strategy is outmoded; the same results can be better achieved by buying a straddle (a call and a put). Hence, the name "simulated straddle" is applied to the reverse hedge strategy. This strategy has limited loss potential, usually amounting to a moderate per­ centage of the initial investment, and theoretically unlimited profit potential. When properly selected (selection criteria are described in great detail in Chapter 36, which deals with volatility trading), the percentage of success can be quite high in straddle or synthetic straddle buying. These features make this an attractive strategy, especially when call premiums are low in comparison to the volatility of underlying stock. Example: XYZ is at 40 and an investor believes that the stock has the potential to move by a relatively large distance, but he is not sure of the direction the stock will take. This investor could short XYZ at 40 and buy 2 XYZ July 40 calls at 3 each to set up a reverse hedge. If XYZ moves up by a large distance, he will incur a loss on his short stock, but the fact that he owns two calls means that the call profits will outdis­ tance the stock loss. If, on the other hand, XYZ drops far enough, the short sale prof­ it will be larger than the loss on the calls, which is limited to 6 points. Table 4-2 and Figure 4-2 show the possible outcomes for various stock prices at July expiration. If XYZ falls, the stock profits on the short sale will accumulate, but the loss on the two calls is limited to $600 (3 points each) so that, below 34, the reverse hedge can make ever-increasing profits. To the upside, even though the short sale is incurring losses, the call profits grow faster because there are two long calls. For example, at 60 at expiration, there will be a 20-point ($2,000) loss on the short stock, but each XYZ July 40 call will be worth 20 points with the stock at 60. Thus, the two calls are worth $4,000, representing a profit of $3,400 over the initial cost of $600 for the calls. Table 4-2 and Figure 4-2 illustrate another important point: The maximum loss would occur if the stock were exactly at the striking price at expiration of the calls. This maximum loss would occur if XYZ were at 40 at expiration and would amount to $600. In actual practice, since the short seller must pay out any dividends paid by the under­ lying stock, the risk in this strategy is increased by the amount of such dividends. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:148 SCORE: 17.00 ================================================================================ 124 TABLE 4-2. Reverse hedge at July expiration. XYZ Price at Stock Expiration Profit 20 +$2,000 25 + 1,500 30 + 1,000 34 + 600 40 0 46 600 50 - 1,000 55 - 1,500 60 - 2,000 FIGURE 4-2. Reverse hedge {simulated straddle). C: 0 ~ ! co (/) (/) .3 ~-$600 e a. Profit on 2 Calls -$ 600 600 600 600 600 + 600 + 1,400 + 2,400 + 3,400 Stock Price at Expiration Part II: Call Option Strategies Total Profit +$ l ,400 + 900 + 400 0 600 0 + 400 + 900 + 1,400 The net margin required for this strategy is 50% of the underlying stock plus the full purchase price of the calls. In the example above, this would be an initial investment of $2,000 (50% of the stock price) plus $600 for the calls, or $2,600 total plus commissions. The short sale is marked to market, so the collateral requirement would grow if the stock rose. Since the maximum risk, before commissions, is $600, this means that the net percentage risk in this transaction is $600/$2,600, about 23%. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:149 SCORE: 21.00 ================================================================================ Cl,opter 4: Other Call Buying Strategies 125 This is a relatively small percentage risk in a position that could have very large prof­ its. There is also very little chance that the entire maximum loss would ever be real­ ized since it occurs only at one specific stock price. One should not be deluded into thinking that this strategy is a sure money-maker. In general, stocks do not move very far in a 3- or 6-month period. With careful selection, though, one can often find sit­ uations in which the stock will be able to move far enough to reach the break-even points. Even when losses are taken, they are counterbalanced by the fact that signif­ icant gains can be realized when the stock moves by a great distance. It is obvious from the information above that profits are made if the stock moves far enough in either direction. In fact, one can determine exactly the prices beyond which the stock would have to move by expiration in order for profits to result. These prices are 34 and 46 in the foregoing example. The downside break-even point is 34 and the upside break-:even point is 46. These break-even points can easily be com­ puted. First, the maximum risk is computed. Then the break-even points are deter­ mined. Maximum risk = Striking price + 2 x Call price - Stock price Upside break-even point = Striking price + Maximum risk Downside break-even point = Striking price - Maximum risk In the preceding example, the striking price was 40, the stock price was also 40, and the call price was 3. Thus, the maximum risk = 40 + 2 x 3 - 40 = 6. This con­ firms that the maximum risk in the position is 6 points, or $600. The upside break­ even point is then 40 + 6, or 46, and the downside break-even point is 40 - 6, or 34. These also agree with Table 4-2 and Figure 4-2. Before expiration, profits can be made even closer to the striking price, because there will be some time value premium left in the purchased calls. Example: IfXYZ moved to 45 in one month, each call might be worth 6. If this hap­ pened, the investor would have a 5-point loss on the stock, but would also have a 3- point gain on each of the two options, for a net overall gain of 1 point, or $100. Before expiration, the break-even point is clearly somewhere below 46, because the position is at a profit at 45. Ideally, one would like to find relatively underpriced calls on a fairly volatile stock in order to implement this strategy most effectively. These situations, while not prevalent, can be found. Normally, call premiums quite accurately reflect the volatil­ ity of the underlying stock. Still, this strategy can be quite viable, because nearly every stock, regardless of its volatility, occasionally experiences a straight-line, fairly large move. It is during these times that the investor can profit from this strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:150 SCORE: 16.00 ================================================================================ 126 Part II: Call Option Strategies Generally, the underlying stock selected for the reverse hedge should be volatile. Even though option premiums are larger on these stocks, they can still be outdistanced by a straight-line move in a volatile situation. Another advantage of uti­ lizing volatile stocks is that they generally pay little or no dividends. This is desirable for the reverse hedge, because the short seller will not be required to pay out as much. The technical pattern of the underlying stock can also be useful when selecting the position. One generally would like to have little or no technical support and resistance within the loss area. This pattern would facilitate the stock's ability to make a fairly quick move either up or down. It is sometimes possible to find a stock that is in a wide trading range, frequently swinging from one side of the range to the other. If a reverse hedge can be set up that has its loss area well within this trading range, the position may also be attractive. Example: The XYZ stock in the previous example is trading in the range 30 to 50, perhaps swinging to one end and then the other rather frequently. Now the reverse hedge example position, which would make profits above 46 or below 34, would appear more attractive. FOLLOW-UP ACTION Since the reverse hedge has a built-in limited loss feature, it is not necessary to take any follow-up action to avoid losses. The investor could quite easily put the position on and take no action at all until expiration. This is often the best method of follow­ up action in this strategy. Another follow-up strategy can be applied, although it has some disadvantages associated with it. This follow-up strategy is sometimes known as trading against the straddle. When the stock moves far enough in either direction, the profit on that side can be taken. Then, if the stock swings back in the opposite direction, a profit can also be made on the other side. Two examples \vill show how this type of follow-up strategy works. Example 1: The XYZ stock in the previous example quickly moves down to 32. At that time, an 8-point profit could be taken on the short sale. This would leave two long calls. Even if they expired worthless, a 6-point loss is all that would be incurred on the calls. Thus, the entire strategy would still have produced a profit of 2 points. However, if the stock should rally above 40, profits could be made on the calls as well. A slight variation would be to sell one of the calls at the same time the stock profit is taken. This would result in a slightly larger realized profit; but if the stock rallied back ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:151 SCORE: 12.00 ================================================================================ Cl,apter 4: Other Call Buying Strategies 127 above 40, the resulting profits there would be smaller because the investor would be long only one call instead of two. Example 2: XYZ has moved up to a price at which the calls are each worth 8 points. One of the calls could then be sold, realizing a 5-point profit. The resulting position would be short 100 shares of stock and long one call, a protected short sale. The pro­ tected short sale has a limited risk, above 40, of 3 points (the stock was sold short at 40 and the call was purchased for 3 points). Even if XYZ remains above 40 and the maximum 3-point loss has to be taken, the overall reverse hedge would still have made a profit of 2 points because of the 5-point profit taken on the one call. Conversely, if XYZ drops below 40, the protected short sale position could add to the profits already taken on the call. There is a variation of this upside protective action. Example 3: Instead of selling the one call, one could instead short an additional 100 shares of stock at 48. If this was done, the overall position would be short 200 shares of stock (100 at 40 and the other 100 at 48) and long two calls - again a protected short sale. If XYZ remained above 40, there would again be an overall gain of 2 points. To see this, suppose that XYZ was above 40 at expiration and the two calls were exercised to buy 200 shares of stock at 40. This would result in an 8-point prof­ it on the 100 shares sold short at 48, and no gain or loss on the 100 shares sold short at 40. The initial call cost of 6 points would be lost. Thus, the overall position would profit by 2 points. This means of follow-up action to the upside is more costly in com­ missions, but would provide bigger profits if XYZ fell back below 40, because there are 200 shares of XYZ short. In theory, if any of the foregoing types of follow-up action were taken and the underlying stock did indeed reverse direction and cross back through the striking price, the original position could again be established. Suppose that, after covering the short stock at 32, XYZ rallied back to 40. Then XYZ could be sold short again, reestablishing the original position. If the stock moved outside the break-even points again, further follow-up action could be taken. This process could theoretically be repeated a number of times. If the stock continued to whipsaw back and forth in a trading range, the repeated follow-up actions could produce potentially large profits on a small net change in the stock price. In actual practice, it is unlikely that one would be fortunate enough to find a stock that moved that far that quickly. The disadvantage of applying these follow-up strategies is obvious: One can never make a large profit if he continually cuts his profits off at a small, limited ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:152 SCORE: 8.00 ================================================================================ 128 Part II: Call Option Strategies amount . .. When XYZ falls to 32, the stock can be covered to ensure an overall profit of 2 points on the transaction. However, if XYZ continued to fall to 20, the investor who took no follow-up action would make 14 points while the one who did take fol­ low-up action would make only 2 points. Recall that it was stated earlier that there is a high probability of realizing limited losses in the reverse hedge strategy, but that this is balanced by the potentially large profits available in the remaining cases. If one takes follow-up action and cuts off these potentially large profits, he is operating at a distinct disadvantage unless he is an extremely adept trader. Proponents of using the follow-up strategy often counter with the argument that it is frustrating to see the stock fall to 32 and then return back to nearly 40 again. If no follow-up action were taken, the unrealized profit would have dissolved into a loss when the stock rallied. This is true as far as it goes, but it is not an effective enough argument to counterbalance the negative effects of cutting off one's profits. ALTERING THE RATIO OF LONG CALLS TO SHORT STOCK Another aspect of this strategy should be discussed. One does not have to buy exact­ ly two calls against 100 shares of short stock. More bullish positions could be con­ structed by buying three or four calls against 100 shares short. More bearish positions could be constructed by buying three calls and shorting 200 shares of stock. One might adopt a ratio other than 2:1, because he is more bullish or bearish. He also might use a different ratio if the stock is between two striking prices, but he still wants to create a position that has break-even points spaced equidistant from the cur­ rent stock price. A few examples will illustrate these points. Example: XYZ is at 40 and the investor is slightly bullish on the stock but still wants to employ the reverse hedge strategy, because he feels there is a chance the stock could drop sharply. He might then short 100 shares of XYZ at 40 and buy 3 July 40 calls for 3 points apiece. Since he paid 9 points for the calls, his maximum risk is that 9 points if XYZ were to be at 40 at expiration. This means his downside break-even price is 31, for at 31 he would have a 9-point profit on the short sale to offset the 9- point loss on the calls. To the upside, his break-even is now 44½. IfXYZ were at 44½ and the calls at 4½ each at expiration, he would lose 4½ points on the short sale, but would make l ½ on each of the three calls, for a total call profit of 4½. A more bearish investor might short 200 XYZ at 40 and buy 3 July 40 calls at 3. His break-even points would be 35½ on the downside and 49 on the upside, and his maximum risk would be 9 points. There is a general formula that one can always ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:154 SCORE: 14.00 ================================================================================ 130 Example: The following prices exist: XYZ, 37½; XYZ July 40 call, 2; and XYZ July 35 call, 4. Part II: Call Option Strategies If one were to short 100 XYZ at 37½ and to buy one July 40 call for 2 and one July 35 call for 4, he would have a position that is similar to a reverse hedge except that the maximum risk would be realized anywhere between 35 and 40 at expiration. Although this risk is over a much wider range than in the normal reverse hedge, it is now much smaller in dimension. Table 4-3 and Figure 4-3 show the results from this type of position at expiration. The maximum loss is 3½ points ($350), which is a smaller amount than could be realized using any ratio strictly with the July 35 or the July 40 call. However, this maximum loss is realizable over the entire range, 35 to 40. Again, large potential profits are available if the stock moves far enough either to the upside or to the downside. This form of the strategy should only be used when the stock is nearly centered between two strikes and the strategist wants a neutral positioning of the break-even points. Similar types of follow-up action to those described earlier can be applied to this form of the reverse hedge strategy as well. TABLE 4-3. Reverse hedge using two strikes. XYZ Price at Stock July 40 Coll July 35 Coll Total Expiration Profit Profit Profit Profit 25 +$1,250 -$200 -$ 400 +$ 650 30 + 750 - 200 400 + 150 31 1/2 + 600 - 200 400 0 35 + 250 - 200 400 350 371/2 0 - 200 150 350 40 - 250 - 200 + 100 350 431/2 - 600 + 150 + 450 0 45 - 750 + 300 + 600 + 150 50 - 1,250 + 800 + 1,100 + 650 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:155 SCORE: 12.00 ================================================================================ Gapter 4: Other Call Buying Strategies 131 FIGURE 4-3. Reverse hedge using two strikes (simulated combination purchase). C: ~ ·5. in ~ l/l .3 0 i.l::-$350 e a. SUMMARY 40 Stock Price at Expiration The strategies described in this chapter would not normally be used if the underly­ ing stock has listed put options. However, if no puts exist, or the puts are very illiq­ uid, and the strategist feels that a volatile stock could move a relatively large distance in either direction during the life of a call option, he should consider using one of the forms of the reverse hedge strategy - shorting a quantity of stock and buying calls on more shares than he is short. If the desired movement does develop, potentially large profits could result. In any case, the loss is limited to a fixed amount, generally around 20 to 30% of the initial investment. Although it is possible to take follow-up action to lock in small profits and attempt to gain on a reversal by the stock, it is wiser to let the position run its course to capitalize on those occasions when the profits become large. Normally a 2:1 ratio (long 2 calls, short 100 shares of stock) is used in this strategy, but this ratio can be adjusted if the investor wants to be more bullish or more bearish. If the stock is initially between two striking prices, a neutral profit range can be set up by shorting the stock and buying calls at both the next higher strike and the next lower strike. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:156 SCORE: 54.00 ================================================================================ CHAPTER 5 Naked Call Writing The next two chapters will concentrate on various aspects of writing uncovered call options. These strategies have risk ofloss if the underlying stock should rise in price, but they offer profits if the underlying stock declines in price. This chapter on naked, or uncovered, call writing - demonstrates some of the risks and rewards inherent in this aggressive strategy. Novice option traders often think that selling naked options is the "best" way to make money, because of time decay. In addition, they often assume that market-makers and other professionals sell a lot of naked options. In reality, neither is true. Yes, options do eventually lose their premium if held all the way until expiration. However, when an option has a good deal of life remaining, its excess value above intrinsic value what we call "time value premium" - is, in reality, heavily influenced by the volatility estimate of the stock. This is called implied volatility and is discussed at length later in the book. For now, though, it is sufficient to understand that a lot can go wrong when one writes a naked option, before it eventually expires. As to professionals selling a lot of naked options, the fact is that most market-makers and other full-time option traders attempt to reduce their exposure to large stock price movements if possible. Hence, they may sell some options naked, but they generally try to hedge them by buying other options or by buying the underlying stock. Many novice option traders hold these misconceptions, probably because there is a general belief that most options expire worthless. Occasionally, one will even hear or see a statement to this effect in the mainstream media, but it is not true that most options expire worthless. In fact, studies conducted by McMillan Analysis Corp. in both bull and bear months indicate that about 65% to 70% of all options have some value (at least half a point) when they expire. This is not to say that all option buyers make money, either, but it does serve to show that many more options do not expire worthless than do. 132 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:157 SCORE: 44.00 ================================================================================ Qapter 5: Naked Call Writing 133 THE UNCOVERED (NAKED) CALL OPTION When one sells a call option without owning the underlying stock or any equivalent security (convertible stock or bond or another call option), he is considered to have written an uncovered call option. This strategy has limited profit potential and theo­ retically unlimited loss. For this reason, this strategy is unsuitable for some investors. This fact is not particularly attractive, but since there is no actual cash investment required to write a naked call ( the position can be financed with collateral loan value of marginable securities), the strategy can be operated as an adjunct to many other investment strategies. A simple example will outline the basic profit and loss potential from naked writing. Example: XYZ is selling at 50 and a July 50 call is selling for 5. If one were to sell the July 50 call naked - that is, without owning XYZ stock, or any security convertible into XYZ, or another call option on XYZ - he could make, at most, 5 points of profit. This profit would accrue if XYZ were at or anywhere below 50 at July expiration, as the call would then expire worthless. If XYZ were to rise, however, the naked writer could potentially lose large sums of money. Should the stock climb to 100, say, the call would be at a price of 50. If the writer then covered (bought back) the call for a price of 50, he would have a loss of 45 points on the transaction. In theory, this loss is unlimited, although in practice the loss is limited by time. The stock cannot rise an infinite amount during the life of the call. Clearly, defensive strategies are important in this approach, as one would never want to let a loss run as far as the one here. Table 5-1 and Figure 5-1 (solid line) depict the results of this position at July expira­ tion. Note that the break-even point in this example is 55. That is, if XYZ rose 10%, or 5 points, at expiration, the naked writer would break even. He could buy the call back at parity, 5 points, which is exactly what he sold it for. There is some room for error to the upside. A naked write will not necessarily lose money if the stock moves up. It will only lose if the stock advances by more than the amount of the time value premium that was in the call when it was originally written. Naked writing is not the same as a short sale of the underlying stock. While both strategies have large potential risk, the short sale has much higher reward potential, but the naked write will do better if the underlying stock remains relatively unchanged. It is possible for the naked writer to make money in situations when the short seller would have lost money. Using the example above, suppose one investor had written the July 50 call naked for 5 points while another investor sold the stock short at 50. If XYZ were at 52 at expiration, the naked writer could buy the call back at parity, 2 points, for a 3-point profit. The short seller would have a 2-point loss. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:158 SCORE: 20.00 ================================================================================ 134 TABLE 5-1. Position at July expiration. XYZ Price at Call Price at Expiration Expiration 30 0 40 0 50 0 55 5 60 10 70 20 80 30 FIGURE 5-1. Uncovered (naked) call write. +$500 C 0 ~ ·15.. X w cu (/J ~ ...I 0 lt, .... ...... ", Naked Write 45 SO', .... .. .... .. .. Short Sale ,, .. .. Stock Price at Expiration .. Part II: Call Option Strategies Profit on Naked Write +$ 500 + 500 + 500 0 500 - 1,500 - 2,500 .. .... .. ~ Moreover, the short seller pays out the dividends on the underlying stock, whereas the naked call writer does not. The naked call will expire, of course, but the short sale does not. This is a situation in which the naked write outperforms the short sale. However, ifXYZ were to fall sharply- to 20, say- the naked writer could only make 5 points while the short seller would make 30 points. The dashed line in Figure 5-1 shows how the short sale of XYZ at 50 would compare with the naked write of the July 50 call. Notice that the two strategies are equal at 45 at expiration; they both ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:159 SCORE: 26.00 ================================================================================ Cl,apter 5: Naked Call Writing 135 make a 5-point profit there. Above 45, the naked write does better; it has larger prof­ its and smaller losses. Below 45, the short sale does better, and the farther the stock falls, the better the short sale becomes in comparison. As will be seen later, one can more closely simulate a short sale by writing an in-the-money naked call. INVESTMENT REQUIRED The margin requirements for writing a naked call are 20% of the stock price plus the call premium, less the amount by which the stock is below the striking price. If the stock is below the striking price, the differential is subtracted from the requirement. However, a minimum of 10% of the stock price is required for each call, even if the C-'Omputation results in a smaller number. Table 5-2 gives four examples of how the ini­ tial margin requirement would be computed for four different stock prices. The 20% collateral figure is the minimum exchange requirement and may vary somewhat among different brokerage houses. The call premium may be applied against the requirement. In the first line of Table 5-2, if the XYZ July 50 call were selling for 7 points, the $700 call premium could be applied against the $1,800 margin requirement, reducing the actual amount that the investor would have to put up as collateral to $1,100. TABLE 5-2. Initial collateral requirements for four stock prices. Coll Written XYZ July 50 XYZ July 50 XYZ July 50 XYZ July 50 Stock Price When Coll Written 55 50 46 40 *Requirement cannot be less than 10%. Coll Price $700 400 200 100 20% of Stock Price $1,100 1,000 920 800 Out-of-the­ Money Differential $ 0 0 400 - 1,000 Total Margin Requirement $1,800 1,400 720 400* In addition to the basic requirements, a brokerage firm may require that for a customer to participate in uncovered writing, he have a minimum equity in his account. This equity requirement may range from as low as $2,000 to as high as $100,000. Since naked call writing is a high-risk strategy, some brokerage firms require that the customer be able to show both financial wherewithal and option ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:160 SCORE: 33.00 ================================================================================ 136 Part II: Call Option Strategies trading experience before the account can be approved for naked call writing. In addition, some brokers require that a maintenance requirement be applied against each option written naked. This requirement, sometimes called a kicker, is usually less than $250 per call and is generally used by the broker to ensure that, should the customer fail to respond to an assignment notice against his naked call, the commis­ sion costs for buying and selling the underlying stock would be defrayed. Naked Option Positions Are Marked to the Market Daily. This means that the collateral requirement for the position is recomputed daily, just as in the short sale of stock. The same margin formula that was described above is applied and, if the stock has risen far enough, the customer will be required to deposit addi­ tional collateral or close the position. The need for such a mark to market is obvious. If the underlying stock should rise, the brokerage firm must ensure that the customer has enough collateral to cover the eventuality of buying the stock in the open market and selling it at the striking price if an assignment notice should be received against the naked call. The mark to market works to the customer's favor if the stock falls in price. Excess collateral is then released back into the customer's margin account, and may be used for other purposes. It is important to realize that, in order to write a naked call, collateral is all that is required. No cash need be "invested" if one owns securities with sufficient collat­ eral loan value. Example: An investor owns 100 shares of a stock selling at $60 per share. This stock is worth $6,000. If the loan rate on stock is 50% of $6,000, this investor has a collat­ eral loan value equal to 50% of $6,000, or $3,000. This investor could write any of the naked calls in Table 5-2 without adding cash or securities to his account. Moreover, he would have satisfied a minimum equity requirement of at least $6,000, since his stock is equity. This aspect of naked call writing - using collateral value to finance the writing - is attractive to many investors, since one is able to write calls and bring in premi­ ums without disturbing his existing portfolio. Of course, if the stock underlying the naked call should rise too far in price, additional collateral may be called for by the broker because of the mark to market. Moreover, there is risk whether cash or col­ lateral is used. If one buys in a naked call at a loss, he will then be spending cash, cre­ ating a debit in his account. Regardless of how one finances a naked option position, it is generally a good idea to allow enough collateral so that the stock can move all the way to the point at which one would cover the option or take follow-up action. For example, suppose a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:163 SCORE: 74.00 ================================================================================ Gapter 5: Naked Call Writing 137 stock is trading at 50 and one sells an April 60 call naked, figuring that he will cover the call if the stock rises to 60 ( that is, if the option becomes an in-the-money option). He should set aside enough collateral to margin the position as if the stock were at 60 (even though the actual margin requirement will be smaller than that). If he allows that extra collateral, then he will never be forced into a margin call at a stock price prior to (that is, below) where he wanted to take follow-up action. Simply stat­ ed, let the market take you out of a position, not a margin call. THE PHILOSOPHY OF SELLING NAKED OPTIONS The first and foremost question one must address when thinking about selling naked options (or any strategy, for that matter) is: "Can I psychologically handle the thought of naked options in my account?" Notice that the question does not have anything to do with whether one has enough collateral or margin to sell calls (although that, too, is important) nor does it ask how much money he will make. First, one must decide if he can be comfortable with the risk of the strategy. Selling naked options means that there is theoretically unlimited risk if the underlying instrument should make a large, sudden, adverse move. It is one's attitude regarding that fact alone that deter­ mines whether he should consider selling naked options. If one feels that he won't be able to sleep at night, then he should not sell naked options, regardless of any profit projections that might seem attractive. If one feels that the psychological suitability aspect is not a roadblock, then he can consider whether he has the financial wherewithal to write naked options. On the surface, naked option margin requirements are not large (although in equity and index options, they are larger than they were prior to the crash of 1987). In general, one would prefer to let the naked options expire worthless, if at all possible, without disturbing them, unless the underlying instrument makes a signifi­ cant adverse move. So, out-of-the-money options are the usual choice for naked sell­ ing. Then, in order to reduce ( or almost eliminate) the chance of a margin call, one should set aside the margin requirement as if the underlying had already rrwved to the strike price of the option sold. By allowing margin as if the underlying were already at the strike, one will almost never experience a margin call before the under­ lying price trades up to the strike price, at which time it is best to close the position or to roll the call to another strike. Thus, for naked equity call options, allow as collateral 20% of the highest naked strike price. In this author's opinion, the biggest mistake a trader can make is to ini­ tiate trades because of margin or taxes. Thus, by allowing the "maximum" margin, one can make trading decisions based on what's happening in the market, as opposed to reacting to a margin call from his broker. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:164 SCORE: 49.00 ================================================================================ 138 Part II: Call Option Strategies "Suitability" also means not risking nwre nwney than one can afford to lose. If one allows the "maximum" margin, then he won't be risking a large portion of his equity unless he is unable to cover when the underlying trades through the strike price of his naked option. Gaps in trading prices would be the culprits that could pre­ vent one from covering. Gaps are common in stocks, less common in futures, and almost nonexistent in indices. Hence, index options are the options of choice when it comes to naked writing. Index options are discussed later in the book. Finally, there is one more "rule" that a naked option writer must follow: Someone has to be watching the position at all times. Disasters could occur if one were to go on vacation and not pay attention to his naked options. Usually, one's bro­ ker can watch the position, even if the trader has to call him from his vacation site. In sum, then, to write naked options, one needs to be prepared psychological­ ly, have sufficient funds, be willing to accept the risk, be able to monitor the position every day, sell options whose implied volatility is extremely high, and cover any naked options that become in-the-money options. RISK AND REWARD One can adjust the apparent risks and rewards from naked call writing by his selec­ tion of an in-the-money or out-of-the-money call. Writing an out-of-the-money call naked, especially one quite deeply out-of-the-money, offers a high probability of achieving a small profit. Writing an in-the-money call naked has the most profit potential, but it also has higher risks. Example: XYZ is selling at 40 and the July 50 is selling for½. This call could be sold naked. The probability that XYZ could rise to 50 by expiration has to be considered small, especially if there is not a large amount of time remaining in the life of the call. In fact, the stock could rise 25%, or 10 points, by expiration to a price of 50, and the call would still expire worthless. Thus, this naked writer has a good chance of realiz­ ing a $50 profit, less commissions. There could, of course, be substantial risk in terms of potential profit versus potential loss if the stock rises substantially in price by expi­ ration. Still, this apparent possibility of achieving additional limited income with a high probability of success has led many investors to use the collateral value of their portfolios to sell deeply out-of-the-money naked calls. For those employing this technique, a favored position is to have a stock at or just about 15 and then sell the near-term option with striking price 20 naked. This option would sell for one-eighth or one-quarter, perhaps, although at times there might not be any bid at all. At this price, the stock would have to rally nearly one- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:165 SCORE: 30.00 ================================================================================ C.,,er 5: Naked Call Writing 139 third, or 33%, for the writer to lose money. Although there are not usually many optionable stocks selling at or just above $10 per share, these same out-of-the-money writers would also be attracted to selling a call with a striking price 15 when the stock is at 10, because a 50% upward move by the stock would be required for a loss to be realized. This strategy of selling deeply out-of-the-money calls has its apparent attraction in that the writer is assured of a profit unless the underlying stock can rally rather substantially before the call expires. The danger in this strategy is that one or two losses, perhaps amounting to only a couple of points each, could wipe out many peri­ ods of profits. The stock market does occasionally rally heavily in a short period, as witnessed repeatedly throughout history. Thus, the writer who is adopting this strat­ egy cannot regard it as a sure thing and certainly cannot afford to establish the writes and forget them. Close monitoring is required in case the market begins to rally, and by no means should losses be allowed to accumulate. The opposite end of the spectrum in naked call writing is the writing of fairly deeply in-the-money calls. Since an in-the-money call would not have much time value premium in it, this writer does not have much leeway to the upside. If the stock rallies at all, the writer of the deeply in-the-money naked call will normally experience a loss. However, should the stock drop in price, this writer will make larger dollar profits than will the writer of the out-of-the-money call. The sale of the deeply in-the-money call simulates the profits that a short seller could make, at least until the stock drops close to the striking price, since the delta of a deeply in-the­ money call is close to 1. Example: XYZ is selling at 60 and the July 50 call is selling for 10½. IfXYZ rises, the naked writer will lose money, because there is only ½ of a point of time value pre­ mium in the call. If XYZ falls, the writer will make profits on a point-for-point basis until the stock falls much closer to 50. That is, if XYZ dropped from 60 to 57, the call price would fall by almost 3 points as well. Thus, for quick declines by the stock, the deeply in-the-money write can provide profits nearly equal to those that the short seller could accumulate. Notice that if XYZ falls all the way to 50, the profits on the written call will be large, but will be accumulating at a slower rate as the time value premium builds up with the stock near the striking price. If one is looking to trade a stock on the short side for just a few points of nwve­ ment, he might use a deeply in-the-nwney naked write instead of shorting the stock. His investment will be smaller - 20% of the stock price for the write as compared to 50% of the stock price for the short sale - and his return will thus be larger. (The requirement for the in-the-money amount is offset by applying the call's premium.) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:166 SCORE: 26.00 ================================================================================ 140 Part II: Call Option Strategies The writer should take great caution in ascertaining that the call does have some time premium in it. He does not want to receive an assignment notice on the written call. It is easiest to find time premium in the more distant expiration series, so the writer would normally be safest from assignment by writing the longest-term deep in-the­ money call if he wants to make a bearish trade in the stock. Example: An investor thinks that XYZ could fall 3 or 4 points from its current price of 60 in a quick downward move, and wants to capitalize on that move by writing a naked call. If the April 40 were the near-term call, he might have the choice of sell­ ing the April 40 at 20, the July 40 at 20¼, or the October 40 at 20½. Since all three calls will drop nearly point for point with the stock in a move to 56 or 57, he should write the October 40, as it has the least risk of being assigned. A trader utilizing this strategy should limit his losses in much the same way a short seller would, by cover­ ing if the stock rallies, perhaps breaking through overhead technical resistance. ROLLING FOR CREDITS Most writers of naked calls prefer to use one of the two strategies described above. The strategy of writing at-the-money calls, when the stock price is initially close to the striking price of the written call, is not widely utilized. This is because the writer who wants to limit risk will write an out-of-the-money call, whereas the writer who wants to make larger, quick trading profits will write an in-the-money call. There is, how­ ever, a strategy that is designed to utilize the at-the-money call. This strategy offers a high degree of eventual success, although there may be an accumulation of losses before the success point is reached. It is a strategy that requires large collateral back­ ing, and is therefore only for the largest investors. We call this strategy "rolling for credits." The strategy is described here in full, although it can, at times, resemble a Martingale strategy; that is, one that requires "doubling up" to succeed, and one that can produce ruin if certain physical limits are reached. The classic Martingale strat­ egy is this: Begin by betting one unit; if you lose, double your bet; if you win that bet, you'll have netted a profit of one unit (you lost one, but won two); if you lost the sec­ ond bet, double your bet again. No matter how many times you lose, keep doubling your bet each time. When you eventually win, you will profit by the amount of your original bet (one unit). Unfortunately, such a strategy cannot be employed in real life. For example, in a gambling casino, after enough losses, one would bump up against the table limit and would no longer be able to double his bet. Consequently, the strat­ egy would be ruined just when it was at its worst point. While "rolling for credits" doesn't exactly call for one to double the number of written calls each time, it does require that one keep increasing his risk exposure in order to profit by the amount of that original credit sold. In general, Martingale strategies should be avoided. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:167 SCORE: 18.00 ================================================================================ Cl,apter 5: Naked Call Writing 141 In essence, the writer who is rollingf or credits sells the most time premium that he can at any point in time. This would generally be the longest-term, at-the-money call. If the stock declines, the writer makes the time premium that he sold. However, if the stock rises in price, the writer rolls up for a credit. That is, when the stock reaches the next higher striking price, the writer buys back the calls that were origi­ nally sold and sells enough long-term calls at the higher strike to generate a credit. In this way, no debits are incurred, although a realized loss is taken on the rolling up. If the stock persists and rises to the next striking price, the process is repeated. Eventually, the stock will stop rising - they always do - and the last set of written options will expire worthless. At that time, the writer would make an overall profit consisting of an amount equal to all the credits that he had taken in so far. In reality, most of that credit will simply be the initial credit received. The "rolls" are done for even money or a small credit. In essence, the increased risk generated by continual­ ly rolling up is all geared toward eventually capturing that initial credit. The similar­ ity to the Martingale strategy is strongest in this regard: One continually increases his risk, knowing that when he eventually wins (i.e., the last set of options expires worth­ less), he profits by the amount of his original "bet." There are really only two requirements for success in this strategy. The first is that the underlying stock eventually fall back, that it does not rise indefinitely. This is hardly a requirement; it is axiomatic that all stocks will eventually undergo a correc­ tion, so this is a simple requirement to satisfy. The second requirement is that the investor have enough collateral backing to stay with the strategy even if the stock runs up heavily against him. This is a much harder requirement to satisfy, and may in fact tum out to be nearly impossible to satisfy. If the stock were to experience a straight-line upward move, the number of calls written might grow so substantially that they would require an unrealistically large amount of collateral (margin). At a minimum, this strategy is applicable only for the largest investors. For such well-collateralized investors, this strategy can be thought of as a way to add income to a portfolio. That is, a large stock portfolio's equity may be used to finance this strategy through its loan value. There would be no margin interest charges, because all transactions are cred­ it transactions. (No debits are created, as long as the Martingale "limits" are not reached.) The securities portfolio would not have to be touched unless the strategy were terminated before the last set of calls expired worthless. This is where the danger comes in: If the stock upon which the calls are written rises so fast that one completely uses up all of his collateral value to finance the naked calls, and then one is required to roll again, the strategy could result in large losses. For a while, one could simply continue to roll the same number of calls up for deb­ its, but eventually those debits would mount in size if the stock persisted in rising. At ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:168 SCORE: 21.00 ================================================================================ 142 Part II: Call Option Strategies this point, even if the stock did finally decline enough for the last set of calls to expire worthless, the overall strategy might still have been operated at a loss. Example: The basic strategy in the case of rising stock is shown in Table 5-3. Note that each transaction is a credit and that all ( except the last) involve taking a realized loss. This example assumes that the stock rose so quickly that a longer-term call was never available to roll into. That is, the October calls were always utilized. If there were a longer-term call available (the January series, for example), the writer should roll up and out as well. In this way, larger credits could be generated. The number of calls written increased from 5 to 15 and the collateral required as backing for the writing of the naked calls also increased heavily. Recall that the collateral require­ ment is equal to 20% of the stock price plus the call premium, less the amount by which the call is out-of-the-money. The premium may be used against the collateral requirements. Using the stock and call prices of the example above, the investment is computed in Table 5-4. While the number of written calls has tripled from 5 to 15, the collateral requirement has more than quadrupled from $5,000 to $21,000. This is why the investor must have ample collateral backing to utilize this strategy. The gen­ eral philosophy of the large investors who do apply this strategy is that they hope to eventually make a profit and, since they are using the collateral value of large securi­ ty positions already held, they are not investing any more money. The strategy does not really "cost" these investors anything. All profits represent additional income and do not in any way disturb the underlying security portfolio. Unfortunately, losses taken due to aborting the strategy could seriously affect the portfolio. This is why the investor must have sufficient collateral to carry through to completion. The sophisticated strategist who implements this strategy will generally do more rolling than that discussed in the simple example above. First, if the stock drops, the calls will be rolled down to the next strike - for a credit - in order to con­ stantly be selling the most time premium, which is always found in the longest-term at-the-money call. Furthermore, the strategist may want to roll out to a more distant expiration series whenever the opportunity presents itself. This rolling out, or for­ ward, action is only taken when the stock is relatively unchanged from the initial price and there is no need to roll up or down. This strategy seems ve:ry attractive as long as one has enough collateral backing. Should one use up all of his available collateral, the strategy could collapse, causing substantial losses. It may not necessarily generate large rates of return in rising mar­ kets, but in stable or declining markets the generation of additional income can be quite substantial. Since the investor is not putting up any additional cash but is uti- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:170 SCORE: 47.00 ================================================================================ 144 Part II: Call Option Strategies security, the strategist should diversify several moderately sized positions throughout a variety of underlying stocks. If he does this, he will probably never have to exceed the position limit of contracts short in any one security. Even with as many precautions as one might take, there is no guarantee that one would have the collateral available to withstand a gain of 1000% or more, such as is occasionally seen with high-flying tech stocks or new IPOs. One would probably be best served, if he really wants to operate this strategy, to stick with stocks that are well capitalized (some of the biggest in the industry), so that they are less suscepti­ ble to such violent upside moves. Even then, though, there is no guarantee that one will not run out of collateral in a sharply rising market, because it is impossible to esti­ mate with complete certainty just how far any one stock might advance in a particu­ lar period of time. TIME VALUE PREMIUM IS A MISNOMER Once again, the topic of time value premium is discussed, as it was in Chapter 3. Many novice option traders think that if they sell an out-of-the-money option (whether covered or naked), all they have to do is sit back and wait to collect the pre­ mium as time wears it away. However, a lot of things can happen between the time an option is sold and its expiration date. The stock can move a great deal, or implied volatility can skyrocket. Both are bad for the option seller and both completely coun­ teract any benefit that time decay might be imparting. The option seller must con­ sider what might happen during the life of the option, and not simply view it as a strategy to hold the option until expiration. Naked call writers, especially, should operate with that thought in mind, but so should covered call writers, even though most don't. What the covered writer gives away is the upside; and if he constantly sells options without regard to the possibilities of volatility or stock price increases, he will be doing himself a disservice. So, while it is still proper to refer to the part of an option's price that is not intrinsic value as "time value premium," the knowledgeable option trader under­ stands that it is also more heavily influenced by volatility and stock price movement than by time. SUMMARY In a majority of cases, naked call writing is applied as a deeply out-of-the-money strategy in which the investor uses the collateral value of his security holdings to par­ ticipate in a strategy that offers a large probability of making a very limited profit. It is a poor strategy, because one loss may wipe out many profits. The trader who ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:172 SCORE: 27.00 ================================================================================ Ratio Call Writing Two basic types of call writing have been described in previous chapters: covered call writing, in which one owns the underlying stock and sells a call; and naked call writ­ ing. Ratio writing is a combination of these two types of positions. THE RATIO WRITE Simply stated, ratio call writing is the strategy in which one owns a certain number of shares of the underlying stock and sells calls against more shares than he owns. Thus, there is a ratio of calls written to stock owned. The most common ratio is the 2:1 ratio, whereby one owns 100 shares of the underlying stock and sells 2 calls. Note that this type of position involves writing a number of naked call options as well as a number of covered options. This resulting position has both downside risk, as does a covered write, and unlimited upside risk, as does a naked write. The ratio write gen­ erally wilI provide much larger profits than either covered writing or naked writing if the underlying stock remains relatively unchanged during the life of the calls. However, the ratio write has two-sided risk, a quality absent from either covered or naked writing. Generally, when an investor establishes a ratio write, he attempts to be neutral in outlook regarding the underlying stock. This means that he writes the calls with striking prices closest to the current stock price. Example: A ratio write is established by buying 100 shares of XYZ at 49 and selling two XYZ October 50 calls at 6 points each. If XYZ should decline in price and be anywhere below 50 at October expiration, the calls will expire worthless and the writer will make 12 points from the sale of the calls. Thus, even if XYZ drops 12 points to a price of 37, the ratio writer will break even. The stock loss of 12 points 146 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:173 SCORE: 21.00 ================================================================================ Otapter 6: Ratio Call Writing 147 would be offset by a 12-point gain on the calls. As with any strategy in which calls are sold, the maximum profit occurs at the striking price of the written calls at expiration. In this example, if XYZ were at 50 at expiration, the calls would still expire worthless for a 12-point gain and the writer would have a 1-point profit on his stock, which has moved up from 49 to 50, for a total gain of 13 points. This position therefore has ample downside protection and a relatively large potential profit. Should XYZ rise above 50 by expiration, the profit will decrease and eventually become a loss if the stock rises too far. To see this, suppose XYZ is at 63 at October expiration. The calls will be at 13 points each, representing a 7-point loss on each call, because they were originally sold for 6 points apiece. However, there would be a 14-poirit gain on the stock, which has risen from 49 to 63. The overall net is a break-even situation at 63 - a 14-point gain on the stock offset by 14 points ofloss on the options (7 points each). Table 6-1 and Figure 6-1 summarize the profit and loss potential of this example at October expiration. The shape of the graph resembles a roof with its peak located at the striking price of the written calls, or 50. It is obvious that the position has both large upside risk above 63 and large downside risk below 37. Therefore, it is imper­ ative that the ratio writer plan to take follow-up action if the stock should move out­ side these prices. Follow-up action is discussed later. If the stock remains within the range 37 to 63, some profit will result before commission charges. This range between the downside break-even point and the upside break-even point is called the profit range. This example represents essentially a neutral position, because the ratio writer will make some profit unless the stock falls by more than 12 points or rises by more than 14 points before the expiration of the calls in October. This is frequently an attractive type of strategy to adopt because, normally, stocks do not move very far in TABLE 6-1. Profit and loss at October expiration. XYZ Price at Stock Call Profit Total Expiration Profit Price on Calls Profit 30 -$1,900 0 +$1,200 -$ 700 37 - 1,200 0 + 1,200 0 45 400 0 + 1,200 + 800 50 + 100 0 + 1,200 + 1,300 55 + 600 5 + 200 + 800 63 + 1,400 13 - 1,400 0 70 + 2,100 20 - 2,800 - 700 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:174 SCORE: 17.00 ================================================================================ 148 FIGURE 6-1. Ratio write (2: 1 ). +$1,300 C 0 e ·5. X LU al rn rn .3 0 -e a. Part II: Call Option Strategies Stock Price at Expiration a 3- or 6-month time period. Consequently, this strategy has a rather high probabili­ ty of making a limited profit. The profit in this example would, of course, be reduced by commission costs and margin interest charges if the stock is bought on margin. Before discussing the specifics of ratio writing, such as investment required, selection criteria, and follow-up action, it may be beneficial to counter two fairly common objections to this strategy. The first objection, although not heard as fre­ quently today as when listed options first began trading, is "Why bother to buy 100 shares of stock and sell 2 calls? You will be naked one call. Why not just sell one naked call?" The ratio writing strategy and the naked writing strategy have very little in common except that both have upside risk. The profit graph for naked writing (Figure 5-1) bears no resemblance to the roof-shaped profit graph for a ratio write (Figure 6-1). Clearly, the two strategies are quite different in profit potential and in many other respects as well. The second objection to ratio writing for the conservative investor is slightly more valid. The conservative investor may not feel comfortable with a position that has risk if the underlying stock moves up in price. This can be a psychological detri­ ment to ratio writing: When stock prices are rising and everyone who owns stocks is happy and making profits, the ratio writer is in danger of losing money. However, in a purely strategic sense, one should be willing to assume some upside risk in exchange for larger profits if the underlying stock does not rise heavily in price. The ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:175 SCORE: 13.00 ================================================================================ Chapter 6: Ratio Call Writing 149 covered writer has upside protection all the way to infinity; that is, he has no upside risk at all. This cannot be the mathematically optimum situation, because stocks never rise to infinity. Rather, the ratio writer is engaged in a strategy that makes its profits in a price range more in line with the way stocks actually behave. In fact, if one were to try to set up the optimum strategy, he would want it to make its most profits in line with the most probable outcomes for a stock's movement. Ratio writ­ ing is such a strategy. Figure 6-2 shows a simple probability curve for a stock's movement. It is most likely that a stock will remain relatively unchanged and there is very little chance that it will rise or fall a great distance. Now compare the results of the ratio writing strat­ egy with the graph of probable stock outcomes. Notice that the ratio write and the probability curve have their "peaks" in the same area; that is, the ratio write makes its profits in the range of most likely stock prices, because there is only a small chance that any stock will increase or decrease by a large amount in a fixed period of time. The large losses are at the edges of the graph, where the probability curve gets very low, approaching zero probability. It should be noted that these graphs show the prof­ it and probability at expiration. Prior to expiration, the break-even points are closer to the original purchase price of the stock because there will still be some time value premium remaining on the options that were sold. FIGURE 6-2. Stock price probability curve overlaid on profit graph of ratio write. +$1,300 Probability Curve Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:176 SCORE: 17.00 ================================================================================ 150 Part II: Call Option Strategies INVESTMENT REQUIRED The ratio writer has a combination of covered writes and naked writes. The margin requirements for each of these strategies have been described previously, and the requirements for a ratio writing strategy are the sum of the requirements for a naked write and a covered write. Ratio writing is normally done in a margin account, although one could technically keep the stock in a cash account. Example: Ignoring commissions, the investment required can be computed as fol­ lows: Buy 100 XYZ at 49 on 50% margin and sell 2 XYZ October 50 calls at 6 points each (Table 6-2). The commissions for buying the stock and selling the calls would be added to these requirements. A shorter formula (Table 6-3) is actually more desirable to use. It is merely a combination of the investment requirements listed in Table 6-2. In addition to the basic requirement, there may be minimum equity require­ ments and maintenance requirements, since naked calls are involved. As these vary from one brokerage firm to another, it is best for the ratio writer to check with his broker to determine the equity and maintenance requirements. Again, since naked calls are involved in ratio writing, there will be a mark to market of the position. If the stock should rise in price, the investor will have to put up more collateral. It is conceivable that the ratio writer would want to stay with his original posi­ tion as long as the stock did not penetrate the upside break-even point of 63. TABLE 6-2. Investment required. Covered writing portion (buy 100 XYZ and sell 1 call) 50% of stock price Less premium received Requirement for covered portion Naked writing portion (sell 1 XYZ call) 20% of stock price Less out-of-the-money amount Plus call premium Less premium received Requirement for naked portion Total requirement for ratio write $2,450 600 $1,850 $ 980 100 + 600 600 $ 880 $2,730 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:177 SCORE: 11.00 ================================================================================ Cl,apter 6: Ratio Call Writing TABLE 6-3. Initial investment required for a ratio write. 70% of stock cost (XYZ = 49) Plus naked call premiums Less total premiums received Plus or minus striking price differential on naked calls $3,430 + 600 - 1,200 100 151 Total requirement $2,730 (plus commissions) TABLE 6-4. Collateral required with stock at upside break-even point of 63. Covered writing requirement $1,850 (see Table 6-2) 20% of stock price (XYZ = 63) 1,260 Plus call premium Less initial call premium received Total requirement with XYZ at 63 1,400 600 $3,910 Therefore, he should allow for enough collateral to cover the eventuality of a move to 63. Assuming the October 50 call is at 14 in this case, he would need $3,910 (see Table 6-4). This is the requirement that the ratio writer should be concerned with, not the initial collateral requirement, and he should therefore plan to invest $3,910 in this position, not $2,730 ( the initial requirement). Obviously, he only has to put up $2,730, but from a strategic point of view, he should allow $3,910 for the position. If the ratio writer does this with all his positions, he would not receive a margin call even if all the stocks in his portfolio climbed to their upside break-even points. SELECTION CRITERIA To decide whether a ratio write is a desirable position, the writer must first determine the break-even points of the position. Once the break-even points are known, the writer can then decide if the position has a wide enough profit range to allow for defensive action if it should become necessary. One simple way to determine if the profit range is wide enough is to require that the next higher and lower striking prices be within the profit range. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:178 SCORE: 17.00 ================================================================================ 152 Part II: Call Option Strategies Example: The writer is buying 100 XYZ at 49 and selling 2 October 50 calls at 6 points apiece. It was seen, by inspection, that the break-even points in the position are 37 on the downside and 63 on the upside. A mathematical formula allows one to quickly compute the break-even points for a 2:1 ratio write. Points of maximum profit = Strike price - Stock price + 2 x Call price Downside break-even point = Strike price - Points of maximum profit = Stock price - 2 x Call price Upside break-even point = Strike price + Points of maximum profit In this example, the points of maximum profit are 50 - 49 + 2 x 6, or 13. Thus, the downside break-even point would be 37 (50 - 13) and the upside break-even point would be 63 (50 + 13). These numbers agree with the figures determined ear­ lier by analyzing the position. This profit range is quite clearly wide enough to allow for defensive action should the underlying stock rise to the next highest strikes of 55 or 60, or fall to the next two lower strikes, at 45 and 40. In practice, a ratio write is not automatically a good position merely because the profit range extends far enough. Theoretically, one would want the profit range to be wide in relation to the volatility of the under­ lying stock. If the range is wide in relation to the volatility and the break-even points encompass the next higher and lower striking prices, a desirable position is available. Volatile stocks are the best candidates for ratio writing, since their pre­ miums will more easily satisfy both these conditions. A nonvolatile stock may, at times, have relatively large premiums in its calls, but the resulting profit range may still not be wide enough numerically to ensure that follow-up action could be taken. Specific measures for determining volatility may be obtained from many data serv­ ices and brokerage firms. Moreover, methods of computing volatility are present­ ed later in the chapter on mathematical applications, and probabilities are further addressed in the chapters on volatility trading. Technical support and resistance levels are also important in establishing the position. If both support and resistance lie within the profit range, there is a better chance that the stock will remain within the range. A position should not necessarily be rejected if there is not support and resistance within the profit range, but the writer is then subjecting himself to a possible undeterred move by the stock in one direction or the other. The ratio writer is generally a neutral strategist. He tries to take in the most time premium that he can to earn the premium erosion while the stock remains rel­ atively unchanged. If one is more bullish on a particular stock, he can set up a 2:1 ratio write with out-of~the-money calls. This allows more room to the upside than to the downside, and therefore makes the position slightly more bullish. Conversely, if ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:179 SCORE: 17.00 ================================================================================ Cl,apter 6: Ratio Call Writing 153 one is more bearish on the underlying stock, he can write in-the-money calls in a 2:1 ratio. There is another way to produce a slightly more bullish or bearish ratio write. This is to change the ratio of calls written to stock purchased. This method is also used to construct a neutral profit range when the stock is not close to a striking price. Example: An investor is slightly bearishly inclined in his outlook for the underlying stock, so he might write more than two calls for each 100 shares of stock purchased. His position might be to buy 100 XYZ at 49 and sell 3 XYZ October 50 calls at 6 points each. This position breaks even at 31 on the downside, because if the stock dropped by 18 points at expiration, the call profits would amount to 18 points and would pro­ duce a break-even situation. To the upside, the break-even point lies at 59½ for the stock at expiration. Each call would be worth 9½ at expiration with the stock at 59½, and each call would thus lose 3½ points, for a total loss of 10½ points on the three calls. However, XYZ would have risen from 49 to 59½ - a 10½-point gain - therefore producing a break-even situation. Again, a formula is available to aid in determining the break-even point for any ratio. Maximum profit= (Striking price - Stock price) x Round lots purchased+ Number of calls written x Call price D •d b ak Striking Maximum profit owns1 e re -even = - ------~~----price Number of round lots purchased U .d b ak Striking Maximum profit psi e re -even = + price ( Calls written - Round lots purchased) Note that in the case of a 2:1 ratio write, where the number of round lots purchased equals 1 and the number of calls written equals 2, these formulae reduce to the ones given earlier for the more common 2:1 ratio write. To verify that the formulae above are correct, insert the numbers from the most recent example. Example: Three XYZ October 50 calls at a price of 6 were sold against the purchase of 100 XYZ at 49. The number of round lots purchased is 1. Maximum profit = (50 - 49) x 1 + 3 x 6 = 19 Downside break-even= 50-19/1 = 31 Upside break-even= 50 + 19/(3 1) = 59½ In the 2:1 ratio writing example given earlier, the break-even points were 37 and 63. The 3:1 write has lower break-even points of 31 and 59½, reflecting the more bear­ ish posture on the underlying stock. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:180 SCORE: 27.00 ================================================================================ 154 Part II: Call Option Strategies A more bullish write is constructed by buying 200 shares of the underlying stock and writing three calls. To quickly verify that this ratio (3:2) is more bullish, again use 49 for the stock price and 6 for the call price, and now assume that two round lots were purchased. Maximum profit= (50-49) x 2 + 3 x 6 = 20 Downside break-even = 50 - 20/2 = 40 Upside break-even= 50 + 20/(3 - 2) = 70 Thus, this ratio of 3 calls against 200 shares of stock has break-even points of 40 and 70, reflecting a more bullish posture on the underlying stock. A 2: 1 ratio may not necessarily be neutral. There is, in fact, a mathematically correct way of determining exactly what a neutral ratio should be. The neutral ratio is determined by dividing the delta of the written call into 1. Assume that the delta of the XYZ October 50 call in the previous example is .60. Then the neutral ratio is 1.0/.60, or 5 to 3. This means that one might buy 300 shares and sell 5 calls. Using the formulae above, the details of this position can be observed: Maximum profit= (50 -49) x 3 + 5 x 6 = 33 Downside break-even = 50 - 33/3 = 39 Upside break-even = 50 + 33/(5 --3) = 66½ According to the mathematics of the situation, then, this would be a neutral position initially. It is often the case that a 5:3 ratio is approximately neutral for an at-the­ money call. By now, the reader should have recognized a similarity between the ratio writ­ ing strategy and the reverse hedge (or simulated straddle) strategy presented in Chapter 4. The two strategies are the reverse of each other; in fact, this is how the reverse hedge strategy acquired its name. The ratio write has a profit graph that looks like a roof, while the reverse hedge has a profit graph that looks like a trough - the roof upside down. In one strategy the investor buys stock and sells calls, while the other strategy is just the opposite - the investor shorts stock and buys calls. Which one is better? The answer depends on whether the calls are "cheap" or "expensive." Even though ratio writing has limited profits and potentially large losses, the strate­ gy will result in a profit in a large majority of cases, if held to expiration. However, one may be forced to make adjustments to stock moves that occur prior to expiration. The reverse hedge strategy, with its limited losses and potentially large profits, pro­ vides profits only on large stock moves - a less frequent event. Thus, in stable mar­ kets, the ratio writing strategy is generally superior. However, in times of depressed option premiums, the reverse hedge strategy gains a distinct advantage. If calls are ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:181 SCORE: 18.00 ================================================================================ Chapter 6: Ratio Call Writing 155 underpriced, the advantage lies with the buyer of calls, and that situation is inherent in the reverse hedge strategy. The summaries stated in the above paragraph are rather simplistic ones, refer­ ring mostly to what one can expect from the strategies if they are held until expira­ tion, without adjustment. In actual trading situations, it is much more likely that one would have to make adjustments to the ratio write along the way, thus disturbing or perhaps even eliminating the profit range. Such travails do not befall the reverse hedge (simulated straddle buy). Consequently, when one takes into consideration the stock movements that can take place prior to expiration, the ratio write loses some of its attractiveness and the reverse hedge gains some. THE VARIABLE RATIO WRITE In ratio writing, one generally likes to establish the position when the stock is trading relatively close to the striking price of the written calls. However, it is sometimes the case that the stock is nearly exactly between two striking prices and neither the in­ the-money nor the out-of-the-money call offers a neutral profit range. If this is the case, and one still wants to be in a 2:1 ratio of calls written to stock owned, he can sometimes write one in-the-money call and one out-of-the-money call against each 100 shares of common. This strategy, often termed a variable ratio write or trape­ zoidal hedge, serves to establish a more neutral profit range. Example: Given the following prices: XYZ common, 65; XYZ October 60 call, 8; and XYZ October 70 call, 3. If one were to establish a 2:1 ratio write with only the October 60's, he would have a somewhat bearish position. His profit range would be 49 to 71 at expiration. Since the stock is already at 65, this means that he would be allowing room for 16 points of downside movement and only 6 points on the upside. This is certainly not neutral. On the other hand, if he were to attempt to utilize only the October 70 calls in his ratio write, he would have a bullish position. This profit range for the October 70 ratio write would be 59 to 81 at expiration. In this case, the stock at 65 is too close to the downside break-even point in comparison to its distance from the upside break-even point. A more neutral position can be established by buying 100 XYZ and selling one October 60 and one October 70. This position has a profit range that is centered about the current stock price. Moreover, the new position has both an upside and a downside risk, as does a more normal ratio write. However, now the maximum prof­ it can be obtained anywhere between the two strikes at expiration. To see this, note ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:182 SCORE: 17.00 ================================================================================ 156 Part II: Call Option Strategies that if XYZ is anywhere between 60 and 70 at expiration, the stock will be called away at 60 against the sale of the October 60 call, and the October 70 call will expire worth­ less. It makes no difference whether the stock is at 61 or at 69; the same result will occur. Table 6-5 and Figure 6-3 depict the results from this variable hedge at expira­ tion. In the table, it is assumed that the option is bought back at parity to close the position, but if the stock were called away, the results would be the same. Note that the shape of Figure 6-3 is something like a trapezoid. This is the source of the name "trapezoidal hedge," although the strategy is more commonly known as a variable hedge or variable ratio write. The reader should observe that the maximum profit is indeed obtained if the stock is anywhere between the two strikes at eiqJiration. The maximum profit potential in this position, $600, is smaller than the maximum profit potential available from writing only the October 60's or only the October 70's. However, there is a vastly greater probability of realizing the maximum profit in a variable ratio write than there is of realizing the maximum profit in a nor­ mal ratio write. The break-even points for a variable ratio write can be computed most quickly by first computing the maximum profit potential, which is equal to the time value that the writer takes in. The break-even points are then computed directly by sub­ tracting the points of maximum profit from the lower striking price to get the down­ side break-even point and adding the points of maximum profit to the upper striking price to arrive at the upside break-even point. This is a similar procedure to that fol­ lowed for a normal ratio write: TABLE 6-5. Results at expiration of variable hedge. XYZ Price at XYZ October 60 October 70 Total Expiration Profit Profit Profit Profit 45 -$2,000 +$ 800 +$ 300 -$900 50 - 1,500 + 800 + 300 - 400 54 - 1,100 + 800 + 300 0 60 500 + 800 + 300 + 600 65 0 + 300 + 300 + 600 70 + 500 - 200 + 300 + 600 76 + 1,100 - 800 300 0 80 + 1,500 -$1,200 700 - 400 85 + 2,000 -1,700 - 1,200 - 900 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:183 SCORE: 9.00 ================================================================================ Gopter 6: Ratio Call Writing FIGURE 6-3. Variable ratio write (trapezoidal hedge). +$600 C: i $ al "' "' .3 5 ;t: e 0. $0 Stock Price at Expiration Points of maximum profit = Total option premiums + Lower striking price - Stock price Downside break-even point = Lower striking price - Points of maximum profit Upside break-even point = Higher striking price + Points of maximum profit 157 Substituting the numbers from the example above will help to verify the formula. The total points of option premium brought in were 11 (8 for the October 60 and 3 for the October 70). The stock price was 65, and the striking prices involved were 60 and 70. Points of maximum profit = 11 + 60 - 65 = 6 Downside break-even point= 60- 6 = 54 Upside break-even point= 70 + 6 = 76 Thus, the break-even points as computed by the formula agree with Table 6-5 and Figure 6-3. Nate that the formula applies only if the stock is initially between the two striking prices and the ratio is 2:1. If the stock is above both striking prices, the for­ mula is not correct. However, the writer should not be attempting to establish a vari­ able ratio write with two in-the-money calls. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:184 SCORE: 16.00 ================================================================================ 158 Part II: Call Option Strategies FOLLOW-UP ACTION Aside from closing the position completely, there are three reasonable approaches to follow-up action in a ratio writing situation. The first, and most popular, is to roll the written calls up if the stock rises too far, or to roll down if the stock drops too far. A second method uses the delta of the written calls. The third follow-up method is to utilize stops on the underlying stock to alter the ratio of the position as the stock moves either up or down. In addition to these types of defensive follow-up action, the investor must also have a plan in mind for taking profits as the written calls approach expiration. These types of follow-up action are discussed separately. ROLLING UP OR DOWN AS A DEFENSIVE ACTION The reader should already be familiar with the definition of a rolling action: The cur­ rently written calls are bought back and calls at a different striking price are written. The ratio writer can use rolling actions to his advantage to readjust his position if the underlying stock moves to the edges of his profit range. The reason one of the selection criteria for a ratio write was the availability of both the next higher and next lower striking prices was to facilitate the rolling actions that might become necessary as a follow-up measure. Since an option has its great­ est time premium when the stock price and the striking price are the same, one would normally want to roll exactly at a striking price. Example: A ratio writer bought 100 XYZ at 49 and sold two October 50 calls at 6 points each. Subsequently, the stock drops in price and the following prices exist: XYZ, 40; XYZ October 50, l; and XYZ October 40, 4. One would roll down to the October 40 calls by buying back the 2 October 50's that he is short and selling 2 October 40's. In so doing, he would reestablish a somewhat neutral position. His profit on the buy-back of the October 50 calls would be 5 points each - they were originally sold for 6 - and he would realize a 10-point gain on the two calls. This 10-point gain effectively reduces his stock cost from 49 to 39, so that he now has the equivalent of the following position: long 100 XYZ at 39 and short 2 XYZ October 40 calls at 4. This adjusted ratio write has a profit range of 31 to 49 and is thus a new, neutral position with the stock currently at 40. The investor is now in a position to make profits if XYZ remains near this level, or to take further defensive action if the stock experiences a relatively large change in price again. Defensive action to the upside - rolling up -works in much the same manner. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:185 SCORE: 36.00 ================================================================================ Chapter 6: Ratio Call Writing 159 Example: The initial position again consists of buying 100 XYZ at 49 and selling two October 50 calls at 6. If XYZ then rose to 60, the following prices might exist: XYZ, 60; XYZ October 50, 11; and XYZ October 60, 6. The ratio writer could thus roll this position up to reestablish a neutral profit range. If he bought back the two October 50 calls, he would take a 5-point loss on each one for a net loss on the calls of 10 points. This would effectively raise his stock cost by 10 points, to a price of 59. The rolled-up position would then be long 100 XYZ at 59 and short 2 October 60 calls at 6. This new, neutral position has a profit range of 47 to 73 at October expiration. In both of the examples above, the writer could have closed out the ratio write at a very small profit of about 1 point before commissions. This would not be advis­ able, because of the relatively large stock commissions, unless he expects the stock to continue to move dramatically. Either rolling up or rolling down gives the writer a fairly wide new profit range to work with, and he could easily expect to make more than 1 point of profit if the underlying stock stabilizes at all. Having to take rolling defensive action immediately after the position is estab­ lished is the most detrimental case. If the stock moves very quickly after having set up the position, there will not be much time for time value premium erosion in the written calls, and this will make for smaller profit ranges after the roll is done. It may be useful to use technical support and resistance levels as keys for when to take rolling action if these levels are near the break-even points and/or striking prices. It should be noted that this method of defensive action - rolling at or near strik­ ing prices - automatically means that one is buying back little or no time premium and is selling the greatest amount of time premium currently available. That is, if the stock rises, the call's premium will consist mostly of intrinsic value and very little of time premium value, since it is substantially in-the-money. Thus, the writer who rolls up by buying back this in-the-money call is buying back mostly intrinsic value and is selling a call at the next strike. This newly sold call consists mostly of time value. By continually buying back "real" or intrinsic value and by selling "thin air" or time value, the writer is taking the optimum neutral action at any given time. If a stock undergoes a dramatic move in one direction or the other, the ratio writer will not be able to keep pace with the dramatic movement by remaining in the same ratio. Example: If XYZ was originally at 49, but then undergoes a fairly straight-line move to 80 or 90, the ratio writer who maintains a 2:1 ratio will find himself in a deplorable situation. He will have accumulated rather substantial losses on the calls and will not be able to compensate for these losses by the gain in the underlying stock. A similar ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:186 SCORE: 15.00 ================================================================================ 160 Part II: Call Option Strategies situation could arise to the downside. If:X'YZ were to plunge from 49 to 20, the ratio writer would make a good deal of profit from the calls by rolling down, but may still have a larger loss in the stock itself than the call profits can compensate for. Many ratio writers who are large enough to diversify their positions into a num­ ber of stocks will continue to maintain 2:1 ratios on all their positions and will simply close out a position that has gotten out of hand by running dramatically to the upside or to the downside. These traders believe that the chances of such a dramatic move occurring are small, and that they will take the infrequent losses in such cases in order to be basically neutral on the other stocks in their portfolios. There is, however, a way to combat this sort of dramatic move. This is done by altering the ratio of the covered write as the stock moves either up or down. For example, as the underlying stock moves up dramatically in price, the ratio writer can decrease the number of calls outstanding against his long stock each time he rolls. Eventually, the ratio might decrease as far as 1:1, which is nothing more than a cov­ ered writing situation. As long as the stock continues to move in the same upward direction, the ratio writer who is decreasing his ratio of calls outstanding will be giv­ ing more and more weight to the stock gains in the ratio write and less and less weight to the call losses. It is interesting to note that this decreasing ratio effect can also be produced by buying extra shares of stock at each new striking price as the stock moves up, and simultaneously keeping the number of outstanding calls written con­ stant. In either case, the ratio of calls outstanding to stock owned is reduced. When the stock moves down dramatically, a similar action can be taken to increase the number of calls written to stock owned. Normally, as the stock falls, one would sell out some of his long stock and roll the calls down. Eventually, after the stock falls far enough, he would be in a naked writing position. The idea is the same here: As the stock falls, more weight is given to the call profits and less weight is given to the stock losses that are accumulating. This sort of strategy is more oriented to extremely large investors or to firm traders, market-makers, and the like. Commissions will be exorbitant if frequent rolls are to be made, and only those investors who pay very small commissions or who have such a large holding that their commissions are quite small on a percentage basis will be able to profit substantially from such a strategy. ADJUSTING WITH THE DELTA The delta of the written calls can be used to determine the correct ratio to be used in this ratio-adjusting defensive strategy. The basic idea is to use the call's delta to remain as neutral as possible at all times. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:187 SCORE: 27.00 ================================================================================ Cl,apter 6: Ratio Call Writing 161 Example: An investor initially sets up a neutral 5:3 ratio of XYZ October 50 calls to XYZ stock, as was determined previously. The stock is at 49 and the delta is .60. Furthermore, suppose the stock rises to 57 and the call now has a delta of .80. The neutral ratio would currently be 1/.80 ( = 1.20) or 5:4. The ratio writer could thus buy another 100 shares of the underlying stock. Alternatively, he might buy in one of the short calls. In this particular example, buying in one call would produce a 4:3 ratio, which is not absolutely correct. If he had had a larger position initially, it would be easier to adjust to fractional ratios. When the stock declines, it is necessary to increase the ratio. This can be accom­ plished by either selling more calls or selling out some of the long stock. In theory, these adjustments could be made constantly to keep the position neutral. In practice, one would allow for a few points of movement by the underlying stock before adjust­ ing. If the underlying stock rises too far, it may be logical for the neutral strategist to adjust by rolling up. Similarly, he would roll down if the stock fell to or below the next lower strike. The neutral ratio in that case is determined by using the delta of the option into which he is rolling. Example: With XYZ at 57, an investor is contemplating rolling up to the October 60's from his present position of long 300 shares and short 5 XYZ October 50's. If the October 60 has a delta of .40, the neutral ratio for the October 60's is 2.5:l (1 + .40). Since he is already long 300 shares of stock, he should now be short 7.5 calls (3 x 2.5). Obviously, he would sell 7 or 8, probably depending on his short-term outlook for the stock. If one prefers to adopt an even more sophisticated approach, he can make adjustments between striking prices by altering his stock position, and can make adjustments by rolling up or down if the stock reaches a new striking price. For those who prefer formulae, the following ones summarize this information: 1. When establishing a new position or when rolling up or down, at the next strike: N b f all t 11 Round lots held long um er o c s o se = Delta of call to be sold Note: When establishing a new position, one must first decide how many shares of the underlying stock he can buy before utilizing the formula; 1,000 shares would be a workable amount. 2. When adjusting between strikes by buying or selling stock: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:188 SCORE: 45.00 ================================================================================ 162 Part II: Call Option Strategies Number of round lots = Current delta x Number of short calls - Round lots held long to buy Note: If a negative number results, stock should be sold, not bought. These formulae can be verified by using the numbers from the examples above. For example, when the delta of the October 50 was .80 with the stock at 57, it was seen that buying 100 shares of stock would reestablish a neutral ratio. Number of round lots to buy= .80 x 5 3 = 4- 3 = 1 Also, if the position was to be rolled up to the October 60 (delta = .40), it was seen that 7.5 October 60's would theoretically be sold: Number of calls to sell = __l_ = 7.5 .40 There is a more general approach to this problem, one that can be applied to any strategy, no matter how complicated. It involves computing whether the position is net short or net long. The net position is reduced to an equivalent number of shares of common stock and is commonly called the "equivalent stock position" (ESP). Here is a simple formula for the equivalent stock position of any option position: ESP = Option quantity x Delta x Shares per option Example: Suppose that one is long 10 XYZ July 50 calls, which currently have a delta of .45. The option is an option on 100 shares of XYZ. Thus, the ESP can be computed: ESP = 10 x .45 x 100 = 450 shares This is merely saying that owning 10 of these options is equivalent to owning 450 shares of the underlying common stock, XYZ. The reader should already understand this, in that an option with a delta of .45 would appreciate by .45 points if the com­ mon stock moved up 1 dollar. Thus, 10 options would appreciate by 4.5 points, or $450. Obviously, 450 shares of common stock would also appreciate by $450 if they moved up by one point. Note that there are some options - those that result from a stock split- that are for more than 100 shares. The inclusion of the term "shares per option" in the for­ mula accounts for the fact that such options are equivalent to a different amount of stock than most options. The ESP of an entire option and stock position can be computed, even if sev­ eral different options are included in the position. The advantage of this simple cal- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:189 SCORE: 28.00 ================================================================================ Chapter 6: Ratio Call Writing 163 culation is that an entire, possibly complex option position can be reduced to one number. The ESP shows how the position will behave for short-term market move­ ments. Look again at the previous example of a ratio write. The position was long 300 shares and short 5 options with a current delta of .80 after the stock had risen to 57. The ESP of the 5 October 50's is short 400 shares (5 x .80 x 100 shares per option). The position is also long 300 shares of stock, so the total ESP of this ratio write is short 100 shares. This figure gives the strategist a measure of perspective on his position. He now knows that he has a position that is the equivalent of being short 100 shares of XYZ. Perhaps he is bearish on XYZ and therefore decides to do nothing. That would be fine; at least he knows that his position is short. Normally, however, the strategist would want to adjust his position. Again returning to the previous example, he has several choices in reducing the ESP back to neutral. An ESP of O is considered to be a perfectly neutral position. Obviously, one could buy 100 shares of XYZ to reduce the 100-share delta short. Or, given that the delta of the October 50 call is .80, he could buy in 1.25 of these short calls (obvi­ ously he could only buy l; fractional options cannot be purchased). Later chapters include more discussions and examples using the ESP. It is a vital concept that no strategist who is operating positions involving multiple options should be without. The only requirement for calculating it is to know the delta of the options in one's position. Those are easily obtainable from one's broker or from a number of computer services, software programs, or Web sites. For investors who do not have the funds or are not in a position to utilize such a ratio adjusting strategy, there is a less time-consuming method of taking defensive action in a ratio write. USING STOP ORDERS AS A DEFENSIVE STRATEGY A ratio writer can use buy or sell stops on his stock position in order to automatical­ ly and unemotionally adjust the ratio of his position. This type of defensive strategy is not an aggressive one and will provide some profits unless a whipsaw occurs in the underlying stock. As an example of how the use of stop orders can aid the ratio writer, let us again assume that the same basic position was established by buying XYZ at 49 and selling two October 50 calls at 6 points each. This produces a profit range of 37 to 63 at expi­ ration. If the stock begins to move up too far or to fall too far, the ratio writer can adjust the ratio of calls short to stock long automatically, through the use of stop orders on his stock. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:190 SCORE: 13.00 ================================================================================ 164 Part II: Call Option Strategies Example: An investor places a "good until canceled" stop order to buy 100 shares of XYZ at 57 at the same time that he establishes the original position. If XYZ should get to 57, the stop would be set off and he would then own 200 shares ofXYZ and be short 2 calls. That is, he would have a 200-share covered write of XYZ October 50 calls. To see how such an action affects his overall profit picture, note that his average stock cost is now 53; he paid 49 for the first 100 shares and paid 57 for the second 100 shares bought via the stop order. Since he sold the calls at 6 each, he essentially has a covered write in which he bought stock at 53 and sold calls for 6 points. This does not represent a lot of profit potential, but it will ensure some profit unless the stock falls back below the new break-even point. This new break-even point is 47 - the stock cost, 53, less the 6 points received for the call. He will realize the maximum profit potential from the covered write as long as the stock remains above 50 until expira­ tion. Since the stock is already at 57, the probabilities are relatively strong that it will remain above 50, and even stronger that it will remain above 47, until the expiration date. If the buy stop order was placed just above a technical resistance area, this prob­ ability is even better. Hence, the use of a buy stop order on the upside allows the ratio writer to auto­ matically convert the ratio write into a covered write if the stock moves up too far. Once the stop goes off, he has a position that will make some profit as long as the stock does not experience a fairly substantial price reversal. Downside protective action using a sell stop order works in a similar manner. Example: The investor placed a "good until canceled" sell stop for 100 shares of stock after establishing the original position. If this sell stop were placed at 41, for example, the position would become a naked call writer's position if the stock fell to 41. At that time, the 100 shares of stock that he owned would be sold, at an 8-point loss, but he would have the capability of making 12 points from the sale of his two calls as long as the stock remained below 50 until expiration. In fact, his break-even point after converting into the naked write would actually be 52 at expiration, since at that price, the calls could be bought back for 2 points each, or 8 points total prof­ it, to offset the 8-point loss on the stock. This action limits his profit potential, but will allow him to make some profit as long as the stock does not experience a strong price reversal and climb back above 52 by expiration. There are several advantages for inexperienced ratio writers to using this method of protection. First, the implementation of the protective strategies - buying an extra 100 shares of stock if the stock moves up, or selling out the 100 shares that are long if the stock moves down - is unemotional if the stop orders are placed at the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:192 SCORE: 19.00 ================================================================================ 166 Part II: Call Option Strategies option investment, the writer who operates in large size will experience less of a commission charge, percentagewise. That is, the writer who is buying 500 shares of stock and selling 10 calls to start with will be able to place his stop points far­ ther out than the writer who is buying 100 shares of stock and selling 2 calls. Technical analysis can be helpful in selecting the stop points as well. If there is resistance overhead, the buy stop should be placed above that resistance. Similarly, if there is support, the sell stop should be placed beneath the support point. Later, when straddles are discussed, it will be seen that this type of strategy can be operat­ ed at less of a net commission charge, since the purchase and sale of stock will not be involved. CLOSING OUT THE WRITE The methods of follow-up action discussed above deal ,vith the eventuality of pre­ venting losses. However, if all goes well, the ratio write will begin to accrue profits as the stock remains relatively close to the original striking price. To retain these paper profits that have accrued, it is necessary to move the protective action points closer together. Example: XYZ is at 51 after some time has passed, and the calls are at 3 points each. The writer would, at this time, have an unrealized profit of $800 - $200 from the stock purchase at 49, and $300 each on the two calls, which were originally sold at 6 points each. Recall that the maximum potential profit from the position, ifXYZ were exactly at 50 at expiration, is $1,300. The writer would like to adjust the protective points so that nearly all of the $800 paper profit might be retained while still allow­ ing for the profit to grow to the $1,300 maximum. At expiration, $800 profit would be realized ifXYZ were at 45 or at 55. This can be verified by referring again to Table 6-1 and Figure 6-1. The 45 to 55 range is now the area that the writer must be concerned with. The original profit range of 39 to 61 has become meaningless, since the position has performed well to this point in time. If the writer is using the rolling method of protection, he would roll forward to the next expiration series if the stock were to reach 45 or 55. If he is using the stop-out method of protection, he could either close the position at 45 or 55 or he could roll to the next expiration series and readjust his stop points. The neutral strategist using deltas would determine the number of calls to roll forward to by using the delta of the longer-term call. By moving the protective action points closer together, the ratio writer can then adjust his position while he still has a profit; he is attempting to "lock in" his profit. As even more time passes and expiration draws nearer, it may be possible to move ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:193 SCORE: 53.00 ================================================================================ Chapter 6: Ratio Call Writing 167 the protective points even closer together. Thus, as the position continues to improve over time, the writer should be constantly "telescoping" his action points and finally roll out to the next expiration series. This is generally the more prudent move, because the commissions to sell stock to close the position and then buy another stock to establish yet another position may prove to be prohibitive. In summary, then, as a ratio write nears expiration, the writer should be concerned with an ever-nar­ rowing range within which his profits can grow but outside of which his profits could dissipate if he does not take action. COMMENTS ON DELTA-NEUTRAL TRADING Since the concept of delta-neutral positions was introduced in this chapter, this is an appropriate time to discuss them in a general way. Essentially, a delta-neutral position is a hedged position in which at least two securities are used - two or more different options, or at least one option plus the underlying. The deltas of the two securities offset each other so that the position starts out with an "equivalent stock position" (ESP) of 0. Another term for ESP is "position delta." Thus, in theory, there is no price risk to begin with; the position is neutral with respect to price movement of the underlying. That definition lasts for about a nanosecond. As soon as time passes, or the stock moves, or implied volatility changes, the deltas change and therefore the position is no longer delta-neutral. Many people seem to have the feeling that a delta-neutral position is somehow one in which it is easy to make money without predicting the price direction of the underlying. That is not true. Delta-neutral trading is not "easy": Either (1) one assumes some price risk as soon as the stock begins to move, or (2) one keeps constantly adjusting his deltas to keep them neutral. Method 2 is not feasible for public traders because of commis­ sions. It is even difficult for market-makers, who pay no commissions. Most public practitioners of delta-neutral trading establish a neutral position, but then refrain from adjusting it too often. A common mistake that novice traders make with delta-neutral trading is to short options in a neutral manner, figuring that they have little exposure to price change because the position is delta-neutral. However, a sizeable move by the under­ lying (which often happens in a short period of time) ruins the neutrality of the posi­ tion and inevitably costs the trader a lot of money. A simple example: If one sells a naked straddle (i.e., he sells a naked put and a naked call with both having the same striking price) with the stock initially just below the strike price, that's a delta-ne~tral ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:194 SCORE: 56.00 ================================================================================ 168 Part II: Call Option Strategies position. However, the position has naked options on both sides, and therefore has tremendous liability. In practice, professionals watch more than just the delta; they also watch other measures of the risk of a position. Even then, price and volatility changes can cause problems. Advanced risk concepts are addressed more fully in the chapter on Advanced Concepts. SUMMARY Ratio writing is a viable, neutral strategy that can be employed with differing levels of sophistication. The initial ratio of short calls to long stock can be selected simplis­ tically by comparing one's opinion for the underlying stock with projected break-even points from the position. In a more sophisticated manner, the delta of the written calls can be used to determine the ratio. Since the strategy has potentially large losses either to the upside or the down­ side, follow-up action is mandatory. This action can be taken by simple methods such as rolling up or down in a constant ratio, or by placing stop orders on the underlying stock. A more sophisticated technique involves using the delta of the option to either adjust the stock position or roll to another call. By using the delta, a theoretically neu­ tral position can be maintained at all times. Ratio writing is a relatively sophisticated strategy that involves selling naked calls. It is therefore not suitable for all investors. Its attractiveness lies in the fact that vast quantities of time value premium are sold and the strategy is profitable for the most probable price outcomes of the underlying stock. It has a relatively large prob­ ability of making a limited profit, if the position can be held until expiration without frequent adjustment. AN INTRODUCTION TO CALL SPREAD STRATEGIES A spread is a transaction in which one simultaneously buys one option and sells another option, with different terms, on the same underlying security. In a call spread, the options are all calls. The basic idea behind spreading is that the strategist is using the sale of one call to reduce the risk of buying another call. The short call in a spread is considered covered, for margin purposes, only if the long call has an expi­ ration date equal to or longer than the short call. Before delving into the individual types of spreads, it may be beneficial to cover some general facts that pertain to most spread situations. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:195 SCORE: 46.00 ================================================================================ Chapter 6: Ratio Call Writing 169 All spreads fall into three broad categories: vertical, horizontal, or diagonal. A vertical spread is one in which the calls involved have the same expiration date but different striking prices. An example might be to buy the XYZ October 30 and sell the October 35 simultaneously. A horizontal spread is one in which the calls have the same striking price but different expiration dates. This is a horizontal spread: Sell the XYZ January 35 and buy the XYZ April 35. A diagonal spread is any combination of vertical and horizontal and may involve calls that have different expiration dates as well as different striking prices. These three names that classify the spreads can be related to the way option prices are listed in any newspaper summary of closing option prices. A vertical spread involves two options from the same column in a news­ paper listing. Newspaper columns run vertically. A horizontal spread involves two calls whose prices are listed in the same row in a newspaper listing; rows are hori­ zontal. This relationship to the listing format in newspapers is not important, but it is an easy way to remember what vertical spreads and horizontal spreads are. There are many types of vertical and horizontal spreads, and several of them are discussed in detail in later chapters. SPREAD ORDER The term "spread" designates not only a type of strategy, but a type of order as well. All spread transactions in which both sides of the spread are opening (initial) trans­ actions must be done in a margin account. This means that the customer must gen­ erally maintain a minimum equity in the account, normally $2,000. Some brokerage houses may also have a maintenance requirement, or "kicker." It is possible to transact a spread in a cash account, but one of the sides must be a closing transaction. In fact, many of the follow-up actions taken in the covered writ­ ing strategy are actually spread transactions. Suppose a covered writer is currently short one XYZ April call against 100 shares of the underlying stock. If he wants to roll forward to the July 35 call, he will be buying back the April 35 and selling the July 35 simultaneously. This is a spread transaction, technically, since one call is being bought and the other is being sold. However, in this transaction, the buy side is a closing transaction and the sell side is an opening transaction. This type of spread could be done in a cash account. Whenever a covered writer is rolling - up, down, or fmward he should place the order as a spread order to facilitate a better price execution. The spreads discussed in the following chapters are predominantly spread strategies, ones in which both sides of the spread are opening transactions. These are designed to have their own profit and risk potentials, and are not merely follow-up actions to some previously discussed strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:196 SCORE: 51.00 ================================================================================ 170 Part II: Call Option Strategies When a spread order is entered, the options being bought and sold must be specified. Two other items must be specified as well: the price at which the spread is to be executed, and whether that price is a credit or a debit. If the total price of the spread results in a cash inflow to the spread strategist, the spread is a credit spread. This merely means that the sell side of the spread brings in a higher price than is paid for the buy side of the spread. If the reverse is true - that is, there is a cash outflow from the spread transaction - the spread is said to be a debit spread. This means that the buy side of the spread costs more than is received from the sell side. It is also common to refer to the purchased side of the spread as the long side and to refer to the written side of the spread as the short side. The price at which a certain spread can be executed is generally not the differ­ ence between the last sale prices of the two options involved in the spread. Example: An investor wants to buy an XYZ October 30 and simultaneously sell an XYZ October 35 call. If the last sale price of the October 30 was 4 points and the last sale price of the October 35 was 2 points, it does not necessarily mean that the spread could be done for a 2-point debit (the difference in the last sale prices). In fact, the only way to detennine the market price for a spread transaction is to know what the bid and asked prices of the options involved are. Suppose the following quotes are available on these two calls: October 30 call October 35 call Bid 37/s F/s Asked 41/s 2 Lost Sole 4 2 Since the spread in question involves buying the October 30 call and selling the October 35, the spreader will, at market, have to pay 41/s for the October 30 ( the asked or offering quote) and will receive only F/s (the bid quote) for the October 35. This results in a debit of 2¼ points, significantly more than the 2-point difference in the last sale prices. Of course, one is free to specify any price he wants for any type of transaction. One might enter this spread order at a 21/s-point debit and could have a reasonable chance of having the order filled if the floor broker can do better than the bid side on the October 35 or better than the offering side on the October 30. The point to be learned here is that one cannot assume that last sale prices are indicative of the price at which a spread transaction can be executed. This makes computer analysis of spread transactions via closing price data somewhat difficult. Some computer data services offer (generally at a higher cost) closing bid and asked prices as well as closing sale prices. If a strategist is forced to operate with closing ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:197 SCORE: 15.00 ================================================================================ O,apter 6: Ratio Call Writing 171 prices only, however, he should attempt to build some screens into his output to allow for the fact that last sale prices might not be indicative of the price at which the spread can be executed. One simple method for screening is to look only at relative­ ly liquid options - that is, those that have traded a substantial number of contracts during the previous trading day. If an option is experiencing a great deal of trading activity, there is a much better chance that the current quote is "tight," meaning that the bid and offering prices are quite close to the last sale price. In the early days of listed options, it was somewhat common practice to "leg" into a spread. That is, the strategist would place separate buy and sell orders for the two transactions comprising his spread. As the listed markets have developed, adding depth and liquidity, it is generally a poor idea to leg into a spread. If the floor broker handling the transaction knows the entire transaction, he has a much better chance of "splitting a quote," buying on the bid, or selling on the offering. Splitting a quote merely means executing at a price that is between the current bid and asked prices. For example, if the bid is 37/s and the offering is 41/s, a transaction at a price of 4 would be "splitting the quote." The public customer must be aware that spread transactions may involve sub­ stantially higher commission costs, because there are twice as many calls involved in any one transaction. Some brokers offer slightly lower rates for spread transactions, but these are not nearly as low as spreads in commodity trading, for example. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:198 SCORE: 44.00 ================================================================================ CHAPTER 7 Bull Spreads The bull spread is one of the most popular forms of spreading. In this type of spread, one buys a call at a certain striking price and sells a call at a higher striking price. Generally, both options have the same expiration date. This is a vertical spread. A bull spread tends to be profitable if the underlying stock rrwves up in price; hence, it is a bullish position. The spread has both limited profit potential and limited risk. Although both can be substantial percentagewise, the risk can never exceed the net investment. In fact, a bull spread requires a smaller dollar investment and therefore has a smaller maximum dollar loss potential than does an outright call purchase of a similar call. Example: The following prices exist: XYZ common, 32; XYZ October 30 call, 3; and XYZ October 35 call, 1. A bull spread would be established by buying the October 30 call and simultaneous­ ly selling the October 35 call. Assume that this could be done at the indicated 2-point debit. A call bull spread is always a debit transaction, since the call with the lower striking price must always trade for more than a call with a higher price, if both have the same expiration date. Table 7-1 and Figure 7-1 depict the results of this transac­ tion at expiration. The indicated call profits or losses would be realized if the calls were liquidated at parity at expiration. Note that the spread has a maximum profit and this profit is realized if the stock is anywhere above the higher striking price at expiration. The maxipmm loss is realized if the stock is anywhere below the lower strike at expiration, and is equal to the net investment, 2 points in this example. 172 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:199 SCORE: 17.00 ================================================================================ Chapter 7: Bull Spreads 173 Moreover, there is a break-even point that always lies between the two striking prices at expiration. In this example, the break-even point is 32. All bull spreads have prof­ it graphs with the same shape as the one shown in Figure 7-1 when the expiration dates are the same for both calls. The investor who establishes this position is bullish on the underlying stock, but is generally looking for a way to hedge himself. If he were rampantly bullish, he TABLE 7-1. Results at expiration of bull spread. XYZ Price of Expiration 25 30 32 35 40 45 FIGURE 7-1. Bull spread. c: +$300 .Q ~ -~ w October 30 Profit -$ 300 - 300 100 + 200 + 700 + 1,200 October 35 Profit +$100 + 100 + 100 + 100 - 400 - 900 ,, ,,,' ;ff ,,,' ,,' iii ~ ,,,,' $01---------'----J...__.... _ ___. _____ _ 30 3:?,,' 35 0 ::: -$200 e 0..-$300 , , ..------,,,,,' Call Purchase •-----------,' Stock Price at Expiration Total Profit -$200 - 200 0 + 300 + 300 + 300 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:200 SCORE: 39.00 ================================================================================ 174 Part II: Call Option Strategies would merely buy the October 30 call outright. However, the sale of the October 35 call against the purchase of the October 30 allows him to take a position that will out­ perform the outright purchase of the October 30, dollarwise, as long as the stock does not rise above 36 by expiration. This fact is demonstrated by the dashed line in Figure 7-1. Therefore, the strategist establishing the bull spread is bullish, but not overly so. To verify that this comparison is correct, note that if one bought the October 30 call outright for 3 points, he would have a 3-point profit at expiration if XYZ were at 36. Both strategies have a 3-point profit at 36 at expiration. Below 36, the bull spread does better because the sale of the October 35 call brings in the extra point of pre­ mium. Above 36 at expiration, the outright purchase outperforms the bull spread, because there is no limit on the profits that can occur in an outright purchase situa­ tion. The net investment required for a bull spread is the net debit plus commissions. Since. the spread must be transacted in a margin account, there will generally be a minimum equity requirement imposed by the brokerage firm. In addition, there may be a maintenance requirement by some brokers. Suppose that one was establishing 10 spreads at the prices given in the example above. His investment, before com­ missions, would be $2,000 ($200 per spread), plus commissions. It is a simple matter to compute the break-even point and the maximum profit potential of a call bull spread: Break-even point= Lower striking price+ Net debit of spread Maximum profit _ Higher striking _ Lower striking _ Net debit potential - price price of spread In the example above, the net debit was 2 points. Therefore, the break-even point would be 30 + 2, or 32. The maximum profit potential would be 35 - 30 - 2, or 3 points. These figures agree with Table 7-1 and Figure 7-1. Commissions may rep­ resent a significant percentage of the profit and net investment, and should therefore be calculated before establishing the position. If these commissions are included in the net debit to establish the spread, they conveniently fit into the preceding formu­ lae. Commission charges can be reduced percentagewise by spreading a larger quan­ tity of calls. For this reason, it is generally advisable to spread at least 5 options at a time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:201 SCORE: 57.00 ================================================================================ Chapter 7: Bull Spreads 175 DEGREES OF AGGRESSIVENESS AGGRESSIVE BULL SPREAD Depending on how the bull spread is constructed, it may be an extremely aggressive or more conservative position. The most commonly used bull spread is of the aggres­ sive type; the stock is generally well below the higher striking price when the spread is established. This aggressive bull spread generally has the ability to generate sub­ stantial percentage returns if the underlying stock should rise in price far enough by expiration. Aggressive bull spreads are most attractive when the underlying common stock is relatively close to the lower striking price at the time the spread is established. A bull spread established under these conditions will generally be a low-cost spread with substantial profit potential, even after commissions are included. EXTREMELY AGGRESSIVE BULL SPREAD An extremely aggressive type of bull spread is the "out-of-the-money" spread. In such a spread, both calls are out-of-the-money when the spread is established. These spreads are extremely inexpensive to establish and have large potential profits if the stock should climb to the higher striking price by expiration. However, they are usu­ ally quite deceptive in nature. The underlying stock has only a relatively remote chance of advancing such a great deal by expiration, and the spreader could realize a 100% loss of his investment even if the underlying stock advances moderately, since both calls are out-of-the-money. This spread is akin to buying a deeply out-of-the­ money call as an outright speculation. It is not recommended that such a strategy be pursued with more than a very small percentage of one's speculative funds. LEAST AGGRESSIVE BULL SPREAD Another type of bull spread can be found occasionally - the "in-the-money" spread. In this situation, both calls are in-the-money. This is a much less aggressive position, since it offers a large probability of realizing the maximum profit potential, although that profit potential will be substantially smaller than the profit potentials offered by the more aggressive bull spreads. Example: XYZ is at 37 some time before expiration, and the October 30 call is at 7 while the October 35 call is at 4. Both calls are in-the-money and the spread would cost 3 points (debit) to establish. The maximum profit potential is 2 points, but it would be realized as long as XYZ were above 35 at expiration. That is, XYZ could fall by 2 points and the spreader would still make his maximum profit. This is certainly a more conservative position than the aggressive spread described above. The com- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:202 SCORE: 52.00 ================================================================================ 176 Part II: Call Option Strategies mission costs in this spread would be substantially larger than those in the spreads above, which involve less expensive options initially, and they should therefore be fig­ ured into one's profit calculations before entering into the spread transaction. Since this stock would have to decline 7 points to fall below 30 and cause a loss of the entire investment, it would have to be considered a rather low-probability event. This fact adds to the less aggressive nature of this type of spread. RANKING BULL SPREADS To accurately compare the risk and reward potentials of the many bull spreads that are available in a given day, one has to use a computer to perform the mass calcula­ tions. It is possible to use a strictly arithmetic method of ranking bull spreads, but such a list will not be as accurate as the correct method of analysis. In reality, it is necessary to incorporate the volatility of the underlying stock, and possibly the expected return from the spread as well, into one's calculations. The concept of expected return is described in detail in Chapter 28, where a bull spread is used as an example. The exact method for using volatility and predicting an option's price after an upward movement are presented later. Many data services offer such information. However, if the reader wants to attempt a simpler method of analysis, the following one may suffice. In any ranking of bull spreads, it is important not to rank the spreads by their maximum potential profits at expiration. Such a ranking will always give the most weight to deeply out-of-the-money spreads, which can rarely achieve their max­ imum profit potential. It would be better to screen out any spreads whose maximum profit prices are too far away from the current stock price. A simple method of allow­ ing for a stock's movement might be to assume that the stock could, at expiration, advance by an amount equal to twice the time value premium in an at-the-money call. Since more volatile stocks have options with greater time value premium, this is a simple attempt to incorporate volatility into the analysis. Also, since longer-term options have more time value premium than do short-term options, this will allow for larger movements during a longer time period. Percentage returns should include commission costs. This simple analysis is not completely correct, but it may prove useful to those traders looking for a simple arithmetic method of analysis that can be computed quickly. FURTHER CONSIDERATIONS The bull spreads described in previous examples utilize the same expiration date for both the short call and the long call. It is sometimes useful to buy a call with a longer ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:203 SCORE: 79.00 ================================================================================ Chapter 7: Bull Spreads 177 time to maturity than the short call has. Such a position is known as a diagonal bull spread and is discussed in a later chapter. Experienced traders often tum to bull spreads when options are expensive. The sale of the option at the higher strike partially mitigates the cost of buying an expen­ sive option at the lower strike. However, one should not always use the bull spread approach just because the options have a lot of time value premium, for he would be giving up a lot of upside profit potential in order to have a hedged position. With most types of spreads, it is necessary for some time to pass for the spread to become significantly profitable, even if the underlying stock moves in favor of the spreader. For this reason, bull spreads are not for traders unless the options involved are very short-term in nature. If a speculator is bullishly oriented for a short-term upward move in an underlying stock, it is generally better for him to buy a call out­ right than to establish a bull spread. Since the spread differential changes mainly as a function of time, small movements in price by the underlying stock will not cause much of a short-term change in the price of the spread. However, the bull spread has a distinct advantage over the purchase of a call if the underlying stock advances mod­ erately by expiration. In the previous example, a bull spread was established by buying the XYZ October 30 call for 3 points and simultaneously selling the October 35 call for 1 point. This spread can be compared to the outright purchase of the XYZ October 30 alone. There is a short-term advantage in using the outright purchase. Example: The underlying stock jumps from 32 to 35 in one day's time. The October 30 would be selling for approximately 5½ points if that happened, and the outright purchaser would be ahead by 2½ points, less one option commission. The long side of the bull spread would do as well, of course, since it utilizes the same option, but the short side, the October 35, would probably be selling for about 2½ points. Thus, the bull spread would be worth 3 points in total (5½ points on the long side, less 2½ points loss on the short side). This represents a 1-point profit to the spreader, less two option commissions, since the spread was initially established at a debit of 2 points. Clearly, then, for the shortest time period one day - the outright purchase outper­ forms the bull spread on a quick rise. For a slightly longer time period, such as 30 days, the outright purchase still has the advantage if the underlying stock moves up quickly. Even if the stock should advance above 35 in 30 days, the bull spread will still have time premium in it and thus will not yet have reached its maximum spread potential of 5 points. Recall that the maximum potential of a bull spread is always equal to the difference between the striking prices. Clearly, the outright purchaser will do very well if the underlying stock should advance that far in 30 days' time. When risk is considered, however, it ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:204 SCORE: 57.00 ================================================================================ 178 Part II: Call Option Strategies must be pointed out that the bull spread has fewer dollars at risk and, if the under­ lying stock should drop rather than rise, the bull spread will often have a smaller loss than the outright call purchase would. The longer it takes for the underlying stock to advance, the more the advantage swings to the spread. Suppose XYZ does not get to 35 until expiration. In this case, the October 30 call would be worth 5 points and the October 35 call would be worth­ less. The outright purchase of the October 30 call would make a 2-point profit less one commission, but the spread would now have a 3-point profit, less two commis­ sions. Even with the increased commissions, the spreader will make more of a prof­ it, both dollarwise and percentagewise. Many traders are disappointed with the low profits available from a bull spread when the stock rises almost immediately after the position is established. One way to partially off set the problem with the spread not widening out right away is to use a greater distance between the two strikes. When the distance is great, the spread has room to widen out, even though it won't reach its maximum profit potential right away. Still, since the strikes are "far apart," there is more room for the spread to widen even if the underlying stock rises immediately. The conclusion that can be drawn from these examples is that, in general, the outright purchase is a better strategy if one is looking for a quick rise by the under­ lying stock. Overall, the bull spread is a less aggressive strategy than the outright pur­ chase of a call. The spread will not produce as much of a profit on a short-term move, or on a sustained, large upward move. It will, however, outperform the outright pur­ chase of a call if the stock advances slowly and moderately by expiration. Also, the spread always involves fewer actual dollars of risk, because it requires a smaller debit to establish initially. Table 7-2 summarizes which strategy has the upper hand for var­ ious stock movements over differing time periods. TABLE 7-2. Bull spread and outright purchase compared. If the underlying stock ... Remains Relatively Advonces Advances Declines Unchanged Moderately Substantially in ... 1 week Bull spread Bull spread Outright purchase Outright purchase 1 month Bull spread Bull spread Outright purchase Outright purchase At expiration Bull spread Bull spread Bull spread Outright purchase ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:205 SCORE: 79.00 ================================================================================ Chapter 7: Bull Spreads FOLLOW-UP ACTION 179 Since the strategy has both limited profit and limited risk, it is not mandatory for the spreader to take any follow-up action prior to expiration. If the underlying stock advances substantially, the spreader should watch the time value premium in the short call closely in order to close the spread if it appears that there is a possibility of assignment. This possibility would increase substantially if the time value premium disappeared from the short call. If the stock falls, the trader may want to close the spread in order to limit his losses even further. When the spread is closed, the order should also be entered as a spread trans­ action. If the underlying stock has moved up in price, the order to liquidate would be a credit spread involving two closing transactions. The maximum credit that can be recovered from a bull spread is an amount equal to the difference between the striking prices. In the previous example, if XYZ were above 35 at expiration, one might enter an order to liquidate the spread as follows: Buy the October 35 (it is common practice to specify the buy side of a spread first when placing an order); sell the October 30 at a 5-point credit. In reality, because of the difference between bids and offers, it is quite difficult to obtain the entire 5-point credit even if expira­ tion is quite near. Generally, one might ask for a 4¼ or 47/s credit. It is possible to close the spread via exercise, although this method is normally advisable only for traders who pay little or no commissions. If the short side of a spread is assigned, the spreader may satisfy the assignment notice by exercising the long side of his spread. There is no margin required to do so, but there are stock commissions involved. Since these stock commissions to a public customer would be substantial­ ly larger than the option commissions involved in closing the spread by liquidating the options, it is recommended that the public customer attempt to liquidate rather than exercise. A minor point should be made here. Since the amount of commissions paid to liquidate the spread would be larger if higher call prices are involved, the actual net maximum profit point for a bull spread is for the stock to be exactly at the higher striking price at expiration. If the stock exceeds the higher striking price by a great deal, the gross profit will be the same (it was demonstrated earlier that this gross profit is the same anywhere above the higher strike at expiration), but the net profit will be slightly smaller, since the investor will pay more in commissions to liquidate the spread. Some spreaders prefer to buy back the short call if the underlying stock drops in price, in order to lock in the profit on the short side. They will then hold the long call in hopes of a rise in price by the underlying stock, in order to make the long side of the spread profitable as well. This amounts to "legging" out of the spread, although ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:206 SCORE: 37.00 ================================================================================ 180 Part II: Call Option Strategies the overall increase in risk is small - the amount paid to repurchase the short call. If he attempts to "leg" out of the spread in such a manner, the spreader should not attempt to buy back the short call at too high a price. If it can be repurchased at 1/s or 1/16, the spreader will be giving away virtually nothing by buying back the short call. However, he should not be quick to repurchase it if it still has much more value than that, unless he is closing out the entire spread. At no time should one attempt to "leg" out after a stock price increase, taking the profit on the long side and hoping for a stock price decline to make the short side profitable as well. The risk is too great. Many traders find themselves in the somewhat perplexing situation of having seen the underlying make a large, quick move, only to find that their spread has not widened out much. They often try to figure out a way to perhaps lock in some gains in case the underlying subsequently drops in price, but they want to be able to wait around for the spread to widen out more toward its maximum profit potential. There really isn't any hedge that can accomplish all of these things. The only position that can lock in the profits in a call bull spread is to purchase the accompanying put bear spread. This strategy is discussed in Chapter 23, Spreads Combining Calls and Puts. OTHER USES OF BULL SPREADS Superficially, the bull spread is one of the simplest forms of spreading. However, it can be an extremely useful tool in a wide variety of situations. Two such situations were described in Chapter 3. If the outright purchaser of a call finds himself with an unrealized loss, he may be able to substantially improve his chances of getting out even by "rolling down" into a bull spread. If, however, he has an unrealized profit, he may be able to sell a call at the next higher strike, creating a bull spread, in an attempt to lock in some of his profit. In a somewhat similar manner, a common stockholder who is faced with an unrealized loss may be able to utilize a bull spread to lower the price at which he can break even. He may often have a significantly better chance of breaking even or making a profit by using options. The following example illustrates the stockholder's strategy. Example: An investor buys 100 shares of XYZ at 48, and later finds himself with an unrealized loss with the stock at 42. A 6-point rally in the stock would be necessary in order to break even. However, if XYZ has listed options trading, he may be able to significantly reduce his break-even price. The prices are: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:207 SCORE: 37.00 ================================================================================ Chapter 7: Bull Spreads XYZ common, 42; XYZ October 40, 4; and XYZ October 45, 2. 181 The stock owner could enhance his overall position by buying one October 40 call and selling two October 45 calls. Note that no extra money, except commissions, is required for this transaction, because the credit received from selling two October 45's is $400 and is equal to the cost of buying the October 40 call. However, mainte­ nance and equity requirements still apply, because a spread has been established. The resulting position does not have an uncovered, or naked, option in it. One of the October 45 calls that was sold is covered by the underlying stock itself. The other is part of a bull spread with the October 40 call. It is not particularly important that the resulting position is a combination of both a bull spread and a covered write. What is important is the profit characteristic of this new total position. If XYZ should continue to decline in price and be below 40 at October expira­ tion, all the calls will expire worthless, and the resulting loss to the stock owner will be the same (except for the option commissions spent) as if he had merely held onto his stock without having done any option trading. Since both a covered write and a bull spread are strategies with limited profit potential, this new position obviously must have a limited profit. If XYZ is anywhere above 45 at October expiration, the maximum profit will be realized. To determine the size of the maximum profit, assume that XYZ is at exactly 45 at expiration. In that case, the two short October 45's would expire worthless and the long October 40 call would be worth 5 points. The option trades would have resulted in a $400 profit on the short side ($200 from each October 45 call) plus a $100 profit on the long side, for a total profit of $500 from the option trades. Since the stock was originally bought at 48 in this example, the stock portion of the position is a $300 loss with XYZ at 45 at expiration. The overall profit of the position is thus $500 less $300, or $200. For stock prices between 40 and 45 at expiration, the results are shown in Table 7-3 and Figure 7-2. Figure 7-2 depicts the two columns from the table labeled "Profit on Stock" and "Total Profit," so that one can visualize how the new total posi­ tion compares with the original stockholder's profit. Several points should be noted from either the graph or the table. First, the break-even point is lowered from 48 to 44. The new total position breaks even at 44, so that only a 2-point rally by the stock by expiration is necessary in order to break even. The two strategies are equal at 50 at expiration. That is, the stock would have to rally more than 8 points, from 42 to 50, by expiration for the original stockholder's position to outperform the new posi- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:208 SCORE: 21.00 ================================================================================ 182 Part II: Call Option Strategies TABLE 7-3. Lowering the break-even price on common stock. XYZ Price at Profit on Profit on Short Profit on long Total Expiration Stock October 45's October 40 Profit 35 -$1,300 +$400 -$400 -$1,300 38 - 1,000 + 400 - 400 - 1,000 40 800 + 400 - 400 800 42 600 + 400 - 200 400 43 500 + 400 - 100 200 44 400 + 400 0 0 45 300 + 400 + 100 + 200 48 0 - 200 + 400 + 200 50 + 200 - 600 + 600 + 200 tion. Below 40, the two strategies produce the same result. Finally, between 40 and 50, the new position outperforms the original stockholder's position. In summary, then, the stockholder stands to gain much and gives away very lit­ tle by adding the indicated options to his stock position. If the stock stabilizes at all - anywhere between 40 and 50 in the example above - the new position would be an improvement. Moreover, the investor can break even or make profits on a small rally. If the stock continues to drop heavily, nothing additional will be lost except for option commissions. Only if the stock rallies very sharply will the stock position outperform the total position. This strategy- combining a covered write and a bull spread - is sometimes used as an initial ( opening) trade as well. That is, an investor who is considering buying XYZ at 42 might decide to buy the October 40 and sell two October 45's (for even money) at the outset. The resulting position would not be inferior to the outright pur­ chase of XYZ stock, in terms of profit potential, unless XYZ rose above 46 by October expiration. Bull spreads may also be used as a "substitute" for covered writing. Recall from Chapter 2 that writing against warrants can be useful because of the smaller invest­ ment required, especially if the warrant was in-the-money and was not selling at much of a premium. The same thinking applies to call options. If there is an in-the­ money call with little or no time premium remaining in it, its purchase may be used as a substitute for buying the stock itself Of course, the call will expire, whereas the stock will not; but the profit potential of owning a deeply in-the-money call can be ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:209 SCORE: 12.00 ================================================================================ Chapter 7: Bull Spreads FIGURE 7-2. Lowering the break-even price on common stock. C: 0 I +$200 iii (/) $0 (/) .:l 0 i5 e Q. -$800 40 Profit with Options , ,,,' , , ,,,' 50 Stock Price at Expiration 183 ;f ,, very similar to owning the stock. Since such a call costs less to purchase than the stock itself would, the buyer is getting essentially the same profit or loss potential with a smaller investment. It is natural, then, to think that one might write another call - one closer to the money- against the deeply in-the-money purchased call. This posi­ tion would have profit characteristics much like a covered write, since the long call "simulates" the purchase of stock This position really is, of course, a bull spread, in which the purchased call is well in-the-money and the written call is closer to the money. Clearly, one would not want to put all of his money into such a strategy and forsake covered writing, since, with bull spreads, he could be entirely wiped out in a moderate market decline. In a covered writing strategy, one still owns the stocks even after a severe market decline. However, one may achieve something of a compromise by investing a much smaller amount of money in bull spreads than he might have invested in covered writes. He can still retain the same profit potential. The balance of the investor's funds could then be placed in interest-bearing securities. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:210 SCORE: 34.00 ================================================================================ 184 Example: The following prices exist: XYZ common, 49; XYZ April 50 call, 3; and XYZ April 35 call, 14. Part II: Call Option Strategies Since the deeply in-the-money call has no time premium, its purchase will perform much like the purchase of the stock until April expiration. Table 7-4 summarizes the profit potential from the covered write or the bull spread. The profit potentials are the same from a cash covered write or the bull spread. Both would yield a $400 prof­ it before commissions if XYZ were above 50 at April expiration. However, since the bull spread requires a much smaller investment, the spreader could put $3,500 into interest-bearing securities. This interest could be considered the equivalent of receiving the dividends on the stock. In any case, the spreader can lose only $1,100, even if the stock declines substantially. The covered writer could have a larger unre­ alized loss than that if XYZ were below 35 at expiration. Also, in the bull spread sit­ uation, the writer can "roll down" the April 50 call if the stock declines in price, just as he might do in a covered writing situation. TABLE 7-4. Results for covered write and bull spread compared. Maximum profit potential (stock over 50 in April) Break-even point Investment Covered Write: Buy XYZ and Sell April 50 Coll $ 400 46 $4,600 Bull Spread: Buy XYZ April 35 Call and Sell April 50 Coll $ 400 46 $1,100 Thus, the bull spread offers the same dollar rewards, the same break-even point, smaller commission costs, less potential risk, and interest income from the fixed-income portion of the investment. While it is not always possible to find a deeply in-the-money call to use as a "substitute" for buying the stock, when one does exist, the strategist should consider using the bull spread instead of the covered write. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:211 SCORE: 10.00 ================================================================================ Chapter 7: Bull Spreads SUMMARY 185 The bull spread is one of the simplest and most popular forms of spreading. It will generally perform best in a moderately bullish environment. A bull spread will not widen out to its maximum profit potential right away, though; so for short-term trades, the outright purchase of a call is a better choice. The bull spread can also be applied for more sophisticated purposes in a far wider range of situations than mere­ ly wanting to attempt to capitalize on a moderate advance by the underlying stock. Both call buyers and stock buyers may be able to use bull spreads to "roll down" and produce lower break-even points for their positions. The covered writer may also be able to use bull spreads as a substitute for covered writes in certain situations in which a deeply in-the-money call exists. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:212 SCORE: 55.00 ================================================================================ Bear Spreads Using Call Options Options are versatile investment vehicles. For every type of bullish position that can be established, there is normally a corresponding bearish type of strategy. For every neutral strategy, there is an aggressive strategy for the investor with an opposite opin­ ion. One such case has already been explored in some detail; the straddle buy or reverse hedge strategy is the opposite side of the spectrum. For many of the strate­ gies to be described from this point on, there is a corresponding strategy designed for the strategist with the opposite point of view. In this vein, a bear spread is the oppo­ site of a bull spread. THE BEAR SPREAD In a call bear spread, one buys a call at a certain striking price and sells a call at a lower striking price. This is a vertical spread, as was the bull spread. The bear spread tends to be profitable if the underlying stock declines in price. Llke the bull spread, it has limited profit and loss potential. However, unlike the bull spread, the bear spread is a credit spread when the spread is set up with call options. Since one is sell­ ing the call with the lower strike, and a call at a lower strike always trades at a high­ er price than a call at a higher strike with the same expiration, the bear spread must be a credit position. It should be pointed out that most bearish strategies that can be established with call options may be more advantageously constructed using put options. Many of these same strategies are therefore discussed again in Part III. 186 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:213 SCORE: 43.00 ================================================================================ Chapter 8: Bear Spreads Using Call Options 187 Example: An investor is bearish on XYZ. Using the same prices that were used for the examples in Chapter 7, an example of a bear spread can be constructed for: XYZ common, 32; XYZ October 30 call, 3; and XYZ October 35 call, 1. A bear spread would be established by buying the October 35 call and selling the October 30 call. This would be done for a 2-point credit, before commissions. In a bear spread situation, the strategist is hoping that the stock will drop in price and that both options will expire worthless. If this happens, he will not have to pay anything to close his spread; he will profit by the entire amount of the original credit taken in. In this example, then, the maximum profit potential is 2 points, since that is the amount of the initial credit. This profit would be realized if XYZ were anywhere below 30 at expiration, because both options would expire worthless in that case. If the spread expands in price, rather than contracts, the bear spreader will be losing money. This expansion would occur in a rising market. The maximum amount that this spread could expand to is 5 points - the difference between the striking prices. Hence, the most that the bear spreader would have to pay to buy back this spread would be 5 points, resulting in a maximum potential loss of 3 points. This loss would be realized if XYZ were anywhere above 35 at October expiration. Table 8-1 and Figure 8-1 depict the actual profit and loss potential of this example at expiration (commissions are not included). The astute reader will note that the figures in the table are exactly the reverse of those shown for the bull spread example in Chapter 7. Also, the profit graph of the bear spread looks like a bull spread profit graph that has been turned upside down. All bear spreads have a profit graph with the same shape at expiration as the graph shown in Figure 8-1. TABLE 8-1. Bear spread. XYZ Price at October 30 October 35 Total Expiration Profit Profit Profit 25 +$300 -$100 +$200 30 + 300 - 100 + 200 32 + 100 - 100 0 35 - 200 - 100 - 300 40 - 700 + 400 - 300 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:214 SCORE: 23.00 ================================================================================ 188 FIGURE 8-1. Bear spread • . § +$200 "it! -~ w CJ) 30 ig ..J 0 :!: e a. -$300 Part II: Call Option Strategies Stock Price at Expiration The break-even point, maximum profit potential, and investment required are all quite simple computations for a bear spread. Maximum profit potential== Net credit received Break-even point== Lower striking price + Amount of credit Maximum Collateral investment = = risk required Difference in striking prices Credit + Commissions received In the example above, the net credit received from the sale of the October 30 call at 3 and the purchase of the October 35 call at 1 was two points. This is the max­ imum profit potential. The break-even point is then easily computed as the lower striking price, 30, plus the amount of the credit, 2, or 32. The risk is equal to the investment. It is the difference between the striking prices - 5 points - less the net credit received - 2 points - for a total investment of 3 points plus commissions. Since this spread involves a call that is not "covered" by a long call with a striking price equal to or lower than that of the short call, some brokerage firms may require a higher maintenance requirement per spread than would be required for a bull spread. Again, since a spread must be done in a margin account, most brokerage firms require that a minimum amount of equity be in the account as well. Since this is a credit spread, the investor does not really "spend" any dollars to establish the spread. The investment is really a reduction in the buying power of the customer's margin account, but it does not actually require dollars to be spent when the transaction is initiated. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:215 SCORE: 66.00 ================================================================================ Chapter 8: Bear Spreads Using Call Options SELECTING A BEAR SPREAD 189 Depending on where the underlying stock is trading with respect to the two striking prices, the bear spread may be very aggressive, with a high profit potential, or it may be less aggressive, with a low profit potential. If a large credit is initially taken in, there is obviously the potential for a good deal of profit. However, for the spread to take in a large credit, the underlying stock must be well above the lower striking price. This means that a relatively substantial downward move would be necessary in order for the maximum profit potential to be realized. Thus, a large credit bear spread is usually an aggressive position; the spreader needs a substantial move by the underlying stock in order to make his maximum profit. The probabilities of this occurring cannot be considered large. A less aggressive type of bear spread is one in which the underlying stock is actually below the lower striking price when the spread is established. The credit received from establishing a bear spread in such a situation would be small, but the spreader would realize his maximum profit even if the underlying stock remained unchanged or actually rose slightly in price by expiration. Example: XYZ is trading at a price of 25. The October 30 call might be sold for 1 ½ points and the October 35 call bought for½ point with the stock at 29. While the net credit, and hence the maximum profit potential, is a small dollar amount, 1 point, it will be realized even if XYZ rises slightly by expiration, as long as it does not rise above 30. It is not always clear which type of spread is better, the large credit bear spread or the small credit bear spread. One has a small probability of making a large profit and the other has a much larger probability of making a much smaller profit. In gen­ eral, bear spreads established when the underlying stock is closer to the lower strik­ ing price will be the best ones. To see this, note that if a bear spread is initiated when the stock is at the higher striking price, the spreader is selling a call that has mostly intrinsic value and little time value premium (since it is in-the-money), and is buying a call that is nearly all time value. This is just the opposite of what the option strate­ gist should be attempting to do. The basic philosophy of option strategy is to sell time value and buy intrinsic value. For this reason, the large credit bear spread is not an optimum strategy. It will be interesting to observe later that bear spreads with puts are more attractive when the underlying stock is at the higher striking price! A bear spread will not collapse right away, even if the underlying stock drops in price. This is somewhat similar to the effect that was observed with the call bull spreads in Chapter 7. They, too, do not accelerate to their maximum profit potential right away. Of course, as time winds down and expiration approaches, then the spread ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:216 SCORE: 69.00 ================================================================================ 190 Part II: Call Option Strategies will approach its maximum profit potential. This is important to understand because, if one is expecting a quick move down by the underlying stock, he might need to use a call bear spread in which the lower strike is actually somewhat deeply in-the­ money, while the upper strike is out-of-the-money. In this case, the in-the-money call will decline in value as the stock moves down, even if that downward move happens immediately. Meanwhile, the out-of-the-money long call protects against a disastrous upside breakout by the stock. This type of bear spread is really akin to selling a deep in-the-money call for its raw downside profit potential and buying an out-of-the­ money call merely as disaster insurance. FOLLOW-UP ACTION Follow-up strategies are not difficult, in general, for bear spreads. The major thing that the strategist must be aware of is impending assignment of the short call. If the short side of the spread is in-the-money and has no time premium remaining, the spread should be closed regardless of how much time remains until expiration. This disappearance of time value premium could be caused either by the stock being significantly above the striking price of the stock call, or by an impending dividend payment. In either case, the spread should be closed to avoid assignment and the resultant large commission costs on stock transactions. Note that the large credit bear spread (one established with the stock well above the lower striking price) is dangerous from the viewpoint of early assignment, since the time value premium in the call will be small to begin with. SUMMARY The call bear spread is a bearishly oriented strategy. Since the spread is a credit spread, requiring only a reduction in buying power but no actual layout of cash to establish, it is a moderately popular strategy. The bear spread using calls may not be the optimum type of bearish spread that is available; a bear spread using put options maybe. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:217 SCORE: 48.00 ================================================================================ Calendar Spreads A calendar spread, also frequently called a time spread, involves the sale of one option and the simultaneous purchase of a more distant option, both with the same striking price. In the broad definition, the calendar spread is a horizontal spread. The neutral philosophy for using calendar spreads is that time will erode the value of the near-term option at a faster rate than it will the far-term option. If this happens, the spread will widen and a profit may result at near-term expiration. With call options, one may construct a more aggressive, bullish calendar spread. Both types of spreads are discussed. Example: The following prices exist sometime in late January: XYZ:50 April 50 Call (3-month call) 5 July 50 Call (6-month call) 8 October 50 Call (9-month call) 10 If one sells the April 50 call and buys the July 50 at the same time, he will pay a debit of 3 points - the difference in the call prices plus commissions. That is, his invest­ ment is the net debit of the spread plus commissions. Furthermore, suppose that in 3 months, at April expiration, XYZ is unchanged at 50. Then the 3-month call should be worth 5 points, and the 6-month call should be worth 8 points, as they were pre­ viously, all other factors being equal. XYZ:50 April 50 Call (Expiring) 0 July 50 Call (3-month call) 5 October 50 Call (6-month call) 8 191 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:218 SCORE: 82.00 ================================================================================ 192 Part II: Call Option Strategies The spread between the April 50 and the July 50 has now widened to 5 points. Since the spread cost 3 points originally, this widening effect has produced a 2-point prof­ it. The spread could be closed at this time in order to realize the profit, or the spread­ er may decide to continue to hold the July 50 call that he is long. By continuing to hold the July 50 call, he is risking the profits that have accrued to date, but he could profit handsomely if the underlying stock rises in price over the next 3 months, before July expiration. It is not necessary for the underlying stock to be exactly at the striking price of the options at near-term expiration for a profit to result. In fact, some profit can be made in a range that extends both below and above the striking price. The risk in this type of position is that the stock will drop a great deal or rise a great deal, in which case the spread between the two options will shrink and the spreader will lose money. Since the spread between two calls at the same strike cannot shrink to less than zero, however, the risk is limited to the amount of the original debit spent to establish the spread, plus commissions. THE NEUTRAL CALENDAR SPREAD As mentioned earlier, the calendar spreader can either have a neutral outlook on the stock or he can construct the spread for an aggressively bullish outlook. The neutral outlook is described first. The calendar spread that is established when the underly­ ing stock is at or near the striking price of the options used is a neutral spread. The strategist is interested in selling time and not in predicting the direction of the under­ lying stock. If the stock is relatively unchanged when the near-term option expires, the neutral spread will make a profit. In a neutral spread, one should initially have the intent of closing the spread by the time the near-tenn option expires. Let us again tum to our example calendar spread described earlier in order to more accurately demonstrate the potential risks and rewards from that spread when the near-term, April, call expires. To do this, it is necessary to estimate the price of the July 50 call at that time. Notice that, with XYZ at 50 at expiration, the results agree with the less detailed example presented earlier. The graph shown in Figure 9-1 is the "total profit" from Table 9-1. The graph is a curved rather than straight line, since the July 50 call still has time premium. There is a slightly bullish bias to this graph: The profit range extends slightly farther above the striking price than it does below the striking price. This is due to the fact that the spread is a call spread. If puts had been used, the profit range would have a bearish bias. The total width of the profit range is a function of the volatility of the underlying stock, since that will determine the price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:219 SCORE: 19.00 ================================================================================ Chapter 9: Calendar Spreads FIGURE 9-1. Calendar spread at near-term expiration. C: i +$200 $ 1i:i ~ 0 ~ o. -$300 Stock Price at Expiration TABLE 9-1. Estimated profit or losses at April expiration. XYZ Stock April 50 April 50 July 50 Price Price Profit Price 40 0 +$500 1/2 45 0 + 500 21/2 48 0 + 500 4 50 0 + 500 5 52 2 + 300 6 55 5 0 8 60 10 - 500 l 01/2 193 July 50 Total Profit Profit -$750 -$250 - 550 - 50 - 400 + 100 - 300 + 200 - 200 + 100 0 0 + 250 - 250 of the remaining long call at expiration, as well as a function of the time remaining to near-term expiration. Table 9-1 and Figure 9-1 clearly depict several of the more significant aspects of the calendar spread. There is a range within which the spread is profitable at near­ term expiration. That range would appear to be about 46 to 55 in the example. Outside that range, losses can occur, but they are limited to the amount of the initial debit. Notice in the example that the stock would have to be well below 40 or well ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:220 SCORE: 74.00 ================================================================================ 194 Part II: Call Option Strategies above 60 for the maximum loss to occur. Even if the stock is at 40 or 60, there is some time premium left in the longer-term option, and the loss is not quite as large as the maximum possible loss of $300. This type of calendar spread has limited profits and relatively large commission costs. It is generally best to establish such a spread 8 to 12 weeks before the near­ term option expires. If this is done, one is capitalizing on the maximum rate of decay of the near-term option with respect to the longer-term option. That is, when a call has less than 8 weeks of life, the rate of decay of its time value premium increases substantially with respect to the longer-term options on the same stock. THE EFFECT OF VOLATILITY The implied volatility of the options (and hence the actual volatility of the underly­ ing stock) will have an effect on the calendar spread. As volatility increases, the spread widens; as volatility contracts, the spread shrinks. This is important to know. In effect, buying a calendar spread is an antivolatility strategy: One wants the under­ lying to remain somewhat unchanged. Sometimes, calendar spreads look especially attractive when the underlying stock is volatile. However, this can be misleading for two reasons. First of all, since the stock is volatile, there is a greater chance that it will move outside of the profit area. Second, if the stock does stabilize and trades in a range near the striking price, the spread will lose value because of the decrease in volatility. That loss may be greater than the gain from time decay! FOLLOW-UP ACTION Ideally, the spreader would like to have the stock be just below the striking price when the near-term call expires. If this happens, he can close the spread with only one commission cost, that of selling out the long call. If the calls are in-the-money at the expiration date, he will, of course, have to pay two commissions to close the spread. As with all spread positions, the order to close the spread should be placed as a single order. "Legging" out of a spread is highly risky and is not recommended. Prior to expiration, the spreader should close the spread if the near-term short call is trading at parity. He does this to avoid assignment. Being called out of spread position is devastating from the viewpoint of the stock commissions involved for the public customer. The near-term call would not normally be trading at parity until quite close to the last day of trading, unless the stock has undergone a substantial rise in price. In the case of an early downside breakout by the underlying stock, the spread­ er has several choices. He could immediately close the spread and take a small loss ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:221 SCORE: 61.00 ================================================================================ Chapter 9: Calendar Spreads 195 on the position. Another choice is to leave the spread alone until the near-term call expires and then to hope for a partial recovery from the stock in order to be able to recover some value from the long side of the spread. Such a holding action is often better than the immediate close-out, because the expense of buying back the short call can be quite large percentagewise. A riskier downside defensive action is to sell out the long call if the stock begins to break down heavily. In this way, the spreader recovers something from the long side of his spread immediately, and then looks for the stock to remain depressed so that the short side of the spread will expire worth­ less. This action requires that one have enough collateral available to margin the resulting naked call, often an amount substantially in excess of the original debit paid for the spread. Moreover, if the underlying stock should reverse direction and rally back to or above the striking price, the short side of the spread is naked and could produce substantial losses. The risk assumed by such a follow-up violates the initial neutral premise of the spread, and should therefore be avoided. Of these three types of downside defensive action, the easiest and rrwst conservative one is to do nothing at all, letting the short call expire worthless and then hoping for a recovery by the underlying stock. If this tack is taken, the risk remains fixed at the original debit paid for the spread, and occasionally a rally may produce large profits on the long call. Although this rally is a nonfrequent event, it generally costs the spreader very little to allow himself the opportunity to take advantage of such a rally if it should occur. In fact, the strategist can employ a slight modification of this sort of action, even if the spread is not at a large loss. If the underlying stock is moderately below the striking price at near-term expiration, the short option will expire worthless and the spreader will be left holding the long option. He could sell the long side immediate­ ly and perhaps take a small gain or loss. However, it is often a reasonable strategy to sell out a portion of the long side - recovering all or a substantial portion of the ini­ tial investment - and hold the remainder. If the stock rises, the remaining long posi­ tion may appreciate substantially. Although this sort of action deviates from the true nature of the time spread, it is not overly risky. An early breakout to the upside by the underlying stock is generally handled in much the same way as a downside breakout. Doing nothing is often the best course of action. If the underlying stock rallies shortly after the spread is established, the spread will shrink by a small amount, but not substantially, because both options will hold premium in a rally. If the spreader were to rush in to close the position, he would be paying commissions on two rather expensive options. He will usually do better to wait and give himself as much of a chance for a reversal as possible. In fact, even at near-term expiration, there will normally be some time premium left in the long option so that the maximum loss would not have to be realized. A highly risk­ oriented upside defensive action is to cover the short call on a technical breakout and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:222 SCORE: 48.00 ================================================================================ 196 Part II: Call Option Strategies continue to hold the long call. This can become disastrous if the breakout fails and the stock drops, possibly resulting in losses far in excess of the original debit. Therefore, this action cannot be considered anything but extremely aggressive and illogical for the neutral strategist. If a breakout does not occur, the spreader will normally be making unrealized profits as time passes. Should this be the case, he may want to set some mental stop­ out points for himself. For example, if the underlying stock is quite close to the strik­ ing price with only two weeks to go, there will be some more profit potential left in the spread, but the spreader should be ready to close the position quickly if the stock begins to get too far away from the striking price. In this manner, he can leave room for more profits to accrue, but he is also attempting to protect the profits that have already built up. This is somewhat similar to the action that the ratio writer takes when he narrows the range of his action points as more and more time passes. THE BULLISH CALENDAR SPREAD A less neutral and more bullish type of calendar spread is preferred by the more aggressive investor. In a bullish calendar spread, one sells the near-term call and buys a longer-term call, but he does this when the underlying stock is some distance below the striking price of the calls. This type of position has the attractive features of low dollar investment and large potential profits. Of course, there is risk involved as well. Example: One might set up a bullish calendar spread in the following manner: XYZ common, 45; sell the XYZ April 50 for l; and buy the XYZ July 50 for 1 ½. This investor ideally wants two things to happen. First, he would like the near­ term call to expire worthless. That is why the bullish calendar spread is established with out-of-the-money calls: to increase the chances of the short call expiring worth­ less. If this happens, the investor will then own the longer-term call at a net cost of his original debit. In this example, his original debit was only ½ of a point to create the spread. If the April 50 call expires worthless, the investor will own the July 50 call at a net cost of ½ point, plus commissions. The investor now needs a second criterion to be fulfilled: The stock must rise in price by the time the July 50 call expires. In this example, even if XYZ were to rally to only 52 between April and July, the July 50 call could be sold for at least 2 points. This represents a substantial percentage gain, because the cost of the call has been ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:223 SCORE: 31.00 ================================================================================ Chapter 9: Calendar Spreads 197 reduced to ¼ point. Thus, there is the potential for large profits in bullish calendar spreads if the underlying stock rallies above the striking price before the longer-term call expires, provided that the short-term call has already expired worthless. What chance does the investor have that both ideal conditions will occur? There is a reasonably good chance that the written call will expire worthless, since it is a short-term call and the stock is below the striking price to start with. If the stock falls, or even rises a little - up to, but not above, the striking price the first condition will have been met. It is the second condition, a rally above the striking price by the underlying stock before the longer-term expiration date, that normally presents the biggest problem. The chances of this happening are usually small, but the rewards can be large when it does happen. Thus, this strategy offers a small probability of making a large profit. In fact, one large profit can easily offset several losses, because the losses are small, dollarwise. Even if the stock remains depressed and the July 50 call in the example expires worthless, the loss is limited to the initial debit of¼ point. Of course, this loss represents 100% of the initial investment, so one cannot put all his money into bullish calendar spreads. This strategy is a reasonable way to speculate, provided that the spreader adheres to the following criteria when establishing the spread: 1. Select underlying stocks that are volatile enough to move above the striking price within the allotted time. Bullish calendar spreads may appear to be very "cheap" on nonvolatile stocks that are well below the striking price. But if a large stock move, say 20%, is required in only a few months, the spread is not worthwhile for a nonvolatile stock. 2. Do not use options more than one striking price above the current market. For example, if XYZ were 26, use the 30 strike, not the 35 strike, since the chances of a rally to 30 are many times greater than the chances of a rally to 35. 3. Do not invest a large percentage of available trading capital in bullish calendar spreads. Since these are such low-cost spreads, one should be able to follow this rule easily and still diversify into several positions. FOLLOW-UP ACTION If the underlying stock should rally before the near-term call expires, the bullish cal­ endar spreader must never consider "legging" out of the spread, or consider cover­ ing the short call at a loss and attempting to ride the long call. Either action could turn the initial small, limited loss into a disastrous loss. Since the strategy hinges on ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:224 SCORE: 59.00 ================================================================================ 198 Part II: Call Option Strategies the fact that all the losses will be small and the infrequent large profits will be able to overcome these small losses, one should do nothing to jeopardize the strategy and possibly generate a large loss. The only reasonable sort of follow-up action that the bullish calendar spreader can take in advance of expiration is to close the spread if the underlying stock has moved up in price and the spread has widened to become profitable. This might occur if the stock moves up to the striking price after some time has passed. In the example above, if XYZ moved up to 50 with a month or so of life left in the April 50 call, the call might be selling for I½ while the July 50 call might be selling for 3 points. Thus, the spread could be closed at I½ points, representing a I-point gain over the initial debit of 1/2 point. Two commissions would have to be paid to close the spread, of course, but there would still be a net profit in the spread. USING ALL THREE EXPIRATION SERIES In either the neutral calendar spread or the bullish calendar spread, the investor has three choices of which months to use. He could sell the nearest-term call and buy the intermediate-term call. This is usually the most common way to set up these spreads. However, there is no rule that prevents him from selling the intermediate-term and buying the longest-term, or possibly selling the near-term and buying the long-term. Any of these situations would still be calendar spreads. Some proponents of calendar spreads prefer initially to sell the near-term and buy the long-term call. Then, if the near-term call expires worthless, they have an opportunity to sell the intermediate-term call if they so desire. Example: An investor establishes a calendar spread by selling the April 50 call and buying the October 50 call. The April call would have less than 3 months remaining and the October call would be the long-term call. At April expiration, if XYZ is below 50, the April call will expire worthless. At that time, the July 50 call could be sold against the October 50 that is held long, thereby creating another calendar spread with no additional commission cost on the long side. The advantage of this type of strategy is that it is possible for the two sales (April 50 and July 50 in this example) to actually bring in more credits than were spent for the one purchase (October 50). Thus, the spreader might be able to create a position in which he has a guaranteed profit. That is, if the sum of his transactions is actually a credit, he cannot lose money in the spread (provided that he does not attempt to "leg" out of the spread). The disadvantage of using the long-term call in the calendar spread is that the initial debit is larger, and therefore more dollars are initially at risk. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:225 SCORE: 34.00 ================================================================================ Chapter 9: Calendar Spreads 199 If the underlying stock moves substantially up or down in the first 3 months, the spreader could realize a larger dollar loss with the October/ April spread because his loss will approach the initial debit. The remaining combination of the expiration series is to initially buy the longest-term call and sell the intermediate-term call against it. This combination will generally require the smallest initial debit, but there is not much profit potential in the spread until the intermediate-term expiration date draws near. Thus, there is a lot of time for the underlying stock to move some distance away from the initial strik­ ing price. For this reason, this is generally an inferior approach to calendar spread­ ing. SUMMARY Calendar spreading is a low-dollar-cost strategy that is a nonaggressive approach, pro­ vided that the spreader does not invest a large percentage of his trading capital in the strategy, and provided that he does not attempt to "leg" into or out of the spreads. The neutral calendar spread is one in which the strategist is mainly selling time; he is attempting to capitalize on the known fact that the near-term call will lose time pre­ mium more rapidly than will a longer-term call. A more aggressive approach is the bullish calendar spread, in which the speculator is essentially trying to reduce the net cost of a longer-term call by the amount of credits taken in from the sale of a nearer­ term call. This bullish strategy requires that the near-term call expire worthless and then that the underlying stock rise in price. In either strategy, the most common approach is to sell the nearest-term call and buy the intermediate-term call. However, it may sometimes prove advantageous to sell the near-term and buy the longest-term initially, with the intention of letting the near-term expire and then pos­ sibly writing against the longer-term call a second time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:226 SCORE: 57.00 ================================================================================ . CHAPTER 10 The Butterfly Spread The recipient of one of the more exotic names given to spread positions, the butter­ fly spread is a neutral position that is a combination of both a bull spread and a bear spread. This spread is for the neutral strategist, one who thinks the underlying stock will not experience much of a net rise or decline by expiration. It generally requires only a small investment and has limited risk. Although profits are limited as well, they are larger than the potential risk. For this reason, the butterfly spread is a viable strat­ egy. However, it is costly in terms of commissions. In this chapter, the strategy is explained using only calls. The strategy can also be implemented using a combination of puts and calls, or with puts only, as will be demonstrated later. There are three striking prices involved in a butterfiy spread. Using only calls, the butterfly spread consists of buying one call at the lowest striking price, selling two calls at the middle striking price, and buying one call at the highest striking price. The following example will demonstrate how the butterfly spread works. Example: A butterfly spread is established by buying a July 50 call for 12, selling 2 July 60 calls for 6 each, and buying a July 70 call for 3. The spread requires a rela­ tively low debit of $300 (Table 10-1), although there are four option commissions involved and these may represent a substantial percentage of the net investment. As usual, the maximum amount of profit is realized at the striking price of the written calls. With most types of spreads, this is a useful fact to remember, for it can aid in quick computation of the potential of the spread. In this example, if the stock were at the striking price of the written options at expiration (60), the two July 60's that are short would expire worthless for a $1,200 gain. The long July 70 call would expire worthless for a $300 loss, and the long July 50 call would be worth 10 points, for a $200 loss on that call. The sum of the gains and losses would thus be a $700 gain, less commissions. This is the maximum profit potential of the spread. 200 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:227 SCORE: 63.00 ================================================================================ Chapter 10: The Butterfly Spread TABLE 10-1. Butterfly spread example. Current prices: XYZ common: XYZ July 50 call: XYZ July 60 call: XYZ July 70 call: Butterfly spread: Buy 1 July 50 call Sell 2 July 60 calls Buy 1 July 70 call Net debit 60 12 6 3 $1 ,200 debit $1,200 credit $300 debit $300 (plus commissions) 201 The risk is limited in a butterfly spread, both to the upside and to the downside, and is equal to the amount of the net debit required to establish the spread. In the example above, the risk is limited to $300 plus commissions. Table 10-2 and Figure 10-1 depict the results of this butterfly spread at various prices at expiration. The profit graph resembles that of a ratio write, except that the loss is limited on both the upside and the downside. There is a profit range within which the butterfly spread makes money - 53 to 67 in the example, before commis­ sions are included. Outside this profit range, losses will occur at expiration, but these losses are limited to the amount of the original debit plus commissions. In accordance with more lenient margin requirements passed in 2000, the investment required for a butterfly spread is equal to the net debit expended, which is the risk in the spread. When the options expire in the same month and the strik­ ing prices are evenly spaced (the spacing is 10 points in this example), the following formulae can be used to quickly compute the important details of the butterfly spread: Net investment= Net debit of the spread Maximum profit = Distance between strikes - Net debit Downside break-even= Lowest strike+ Net debit Upside break-even= Highest strike - Net debit In the example, the distance between strikes is 10 points, the net debit is 3 points (before commissions), the lowest strike used is 50, and the highest strike is 70. These formulae would then yield the following results for this example spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:229 SCORE: 49.00 ================================================================================ Chapter 10: The Butterfly Spread 203 Note that all of these answers agree with the results that were previously obtained by analyzing the example spread in detail. In this example, the maximum profit potential is $700, the maximum risk is $300, and the investment required is also $300, commissions excluded. In percent­ age terms, this means that the butterfly spread has a loss limited to about 100% of capital invested and could make profits of nearly 133% in this case. These represent an attractive risk/reward relationship. This is, however, just an example, and two fac­ tors that exist in the actual marketplace may greatly affect these numbers. First, com­ missions are large; it is possible that eight commissions might have to be paid to establish and liquidate the spread. Second, depending on the level of premiums to be found in the market at any point in time, it may not be possible to establish a spread for a debit as low as 3 points when the strikes are 10 points apart. SELECTING THE SPREAD Ideally, one would want to establish a butterfly spread at as small of a debit as pos­ sible in order to limit his risk to a small amount, although that risk is still equal to 100% of the dollars invested in the spread. One would also like to have the stock be near the middle striking price to begin with, because he will then be in his maximum profit area if the stock remains relatively unchanged. Unfortunately, it is difficult to satisfy both conditions simultaneously. The smallest-debit butterfly spreads are those in which the stock is some dis­ tance away from the middle striking price. To see this, note that if the stock were well above the middle strike and all the options were at parity, the net debit would be zero. Although no one would attempt to establish a butterfly spread with parity options because of the risk of early assignment, it may be somewhat useful to try to obtain a small debit by taking an opinion on the underlying stock. For example, if the stock is close to the higher striking price, the debit would be small normally, but the investor would have to be somewhat bearish on the underlying stock in order to maximize his profit; that is, the stock would have to decline in price from the upper striking price to the middle striking price for the maximum profit to be realized. An analogous situation exists when the underlying stock is originally close to the lower striking price. The investor could establish the spread for a small debit in this case also, but he would now have to be somewhat bullish on the underlying stock in order to attempt to realize his maximum profit. Example: XYZ is at 70. One may be able to establish a low-debit butterfly spread with the 50's, 60's, and 70's if the following prices exist: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:230 SCORE: 53.00 ================================================================================ 204 XYZ common, 70; XYZ July 50, 20; XYZ July 60, 12; and XYZ July 70, 5. Part II: Call Option Strategies The butterfly spread would require a debit of only $100 plus commissions to estab­ lish, because the cost of the calls at the higher and lower strike is 25 points, and a 24- point credit would be obtained by selling two calls at the middle strike. This is indeed a low-cost butterfly spread, but the stock will have to move down in price for much of a profit to be realized. The maximum profit of $900 less commissions would be realized at 60 at expiration. The strategist would have to be bearish on XYZ to want to establish such a spread. Without the aid of an example, the reader should be able to determine that if XYZ were originally at 50, a low-cost butterfly spread could be established by buying the 50, selling two 60's, and buying a 70. In this case, however, the investor would have to be bullish on the stock, because he would want it to move up to 60 by expi­ ration in order for the maximum profit to be realized. In general, then, if the butterfly spread is to be established at an extremely low debit, the spreader will have to make a decision as to whether he wants to be bullish or bearish on the underlying stock. Many strategists prefer to remain as neutral as possible on the underlying stock at all times in any strategy. This philosophy would lead to slightly higher debits, such as the $300 debit in the example at the beginning of this chapter, but would theoretically have a better chance of making money because there would be a profit if the stock remained relatively unchanged, the most probable occurrence. In either philosophy, there are other considerations for the butterfly spread. The best butterfly spreads are generally found on the more expensive and/or more volatile stocks that have striking prices spaced 10 or 20 points apart. In these situa­ tions, the maximum profit is large enough to overcome the weight of the commission costs involved in the butterfly spread. When one establishes butterfly spreads on lower-priced stocks whose striking prices are only 5 points apart, he is normally put­ ting himself at a disadvantage unless the debit is extremely small. One exception to this rule is that attractive situations are often found on higher-priced stocks with striking prices 5 points apart (50, 55, and 60, for example). They do exist from time to time. In analyzing butterfly spreads, one commonly works with closing prices. It was mentioned earlier that using closing prices for analysis can prove somewhat mislead­ ing, since the actual execution will have to be done at bid and asked prices, and these ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:231 SCORE: 48.00 ================================================================================ Chapter 10: The Butterfly Spread 205 may differ somewhat from closing prices. Normally, this difference is small, but since there are three different calls involved in a butterfly spread, the difference could be substantial. Therefore, it is usually necessary to check the appropriate bid and asked price for each call before entering the spread, in order to be able to place a reason­ able debit on the order. As with other types of spreads, the butterfly spread order can be placed as one order. Before moving on to discuss follow-up action, it may be worthwhile to describe a tactic for stocks with 5 points between striking prices. For example, the butterfly spreader might work with strikes of 45, 50, and 60. If he sets up the usual type of but­ terfly spread, he would end up with a position that has too much risk near 60 and very little or none at all near 45. If this is what he wants, fine; but if he wants to remain neutral, the standard type of butterfly spread will have to be modified slightly. Example: The following prices exist: XYZ common, 50; July 45 call, 7; July 50 call, 5; and July 60 call, 2. The normal type of butterfly spread- buying one 45, selling two 50's, and buying one 60 - can actually be done for a credit of 1 point. However, the profitability is no longer symmetric about the middle striking price. In this example, the investor can­ not lose to the downside because, even if the stock collapses and all the calls expire worthless, he will still make his I-point credit. However, to the upside, there is risk: If XYZ is anywhere above 60 at expiration, the risk is 4 points. This is no longer a neu­ tral position. The fact that the lower strike is only 5 points from the middle strike while the higher strike is 10 points away has made this a somewhat bearish position. If the spreader wants to be neutral and still use these striking prices, he will have to put on two bull spreads and only one bear spread. That is, he should: Buy 2 July 45's: Sell 3 July 50's: Buy 1 July 60: $1,400 debit $1,500 credit $200 debit This position now has a net debit of $100 but has a better balance of risk at either end. If XYZ drops and is below 45 at expiration, the spreader will lose his $100 ini­ tial debit. But now, if XYZ is at or above 60 at expiration, he will lose $100 in that range also. Thus, by establishing two bull spreads with a 5-point difference between ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:232 SCORE: 65.00 ================================================================================ 206 Part II: Call Option Strategies strikes versus one bear spread with a IO-point difference between strikes, the risk has been balanced at both ends. When one uses strike prices that are not evenly spaced apart, his margin requirement increases substantially. In such a case, one has to mar­ gin the individual component spreads separately. Therefore, in this example, he would have to pay for the two bull spreads ( $200 each, for a total of $400) and then margin the additional call bear spread ($700: the $1,000 difference in the strikes, less the $300 credit taken in for that portion of the spread). Hence, in this example, the margin requirement would be $1,100, even though the risk is only $100. Technically, of that $1,100 requirement, the spread trader pays out only $100 in cash (the actual debit of the spread), and the rest of the requirement can be satisfied with excess equity in his account. The same analysis obviously applies whenever 5-point striking price intervals exist. There are numerous combinations that could be worked out for lower-priced stocks by merely skipping over a striking price ( using the 25's, 30's, and 40's, for exam­ ple). Although there are not normally many stocks trading over $100 per share, the same analysis is applicable using 130's, 140's, and 160's, for example. FOLLOW-UP ACTION Since the butterfly spread has limited risk by its construction, there is usually little that the spreader has to do in the way of follow-up action other than avoiding early exercise or possibly dosing out the position early to take profits or limit losses even further. The only part of the spread that is subject to assignment is the call at the mid­ dle strike. If this call trades at or near parity, in-the-money, the spread should be closed. This may happen before expiration if the underlying stock is about to go ex­ dividend. It should be noted that accepting assignment will not increase the risk of the spread (because any short calls assigned would still be protected by the remain­ ing long calls). However, the margin requirement would change substantially, since one would now have a synthetic put (long calls, short stock) in place. Plus, there may be more onerous commissions for trading stock. Therefore, it is usually wise to avoid assignment in a butterfly spread, or in any spread, for that matter. If the stock is near the middle strike after a reasonable amount of time has passed, an unrealized profit will begin to accrue to the spreader. If one feels that the underlying stock is about to move away from the middle striking price and thereby jeopardize these profits, it may be advantageous to close the spread to take the avail­ able profit. Be certain to include commission costs when determining if an unreal­ ized profit exists. As a general rule of thumb, if one is doing 10 spreads at a time, he ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:233 SCORE: 75.00 ================================================================================ Chapter 10: Tire Butterfly Spread 207 can estimate that the commission cost for each option is about 1/s point. That is, if one has 10 butterfly spreads and the spread is currently at 6 points, he could figure that he would net about 5½ points after commissions to close the spread. This 1/s estimate is only valid if the spreader has at least 10 options at each strike involved in a spread. Normally, one would not close the spread early to limit losses, since these loss­ es are limited to the original net debit in any case. However, if the original debit was large and the stock is beginning to break out above the higher strike or to break down below the lower strike, the spreader may want to close the spread to limit losses even further. It has been repeatedly stated that one should not attempt to ''leg" out of a spread because of the risk that is incurred if one is wrong. However, there is a method of legging out of a butterfly spread that is acceptable and may even be pru­ dent. Since the spread consists of both a bull spread and a bear spread, it may often be the case that the stock experiences a relatively substantial move in one direction or the other during the life of the butterfly spread, and that the bull spread portion or the bear spread portion could be closed out near their maximum profit potentials. If this situation arises, the spreader may want to take advantage of it in order to be able to profit more if the underlying stock reverses direction and comes back into the profit range. Exampk: This strategy can be explained by using the initial example from this chap­ ter and then assuming that the stock falls from 60 to 45. Recall that this spread was initially established with a 3-point debit and a maximum profit potential of 7 points. The profit range was 53 to 67 at July expiration. However, a rather unpleasant situa­ tion has occurred: The stock has fallen quickly and is below the profit range. If the spreader does nothing and keeps the spread on, he will lose 3 points at most if the stock remains below 50 until July expiration. However, by increasing his risk slightly, he may be able to improve his position. Notice in Table 10-3 that the bear spread por­ tion of the overall spread - short July 60, long July 70 - has very nearly reached its maximum potential. The bear spread could be bought back for ½ point total (pay 1 point to buy back the July 60 and receive½ point from selling out the July 70). Thus, the spreader could convert the butterfly spread to a bull spread by spending ½ point. What would such an action do to his overall position? First, his risk would be increased by the ½ point spent to close the bear spread. That is, if XYZ continues to remain below 50 until July expiration, he would now lose 3½ rather than 3 points, plus commissions in either case. He has, however, potentially helped his chances of realizing something close to the maximum profit available from the original butterfly spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:234 SCORE: 63.00 ================================================================================ 208 Part II: Call Option Strategies TABLE 10-3. Initial spread and current prices. Initial Spread Current Prices XYZ common: 60 XYZ common: 45 July 50 call: 12 July 50 call: 2 July 60 call: 6 July 60 call: 1 July 70 call: 3 July 70 call: 1/2 After buying back the bear spread, he is left with the following bull spread: Long July 50 call _ N t d b·t 3u, . t h l all e e 1 ,2 pom s S ort Ju y 60 c He has a bull spread at the total cost paid to date - 3½ points. From the earlier dis­ cussion of bull spreads, the reader should know that the break-even point for this position is 53½ at expiration, and it could make a 6½ point profit if XYZ is anywhere over 60 at July expiration. Hence, the break-even point for the position was raised from 53 to 53½ by the expense of the ½ point to buy back the bear spread. However, if the stock should rally back above 60, the strategist will be making a profit nearly equal to the original maximum profit that he was aiming for (7 points). Moreover, this profit is now available anywhere over 60, not just exactly at 60 as it was in the origi­ nal position. Although the chances of such a rally cannot be considered great, it does not cost the spreader much to restructure himself into a position with a much broad­ er maximum profit area. A similar situation is available if the underlying stock moves up in price. In that case, the bull spread may be able to be removed at nearly its maximum profit poten­ tial, thereby leaving a bear spread. Again, suppose that the same initial spread was established but that XYZ has risen to 75. When the underlying stock advances sub­ stantially, the bull spread portion of the butterfly spread may expand to near its max­ imum potential. Since the strikes are 10 points apart in this bull spread, the widest it can grow to is 10 points. At the prices shown in Table 10-4, the bull spread - long July 50 and short July 60 - has grown to 9½ points. Thus, the bull spread position could be removed within ½ point of its maximum profit potential and the original butterfly spread would become a bear spread. Note that the closing of the bull spread portion generates a 9½ point credit: The July 50 is sold at 25½ and the July 60 is bought back at 16. The original butterfly spread was established at a 3-point debit, so the net position is the remaining position: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:235 SCORE: 57.00 ================================================================================ Chapter 10: The BatterRy Spread 209 Long July 70 call . Short July 60 call - Net credit 6½ points This bear spread has a maximum profit potential of 6½ points anywhere below 60 at July expiration. The maximum risk is 3½ points anywhere above 70 at expiration. Thus, the original butterfly spread was again converted into a position such that a stock price reversal to any price below 60 could produce something close to the max­ imum profit. Moreover, the risk was only increased by an additional ½ point. TABLE 10-4. Initial spread and new current prices. I nitiol Spread XYZ common: 60 XYZ July 50 call: 12 July 60 call: 6 July 70 call: 3 SUMMARY Current Prices XYZ common: July 50 call: July 60 call: July 70 call: 75 251/2 16 7 The butterfly spread is a viable, low-cost strategy with both limited profit potential and limited risk. It is actually a combination of a bull spread and a bear spread, and involves using three striking prices. The risk is limited should the underlying stock fall below the lowest strike or rise above the highest strike. The maximum profit is obtained at the middle strike. One can keep his initial debits to a minimum by ini­ tially assuming a bullish or bearish posture on the underlying stock. If he would rather remain neutral, he will normally have to pay a slightly larger debit to establish the spread, but may have a better chance of making money. If the underlying stock experiences a large move in one direction or the other prior to expiration, the spread­ er may want to close the profitable side of his butterfly spread near its maximum profit potential in order to be able to capitalize on a stock price reversal, should one occur. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:236 SCORE: 46.00 ================================================================================ Ratio Call Spreads A ratio call spread is a neutral strategy in which one buys a number of calls at a lower strike and sells more calls at a higher strike. It is somewhat similar to a ratio write in concept, although the spread has less downside risk and normally requires a smaller investment than does a ratio write. The ratio spread and ratio write are similar in that both involve uncovered calls, and both have profit ranges within which a profit can be made at expiration. Other comparisons are demonstrated throughout the chapter. Example: The following prices exist: XYZ common, 44; XYZ April 40 call, 5; and XYZ April 45 call, 3. A 2:1 ratio call spread could be established by buying one April 40 call and simulta­ neously selling two April 45's. This spread would be done for a credit of 1 point - the sale of the two April 45's bringing in 6 points and the purchase of the April 40 cost­ ing 5 points. This spread can be entered as one spread order, specifying the net cred­ it or debit for the position. In this case, the spread would be entered at a net credit of 1 point. Ratio spreads, unlike ratio writes, have a relatively small, limited downside risk. In fact, if the spread is established at an initial credit, there is no downside risk at all. In a ratio spread, the profit or loss at expiration is constant below the lower striking price, because both options would be worthless in that area. In the example above, if XYZ is below 40 at April expiration, all the options would expire worthless and the spreader would have made a profit of his initial I-point credit, less commissions. This I-point gain would occur anywhere below 40 at expiration; it is a constant. 210 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:237 SCORE: 27.00 ================================================================================ Chapter 11: Ratio Call Spreads 211 The maximum profit at expiration for a ratio spread occurs if the stock is exact­ ly at the striking price of the written options. This is true for nearly all types of strate­ gies involving written options. In the example, if XYZ were at 45 at April expiration, the April 45 calls would expire worthless for a gain of $600 on the two of them, and the April 40 call would be worth 5 points, resulting in no gain or loss on that call. Thus, the total profit would be $600 less commissions. The greatest risk in a ratio call spread lies to the upside, where the loss may the­ oretically be unlimited. The upside break-even point in this example is 51, as shown in Table 11-1. The table and Figure 11-1 illustrate the statements made in the pre­ ceding paragraphs. In a 2:1 ratio spread, two calls are sold for each one purchased. The maximum profit amount and the upside break-even point can easily be computed by using the following formulae: Points of maximum profit = Initial credit + Difference between strikes or = Difference between strikes - Initial debit Upside break-even point= Higher strike price+ Points of maximum profit In the preceding example, the initial credit was 1 point, so the points of maxi­ mum profit = 1 + 5 = 6, or $600. The upside break-even point is then 45 + 6, or 51. This agrees with the results determined earlier. Note that if the spread is established at a debit rather than a credit, the debit is subtracted from the striking price differ­ ential to determine the points of maximum profit. Many neutral investors prefer ratio spreads over ratio writes for two reasons: TABLE 11-1. Ratio call spread. XYZ Price of April 40 Coll April 45 Coll Total Expiration Profits Profits Profits 35 -$ 500 +$ 600 +$100 40 - 500 + 600 + 100 42 - 300 + 600 + 300 45 0 + 600 + 600 48 + 300 0 + 300 51 + 600 - 600 0 55 +1,000 -1,400 - 400 60 + 1,500 -2,400 - 900 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:238 SCORE: 57.00 ================================================================================ 212 Part II: Call Option Strategies FIGURE 11 • 1. Ratio call spread (2: 1 ). Stock Price at Expiration 1. The downside risk or gain is predetermined in the ratio spread at expiration, and therefore the position does not require much monitoring on the downside. 2. The margin investment required for a ratio spread is normally smaller than that required for a ratio write, since on the long side one is buying a call rather than buying the common stock itself. For margin purposes, a ratio spread is really the combination of a bull spread and a naked call write. There is no margin requirement for a bull spread other than the net debit to establish the bull spread. The net investment for the ratio spread is thus equal to the collateral required for the naked calls in the spread plus or minus the net debit or credit of the spread. In the example above, there is one naked call. The requirement for the naked call is 20% of the stock price plus the call premium, less the out-of-the-money amount. So the requirement in the example would be 20% of 44, or $880, plus the call premium of $300, less the one point that the stock is below the striking price - a $1,080 requirement for the naked call. Since the spread was established at a credit of one point, this credit can also be applied against the ini­ tial requirement, thereby reducing that requirement to $980. Since there is a naked call in this spread, there will be a mark to market if the stock moves up. Just as was recommended for the ratio write, it is recommended that the ratio spreader allow at least enough collateral to reach the upside break-even point. Since the upside break­ even point is 51 in this example, the spreader should allow 20% of 51, or $1,020, plus ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:239 SCORE: 64.00 ================================================================================ Chapter 11: Ratio Call Spreads 213 the 6 points that the call would be worth less the 1-point initial net credit - a total of $1,520 for this spread ($1,020 + $600 - $100). DIFFERING PHILOSOPHIES For many strategies, there is more than one philosophy of how to implement the strategy. Ratio spreads are no exception, with three philosophies being predominant. One philosophy holds that ratio spreading is quite similar to ratio writing - that one should be looking for opportunities to purchase an in-the-money call with little or no time premium in it so that the ratio spread simulates the profit opportunities from the ratio write as closely as possible with a smaller investment. The ratio spreads established under this philosophy may have rather large debits if the purchased call is substantially in-the-money. Another philosophy of ratio spreading is that spreads should be established for credits so that there is no chance of losing money on the downside. Both philosophies have merit and both are described. A third philosophy, called the "delta spread," is more concerned with neutrality, regardless of the initial debit or credit. It is also described. RATIO SPREAD AS RATIO WRITE There are several spread strategies similar to strategies that involve common stock. In this case, the ratio spread is similar to the ratio write. Whenever such a similarity exists, it may be possible for the strategist to buy an in-the-money call with little or no time premium as a substitute for buying the common stock. This was seen earlier in the covered call writing strategy, where it was shown that the purchase of in-the­ money calls or warrants might be a viable substitute for the purchase of stock. If one is able to buy an in-the-rrwney call as a substitute for the stock, he will not affect his profit potential substantially. When comparing a ratio spread to a ratio write, the max­ imum profit potential and the profit range are reduced by the time value premium paid for the long call. If this call is at parity (the time value premium is thus zero), the ratio spread and the ratio write have exactly the same profit potential. Moreover, the net investment is reduced and there is less downside risk should the stock fall in price below the striking price of the purchased call. The spread also involves smaller com­ mission costs than does the ratio write, which involves a stock purchase. The ratio writer does receive stock dividends, if any are paid, whereas the spreader does not. Example: XYZ is at 50, and an XYZ July 40 call is selling for 11 while an XYZ July 50 call is selling for 5. Table 11-2 compares the important points between the ratio write and the ratio spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:240 SCORE: 55.00 ================================================================================ 214 TABLE 11-2. Ratio write and ratio spread compared. Profit range Maximum profit Downside risk Upside risk Initial investment Ratio Write: Buy XYZ of 50 and Sell 2 July SO's at 5 40 to 60 10 points 40 points 40 points $3,000 Part II: Call Option Strategies Ratio Spread: Buy 1 July 40 of 11 and Sell 2 July SO's at 5 41 to 59 9 points 1 point Unlimited $1,600 In Chapter 6, it was pointed out that ratio writing was one of the better strate­ gies from a probability of profit viewpoint. That is, the profit potential conforms well to the expected movement of the underlying stock. The same statement holds true for ratio spreads as substitutes for ratio writes. In fact, the ratio spread may often be a better position than the ratio write itself, when the long call can be purchased with little or no time value premium in it. RATIO SPREAD FOR CREDITS The second philosophy of ratio spreads is to establish them only for credits. Strategists who follow this philosophy generally want a second criterion fulfilled also: that the underlying stock be below the striking price of the written calls when the spread is established. In fact, the farther the stock is below the strike, the more attractive the spread would be. This type of ratio spread has no downside risk because, even if the stock collapses, the spreader will still make a profit equal to the initial credit received. This application of the ratio spread strategy is actually a sub­ case of the application discussed above. That is, it may be possible both to buy a long call for little or no time premium, thereby simulating a ratio write, and also to be able to set up the position for a credit. Since the underlying stock is generally below the maximum profit point when one establishes a ratio spread for a credit, this is actually a mildly bullish position. The investor would want the stock to move up slightly in order for his maximum prof­ it potential to be realized. Of course, the position does have unlimited upside risk, so it is not an overly bullish strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:241 SCORE: 12.00 ================================================================================ Chapter 11: Ratio Call Spreads 215 These two philosophies are not mutually exclusive. The strategist who uses ratio spreads without regard for whether they are debit or credit spreads will generally have a broader array of spreads to choose from and will also be able to assume a more neutral posture on the stock. The spreader who insists on generating credits only will be forced to establish spreads on which his return will be slightly smaller if the under­ lying stock remains relatively unchanged. However, he will not have to worry about downside defensive action, since he has no risk to the downside. The third philoso­ phy, the "delta spread," is described after the next section, in which the uses of ratios other than 2: 1 are described. ALTERING THE RATIO Under either of the two philosophies discussed above, the strategist may find that a 3:1 ratio or a 3:2 ratio better suits his purposes than the 2:1 ratio. It is not common to write in a ratio of greater than 4: 1 because of the large increase in upside risk at such high ratios. The higher the ratio that is used, the higher will be the credits of the spread. This means that the profits to the downside will be greater if the stock collapses. The lower the ratio that is used, the higher the upside break-even point will be, thereby reducing upside risk. Example: If the same prices are used as in the initial example in this chapter, it will be possible to demonstrate these facts using three different ratios (Table 11-3): XYZ common, 44; XYZ April 40 call, 5; and XYZ April 45 call, 3. TABLE 11-3. Comparison of three ratios. Price of spread (downside risk) Upside break-even Downside break-even Maximum profit 3:2 Ratio: Buy 2 April 40's Sell 3 April 45's 1 debit 54 401/2 9 2:1 Ratio: 3:1 Ratio: By 1 April 40 Buy 1 April 40 Sell 2 April 45's Sell 3 April 45's 1 credit 4 credit 51 49½ None None 6 9 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:242 SCORE: 49.00 ================================================================================ 216 Part II: Call Option Strategies In Chapter 6 on ratio writing, it was seen that it was possible to alter the ratio to adjust the position to one's outlook for the underlying stock The altering of the ratio in a ratio spread accomplishes the same objective. In fact, as will be pointed out later in the chapter, the ratio may be adjusted continuously to achieve what is con­ sidered to be a "neutral spread." A similar tactic, using the option's delta, was described for ratio writes. The following formulae allow one to determine the maximum profit potential and upside break~even point for any ratio: Points of maximum = Net credit+ Number oflong calls x profit Difference in striking prices or = Number of long calls X Difference in striking prices - Net debit Upside break-even = Points of maximum profit ff h t "ki . point Number of naked calls + ig er s n ng pnce These formulae can easily be verified by checking the numbers in Table 11-3. THE "DELTA SPREAD" The third philosophy of ratio spreading is a more sophisticated approach that is often referred to as the delta spread, because the deltas of the options are used to estab­ lish and monitor the spread. Recall that the delta of a call option is the amount by which the option is expected to increase in price if the underlying stock should rise by one point. Delta spreads are neutral spreads in that one uses the deltas of the two calls to set up a position that is initially neutral. Example: The deltas of the two calls that appeared in the previous examples were .80 and .50 for the April 40 and April 45, respectively. If one were to buy 5 of the April 40's and simultaneously sell 8 of the April 45's, he would have a delta-neutral spread. That is, if XYZ moved up by one point, the 5 April 40 calls would appreciate by .80 point each, for a net gain of 4 points. Similarly, the 8 April 45 calls that he is short would each appreciate by .50 point for a net loss of 4 points on the short side. Thus, the spread is initially neutral - the long side and the short side will offset each other. The idea of setting up this type of neutral spread is to be able to capture the time value premium decay in the preponderance of short calls without subjecting the spread to an inordinate amount of market risk. The actual credit or debit of the spread is not a determining factor. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:243 SCORE: 52.00 ================================================================================ Chapter 11: Ratio Call Spreads 217 It is a fairly simple matter to determine the correct ratio to use in the delta spread: Merely divide the delta of the purchased call by the delta of the written call. In the example, this implies that the neutral ratio is .80 divided by .50, or 1.6:1. Obviously, one cannot sell 1.6 calls, so it is common practice to express that ratio as 16:10. Thus, the neutral spread would consist of buying 10 April 40's and selling 16 April 45's. This is the same as an 8:5 ratio. Notice that this calculation does not include anything about debits or credits involved in the spread. In this example, an 8:5 ratio would involve a small debit of one point (5 April 40's cost 25 points and 8 April 45's bring in 24 points). Generally, reasonably selected delta spreads involve small debits. Certain selection criteria can be offered to help the spreader eliminate some of the myriad possibilities of delta spreads on a day-to-day basis. First, one does not want the ratio of the spread to be too large. An absolute limit, such as 4:1, can be placed on all spread candidates. Also, if one eliminates any options selling for less than ½ point as candidates for the short side of the spread, the higher ratios will be eliminated. Second, one does not want the ratio to be too small. If the delta-neutral ratio is less than 1.2:1 (6:5), the spread should probably be rejected. Finally, if one is concerned with downside risk, he might want to limit the total debit outlay. This might be done with a simple parameter, such as not paying a debit of more than 1 point per long option. Thus, in a spread involving 10 long calls, the total debit must be 10 points or less. These screens are easily applied, especially with the aid of a com­ puter analysis. One merely uses the deltas to determine the neutral ratio. Then, if it is too small or too large, or if it requires the outlay of too large a debit, the spread is rejected from consideration. If not, it is a potential candidate for investment. FOLLOW-UP ACTION Depending on the initial credit or debit of the spread, it may not be necessary to take any downside defensive action at all. If the initial debit was large, the writer may roll down the written calls as in a ratio write. Example: An investor has established the ratio write by buying an XYZ July 40 call and selling two July 60 calls with the stock near 60. He might have done this because the July 40 was selling at parity. If the underlying stock declines, this spreader could roll down to the 50's and then to the 45's, in the same manner as he would with a ratio write. On the other hand, if the spread was initially set up with contiguous striking prices, the lower strike being just below the higher strike, no rolling-down action would be necessary. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:244 SCORE: 41.00 ================================================================================ 218 Part II: Call Option Strategies REDUCING THE RATIO Upside fallow-up action does not normally consist of rolling up as it does in a ratio write. Rather, one should usually buy some more long calls to reduce the ratio in the spread. Eventually, he would want to reduce the spread to 1:1, or a normal bull spread. An example may help to illustrate this concept. Example: In the initial example, one April 40 call was bought and two April 45's were sold, for a net credit of one point. Assume that the spreader is going to buy one more April 40 as a means of upside defensive action if he has to. When and if he buys this second long call, his total position will be a normal bull spread - long 2 April 40's and short 2 April 45's. The liquidating value of this bull spread would be 10 points if XYZ were above 45 at April expiration, since each of the two bull spreads would widen to its maximum potential (5 points) with the stock above 45 in April. The ratio spread­ er originally brought in a one-point credit for the 2:1 spread. If he were later to pay 11 points to buy the additional long April 40 call, his total outlay would have been 10 points. This would represent a break-even situation at April expiration if XYZ were above 45 at that time, since it was just shown that the spread could be liquidated for 10 points in that case. So the ratio spreader could wait to take defensive action until the April call was selling for 11 points. This is a dynamic type of follow-up action, one that is dependent on the options' price, not the stock price per se. This outlay of 11 points for the April 40 would leave a break-even situation as long as the stock did not reverse and fall in price below 45 after the call was bought. The spreader may decide that he would rather leave some room for upside profit rather than merely trying to break even if the stock rallies too far. He might thus decide to buy the additional long call at 9 or 10 points rather than waiting for it to get to 11. Of course, this might increase the chances of a whipsaw occurring, but it would leave some room for upside profits if the stock continues to rise. Where ratios other than 2:1 are involved initially, the same thinking can be applied. In fact, the purchase of the additional long calls might take place in a two­ step process. Example: If the spread was initially long 5 calls and short 10 calls, the spreader would not necessarily have to wait until the April 40's were selling at 11 and then buy all 5 needed to make the spread a normal bull spread. He might decide to buy 2 or 3 at a lower price, thereby reducing his ratio somewhat. Then, if the stock rallied even further, he could buy the needed long calls. By buying a few at a cheaper price, the spreader gives himself the leeway to wait considerably longer to the upside. In essence, all 5 additional long calls in this spread would have to be bought at an aver­ age price of 11 or lower in order for the spread to break even. However, if the first 2 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:245 SCORE: 47.00 ================================================================================ Chapter 11: Ratio Call Spreads 219 of them are bought for 8 points, the spreader would not have to buy the remaining 3 until they were selling around 13. Thus, he could wait longer to the upside before reducing the spread ratio to 1:1 (a bull spread). A formula can be applied to deter­ mine the price one would have to pay for the additional long calls, to convert the ratio spread into a bull spread. If the calls are bought, such a bull spread would break even with the stock above the higher striking price at expiration: Break-even cost of Number of short calls x Difference in strikes -Total debit to date long calls - Number of naked calls In the simple 2: 1 example, the number of short calls was 2, the difference in the strikes was 5, the total debit was minus one (-1) (since it was actually a 1.:.point cred­ it), and the number of naked calls is 1. Thus, the break-even cost of the additional long call is [2 x 5- (-1)(1)]/l = 11. As another verification of the formula, consider the 10:5 spread at the same prices. The initial credit of this spread would be 5 points, and the break-even cost of the five additional long calls is 11 points each. Assume that the spreader bought two additional April 40's for 8 points each (16 debit). This would make the total debit to date of the spread equal to 11 points, and reduce the number of naked calls to 3. The break-even cost of the remaining 3 long calls that would need to be purchased if the stock continued to rally would be (10 x 5 - 11)/3 = 13. This agrees with the observation made earlier. This formula can be used before actual fol­ low-up action is implemented. For example, in the 10:5 spread, if the April 40's were . selling for 8, the spreader might ask: "To what would I raise the purchase price of the remaining long calls if I buy 2 April 40's for 8 right now?" By using the formula, he could easily see that the answer would be 13. ADJUSTING WITH THE DELTA The theoretically-oriented spreader can use the delta-neutral ratio to monitor his spreads as well as to establish them. If the underlying stock moves up in price too far or down in price too far, the delta-neutral ratio of the spread will change. The spread­ er can then readjust his spread to a neutral status by buying some additional long calls on an upside movement by the stock, or by selling some additional short calls on a downward movement by the stock Either action will serve to make the spread delta­ neutral again. The public customer who is employing the delta-neutral adjustment method of follow-up action should be careful not to overadjust, because the com­ mission costs would become prohibitive. A more detailed description of the use of deltas as a means of follow-up action is contained in Chapter 28 on mathematical applications, under the heading "Facilitation or Institutional Block Positioning." The general concept, however, is the same as that shown earlier for ratio writing. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:246 SCORE: 49.00 ================================================================================ 220 Part II: Call Option Strategies Example: Early in this chapter, when selection criteria were described, a neutral ratio was determined to be 16:10, with XYZ at 44. Suppose, after establishing the spread, that the common rallied to 4 7. One could use the current deltas to adjust. This information is summarized in Table 11-4. The current neutral ratio is approxi­ mately 14:10. Thus, two of the short April 45's could be bought closing. In practice, one usually decreases his ratio by adding to the long side. Consequently, one would buy two April 40's, decreasing his overall ratio to 16:12, which is 1.33 and is close to the actual neutral ratio of 1.38. The position would therefore be delta-neutral once more. An alternative way of looking at this is to use the equivalent stock position (ESP), which, for any option, is the multiple of the quantity times the delta times the shares per option. The last three lines of Table 11-4 show the ESP for each call and for the position as a whole. Initially, the position has an ESP of 0, indicating that it is perfectly delta-neutral. In the current situation, however, the position is delta short 140 shares. Thus, one could adjust the position to be delta-neutral by buying 140 shares of XYZ. If he wanted to use the options rather than the stock, he could buy two April 45's, which would add a delta long of 130 ESP (2 x .65 x 100), leaving the position delta short 10 shares, which is very near neutral. As pointed out in the above paragraph, the spreader probably should buy the call with the most intrinsic value - the April 40. Each one of these has an ESP of 90 (1 x .9 x 100). Thus, if one were bought, the position would be delta short 50 shares; if two were bought, the total position would be delta long 40 shares. It would be a matter of individual preference whether the spreader wanted to be long or short the "odd lot" of 40 or 50 shares, respectively. TABLE 11-4. Original and current prices and deltas. XYZ common April 40 call April 45 call April 40 delta April 45 delta Neutral ratio April 40 ESP April 45 ESP Total ESP Original Situation 44 5 3 .80 .50 16:10 (.80/.50) 800 long (l Ox .8 x 100) 800 shrt ( 16 x .5 x l 00) 0 (neutral) Current Situation 47 8 5 .90 .65 14:10 (.90/.65 = 1.38) 900 long (10 x .9 x 100) l ,040 shrt ( 16 x .65 x l 00) 140 shrt ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:247 SCORE: 44.00 ================================================================================ Chapter 11: Ratio Call Spreads 221 The ESP method is merely a confirmation of the other method. Either one works well. The spreader should become familiar with the ESP method because, in a position with many different options, it reduces the exposure of the entire position to a single number. TAKING PROFITS In addition to defensive action, the spreader may find that he can close the spread early to take a profit or to limit losses. If enough time has passed and the underlying stock is close to the maximum profit point - the higher striking price - the spreader may want to consider closing the spread and taking his profit. Similarly, if the under­ lying stock is somewhere between the two strikes as expiration draws near, the writer will normally find himself with a profit as the long call retains some intrinsic value and the short calls are nearly worthless. If at this time one feels that there is little to gain (a price decline might wipe out the long call value), he should close the spread and take his profit. SUMMARY Ratio spreads can be an attractive strategy, similar in some ways to ratio writing. Both strategies offer a large probability of making a limited profit. The ratio spread has limited downside risk, or possibly no downside risk at all. In addition, if the long call(s) in the spread can be bought with little or no time value premium in them, the ratio spread becomes a superior strategy to the ratio write. One can adjust the ratio used to reflect his opinion of the underlying stock or to make a neutral profit range if desired. The ratio adjustment can be accomplished by using the deltas of the options. In a broad sense, this is one of the more attractive forms of spreading, since the strategist is buying mostly intrinsic value and is selling a relatively large amount of time value. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:248 SCORE: 50.00 ================================================================================ Cotnbining Calendar and Ratio Spreads The previous chapters on spreading introduced the basic types of spreads. The sim­ plest forms of bull spreads, bear spreads, or calendar spreads can often be combined to produce a position with a more attractive potential. The butterfly spread, which is a combination of a bull spread and a bear spread, is an example of such a combina­ tion. The next three chapters are devoted to describing other combinations of spreads, wherein the strategist not only mixes basic strategies ..:... bull, bear, and calen­ dar - but uses varying expiration dates as well. Although they may seem overly com­ plicated at first glance, these combinations are often employed by professionals in the field. RATIO CALENDAR SPREAD The ratio cdendar spread is a combination of the techniques used in the calendar and ratio spreads. Recall that one philosophy of the calendar spread strategy was to sell the near-term call and buy a longer-term call, with both being out-of-the-money. This is a bullish calendar spread. If the underlying stock never advances, the spread­ er loses the entire amount of the relatively small debit that he paid for the spread. However, if the stock advances after the near-term call expires worthless, large prof­ its are possible. It was stated that this bullish calendar spread philosophy had a small probability of attaining large profits, and that the few profits could easily exceed the preponderance of small losses. The ratio calendar spread is an attempt to raise the probabilities while allowing for large potential profits. In the ratio calendar spread, one sells a number of near- 222 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:249 SCORE: 63.00 ================================================================================ Chapter 12: Combining Calendar and Ratio Spreads 223 term calls while buyingfewer of the intermediate-term or long-term calls. Since more calls are being sold than are being bought, naked options are involved. It is often pos­ sible to set up a ratio calendar spread for a credit, meaning that if the underlying stock never rallies above the strike, the strategist will still make money. However, since naked calls are involved, the collateral requirements for participating in this strategy may be large. Example: As in the bullish calendar spreads described in Chapter 9, the prices are: XYZ common, 45; XYZ April 50 call, l; and XYZ July 50 call, l½. In the bullish calendar spread strategy, one July 50 is bought for each April 50 sold. This means that the spread is established for a debit of½ point and that the invest­ ment is $50 per spread, plus commissions. The strategist using the ratio calendar / spread has essentially the same philosophy as the bullish calendar spreader: The stock will remain below 50 until April expiration and may then rally. The ratio calen­ dar spread might be set up as follows: Buy 1 XYZ July 50 call at l½ Sell 2 XYZ April 50 calls at 1 each Net l½ debit 2 credit ½ credit Although there is no cash involved in setting up the ratio spread since it is done for a credit, there is a collateral requirement for the naked April 50 call. If the stock remains below 50 until April expiration, the long call - the July 50 - will be owned free. After that, no matter what happens to the underlying stock, the spread cannot lose money. In fact, if the underlying stock advances dramatically after near-term expiration, large profits will accrue as the July 50 call increases in value. Of course, this is entirely dependent on the near-term call expiring worthless. If the underlying stock should rally above 50 before the April calls expire, the ratio calen­ dar spread is in danger of losing a large amount of money because of the naked calls, and defensive action must be taken. Follow-up actions are described later. The collateral required for the ratio calendar spread is equal to the amount of collateral required for the naked calls less the credit taken in for the spread. Since naked calls will be marked to market as the stock moves up, it is always best to allow enough collateral to get to a defensive action point. In the example above, suppose that one felt he would definitely be taking defensive action if the stock rallied to 53 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:250 SCORE: 35.00 ================================================================================ 224 Part II: Call Option Strategies before April expiration. He should then figure his collateral requirement as if the stock were at 53, regardless of what the collateral requirement is at the current time. This is a prudent tactic whenever naked options are involved, since the strategist will never be forced into an unwanted close-out before his defensive action point is reached. The collateral required for this example would then be as follows, assuming the call is trading at 3½: 20% of 53 Call premium Less initial credit Total collateral to set aside $1,060 + 350 -___fill $1,360 The strategist is not really "investing" anything in this strategy, because his require­ ment is in the form of collateral, not cash. That is, his current portfolio assets need not be disturbed to set up this spread, although losses would, of course, create deb­ its in the account. Many naked option strategies are similar in this respect, and the strategist may earn additional money from the collateral value of his portfolio with­ out disturbing the portfolio itself. However, he should take care to operate such strategies in a conservative manner, since any income earned is "free," but losses may force him to disturb his portfolio. In light of this fact, it is always difficult to compute returns on investment in a strategy that requires only collateral to operate. One can, of course, compute the return on the maximum collateral required during the life of the position. The large investor participating in such a strategy should be satisfied with any sort of positive return. Returning to the example above, the strategist would make his $50 credit, less commissions, if the underlying stock remained below 50 until July expiration. It is not possible to determine the results to the upside so definitively. If the April 50 calls expire worthless and then the stock rallies, the potential profits are limited only by time. The case in which the stock rallies before April expiration is of the most con­ cern. If the stock rallies immediately, the spread will undoubtedly show a loss. If the stock rallies to 50 more slowly, but still before April expiration, it is possible that the spread will not have changed much. Using the same example, suppose that XYZ ral­ lies to 50 with only a few weeks of life remaining in the April 50 calls. Then the April 50 calls might be selling at l ½ while the July 50 call might be selling at 3. The ratio spread could be closed for even money at that point; the cost of buying back the 2 April 50's would equal the credit received from selling the one July 50. He would thus make½ point, less commissions, on the entire spread transaction. Finally, at the expi­ ration date of the April 50 calls, one can estimate where he would break even. Suppose one estimated that the July 50 call would be selling for 5½ points if XYZ were at 53 at April expiration. Since the April 50 calls would be selling for 3 at that ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:251 SCORE: 51.00 ================================================================================ Chapter 12: Combining Calendar and Ratio Spreads 225 time (they would be at parity), there would be a debit of½ point to close the ratio spread. The two April 50 calls would be bought for 6 points and the July 50 call sold for 5½ - a ½ debit. The entire spread transaction would thus have broken even, less commissions, at 53 at April expiration, since the spread was put on for a ½ credit and was taken off for a ½ debit. The risk to the upside depends clearly, then, on how quickly the stock rallies above 50 before April expiration. CHOOSING THE SPREAD Some of the same criteria used in setting up a bullish calendar spread apply here as well. Select a stock that is volatile enough to move above the striking price in the allotted time - after the near-term expires, but before the long call expires. Do not use calls that are so far out-of-the-money that it would be virtually impossible for the stock to reach the striking price. Always set up the spread for a credit, commissions included. This will assure that a profit will be made even if the stock goes nowhere. However, if the credit has to be generated by using an extremely large ratio - greater than 3 short calls to every long one - one should probably reject that choice, since the potential losses in an immediate rally would be large. The upside break-even point prior to April expiration should be determined using a pricing model. Such a model, or the output from one, can generally be obtained from a data service or from some brokerage firms. It is useful to the strate­ gist to know exactly how much room he has to the upside if the stock begins to rally. This will allow him to take defensive action in the form of closing out the spread before his break-even point is reached. Since a pricing model can estimate a call price for any length of time, the strategist can compute his break-even points at April expiration, 1 month before April expiration, 6 weeks before, and so on. When the long option in a spread expires at a different time from the short option, the break-even point is dynamic. That is, it changes with time. Table 12-1 shows how this information might be accumulated for the example spread used above. Since this example spread was established for a ½-point credit with the stock at 45, the break-even points would be at stock prices where the spread could be removed for a ½-point debit. Suppose the spread was initiated with 95 days remaining until April expiration. In each line of the table, the cost for buying 2 April 50's is ½ point more than the price of the July 50. That is, there would be a ½-point debit involved in closing the spread at those prices. Notice that the break-even price increases as time passes. Initially, the spread would show a loss if the stock moved up at all. This is to be expected, since an immediate move would not allow for any erosion in the time value premium of the near-term calls. As more and more time passes, time weighs ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:252 SCORE: 29.00 ================================================================================ 226 Part II: Call Option Strategies more heavily on the near-term April calls than on the longer-term July call. Once the strategist has this information, he might then look at a chart of the underlying stock. If there is resistance for XYZ below 53, his eventual break-even point at April expi­ ration, he could then feel more confident about this spread. FOLLOW-UP ACTION The main purpose of defensive action in this strategy is to limit losses if the stock should rally before April e:xJ)iration. The strategist should be quick to close out the spread before any serious losses accrue. The long call quite adequately compen­ sates for the losses on the short calls up to a certain point, a fact demonstrated in Table 12-1. However, the stock cannot be allowed to run. A rule of thumb that is often useful is to close the spread if the stock breaks out above technical resistance or if it breaks above the eventual break-even point at expiration. In the example above, the strategist would close the spread if, at any time, XYZ rose above 53 (before April expiration, of course). If a significant amount of time has passed, the strategist might act even more quickly in closing the spread. As was shown earlier, if the stock rallies to 50 with only a few weeks of time remaining, the spread may actually be at a slight profit at that time. It is often the best course of action to take the small profit, if the stock rises above the striking price. TABLE 12-1. Break-even points changing over time. Estimated Estimated Days Remaining until Break-Even Point April 50 July 50 April Expiration (Stock Price) Price Price 90 45 11/2 60 48 Jl/2 21/2 30 51 21/2 4 1/2 0 53 3 51/2 THE PROBABILITIES ARE GOOD This is a strategy with a rather large probability of profit, provided that the defensive action described above is adhered to. The spread will make money if the stock never rallies above the striking price, since the spread is established for a credit. This in ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:253 SCORE: 39.00 ================================================================================ Chapter 12: Combining Calendar and Ratio Spreads 227 itself is a rather high-probability event, because the stock is initially below the strik­ ing price. In addition, the spread can make large potential profits if the stock rallies after the near-term calls expire. Although this is a much less probable event, the prof­ its that can accrue add to the expected return of the spread. The only time the spread loses is when the stock rallies quickly, and the strategist should close out the spread in that case to limit losses. Although Table 12-2 is not mathematically definitive, it can be seen that this strategy has a positive expected return. Small profits occur more frequently than small losses do, and sometimes large profits can occur. These expected outcomes, when coupled with the fact that the strategist may utilize collateral such as stocks, bonds, or government securities to set up these spreads, demonstrate that this is a viable strategy for the advanced investor. TABLE 12-2. Profitability of ratio calendar spreading. Event Stock never rallies above strike Stock rallies above strike in a short time Stock rallies above strike after near-term call expires Outcome Small profit. Small loss if defensive action employed Large potential profit DELTA-NEUTRAL CALENDAR SPREADS Probability Large probability Small probability Small probability The preceding discussion dealt with a specific kind of ratio calendar spread, the out­ of-the-money call spread. A more accurate ratio can be constructed using the deltas of the calls involved, similar to the ratio spreads in Chapter 11. The spread can be created with either out-of-the-money calls or in-the-money calls. The former has naked calls, while the latter has extra long calls. Both types of ratio calendars are described. In either case, the number of calls to sell for each one purchased is determined by dividing the delta of the long call by the delta of the short call. This is the same for any ratio spread, not just calendars. Example: Suppose XYZ is trading at 45 and one is considering using the July 50 call and the April 50 call to establish a ratio calendar spread. This is the same situation ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:254 SCORE: 43.00 ================================================================================ 228 Part II: Call Option Strategies that was described earlier in this chapter. Furthermore, assume that the deltas of the calls in question are .25 for the July and .15 for the April. Given that information, one can compute the neutral ratio to be 1.667 to 1 (.25/.15). That is, one would sell 1.667 calls for each one he bought; restated, he would sell 5 for each 3 bought. This out-of-the-money neutral calendar is typical. One normally sells more calls than he buys to establish a neutral calendar when the calls are out-of-the-money. The ramifications of this strategy have already been described in this chapter. Follow-up strategy is slightly different, though, and is described later. THE IN-THE-MONEY CALENDAR SPREAD When the calls are in-the-money, the neutral spread has a distinctly different look. An example will help in describing the situation. Example: XYZ is trading at 49, and one wants to establish a neutral calendar spread using the July 45 and April 45 calls. The deltas of these in-the-money calls are .8 for the April and .7 for the July. Note that for in-the-rrwney calls, a shorter-term call has a higher delta than a longer-term call. The neutral ratio for this in-the-money spread would be .875 to 1 (.7/.8). This means that .875 calls would be sold for each one bought; restated, 7 calls would be sold and 8 bought. Thus, the spreader is buying more calls than he is selling when establishing an in-the-money neutral calendar. In some sense, one is establishing some "regular'' calendar spreads (seven of them, in this example) and simultaneous­ ly buying a few extra long calls to go along with them ( one extra long call, in this example). This type of position can be quite attractive. First of all, there is no risk to the upside as there is with the out-of-the-money calendar; the in-the-money calendar would make money, because there are extra long calls in the position. Thus, if there were to be a large gap to the upside in XYZ perhaps caused by a takeover attempt - the in-the-money calendar would make money. If, on the other hand, XYZ stays in the same area, then the regular calendar spread portion of the strategy will make money. Even though the extra call would probably lose some time value premium in that event, the other seven spreads would make a large enough profit to easily com­ pensate for the loss on the one long call. The least desirable result would be for XYZ to drop precipitously. However, in that case, the loss is limited to the amount of the initial debit of the spread. Even in the case of XYZ dropping, though, follow-up action can be taken. There are no naked calls to margin with this strategy, making it attractive to many smaller investors. In the above example, one would need to pay for the entire debit of the position, but there would be no further requirements. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:255 SCORE: 24.00 ================================================================================ Chapter 12: Combining Calendar and Ratio Spreads FOLLOW-UP ACTION 229 If one decides to preserve a neutral strategy with follow-up action in either type of ratio call calendar, he would merely need to look at the deltas of the calls and keep the ratio neutral. Doing so might mean that one would switch from one type of cal­ endar spread to the other, from the out-of-the-money with naked calls to the in-the­ money with extra long calls, or vice versa. For example, if XYZ started at 45, as in the first example, one would have sold more calls than he bought. If XYZ then rallied above 50, he would have to move his position into the in-the-money ratio and get long more calls than he is short. While such follow-up action is strategically correct maintaining the neutral ratio - it might not make sense practically, especially if the size of the original spread were small. If one had originally sold 5 and bought 3, he would be better to adhere to the follow-up strategy outlined earlier in this chapter. The spread is not large enough to dictate adjusting via the delta-neutral ratios. If, however, a large trader had originally sold 500 calls and bought 300, then he has enough profitability in the spread to make several adjustments along the way. In a similar manner, the spreader who had established a small in-the-money cal­ endar might decide not to bother rationing the spread if the stock dropped below the strike. He knows his risk is limited to his initial debit, and that would be small for a small spread. He might not want to introduce naked options into the position if XYZ declines. However, if the same spread were established by a large trader, it should be adjusted because of the greater tolerance of the spread to being adjusted, merely because of its size. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:256 SCORE: 52.00 ================================================================================ Reverse Spreads In general, when a strategy has the term "reverse" in its name, the strategy is the opposite of a more commonly used strategy. The reader should be familiar with this nomenclature from the earlier discussions comparing ratio writing (buying stock and selling calls) with reverse hedging (shorting stock and buying calls). If the reverse strategy is sufficiently well-known, it usually acquires a name of its own. For exam­ ple, the bear spread is really the reverse of the bull spread, but the bear spread is a popular enough strategy in its own right to have acquired a shorter, unique name. REVERSE CALENDAR SPREAD The reverse calendar spread is an infrequently used strategy, at least for public cus­ tomers trading stock or index options, because of the margin requirements. However, even then, it does have a place in the arsenal of the option strategist. Meanwhile, pro­ fessionals and futures option traders use the strategy with more frequency because the margin treatment is more favorable for them. As its name implies, the reverse calendar spread is a position that is just the opposite of a "normal" calendar spread. In the reverse calendar spread, one sells a long-term call option and simultaneously buys a shorter-term call option. The spread can be constructed with puts as well, as will be shown in a later chapter. Both calls have the same striking price. This strategy will make money if one of two things happens: Either (1) the stock price moves away from the striking price by a great deal, or (2) the inplied volatility of the options involved in the spread shrinks. For readers familiar with the "normal" calendar spread strategy, the first way to profit should be obvious, because a "normal" 230 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:257 SCORE: 74.00 ================================================================================ Chapter 13: Reverse Spreads 231 calendar spread makes the most money if the stock is right at the strike price at expi­ ration, and it loses money if the stock rises or falls too far. As with any spread involving options expiring in differing months, it is common practice to look at the profitability of the position at or before the near-term expira­ tion. An example will show how this strategy can profit. Example: Suppose the current month is April and that XYZ is trading at 80. Furthermore, suppose that XYZ's options are quite expensive, and one believes the underlying stock will be volatile. A reverse calendar spread would be a way to profit from these assumptions. The following prices exist: XYZ December 80 call: 12 XYZ July 80 call: 7 A reverse calendar spread is established by selling the December 80 call for 12 points, and buying the July 80 call for 7, a net credit of 5 points for the spread. If, later, XYZ falls dramatically, both call options will be nearly worthless and the spread could be bought back for a price well below 5. For example, if XYZ were to fall to 50 in a month or so, the July 80 call would be nearly worthless and the December 80 call could be bought back for about a point. Thus, the spread would have shrunk from its initial price of 5 to a price of about 1, a profit of 4 points. The other way to make money would be for implied volatility to decrease. Suppose implied volatility dropped after a month had passed. Then the spread might be worth something like 4 points - an unrealized profit of about 1 point, since it was sold for a price of 5 initially. The profit graph in Figure 13-1 shows the profitability of the reverse calendar. There are two lines on the graph, both of which depict the results at the expiration of the near-term option (the July 80 call in the above example). The lower line shows where profits and losses would occur if implied volatility remained unchanged. You can see that the position could profit if XYZ were to rise above 98 or fall below 70. In addition, the higher curve on the graph shows where profits would lie if implied volatility fell prior to expiration of the near-term options. In that case, additional prof­ its would accrue, as depicted on the graph. So there are two ways to make money with this strategy, and it is therefore best to establish it when implied volatility is high and the underlying has a tendency to be volatile. The problem with this spread, for stock and index option traders, is that the call that is sold is considered to be naked. This is preposterous, of course, since the short­ term call is a perfectly valid hedge until it expires. Yet the margin requirements remain onerous. When they were overhauled recently, this glaring inefficiency was ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:258 SCORE: 40.00 ================================================================================ 232 Part II: Call Option Strategies Figure 13-1 • Calendar spread sale at near-term expiration. $400 $300 Implied Volatility Lower $200 \ f/) $100 f/) 0 ~ $0 50 60 110 120 a. -$100 -$200 -$300 Implied Volatility -$400 Remains High -$500 Underlying Price allowed to stand because none of the member firms cared about changing it. Still, if one has excess collateral - perhaps from a large stock portfolio - and is interested in generating excess income in a hedged manner, then the strategy might be applicable for him as well. Futures option traders receive more favorable margin requirements, and it thus might be a more economical strategy for them. REVERSE RATIO SPREAD (BACKSPREAD) A more popular reverse strategy is the reverse ratio call spread, which is comrrwnly known as a backspread. In this type of spread, one would sell a call at one striking price and then would buy several calls at a higher striking price. This is exactly the opposite of the ratio spread described in Chapter 11. Some traders refer to any spread with unlimited profit potential on at least one side as a backspread. Thus, in most backspreading strategies, the spreader wants the stock to rrwve dramatically. He does not generally care whether it moves up or down. Recall that in the reverse hedge strategy (similar to a straddle buy) described in Chapter 4, the strategist had the potential for large profits if the stock moved either up or down by a great deal. In the backspread strategy discussed here, large potential profits exist if the stock moves up dramatically, but there is limited profit potential to the downside. Example: XYZ is selling for 43 and the July 40 call is at 4, with the July 45 call at l. A reverse ratio spread would be established as follows: · ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:259 SCORE: 49.00 ================================================================================ Chapter 13: Reverse Spreads Buy 2 July 45 calls at 1 each Sell 1 July 40 call at 4 Net 2 debit 4 credit 2 credit 233 These spreads are generally established for credits. In fact, if the spread cannot be initiated at a credit, it is usually not attractive. If the underlying stock drops in price and is below 40 at July expiration, all the calls will expire worthless and the strategist will make a profit equal to his initial credit. The maximum downside poten­ tial of the reverse ratio spread is equal to the initial credit received. On the other hand, if the stock rallies substantially, the potential upside profits are unlimited, since the spreader owns more calls than he is short. Simplistically, the investor is bullish and is buying out-of the-money calls but is simultaneously hedging himself by selling another call. He can profit if the stock rises in price, as he thought it would, but he also profits if the stock collapses and all the calls expire worthless. This strategy has limited risk. With most spreads, the maximum loss is attained at expiration at the striking price of the purchased call. This is a true statement for backspreads. Example: IfXYZ is at exactly 45 at July expiration, the July 45 calls will expire worth­ less for a loss of $200 and the July 40 call will have to be bought back for 5 points, a $100 loss on that call. The total loss would thus be $300, and this is the most that can be lost in this example. If the underlying stock should rally dramatically, this strategy has unlimited profit potential, since there are two long calls for each short one. In fact, one can always compute the upside break-even point at expiration. That break­ even point happens to be 48 in this example. At 48 at July expiration, each July 45 call would be worth 3 points, for a net gain of $400 on the two of them. The July 40 call would be worth 8 with the stock at 48 at expiration, representing a $400 loss on that call. Thus, the gain and the loss are offsetting and the spread breaks even, except for commissions, at 48 at expiration. If the stock is higher than 48 at July expiration, profits will result. Table 13-1 and Figure 13-2 depict the potential profits and losses from this example of a reverse ratio spread. Note that the profit graph is exactly like the prof­ it graph of a ratio spread that has been rotated around the stock price axis. Refer to Figure 11-1 for a graph of the ratio spread. There is actually a range outside of which profits can be made - below 42 or above 48 in this example. The maximum loss occurs at the striking price of the purchased calls, or 45, at expiration. There are no naked calls in this strategy, so the investment is relatively small. The strategy is actually a long call added to a bear spread. In this example, the bear ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:260 SCORE: 29.00 ================================================================================ 234 Part II: Call Option Strategies TABLE 13·1. Profits and losses for reverse ratio spread. XYZ Price at Profit on Profit on Total July Expiration 1 July 40 2 July 45's Profit 35 +$ 400 -$ 200 +$ 200 40 + 400 200 + 200 42 + 200 200 0 45 100 200 300 48 400 + 400 0 55 - 1,100 + 1,800 + 700 70 - 2,600 + 4,800 + 2,200 spread portion is long the July 45 and short the July 40. This requires a $500 collat­ eral requirement, because there are 5 points difference in the striking prices. The credit of $200 received for the entire spread can be applied against the initial requirement, so that the total requirement would be $300 plus commissions. There is no increase or decrease in this requirement, since there are no naked calls. Notice that the concept of a delta-neutral spread can be utilized in this strate­ gy, in much the same way that it was used for the ratio call spread. The number of calls to buy and sell can be computed mathematically by using the deltas of the options involved. Example: The neutral ratio is determined by dividing the delta of the July 45 into the delta of the July 40. Prices XYZ common: = 43 XYZ July 40 call: 4 XYZ July 45 call: Delta .80 .35 In this case, that would be a ratio of 2.29:1 (.80/.35). That is, if one sold 5 July 40's, he would buy 11 July 45's (or if he sold 10, he would then buy 23). By beginning with a neutral ratio, the spreader should be able to make money on a quick move by the stock in either direction. The neutral ratio can also help the spreader to avoid being too bearish or too bullish to begin with. For example, a spreader would not be bullish enough if he ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:261 SCORE: 22.00 ================================================================================ Chapter 13: Reverse Spreads FIGURE 13-2. Reverse ratio spread (backspread). C: ~ +$200 ;% :!:: e a. -$300 Stock Price at Expiration 235 merely used a 2:1 ratio for convenience, instead of using the 2.3:l ratio. If anything, one might normally establish the spread with an extra bullish emphasis, since the largest profits are to the upside. There is little reason for the spreader to have too lit­ tle bullishness in this strategy. Thus, if the deltas are correct, the neutral ratio can aid the spreader in the determination of a more accurate initial ratio. The strategist must be alert to the possibility of early exercise in this type of spread, since he has sold a call that is in-the-money. Aside from watching for this pos­ sibility, there is little in the way of defensive follow-up action that needs to be imple­ mented, since the risk is limited by the nature of the position. He might take profits by closing the spread if the stock rallies before expiration. This strategy presents a reasonable method of attempting to capitalize on a large stock movement with little tie-up of collateral. Generally, the strategist would seek out volatile stocks for implementation of this strategy, because he would want as much potential movement as possible by the time the calls expire. In Chapter 14, it will be shown that this strategy can become more attractive by buying calls with a longer maturity than the calls sold. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:262 SCORE: 44.00 ================================================================================ CH.APTER 14 Diagonalizing a Spread When one uses both different striking prices and different expiration dates in a spread, it is a diagonal spread. Generally, the long side of the spread would expire later than the short side of the spread. Note that this is within the definition of a spread for margin purposes: The long side must have a maturity equal to or longer than the maturity of the short side. With the exception of calendar spreads, all the previous chapters on spreads have described ones in which the expiration dates of the short call and the long call were the same. However, any of these spreads can be diag­ onalized; one can replace the long call in any spread with one expiring at a later date. In general, diagonalizing a spread in this manner makes it slightly rrwre bear­ ish at near-term expiration. This can be seen by observing what would happen if the stock fell or rose substantially. If the stock falls, the long side of the spread will retain some value because of its longer maturity. Thus, a diagonal spread will generally do better to the downside than will a regular spread. If the stock rises substantially, all calls will come to parity. Thus, there is no advantage in the long-term call; it will be selling for approximately the same price as the purchased call in a normal spread. However, since the strategist had to pay more originally for the longer-term call, his upside profits would not be as great. A diagonalized position has an advantage in that one can reestablish the posi­ tion if the written calls expire worthless in the spread. Thus, the increased cost of buying a longer-term call initially may prove to be a savings if one can write against it twice. These tactics are described for various spread strategies. THE DIAGONAL BULL SPREAD A vertical call bull spread consists of buying a call at a lower striking price and sell­ ing a call at a higher striking price, both with the same expiration date. The diagonal 236 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:263 SCORE: 105.00 ================================================================================ Chapter 14: Diagonalizing a Spread 231 bull spread would be similar except that one would buy a longer-tenn call at the lower strike and would sell a near-tenn call at the higher strike. The number of calls long and short would still be the same. By diagonalizing the spread, the position is hedged somewhat on the downside in case the stock does not advance by near-term expira­ tion. Moreover, once the near-term option expires, the spread can often be reestab­ lished by selling the call with the next maturity. Example: The following prices exist: Strike April Ju~ October Stock Price XYZ 30 3 4 5 32 XYZ 35 11/2 2 32 A vertical bull spread could be established in any of the expiration series by buying the call with 30 strike and selling the call with 35 strike. A diagonal bull spread would consist of buying the July 30 or October 30 and selling the April 35. To compare a vertical bull spread with a diagonal spread, the following two spreads will be used: Vertical bull spread: buy the April 30 call, sell the April 35 - 2 debit Diagonal bull spread: buy the July 30 call, sell the April 35 3 debit The vertical bull spread has a 3-point potential profit if XYZ is above 35 at April expi­ ration. The maximum risk in the normal bull spread is 2 points (the original debit) if XYZ is anywhere below 30 at April expiration. By diagonalizing the spread, the strate­ gist lowers his potential profit slightly at April expiration, but also lowers the proba­ bility of losing 2 points in the position. Table 14-1 compares the two types of spreads at April expiration. The price of the July 30 call is estimated in order to derive the estimated profits or losses from the diagonal bull spread at that time. If the underly­ ing stock drops too far - to 20, for example - both spreads will experience nearly a total loss at April expiration. However, the diagonal spread will not lose its entire value if XYZ is much above 24 at expiration, according to Table 14-1. The diagonal spread actually has a smaller dollar loss than the normal spread between 27 and 32 at expiration, despite the fact that the diagonal spread was more expensive to estab­ lish. On a percentage basis, the diagonal spread has an even larger advantage in this range. If the stock rallies aboye 35 by expiration, the normal spread will provide a larger profit. There is an interesting characteristic of the diagonal spread that is shown in Table 14-1. If the stock advances substantially and all the calls come to par­ ity, the profit on the diagonal spread is limited to 2 points. However, if the stock is near 35 at April expiration, the long call will have some time premium in it and the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:264 SCORE: 64.00 ================================================================================ 238 Part II: Call Option Strategies TABLE 14-1. Comparison of spreads at expiration. Vertical Bull XYZ Price at April 30 April 35 July 30 Spread Diagonal April Expiration Price Price Price Profit Spread Profit 20 0 0 0 -$200 -$300 24 0 0 1/2 - 200 - 250 27 0 0 1 - 200 - 200 30 0 0 2 - 200 - 100 32 2 0 3 0 0 35 5 0 51/2 + 300 + 250 40 10 5 10 + 300 + 200 45 15 10 15 + 300 + 200 spread will actually widen to more than 5 points. Thus, the maximum area of profit at April expiration for the diagonal spread is to have the stock near the striking price of the written call. The figures demonstrate that the diagonal spread gives up a small portion of potential upside profits to provide a hedge to the downside. Once the April 35 call expires, the diagonal spread can be closed. However, if the stock is below 35 at that time, it may be more prudent to then sell the July 35 call against the July 30 call that is held long. This would establish a normal bull spread for the 3 months remaining until July expiration. Note that ifXYZ were still at 32 at April expiration, the July 35 call might be sold for 1 point if the stock's volatility was about the same. This should be true, since the April 35 call was worth 1 point with the stock at 32 three months before expiration. Consequently, the strategist who had pursued this course of action would end up with a normal July bull spread for a net debit of 2 points: He originally paid 4 for the July 30 call, but then sold the April 35 for 1 point and subsequently sold the July 35 for 1 point. By looking at the table of prices for the first example in this chapter, the reader can see that it would have cost 2½ points to set up the normal July bull spread originally. Thus, by diagonalizing and having the near-term call expire worthless, the strategist is able to acquire the normal July bull spread at a cheaper cost than he could have originally. This is a specific example of how the diagonalizing effect can prove beneficial if the writer is able to write against the same long call two times, or three times if he originally purchased the longest­ term call. In this example, if XYZ were anywhere between 30 and 35 at April expira­ tion, the spread would be converted to a normal July bull spread. If the stock were above 35, the spread should be closed to take the profit. Below 30, the July 30 call would probably be closed or left outright long. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:265 SCORE: 73.00 ================================================================================ Chapter 14: Diagonalizing a Spread 239 In summary, the diagonal bull spread may often be an improvement over the normal bull spread. The diagonal spread is an improvement when the stock remains relatively unchanged or falls, up until the near-term written call expires. At that time, the spread can be converted to a normal bull spread if the stock is at a favorable price. Of course, if at any time the underlying stock rises above the higher striking price at an expiration date, the diagonal spread will be profitable. OWNING A CALL FOR "FREE" Diagonalization can be used in other spread strategies to accomplish much the same purposes already described; but in addition, it may also be possible for the spreader to wind up owning a long call at a substantially reduced cost, possibly even for free. The easiest w~y to see this would be to consider a diagonal bear spread. Example: XYZ is at 32 and the near-term April 30 call is selling for 3 points while the longer-term July 35 call is selling for 1 ½ points. A diagonal bear spread could be established by selling the April 30 and buying the July 35. This is still a bear spread, because a call with a lower striking price is being sold while a call at a higher strike is being purchased. However, since the purchased call has a longer maturity date than the written call, the spread is diagonalized. This diagonal bear spread will make money ifXYZ falls in price before the near­ term April call expires. For example, ifXYZ is at 29 at expiration, the written call will expire worthless and the July 35 will still have some value, perhaps ½. Thus, the prof­ it would be 3 points on the April 30, less a 1-point loss on the July 35, for an overall profit of 2 points. The risk in the position lies to the upside, just as in a regular bear spread. If XYZ should advance by a great deal, both options would be at parity and the spread would have widened to 5 points. Since the initial credit was 1 ½ points, the loss would be 5 minus 1 ½, or 3½ points in that case. As in all diagonal spreads, the spread will do slightly better to the downside because the long call will hold some value, but it will do slightly worse to the upside if the underlying stock advances sub­ stantially. The reason that a strategist might attempt a diagonal bear spread would not be for the slight downside advantage that the diagonalizing effect produces. Rather it would be because he has a chance of owning the July 35 call - the longer-term call - for a substantially reduced cost. In the example, the cost of the July 35 call was 1 ½ points and the premium received from the sale of the April 30 call was 3 points. If the spreader can make 1 ½ points from the sale of the April 30 call, he will have com­ pletely covered the cost of his July option. He can then sit back and hope for a rally ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:266 SCORE: 47.00 ================================================================================ 240 Part II: Call Option Strategies by the underlying stock. If such a rally occurred, he could make unlimited profits on the long side. If it did not, he loses nothing. Example: Assume that the same spread was established as in the last example. Then, if XYZ is at or below 31 ½ at April expiration, the April 30 call can be purchased for 1 ½ points or less. Since the call was originally sold for 3, this would represent a prof­ it of at least 1 ½ points on the April 30 call. This profit on the near-term option cov­ ers the entire cost of the July 35. Consequently, the strategist owns the July 35 for free. If XYZ never rallies above 35, he would make nothing from the overall trade. However, if XYZ were to rally above 35 after April expiration (but before July expi­ ration, of course), he could make potentially large profits. Thus, when one establish­ es a diagonal spread for a credit, there is always the potential that he could own a call for free. That is, the profits from the sale of the near-term call could equal or exceed the original cost of the long call. This is, of course, a desirable position to be in, for if the underlying stock should rally substantially after profits are realized on the short side, large profits could accrue. DIAGONAL BACKSPREADS In an analogous strategy, one might buy more than one longer-term call against the short-term call that is sold. Using the foregoing prices, one might sell the April 30 for 3 points and buy 2 July 35's at 1 ½ points each. This would be an even money spread. . The credits equal the debits when the position is established. If the April 30 call expires worthless, which would happen if the stock was below 30 in April, the spread­ er would own 2 July 35 calls for free. Even if the April 30 does not expire totally worthless, but if some profit can be made on the sale of it, the July 35's will be owned at a reduced cost. In Chapter 13, when reverse spreads were discussed, the strategy in which one sells a call with a lower strike and then buys more calls at a higher strike was termed a reverse ratio spread, or backspread. The strategy just described is merely the diagonalizing of a backspread. This is a strategy that is favored by some professionals, because the short call reduces the risk of owning the longer-term calls if the underlying stock declines. Moreover, if the underlying stock advances, the pre­ ponderance of long calls with a longer maturity will certainly outdistance the losses on the written call. The worst situation that could result would be for the underlying stock to rise very slightly by near-term expiration. If this happened, it might be pos­ sible to lose money on both sides of the spread. This would have to be considered a rather low-probability event, though, and would still represent a limited loss, so it does not substantially offset the positive aspects of the strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:267 SCORE: 61.00 ================================================================================ 0.,ter 14: Diagonalizing a Spread 241 Any type of spread may be diagonalized. There are some who prefer to diago­ nalize even butterfly spreads, figuring that the extra time to maturity in the purchased calls will be of benefit. Overall, the benefits of diagonalizing can be generalized by recalling the way in which the decay of the time value premium of a call takes place. Recall that it was determined that a call loses most of its time value premium in the last stages of its life. When it is a very long-term option, the rate of decay is small. Knowing this fact, it makes sense that one would want to sell options with a short life remaining, so that the maximum benefit of the decay could be obtained. Correspondingly, the purchase of a longer-term call would mean that the buyer is not subjecting himself to a substantial loss in time value premium, at least over the first three months of ownership. A diagonal spread encompasses both of these features - selling a short-term call to try to obtain the maximum rate of time decay, while buy­ ing a longer-term call to try to lessen the effect of time decay on the long side. CALL OPTION SUMMARY This concludes the description of strategies that utilize only call options. The call option has been seen to be a vehicle that the astute strategist can use to set up a wide variety of positions. He can be bullish or bearish, aggressive or conservative. In addi­ tion, he can attempt to be neutral, trying to capitalize on the probability that a stock will not move very far in a short time period. The investor who is not familiar with options should generally begin with a sim­ ple strategy, such as covered call writing or outright call purchases. The simplest types of spreads are the bull spread, the bear spread, and the calendar spread. The more sophisticated investor might consider using ratios in his call strategies - ratio writing against stock or ratio spreading using only calls. Once the strategist feels that he understands the risk and reward relationships between longer-term and short-term calls, between in-the-money and out-of-the­ money calls, and between long calls and short calls, he could then consider utilizing the most advanced types of strategies. This might include reverse ratio spreads, diag­ onal spreads, and more advanced types of ratios, such as the ratio calendar spread. A great deal of information, some of it rather technical in detail, has been pre­ sented in preceding chapters. The best pattern for an investor to follow would be to attempt only strategies that he fully comprehends. This does not mean that he mere­ ly understands the profitability aspects (especially the risk) of the strategy. One must also be able to readily understand the potential effects of early assignments, large div­ idend payments, striking price adjustments, and the like, if he is going to operate advanced strategies. Without a full understanding of how these things might affect one's position, one cannot operate an advanced strategy correctly. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:270 SCORE: 45.00 ================================================================================ INTRODUCTION A put option gives the holder the right to sell the underlying security at the striking price at any time until the expiration date of the option. Listed put options are slightly newer than listed call options, having been introduced on June 3, 1977. The introduction of listed puts has provided a much wider range of strategies for both conservative and aggressive investors. The call option is least effective in strategies in which downward price movement by the underlying stock is concerned. The put option is a useful tool in that case. All stocks with listed call options have listed put options as well. The use of puts or the combination of puts and calls can provide more versatility to the strategist. When listed put options exist, it is no longer necessary to implement strategies involving long calls and short stock. Listed put options can be used more efficiently in such situations. There are many similarities between call strategies and put strategies. For example, put spread strategies and call spread strategies employ sim­ ilar tactics, although there are technical differences, of course. In certain strategies, the tactics for puts may appear largely to be a repetition of those used for calls, but they are nevertheless spelled out in detail here. The strategies that involve the use of both puts and calls together - straddles and combinations - have techniques of their own, but even in these cases the reader will recognize certain similarities to strategies previously discussed. Thus, the introduction of put options not only widens the realm of potential strategies, but also makes more efficient some of the strategies previously described. 244 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:271 SCORE: 53.00 ================================================================================ CH.APTER 15 Put Option Basics Much of the same terminology that is applied to call options also pertains to put options. Underlying security, striking price, and expiration date are all terms that have the same meaning for puts as they do for calls. The expiration dates of listed put options agree with the expiration dates of the calls on the same underlying stock. In addition, puts and calls have the same striking prices. This means that if there are options at a certain strike, say on a particular underlying stock that has both listed puts and calls, both calls at 50 and puts at 50 will be trading, regardless of the price of the underlying stock. Note that it is no longer sufficient to describe an option as an "XYZ July 50." It must also be stated whether the option is a put or a call, for an XYZ July 50 call and an XYZ July 50 put are two different securities. In many respects, the put option and its associated strategies will be very near­ ly the opposite of corresponding call-oriented strategies. However, it is not correct to say that the put is exactly the opposite of a call. In this introductory section on puts, the characteristics of puts are described in an attempt to show how they are similar to calls and how they are not. PUT STRATEGIES In the simplest terms, the outright buyer of a put is hoping for a stock price decline in order for his put to become more valuable. If the stock were to decline well below the striking price of the put option, the put holder could make a profit. The holder of the put could buy stock in the open market and then exercise his put to sell that stock for a profit at the striking price, which is higher. Example: If XYZ stock is at 40, an XYZ July 50 put would be worth at least 10 points, for the put grants the holder the right to sell XYZ at 50 - 10 points above its current 245 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:273 SCORE: 53.00 ================================================================================ CHAPTER 15 Put Option Basics Much of the same terminology that is applied to call options also pertains to put options. Underlying security, striking price, and expiration date are all terms that have the same meaning for puts as they do for calls. The expiration dates of listed put options agree with the expiration dates of the calls on the same underlying stock. In addition, puts and calls have the same striking prices. This means that if there are options at a certain strike, say on a particular underlying stock that has both listed puts and calls, both calls at 50 and puts at 50 will be trading, regardless of the price of the underlying stock. Note that it is no longer sufficient to describe an option as an "XYZ July 50." It must also be stated whether the option is a put or a call, for an XYZ July 50 call and an XYZ July 50 put are two different securities. In many respects, the put option and its associated strategies will be very near­ ly the opposite of corresponding call-oriented strategies. However, it is not correct to say that the put is exactly the opposite of a call. In this introductory section on puts, the characteristics of puts are described in an attempt to show how they are similar to calls and how they are not. PUT STRATEGIES In the simplest terms, the outright buyer of a put is hopingfor a stock price decline in order for his put to become more valuable. If the stock were to decline well below the striking price of the put option, the put holder could make a profit. The holder of the put could buy stock in the open market and then exercise his put to sell that stock for a profit at the striking price, which is higher. Example: If XYZ stock is at 40, an XYZ July 50 put would be worth at least 10 points, for the put grants the holder the right to sell XYZ at 50 10 points above its current 245 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:274 SCORE: 112.00 ================================================================================ 246 Part Ill: Put Option Strategies price. On the other hand, if the stock price were above the striking price of the put option at expiration, the put would be worthless. No one would logically want to exer­ cise a put option to sell stock at the striking price when he could merely go to the open market and sell the stock for a higher price. Thus, as the price of the underly­ ing stock declines, the put becomes more valuable. This is, of course, the opposite of a call option's price action. The meaning of in-the-money and out-of-the-money are altered when one is speaking of put options. A put is considered to be in-the-money when the underlying stock is below the striking price of the put option; it is out-of the-money when the stock is above the striking price. This, again, is the opposite of the call option. IfXYZ is at 45, the XYZ July 50 put is in-the-money and the XYZ July 50 call is out-of-the­ money. However, ifXYZ were at 55, the July 50 put would be out-of-the-money while the July 50 call would be in-the-money. The broad definition of an in-the-money option as "an option that has intrinsic value" would cover the situation for both puts and calls. Note that a put option has intrinsic value when the underlying stock is below the striking price of the put. That is, the put has some "real" value when the stock is below the striking price. The intrinsic value of an in-the-money put is merely the difference between the striking price and the stock price. Since the put is an option (to sell), it will gen­ erally sell for more than its intrinsic value when there is time remaining until the expiration date. This excess value over its intrinsic value is referred to as the time value premium, just as is the case with calls. Example: XYZ is at 47 and the XYZ July 50 put is selling for 5, the intrinsic value is 3 points (50- 47), so the time value premium must be 2 points. The time value pre­ mium of an in-the-money put option can always be quickly computed by the follow­ ing formula: Time value premium p . S k · St "ki · • ) == ut option + toe pnce - n ng pnce (m-the-money put This is not the same formula that was applied to in-the-money call options, although it is always true that the time value premium of an option is the excess value over intrinsic value. Time value premium Call ti S ·ki · St k · . all == op on + tn ng pnce - oc pnce (m-the-money c ) If the put is out-of-the-money, the entire premium of the put is composed of time value premium, for the intrinsic value of an out-of-the-money option is always zero. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:275 SCORE: 130.00 ================================================================================ O.,,ter 15: Put Option Basks 247 The time value premium of a put is largest when the stock is at the striking price of the put. As the option becomes deeply in-the-money or deeply out-of-the-money, the time value premium will shrink substantially. These statements on the magnitude of the time value premium are true for both puts and calls. Table 15-1 will help to illus­ trate the relationship of stock price and option price for both puts and calls. The reader may want to refer to Table 1-1, which described the time value premium rela­ tionship for calls. Table 15-1 describes the prices of an XYZ July 50 call option and an XYZ July 50 put option. Table 15-1 demonstrates several basic facts. As the stock drops, the actual price of a call option decreases while the value of the put option increases. Conversely, as the stock rises, the call option increases in value and the put option decreases in value. Both the put and the call have their maximum time value premium when the stock is exactly at the striking price. However, the call will generally sell for rrwre than the put when the stock is at the strike. Notice in Table 15-1 that, with XYZ at 50, the call is worth 5 points while the put is worth only 4 points. This is true in general, except in the case of a stock that pays a large dividend. This phenomenon has to do with the cost of carrying stock. More will be said about this effect later. Table 15-1 also describes an effect of put options that normally holds true: An in-the-rrwney put ( stock is below strike) loses time value premium rrwre quickly than an in-the-rrwney call does. Notice that with XYZ at 43 in Table 15-1, the put is 7 points in-the-money and has lost all its time value premium. But when the call is 7 points in-the-money, XYZ at 57, the call still has 2 points of time value premium. Again, this is a phenom­ enon that could be affected by the dividend payout of the underlying stock, but is true in general. PRICING PUT OPTIONS The same factors that determine the price of the call option also determine the price of the put option: price of the underlying stock, striking price of the option, time remaining until expiration, volatility of the underlying stock, dividend rate of the underlying stock, and the current risk-free interest rate (Treasury bill rate, for exam­ ple). Market dynamics - supply, demand, and investor psychology - play a part as well. Without going into as much detail as was shown in Chapter 1, the pricing curve of the put option can be developed. Certain facts remain true for the put option as they did for the call option. The rate of decay of the put option is not linear; that is, the time value premium will decay more rapidly in the weeks immediately preced­ ing expiration. The more volatile the underlying stock, the higher will be the price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:276 SCORE: 95.00 ================================================================================ 248 Part Ill: Put Option Strategies TABLE 15-1. Call and put options compared. XYZ XYZ Coll Coll XYZ Put Put Stock July 50 Intrinsic Time Value July 50 Intrinsic Time Value Price Coll Price Value Premium Put Price Value Premium 40 1/2 0 1/2 93/4 10 -1/4* 43 1 0 1 7 7 0 45 2 0 2 6 5 47 3 0 3 5 3 2 50 5 0 5 4 0 4 53 7 3 4 3 0 3 55 8 5 3 2 0 2 57 9 7 2 0 60 101/2 10 1/2 1/2 0 l/2 70 193/4 20 -1/4 * 1/4 0 1/4 * A deeply in-the-money option may actually trade at a discount from intrinsic value in advance of expiration. of its options, both puts and calls. Moreover, the marketplace may at any time value options at a higher or lower volatility than the underlying stock actually exhibits. This is called implied volatility, as distinguished from actual volatility. Also, the put option is usually worth at least its intrinsic value at any time, and should be worth exactly its intrinsic value on the day that it expires. Figure 15-1 shows where one might expect the XYZ July 50 put to sell, for any stock price, if there are 6 months remaining until expiration. Compare this with the similar pricing curve for the call option (Figure 15-2). Note that the intrinsic value line for the put option faces in the opposite direction from the intrinsic value line for call options; that is, it gains value as the stock falls below the striking price. This put option pricing curve demonstrates the effect mentioned earlier, that a put option loses time value pre­ mium more quickly when it is in-the-money, and also shows that an out-of-the­ money put holds a great deal of time value premium. THE EFFECT OF DIVIDENDS ON PUT OPTION PREMIUMS The dividend of the underlying stock is a negative factor on the price of its call options. The opposite is true for puts. The larger the dividend, the nwre valuable the puts will be. This is true because, as the stock goes ex-dividend, it will be reduced in ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:277 SCORE: 25.00 ================================================================================ Cl,opter 15: Put Option Basics FIGURE 1 5-1. Put option price curve. ~ it C: .Q a. 0 FIGURE 1 5-2. Call option price curve. ~ ct C: 0 11 10 9 8 7 6 a 5 Striking Price (50) Greatest Value for Time Value Stock Price 0 4 ---------------------- 3 2 1 0 40 45 represents the option's time value premium. ________ L ________ _ 50\ 55 60 Stock Price Intrinsic value remains at zero until striking price is passed. 249 price by the amount of the dividend. That is, the stock will decrease in price and therefore the put will become more valuable. Consequently, the buyer of the put will be willing to pay a higher price for the put and the seller of the put will also demand a higher price. As with listed calls, listed puts are not adjusted for the payment of cash dividends on the underlying stock. However, the price of the option itself will reflect the dividend payments on the stock. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:278 SCORE: 81.00 ================================================================================ 250 Part Ill: Put Option Strategies Example: XYZ is selling for $25 per share and will pay $1 in dividends over the next 6 months. Then a 6-month put option with strike 25 should automatically be worth at least $1, regardless of any other factor concerning the underlying stock. During the next 6 months, the stock will be reduced in price by the amount of its dividends- $1 - and if everything else remained the same, the stock would then be at 24. With the stock at 24, the put would be 1 point in-the-money and would thus be worth at least its intrinsic value of 1 point. Thus, in advance, this large dividend payout of the underlying stock will help to increase the price of the put options on this stock. On the day before a stock goes ex-dividend, the time value premium of an in­ the-money put should be at least as large as the impending cash dividend payment. That is, if XYZ is 40 and is about to pay a $.50 dividend, an XYZ January 50 put should sell for at least l 0½. This is true because the stock will be reduced in price by the amount of its dividend on the day of the ex-dividend. EXERCISE AND ASSIGNMENT When the holder of a put option exercises his option, he sells stock at the striking price. He may exercise this right at any time during the life of the put option. When this happens, the writer of a put option with the same terms is assigned an obligation to buy stock at the striking price. It is important to notice the difference between puts and calls in this case. The call holder exercises to buy stock and the call writer is obligated to sell stock. The reverse is true for the put holder and writer. The methods of assignment via the OCC and the brokerage firm are the same for puts and calls; any fair method of random or first-in/first-out assignment is allowed. Stock commissions are charged on both the purchase and sale of the stock via the assignment and exercise. When the holder of a put option exercises his right to sell stock, he may be sell­ ing stock that he currently holds in his portfolio. Second, he may simultaneously go into the open market and buy stock for sale via the put exercise. Finally, he may want to sell the stock in his short stock account; that is, he may short the underlying stock by exercising his put option. He would have to be able to borrow stock and supply the margin collateral for a short sale of stock if he chose this third course of action. The writer of the put option also has several choices in how he wants to handle the stock purchase that he is required to make. The put writer who is assigned must receive stock. (The call writer who is assigned delivers stock.) The put writer may cur­ rently be short the underlying stock, in which case he will merely use the receipt of stock from the assignment to cover his short sale. He may also decide to immediate- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:279 SCORE: 61.00 ================================================================================ 0.,ter 15: Put Option Basics 251 ly sell stock in the open market to offset the purchase that he is forced to make via the put assignment. Finally, he may decide to retain the stock that is delivered to him; he merely keeps the stock in his portfolio. He would, of course, have to pay for ( or margin) the stock if he decides to keep it. The mechanics as to how the put holder wants to deliver the stock and how the put writer wants to receive the stock are relatively simple. Each one merely notifies his brokerage firm of the way in which he wants to operate and, provided that he can meet the margin requirements, the exercise or assignment will be made in the desired manner. ANTICIPATING ASSIGNMENT The writer of a put option can anticipate assignment in the same way that the writer of a call can. When the time value premium of an in-the-money put option disappears, there is a risk of assignment, regardless of the time remaining until expiration. In Chapter 1, a form of arbitrage was described in which market-makers or firm traders, who pay little or no commissions, can take advantage of an in-the-money call selling at a discount to parity. Similarly, there is a method for these traders to take advantage of an in-the-money put selling at a discount to parity. Example: XYZ is at 40 and an XYZ July 50 put is selling for 9¾ a ¼ discount from parity. That is, the option is selling for ¼ point below its intrinsic value. The arbi­ trageur could take advantage of this situation through the following actions: 1. Buy the July put at 9¾. 2. Buy XYZ common stock at 40. 3. Exercise the put to sell XYZ at 50. The arbitrageur makes 10 points on the stock portion of the transaction, buying the common at 40 and selling it at 50 via exercise of his put. He paid 9¾ for the put option and he loses this entire amount upon exercise. However, his overall profit is thus ¼ point, the amount of the original discount from parity. Since his commission costs are minimal, he can actually make a net profit on this transaction. As was the case with deeply in-the-money calls, this type of arbitrage with deeply in-the-money puts provides a secondary market that might not otherwise exist. It allows the public holder of an in-the-money put to sell his option at a price near its intrinsic value. Without these arbitrageurs, there might not be a reasonable secondary market in which public put holders could liquidate. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:280 SCORE: 69.00 ================================================================================ 252 Part Ill: Put Option Strategies Dividend payment dates may also have an effect on the frequency of assign­ ment. For call options, the writer might expect to receive an assignment on the day the stock goes ex-dividend. The holder of the call is able to collect the dividend by so exercising. Things are slightly different for the writer of puts. He might expect to receive an assignment on the day after the ex-dividend date of the underlying stock. Since the writer of the put is obligated to buy stock, it is unlikely that any­ one would put the stock to him until after the dividend has been paid. In any case, the writer of the put can use a relatively simple gauge to anticipate assignment near the ex-dividend date. If the time value premium of an in-the-money put is less than the amount of the dividend to be paid, the writer may often anticipate that he will be assigned immediately after the ex-dividend of the stock. An example will show why this is true. Example: XYZ is at 45 and it will pay a $.50 dividend. Furthermore, the XYZ July 50 put is selling at 5¼. Note that the time value premium of the July 50 put is ¼ point - less than the amount of the dividend, which is ½ point. An arbitrageur could take the following actions: 1. Buy XYZ at 45. 2. Buy the July 50 put at 5¼. 3. Collect the ½-point dividend (he must hold the stock until the ex-date to collect the dividend). 4. Exercise his put to sell XYZ at 50 ( writer would receive assignment on the day after the ex-date). The arbitrageur makes 5 points on the stock trades, buying XYZ at 45 and selling it at 50 via exercise of the put. He also collects the ½-point dividend, making his total intake equal to 5½ points. He loses the 5¼ points that he paid for the put but still has a net profit of ¼ point. Thus, as the ex-dividend date of a stock approaches, the time value premium of all in-the-money puts on that stock will tend to equal or exceed the amount of the dividend payment. This is quite different from the call option. It was shown in Chapter 1 that the call writer only needs to observe whether the call was trading at or below parity, regardless of the amount of the dividend, as the ex-dividend date approaches. The put writer must determine if the time value premium of the put exceeds the amount of the dividend to be paid. If it does, there is a much smaller chance of assignment because of the dividend. In any case, the put writer can anticipate the assignment if he carefully monitors his position. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:281 SCORE: 28.00 ================================================================================ O.,ter 15: Put Option Basics POSITION LIMITS 253 Recall that the position limit rule states that one cannot have a position of more than the limit of options on the same side of the market in the same underlying security. The limit varies depending on the trading activity and volatility of the underlying stock and is set by the exchange on which the options are traded. The actual limits are 13,500, 22,500, 31,500, 60,000, or 75,000 contracts, depending on these factors. One cannot have more than 75,000 option contracts on the bullish side of the market - long calls and/or short puts - nor can he have more than 75,000 contracts on the bearish side of the market - short calls and/or long puts. He may, however, have 75,000 con­ tracts on each side of the market; he could simultaneously be long 75,000 calls and long 75,000 puts. For the following examples, assume that one is concerned with an underlying stock whose position limit is 75,000 contracts. Long 75,000 calls, long 75,000 puts - no violation; 75,000 contracts bullish (long calls) and 75,000 contracts bearish (long puts). Long 38,000 calls, short 37,000 puts - no violation; total of 75,000 contracts bullish. Long 38,000 calls, short 38,000 puts - violation; total of 76,000 contracts bullish. Money managers should be aware that these position limits apply to all "related" accounts, so that someone managing several accounts must total all the accounts' positions when considering the position limit rule. CONVERSION Many of the relationships between call prices and put prices relate to a process known as a conversion. This term dates back to the over-the-counter option days when a dealer who owned a put ( or could buy one) was able to satisfy the needs of a potential call buyer by "converting" the put to a call. This terminology is somewhat confusing, and the actual position that the dealer would take is little more than an arbitrage position. In the listed market, arbitrageurs and firm traders can set up the same position that the converter did. The actual details of the conversion process, which must include the carrying cost of owning stock and the inclusion of all dividends to be paid by the stock during the time the position is held, are described later. However, it is important for the put option trader to understand what the arbitrageur is attempting to do in order for him to fully understand the relationship between put and call prices in the listed option market. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:282 SCORE: 42.00 ================================================================================ 254 Part Ill: Put Option Strategies A conversion position has no risk. The arbitrageur will do three things: 1. Buy 100 shares of the underlying stock. 2. Buy 1 put option at a certain striking price. 3. Sell l call option at the same striking price. The arbitrageur has no risk in this position. If the underlying stock drops, he can always exercise his long put to sell the stock at a higher price. If the underlying stock rises, his long stock offsets the loss on his short call. Of course, the prices that the arbitrageur pays for the individual securities determine whether or not a conversion will be profitable. At times, a public customer may look at prices in the newspaper and see that he could establish a position similar to the foregoing one for a profit, even after commissions. However, unless prices are out of line, the public customer would not normally be able to make a better return than he could by putting his money into a bank or a Treasury bill, because of the commission costs he would pay. Without needing to understand, at this time, exactly what prices would make an attractive conversion, it is possible to see that it would not always be possible for the arbitrageur to do a conversion. The mere action of many arbitrageurs doing the same conversion would force the prices into line. The stock price would rise because arbi­ trageurs are buying the stock, as would the put price; and the call price would drop because of the preponderance of sellers. When this happens, another arbitrage, known as a reversal ( or reverse conver­ sion), is possible. In this case, the arbitrageur does the opposite: He shorts the under­ lying stock, sells 1 put, and buys 1 call. Again, this is a position with no risk. If the stock rises, he can always exercise his call to buy stock at a lower price and cover his short sale. If the stock falls, his short stock will offset any losses on his short put. The point of introducing this information, which is relatively complicated, at this place in the text is to demonstrate that there is a relationship between put and call prices, when both have the same striking price and expiration date. They are not independent of one another. If the put becomes "cheap" with respect to the call, arbi­ trageurs will move in to do conversions and force the prices back in line. On the other hand, if the put becomes expensive with relationship to the call, arbitrageurs will do reversals until the prices move back into line. Because of the way in which the carrying cost of the stock and the dividend rate of the stock are involved in doing these conversions or reversals, two facts come to light regarding the relationship of put prices and call prices. Both of these facts have to do with the carrying costs incurred during the conversion. First, a put option will generally sell for less than a call option when the underlying stock is exactly at the striking price, unless the stock pays a large dividend. In the older over-the-counter ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:283 SCORE: 25.00 ================================================================================ a,,pter 15: Put Option Basics 255 option market, it was often stated that the reason for this relationship was that the demand for calls was larger than the demand for puts. This may have been partially true, but certainly it is no longer true in the listed option targets, where a large sup­ ply of both listed puts and calls is available through the OCC. Arbitrageurs again serve a useful function in increasing supply and demand where it might not other­ wise exist. The second fact concerning the relationship of puts and calls is that a put option will lose its time value premium much more quickly in-the-money than a call option will (and, conversely, a put option will generally hold out-of-the-money time value premium better than a call option will). Again, the conversion and reversal processes play a large role in this price action phenomenon of puts and calls. Both of these facts have to do with the carrying costs involved in the conversion. In the chapter on Arbitrage, exact details of conversions and reversals will be spelled out, with specific reasons why these procedures affect the relationship of put and call prices as stated above. However, at this time, it is sufficient for the reader to understand that there is an arbitrage process that is quite widely practiced that will, in fact, make true the foregoing relationships between puts and calls. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:284 SCORE: 43.00 ================================================================================ Put Option Buying The purchase of a put option provides leverage in the case of a downward move by the underlying stock. In this manner, it is an alternative to the short sale of stock, much as the purchase of a call option is a leveraged alternative to the purchase of stock. PUT BUYING VERSUS SHORT SALE In the simplest case, when an investor expects a stock to decline in price, he may either short the underlying stock or buy a put option on the stock. Suppose that XYZ is at 50 and that an XYZ July 50 put option is trading at 5. If the underlying stock declines substantially, the buyer of the put could make profits considerably in excess of his initial investment. However, if the underlying stock rises in price, the put buyer has limited risk; he can lose only the amount of money that he originally paid for the put option. In this example, the most that the put buyer could lose would be 5 points, which is equal to his entire initial investment. Table 16-1 and Figure 16-1 depict the results, at expiration, of this simple purchase of the put option. The put buyer has limited profit potential, since a stock can never drop in price below zero dollars per share. However, his potential profits can be huge, percent­ agewise. His loss, which normally would occur if the stock rises in price, is limited to the amount of his initial investment. The simplest use of a put purchase is for specu­ lative purposes when expecting a price decline in the underlying stock. These results for the profit or loss of the put option purchases can be compared to a similar short sale of XYZ at 50 in order to observe the benefits of leverage and limited risk that the put option buyer achieves. In order to sell short 100 XYZ at 50, assume that the trader would have to use $2,500 in margin. Several points can be ver- 256 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:286 SCORE: 31.00 ================================================================================ 258 Part Ill: Put Option Strategies chase can achieve. If the underlying stock remains relatively unchanged, the short seller would do better because he does not risk losing his entire investment in a lim­ ited amount of time if the underlying stock changes only slightly in price. However, if the underlying stock should rise dramatically, the short seller can actually lose more than his initial investment. The short sale of stock has theoretically unlimited risk. Such is not true of the put option purchase, whereby the risk is limited to the amount of the initial investment. One other point should be made when comparing the pur­ chase of a put and the short sale of stock: The short seller of stock is obligated to pay the dividends on the stock, but the put option holder has no such obligation. This is an additional advantage to the holder of the put. TABLE 16-2. Results of selling short. XYZ Price at Put Option Expiration Short Sale Purchase 20 + $3,000 (+ 120%) +$2,500 (+ 500%) 30 + 2,000 (+ 80%) + 1,500 (+ 300%) 40 + 1,000 (+ 40%) + 500 (+ 100%) 45 + 500(+ 20%) 0( 0%) 48 + 200(+ 80%) 300 (- 60%) 50 0( 0%) 500 (- 100%) 60 - 1,000 (- 40%) 500 (- 100%) 75 - 2,500 (- 100%) 500 (- 100%) 100 - 5,000 (- 200%) 500 (- 100%) SELECTING WHICH PUT TO BUY Many of the same types of analyses that the call buyer goes through in deciding which call to buy can be used by the prospective put buyer as well. First, when approach­ ing put buying as a speculative strategy, one should not place more than 15% of his risk capital in the strategy. Some investors participate in put buying to add some amount of downside protection to their basically bullishly-oriented common stock portfolios. More is said in Chapter 17 about buying puts on stocks that one actually owns. The out-ofthe-nwney put offers both higher reward potentials and higher risk potentials than does the in-the-nwney put. If the underlying stock drops substantial- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:287 SCORE: 83.00 ================================================================================ G,pter 16: Put Option Buying 259 ly, the percentage returns from having purchased a cheaper, out-of-the-money put will be greater. However, should the underlying stock decline only moderately in price, the in-the-rrwney put will often prove to be the better choice. In fact, since a put option tends to lose its time value premium quickly as it becomes an in-the­ money option, there is an even greater advantage to the purchase of the in-the­ money put. Example: XYZ is at 49 and the following prices exist: XYZ, 49; XYZ July 45 put, l; and XYZ July 50 put, 3. If the underlying stock were to drop to 40 by expiration, the July 45 put would be worth 5 points, a 400% profit. The July 50 put would be worth 10 points, a 233% profit over its initial purchase price of 3. Thus, in a substantial downward move, the out-of-the-money put purchase provides higher reward potential. However, if the underlying stock drops only moderately, say to t:15, the purchaser of the July 45 put would lose his entire investment, since the put would be worthless at expiration. The purchaser of the in-the-money July 50 put would have a 2-point profit with XYZ at 45 at expiration. The preceding analysis is based on holding the put until expiration. For the option buyer, this is generally an erroneous form of analysis, because the buyer generally tends to liquidate his option purchase in advance of expiration. When considering what happens to the put option in advance of expiration, it is helpful to remember that an in-the-money put tends to lose its time premium rather quickly. In the example above, the July 45 put is completely composed of time value pre­ mium. If the underlying stock begins to drop below 45, the price of the put will not increase as rapidly as would the price of a call that is going into-the-money. Example: If XYZ fell by 5 points to 44, definitely a move in the put buyer's favor, he may fmd that the July 45 put has increased in value only to 2 or 2½ points. This is somewhat disappointing because, with call options, one would expect to do signifi­ cantly better on a 5-point stock movement in his favor. Thus, when purchasing put options for speculation, it is generally best to concentrate on in-the-rrwney puts unless a very substantial decline in the price of the underlying stock is anticipated. Once the put option is in-the-money, the time value premium will decrease even in the longer-term series. Since this time premium is small in all series, the put ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:288 SCORE: 64.00 ================================================================================ 260 Part Ill: Put Option Strategies buyer can often purchase a longer-term option for very little extra money, thus gain­ ing more time to work with. Call option buyers are generally forced to avoid the longer-term series because the extra cost is not worth the risk involved, especially in a trading situation. However, the put buyer does not necessarily have this disadvan­ tage. If he can purchase the longer-term put for nearly the same price as the near­ term put, he should do so in case the underlying stock takes longer to drop than he had originally anticipated it would. It is not uncommon to see such prices as the following: XYZ common, 46: XYZ April 50 put, 4; XYZ July 50 put, 4½; and XYZ October 50 put, 5. None of these three puts have much time value premium in their prices. Thus, the buyer might be willing to spend the extra 1 point and buy the longest-term put. If the underlying stock should drop in price immediately, he will profit, but not as much as if he had bought one of the less expensive puts. However, should the underlying stock rise in price, he will own the longest-term put and will therefore suffer less of a loss, percentagewise. If the underlying stock rises in price, some amount of time value premium will come back into the various puts, and the longest-term put will have the largest amount of time premium. For example, if the stock rises back to 50, the fol­ lowing prices might exist: XYZ common, 50; XYZ April 50 put, l; XYZ July 50 put, 2½; and XYZ October 50 put, 3½. The purchase of the longer-term October 50 put would have suffered the least loss, percentagewise, in this event. Consequently, when one is purchasing an in-the­ money put, he may often want to consider buying the longest-term put if the time value premium is small when compared to the time premium in the nearer-term puts. In Chapter 3, the delta of an option was described as the amount by which one might expect the option will increase or decrease in price if the underlying stock moves by a fixed amount (generally considered to be one point, for simplicity). Thus, if XYZ is at 49 and a call option is priced at 3 with a delta of ½, one would expect the call to sell for 3½ with XYZ at 50 and to sell at 2¼ with XYZ at 48. In reality, the delta ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:289 SCORE: 73.00 ================================================================================ O.,ter 16: Put Option Buying 261 changes even on a fractional move in the underlying stock, but one generally assumes that it will hold true for a 1-point move. Obviously, put options have deltas as well. The delta of a put is a negative number, reflecting the fact that the put price and the stock price are inversely related. As an approximation, one could say that the delta of the ctill option minus the delta of the put option with the same terms is equal to 1. That is, Delta of put = Delta of call - 1. This is an approximation and is accurate unless the put is deeply in-the-money. It has already been pointed out that the time value premium behavior of puts and calls is different, so it is inaccurate to assume that this formula holds true exactly for all cases. The delta of a put ranges between O and minus 1. If a July 50 put has a delta of -½, and the underlying stock rises by 1 point, the put will lose ½ point. The delta of a deeply out-of-the-money put is close to zero. The put's delta would decrease slow­ ly at first as the stock declined in value, then would begin to decrease much more rapidly as the stock fell through the striking price, and would reach a value of minus 1 (the minimum) as the stock fell only moderately below the striking price. This is reflective of the fact that an out-of-the-money put tends to hold time premium quite well and an in-the-money put comes to parity rather quickly. RANKING PROSPECTIVE PUT PURCHASES In Chapter 3, a method of ranking prospective call purchases was developed that encompassed certain factors, such as the volatility of the underlying stock and the expected holding period of the purchased option. The same sort of analysis should be applied to put option purchases. The steps are summarized below. The reader may refer to the section titled "Advanced Selection Criteria" in Chapter 3 for a more detailed description of why this method of ranking is superior. 1. Assume that each underlying stock can decrease in price in accordance with its volatility over a fixed holding period (30, 60, or 90 days). 2. Estimate the put option prices after the decrease. 3. Rank all potential put purchases by the highest reward opportunity for aggressive purchases. 4. Estimate how much would be lost if the underlying stock instead rose in accor­ dance with its volatility, and rank all potential put purchases by best risk/reward ratio for a more conservative list of put purchases. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:290 SCORE: 40.00 ================================================================================ 262 Part Ill: Put Option Strategies As was stated earlier, it is necessary to have a computer to make an accurate analysis of all listed options. The average customer is forced to obtain such data from a bro­ kerage firm or data service. He should be sure that the list he is using conforms to the above-mentioned criteria. If the data service is ranking option purchases by how well the puts would do if each underlying stock fell by a fixed percentage (such as 5% or 10%), the list should be rejected because it is not incorporating the volatility of the underlying stock into its analysis. Also, if the list is based on holding the put purchase until expiration, the list should be rejected as well, because this is not a realistic assumption. There are enough reliable and sophisticated data services that one should not have to work with inferior analyses in today's option market. For those readers who are more mathematically advanced and have the com­ puter capability to construct their own analyses, the details of implementing an analy­ sis similar to the one described above are presented in Chapter 28, Mathematical Applications. An application of put purchases, combined with fixed-income securi­ ties, is described in Chapter 26, Buying Options and Treasury Bills. FOLLOW-UP ACTION The put buyer can take advantage of strategies that are very similar to those the call buyer uses for follow-up action, either to lock in profits or to attempt to improve a losing situation. Before discussing these specific strategies, it should be stated again that it is rarely to the option buyer's benefit to exercise the option in order to liqui­ date. This precludes, of course, those situations in which the call buyer actually wants to own the stock or the put buyer actually wants to sell the stock. If, however, the option holder is merely looking to liquidate his position, the cost of stock commis­ sions makes exercising a prohibitive move. This is true even ifhe has to accept a price that is a slight discount from parity when he sells his option. LOCKING IN PROFITS The reader may recall that there were four strategies (perhaps "tactics" is a better word) for the call buyer with an unrealized profit. These same four tactics can be used with only slight variations by the put option buyer. Additionally, a fifth strategy can be employed when a stock has both listed puts and calls. After an underlying stock has moved down and the put buyer has a relatively substantial unrealized gain, he might consider taking one of the following actions: 1. Sell the put and liquidate the position for a profit. 2. Do nothing and continue to hold the put. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:291 SCORE: 22.00 ================================================================================ O.,,er 16: Put Option Buying 263 3, Sell the in-the-money long put and use part of the proceeds to purchase out-of­ the-money puts. 4. Create a spread by selling an out-of-the-money put against the one he currently holds. These are the same four tactics that were discussed earlier with respect to call buy­ ing. In the fifth tactic, the holder of a listed put who has an unrealized profit might consider buying a listed call to protect his position. Example: A speculator originally purchased an XYZ October 50 put for 2 points when the stock was 52. If the stock has now fallen to 45, the put might be worth 6 points, representing an unrealized gain of 4 points and placing the put buyer in a position to implement one of these five tactics. After some time has passed, with the stock at 45, an at-the-money October 45 put might be selling for 2 points. Table 16-3 summarizes the situation. If the trader merely liquidates his position by selling out the October 50 put, he would realize a profit of 4 points. Since he is terminating the position, he can make neither more nor less than 4 points. This is the most conservative of the tactics, allowing no additional room for appreciation, but also eliminating any chance of los­ ing the accumulated profits. TABLE 16-3. Background table for profit alternatives. Original Trade Current Prices XYZ common: 52 XYZ common: 45 Bought XYZ October 50 put at 2 XYZ October 50 put: 6 XYZ October 45 put: 2 If the trader does nothing, merely continuing to hold the October 50 put, he is taking an aggressive action. If the stock should reverse and rise back above 50 by expiration, he would lose everything. However, if the stock continues to fall, he could build up substantially larger profits. This is the only tactic that could eventually result in a loss at expiration. These two simple strategies - liquidating or doing nothing are the easiest alternatives. The remaining strategies allow one to attempt to achieve a balance between retaining built-up profits and generating even more profits. The third tactic that the speculator could use would be to sell the put that he is currently holding and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:292 SCORE: 67.00 ================================================================================ 264 Part Ill: Put Option Strategies use some of the proceeds to purchase the October 45 put. The general idea in this tactic is to pull one's initial investment out of the market and then to increase the number of option contracts held by buying the out-of-the-money option. Example: The trader would receive 6 points from the sale of the October 50 put. He should take 2 points of this amount and put it back into his pocket, thus covering his initial investment. Then he could buy 2 October 45 puts at 2 points each with the remaining portion of the proceeds from the sale. He has no risk at expiration with this strategy, since he has recovered his initial investment. Moreover, if the underlying stock should continue to fall rapidly, he could profit handsomely because he has increased the number of put contracts that he holds. The fourth choice that the put holder has is to create a spread by selling the October 45 put against the October 50 that he currently holds. This would create a bear spread, technically. This type of spread is described in more detail later. For the time being, it is sufficient to understand what happens to the trader's risks and rewards by creating this spread. The sale of the October 45 put brings in 2 points, which covers the initial 2-point purchase cost of the October 50 put. Thus, his "cost" for this spread is nothing; he has no risk, except for commissions. If the underlying stock should rise above 50 by expiration, all the puts would expire worthless. (A put expires worthless when the underlying stock is above the striking price at expiration.) This would represent the worst case; he would recover nothing from the spread. If the stock should be below 45 at expiration, he would realize the maximum potential of the spread, which is 5 points. That is, no matter how far XYZ is below 45 at expi­ ration, the October 50 put will be worth 5 points more than the October 45 put, and the spread could thus be liquidated for 5 points. His maximum profit potential in the spread situation is 5 points. This tactic would be the best one if the underlying stock stabilized near 45 until expiration. To analyze the fifth strategy that the put holder could use, it is necessary to introduce a call option into the picture. Example: With XYZ at 45, there is an October 45 call selling for 3 points. The put holder could buy this call in order to limit his risk and still retain the potential for large future profits. If the trader buys the call, he will have the following position: Long l October 50 put C b' d t 5 . t l O b 5 all - om me cos : porn s Long cto er 4 c The total combined cost of this put and call combination is 5 points - 2 points were originally paid for the put, and now 3 points have been paid for the call. No matter where the underlying stock is at expiration, this combination will be worth at least 5 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:293 SCORE: 43.00 ================================================================================ Gapter 16: Put Option Buying 265 points. For example, if XYZ is at 46 at expiration, the put will be worth 4 and the call worth l; or if XYZ is at 48, the put will be worth 2 and the call worth 3. If the stock is above 50 or below 45 at expiration, the combination will be worth more than 5 points. Thus, the trader has no risk in this combination, since he has paid 5 points for it and will be able to sell it for at least 5 points at expiration. In fact, if the underly­ ing stock continues to drop, the put will become more valuable and he could build up substantial profits. Moreover, if the underlying stock should reverse direction and climb substantially, he could still profit, because the call will then become valuable. This tactic is the best one to use if the underlying stock does not stabilize near 45, but instead makes a relatively dramatic move either up or down by expiration. The strategy of simultaneously owning both a put and a call is discussed in much greater detail in Chapter 23. It is introduced here merely for the purposes of the put buyer wanting to obtain protection of his unrealized profits. Each of these five strategies may work out to be the best one under a different set of circumstances. The ultimate result of each tactic is dependent on the direction that XYZ moves in the future. As was the case with call options, the spread tactic never turns out to be the worst tactic, although it is the best one only if the underly­ ing stock stabilizes. Tables 16-4 and 16-5 summarize the results the speculator could expect from invoking each of these five tactics. The tactics are: 1. Liquidate - sell the long put for a profit and do not reinvest. 2. Do nothing - continue to hold the long put. 3. "Roll down" - sell the long put, pocket the initial investment, and invest the remaining proceeds in out-of-the-money puts at a lower strike. 4. "Spread" - create a spread by selling the out-of-the-money put against the put already held. 5. "Combine" create a combination by buying a call at a lower strike while con­ tinuing to hold the put. TABLE 16-4. Comparison of the five tactics. By expiration, if XYZ ... Continues to fall dramatically Falls moderately further Remains relatively unchanged Rises moderately Rises substantially the best strategy was ... "Roll down" Do nothing Spread Liquidate Combine and the worst strategy was ... Liquidate Combine Combine or "roll down" "Roll down" or do nothing Do nothing ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:294 SCORE: 25.00 ================================================================================ 266 Part Ill: Put Option Strategies TABLE 16-5. Results of adopting each of the five tactics. XYZ Price at "Roll Down" Do-Nothing Spread Liquidate Combine Expiration Profit Profit Profit Profit Profit 30 + $3,000 (8) +$1,800 +$500 +$400 (W) +$1,500 35 + 2,000 (8) + 1,300 + 500 + 400 (W) + 1,000 41 + 800 (8) + 700 + 500 + 400 (W) + 400 42 + 600 (8) + 600 (8) + 500 + 400 + 300 (W) 43 + 400 + 500 (8) + 500 (8) + 400 + 200 (W) 45 0(W) + 300 + 500 (8) + 400 0(W) 46 0(W) + 200 + 400 (8) + 400 (8) O(W) 48 0(W) 0(W) + 200 + 400 (8) 0(W) 50 0 200 (W) 0 + 400 (8) 0 54 0 200 (W) 0 + 400 (8) + 400 (8) 60 0 200 (W) 0 + 400 + 1,000 (8) Note that each tactic is the best one under one of the scenarios, but that the spread tactic is never the worst of the five. The actual results of each tactic, using the figures from the example above, are depicted in Table 16-5, where B denotes best tactic and W denotes worst one. All the strategies are profitable if the underlying stock continues to fall dramat­ ically, although the "roll down," "do nothing," and combinations work out best, because they continue to accrue profits if the stock continues to fall. If the underly­ ing stock rises instead, only the combination outdistances the simplest tactic of all, liquidation. If the underlying stock stabilizes, the "do-nothing" and "spread" tactics work out best. It would generally appear that the combination tactic or the "roll-down" tactic would be the most attractive, since neither one has any risk and both could generate large profits if the stock moved substantially. The advantage for the spread was sub­ stantial in call options, but in the case of puts, the premium received for the out-of­ the-money put is not as large, and therefore the spread strategy loses some of its attractiveness. Finally, any of these tactics could be applied partially; for example, one could sell out half of a profitable long position in order to take some profits, and con­ tinue to hold the remainder. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:295 SCORE: 43.00 ================================================================================ Cl,opter 16:PutOptionBuying LOSS-LIMITING ACTIONS 267 The foregoing discussion concentrated on how the put holder could retain or increase his profit. However, it is often the case in option buying that the holder of the option is faced with an unrealized loss. The put holder may also have several choices of action to take in this case. His first, and simplest, course of action would be to sell the put and take his loss. Although this is advisable in certain cases, espe­ cially when the underlying stock seems to have assumed a distinctly bullish stance, it is not always the wisest thing to do. The put holder who has a loss may also consider either "rolling up" to create a bearish spread or entering into a calendar spread. Either of these actions could help him recover part or all of his loss. THE "ROLLING-UP" STRATEGY The reader may recall that a similar action to "rolling up," termed "rolling down," was available for call options held at a loss and was described in Chapter 3. The put buyer who owns a put at a loss may be able to create a spread that allows him to break even at a more favorable price at expiration. Such action will inevitably limit his profit potential, but is generally useful in recovering something from a put that might oth­ erwise expire totally worthless. Example: An investor initially purchases an XYZ October 45 put for 3 points when the underlying stock is at 45. However, the stock rises to 48 at a later date and the put that was originally bought for 3 points is now selling for 1 ¼ points. It is not unusual, by the way, for a put to retain this much of its value even though the stock has moved up and some amount of time has passed, since out-of-the-money puts tend to hold time value premium rather well. With XYZ at 48, an October 50 put might be selling for 3 points. The put holder could create a position designed to per­ mit recovery of some of his losses by selling two of the puts that he is long - October 45's - and simultaneously buying one October 50 put. The net cost for this transac­ tion would be only commissions, since he receives $300 from selling two puts at 1 ¼ each, which completely covers the $300 cost of buying the October 50 put. The transactions are summarized in Table 16-6. By selling 2 of the October 45 puts, the investor is now short an October 45 put. Since he also purchased an October 50 put, he has a spread ( technically, a bear spread). He has spent no additional money, except commissions, to set up this spread, since the sale of the October 45's covered the purchase of the October 50 put. This strategy is most attractive when the debit involved to create the spread is small. In this example, the debit is zero. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:296 SCORE: 48.00 ================================================================================ 268 TABLE 16-6. Summary of rolling-up transactions. Original trade: Later: Net position: Buy 1 October 45 put for 3 with XYZ at 45 With XYZ at 48, sell 2 October 45's for 11/2 each and buy l October 50 put for 3 Long 1 October 50 put Short 1 October 45 put Part Ill: Put Option Strategies $300 debit $300 credit $300 debit $300 debit The effect of creating this spread is that the investor has not increased his risk at all, but has raised the break-even point for his position. That is, if XYZ merely falls a small distance, he will be able to get out even. Without the effect of creating the spread, the put holder would need XYZ to fall back to 42 at expiration in order for him to break even, since he originally paid 3 points for the October 45 put. His orig­ inal risk was $300. IfXYZ continues to rise in price and the puts in the spread expire worthless, the net loss will still be only $300 plus additional commissions. Admittedly, the commissions for the spread will increase the loss slightly, but they are small in comparison to the debit of the position ($300). On the other hand, if the stock should fall back only slightly, to 47 by expiration, the spread will break even. At expiration, with XYZ at 47, the in-the-money October 50 put will be worth 3 points and the out­ of-the-money October 45 put will expire worthless. Thus, the investor will recover his $300 cost, except for commissions, with XYZ at 47 at expiration. His break-even point is raised from 42 to 47, a substantial improvement of his chances for recovery. The implementation of this spread strategy reduces the profit potential of the position, however. The maximum potential of the spread is 2 points. If XYZ is any­ where below 45 at expiration, the spread will be worth 5 points, since the October 50 put will sell for 5 points more than the October 45 put. The investor has limited his potential profit to 2 points - the 5-point maximum width of the spread, less the 3 points that he paid to get into the position. He can no longer gain substantially on a large drop in price by the underlying stock. This is normally of little concern to the put holder faced with an unrealized loss and the potential for a total loss. He gener­ ally would be appreciative of getting out even or of making a small profit. The cre­ ation of the spread accomplishes this objective for him. It should also be pointed out that he does not incur the maximum loss of his entire debit plus commissions, unless XYZ closes above 50 at expiration. If XYZ is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:297 SCORE: 59.00 ================================================================================ O,apter 16: Put Option Buying 269 anywhere below 50, the October 50 will have some value and the investor will be able to recover something from the position. This is distinctly different from the original put holding of the October 45, whereby the maximum loss would be incurred unless the stock were below 45 at expiration. Thus, the introduction of the spread also reduces the chances of having to realize the maximum loss. In summary, the put holder faced with an unrealized loss may be able to create a spread by selling twice the number of puts that he is currently long and simultane­ ously buying the put at the next higher strike. This action should be used only if the spread can be transacted at a small debit or, preferably, at even money (zero debit). The spread position offers a much better chance of breaking even and also reduces the possibility of having to realize the maximum loss in the position. However, the introduction of these loss-limiting measures reduces the maximum potential of the position if the underlying stock should subsequently decline in price by a significant amount. Using this spread strategy for puts would require a margin account, just as calls do. THE CALENDAR SPREAD STRATEGY Another strategy is sometimes available to the put holder who has an unrealized loss. If the put that he is holding has an intermediate-term or long-term expiration date, he might be able to create a calendar spread by selling the near-term put against the put that he currently holds. Example: An investor bought an XYZ October 45 put for 3 points when the stock was at 45. The stock rises to 48, moving in the wrong direction for the put buyer, and his put falls in value to 1 ½. He might, at that time, consider selling the near-term July 45 put for 1 point. The ideal situation would be for the July 45 put to expire worth­ less, reducing the cost of his long put by 1 point. Then, if the underlying stock declined below 45, he could profit after July expiration. The major drawback to this strategy is that little or no profit will be made - in fact, a loss is quite possible - if the underlying stock falls back to 45 or below before the near-term July option expires. Puts display different qualities in their time value premiums than calls do, as has been noted before. With the stock at 45, the differ­ ential between the July 45 put and the October 45 put might not widen much at all. This would mean that the spread has not gained anything, and the spreader has a loss equal to his commissions plus the initial unrealized loss. In the example above, ifXYZ dropped quickly back to 45, the July 45 might be worth 1 ½ and the October worth 2½. At this point, the spreader would have a loss on both sides of his spread: He sold the July 45 put for 1 and it is now 1 ½; he bought the October 45 for 3 and it is now ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:298 SCORE: 25.00 ================================================================================ 270 Part Ill: Put Option Strategies 2½; plus he has spent two commissions to date and would have to spend two more to liquidate the position. At this point, the strategist may decide to do nothing and take his chances that the stock will subsequently rally so that the July 45 put will expire worthless. However, if the stock continues to decline below 45, the spread will most certainly become more of a loss as both puts come closer to parity. This type of spread strategy is not as attractive as the "rolling-up" strategy. In the "rolling-up" strategy, one is not subjected to a loss if the stock declines after the spread is established, although he does limit his profits. The fact that the calendar spread strategy can lead to a loss even if the stock declines makes it a less desirable alternative. EQUIVALENT POSITIONS Before considering other put-oriented strategies, the reader should understand the definition of an equivalent position. Two strategies, or positions, are equivalent when they have the same profit potential. They may have different collateral or investment requirements, but they have similar profit potentials. Many of the call-oriented strategies that were discussed in Part II of the book have an equivalent put strategy. One such case has already been described: The "protected short sale," or shorting the common stock and buying a call, is equivalent to the purchase of a put. That is, both have a limited risk above the striking price of the option and relatively large profit potential to the downside. An easy way to tell if two strategies are equivalent is to see if their profit graphs have the same shape. The put purchase and the "protected short sale" have profit graphs with exactly the same shape (Figures 16-1 and 4-1, respec­ tively). As more put strategies are discussed, it will always be mentioned if the put strategy is equivalent to a previously described call strategy. This may help to clarify the put strategies, which understandably may seem complex to the reader who is not familiar with put options. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:299 SCORE: 24.00 ================================================================================ Put Buying in Conjunction with Com.m.on Stock Ownership Another useful feature of put options, in addition to their speculative leverage in a downward move by the underlying stock, is that the put purchase can be used to limit downside loss in a stock that is owned. When one simultaneously owns both the com­ mon stock and a put on that same stock, he has a position with limited downside risk during the life of the put. This position is also called a synthetic long call, because the profit graph is the same shape as a long call's. Example: An investor owns XYZ stock, which is at 52, and purchases an XYZ October 50 put for 2. The put gives him the right to sell XYZ at 50, so the most that the stock­ holder can lose on his stock is 2 points. Since he pays 2 points for the put protection, his maximum potential loss until October expiration is 4 points, no matter how far XYZ might decline up until that time. If, on the other hand, the price of the stock should move up by October, the investor would realize any gain in the stock, less the 2 points that he paid for the put protection. The put functions much like an insurance policy with a finite life. Table 17-1 and Figure 17-1 depict the results at October expiration for this position: buying the October 50 put for 2 points to protect a holding in XYZ common stock, which is selling at 52. The dashed line on the graph represents the profit poten­ tial of the common stock ownership by itself. Notice that if the stock were below 48 in October, the common stock owner would have been better off buying the put. However, with XYZ above 48 at expiration, the put purchase was a burden that cost a small por­ tion of potential profits. This strategy, however, is not necessarily geared to maximizing 211 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:300 SCORE: 16.00 ================================================================================ 272 Part Ill: Put Option Strategies TABLE 17-1. Results at expiration on a protected stock holding. XYZ Price at Stock Put Expiration Profit Profit 30 -$2,200 +$1,800 40 - 1,200 + 800 50 200 200 54 + 200 200 60 + 800 200 70 + 1,800 200 80 + 2,800 200 FIGURE 17-1. long common stock and long put. C: 0 e ·5. X w 1i'i $0 Cf) Cf) 0 ..J c5 e 0. -$400 , , , , Long ,' Stock ,, ,, ,, , , , 48 50 ,'52 , ,, , ,, , , , ,, , , , ,, Stock Price at Expiration ,, ,, ,, ,, , , Total Profit -$ 400 400 400 0 + 600 + 1,600 + 2,600 one's profit potential on the common stock, but rather provides the stock owner with protection, eliminating the possibility of any devastating loss on the stock holding during the life of the put. In all the put buying strategies discussed in this chapter and Chapter 18, the put must be paid for in full. That is the only increase in investment. Although any common stockholder may use this strategy, two general classes of stock owners find it particularly attractive: First, the long-term holder of the stock who is not considering selling the stock may utilize the put protection to limit losses over a short-term horizon. Second, the buyer of common stock who wants some "insurance" in case he is wrong may also find the put protection attractive. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:301 SCORE: 22.00 ================================================================================ Cl,apter 17: Put Buying in Conjunction with Common Stock Ownership 273 The long-term holder who strongly feels that his stock will drop should proba­ bly sell that stock. However, his cost basis may make the capital gains tax on the sale prohibitive. He also may not be entirely sure that the stock will decline - and may want to continue to hold the stock in case it does go up. In either case, the purchase of a put will limit the stockholder's downside risk while still allowing room for upside appreciation. A large number of individual and institutional investors have holdings that they might find difficult to sell for one reason or another. The purchase of a low­ cost put can often reduce the negative effects of a bear market on their holdings. The second general class of put buyers for protection includes the investor who is establishing a position in the stock. He might want to buy a put at the same time that he buys the stock, thereby creating a position with profitability as depicted in the previous profit graph. He immediately starts out with a position that has limited downside risk with large potential profits if the stock moves up. In this way, he can feel free to hold the stock during the life of the put without worrying about when to sell it if it should experience a temporary setback. Some fairly aggressive stock traders use this technique because it eliminates the necessity of having to place a stop loss order on the stock. It is often frustrating to see a stock fall and touch off one's stop loss limit order, only to subsequently rise in price.' The stock owner who has a put for protection need not overreact to a downward move. He can afford to sit back and wait during the life of the put, since he has built-in protection. WHICH PUT TO BUY The selection of which put the stock owner purchases will determine how much of his profit potential he is giving up and how much risk he is limiting. An out-of-the­ money put will cost very little. Therefore, it will be less of a hindrance on profit potential if the underlying stock rises in price. Unfortunately, the put's protective fea­ ture is small until the stock falls to the striking price of the put. Therefore, the pur­ chase of the out-ofthe-rrwney put will not provide as much downside protection as an at- or in-the-money put would. The purchase of a deeply out-of-the-money put as protection is more like "disaster insurance": It will prevent a stock owner from expe­ riencing a disaster in terms of a downside loss during the life of the put, but will not provide much protection in the case of a limited stock decline. Example: XYZ is at 40 and the October 35 put is selling for ½. The purchase of this put as protection for the common stock would not reduce upside potential much at all, only by ½ point. However, the stock owner could lose 5½ points if XYZ fell to 35 or below. That is his maximum possible loss, for if XYZ were below 35 at October expi­ ration, he could exercise his put to sell the stock at 35, losing 5 points on the stock, and he would have paid ½ point for the put, bringing his total loss to 5½ points. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:302 SCORE: 34.00 ================================================================================ 274 Part Ill: Put Option Strategies At the opposite end of the spectrum, the stock owner might buy an in-the­ money put as protection. This would quite severely limit his profit potential, since the underlying stock would have to rise above the strike and more for him to make a profit. However, the in-the-money put provides vast quantities of downside protec­ tion, limiting his loss to a very small amount. Example: XYZ is again at 40 and there is an October 45 put selling for 5½. The stock owner who purchases the October 45 put would have a maximum risk of½ point, for he could always exercise the put to sell stock at 45, giving him a 5-point gain on the stock, but he paid 5½ points for the put, thereby giving him an overall maximum loss of ½ point. He would have difficulty making any profit during the life of the put, however. XYZ would have to rise by more than 5½ points (the cost of the put) for him to make any total profit on the position by October expiration. The deep in-the-money put purchase is overly conservative and is usually not a good strategy. On the other hand, it is not wise to purchase a put that is too deeply out-of-the-money as protection. Generally, one should purchase a slightly out-ofthe­ money put as protection. This helps to achieve a balance between the positive feature of protection for the common stock and the negative feature of limiting profits. The reader may find it interesting to know that he has actually gone through this analysis, back in Chapter 3. Glance again at the profit graph for this strategy of using the put purchase to protect a common stock holding (Figure 17-1). It has exactly the same shape as the profit graph of a simple call purchase. Therefore, the call purchase and the long put/long stock strategies are equivalent. Again, by equivalent it is meant that they have similar profit potentials. Obviously, the ownership of a call differs sub­ stantially from the ownership of common stock and a put. The stock owner continues to maintain his position for an indefinite period of time, while the call holder does not. Also, the stockholder is forced to pay substantially more for his position than is the call holder, and he also receives dividends whereas the call holder does not. Therefore, "equivalent" does not mean exactly the same when comparing call-oriented and put­ oriented strategies, but rather denotes that they have similar profit potentials. In Chapter 3, it was determined that the slightly in-the-money call often offers the best ratio between risk and reward. When the call is slightly in-the-money, the stock is above the striking price. Similarly, the slightly out-of-the-money put often offers the best ratio between risk and reward for the common stockholder who is buy­ ing the put for protection. Again, the stock is slightly above the striking price. Actually, since the two positions are equivalent, the same conclusions should be arrived at; that is why it was stated that the reader has been through this analysis previously. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:303 SCORE: 39.00 ================================================================================ G,pter 17: Put Buying in Conjunction with Common Stock Ownership TAX CONSIDERATIONS 275 Although tax considerations are covered in detail in a later chapter, an important tax law concerning the purchase of puts against a common stock holding should be men­ tioned at this time. If the stock owner is already a long-term holder of the stock at the time that he buys the put, the put purchase has no effect on his tax status. Similarly, if the stock buyer buys the stock at the time that he buys the put and identifies the position as a hedge, there is no effect on the tax status of his stock. However, if one Is currently a short-tenn holder of the common stock at the time that he buys a put, he eliminates any accrued holding period on his common stock. Moreover, the hold­ ing period for that stock does not begin again until the put is sold. Example: Assume the long-term holding period is 6 months. That is, a stock owner must own the stock for 6 months before it can be considered a long-term capital gain. An investor who bought the stock and held it for 5 months and then purchased a put would wipe out his entire holding period of 5 months. Suppose he then held the put and the stock simultaneously for 6 months, liquidating the put at the end of 6 months. His holding period would start all over again for that common stock. Even though he has owned the stock for 11 months - 5 months prior to the put purchase and 6 months more while he simultaneously owned the put - his holding period for tax pur­ poses is considered to be zero! This law could have important tax ramifications, and one should consult a tax advisor if he is in doubt as to the effect that a put purchase might have on the taxability of his common stock holdings. PUT BUYING AS PROTECTION FOR THE COVERED CALL WRITER Since put purchases afford protection to the owner of common stock, some investors naturally feel that the same protective feature could be used to limit their downside risk in the covered call writing strategy. Recall that the covered call writing strategy involves the purchase of stock and the sale of a call option against that stock. The cov­ ered write has limited upside profit potential and offers protection to the downside in the amount of the call premium. The covered writer will make money if the stock falls a little, remains unchanged, or rises by expiration. The covered writer can actually lose money only if the stock falls by more than the call premium received. He has poten­ tially large downside losses. This strategy is known as a protective collar or, more sim­ ply, a "collar." (It is also called a "hedge wrapper," although that is an outdated term.) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:304 SCORE: 32.00 ================================================================================ 274 Part Ill: Put Option Strategies At the opposite end of the spectrum, the stock owner might buy an in-the­ money put as protection. This would quite severely limit his profit potential, since the underlying stock would have to rise above the stiike and more for him to make a profit. However, the in-the-money put provides vast quantities of downside protec­ tion, limiting his loss to a very small amount. Example: XYZ is again at 40 and there is an October 45 put selling for 5½. The stock owner who purchases the October 45 put would have a maximum risk of½ point, for he could always exercise the put to sell stock at 45, giving him a 5-point gain on the stock, but he paid 5½ points for the put, thereby giving him an overall maximum loss of ½ point. He would have difficulty making any profit during the life of the put, however. XYZ would have to rise by more than 5½ points (the cost of the put) for him to make any total profit on the position by October expiration. The deep in-the-money put purchase is overly conservative and is usually not a good strategy. On the other hand, it is not wise to purchase a put that is too deeply out-of-the-money as protection. Generally, one should purchase a slightly out-ofthe­ nwney put as protection. This helps to achieve a balance between the positive feature of protection for the common stock and the negative feature of limiting profits. The reader may find it interesting to know that he has actually gone through this analysis, back in Chapter 3. Glance again at the profit graph for this strategy of using the put purchase to protect a common stock holding (Figure 17-1). It has exactly the same shape as the profit graph of a simple call purchase. Therefore, the call purchase and the long put/long stock strategies are equivalent. Again, by equivalent it is meant that they have similar profit potentials. Obviously, the ovvnership of a call differs sub­ stantially from the ownership of common stock and a put. The stock owner continues to maintain his position for an indefinite period of time, while the call holder does not. Also, the stockholder is forced to pay substantially more for his position than is the call holder, and he also receives dividends whereas the call holder does not. Therefore, "equivalent" does not mean exactly the same when comparing call-oriented and put­ oriented strategies, but rather denotes that they have similar profit potentials. In Chapter 3, it was determined that the slightly in-the-money call often offers the best ratio between 1isk and reward. When the call is slightly in-the-money, the stock is above the striking price. Similarly, the slightly out-of-the-money put often offers the best ratio between risk and reward for the common stockholder who is buy­ ing the put for protection. Again, the stock is slightly above the striking price. Actually, since the two positions are equivalent, the same conclusions should be arrived at; that is why it was stated that the reader has been through this analysis previously. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:305 SCORE: 39.00 ================================================================================ 0.,,,,, I 7: Put Buying in Conjundion with Common Stock Ownership JAX CONSIDERATIONS 275 Although tax considerations are covered in detail in a later chapter, an important tax law concerning the purchase of puts against a common stock holding should be men­ tioned at this time. If the stock owner is already a long-term holder of the stock at the time that he buys the put, the put purchase has no effect on his tax status. Similarly, if the stock buyer buys the stock at the time that he buys the put and identifies the position as a hedge, there is no effect on the tax status of his stock. However, if one is currently a short-term holder of the comrrwn stock at the time that he buys a put, he eliminates any accrued holding period on his comrrwn stock. Moreover, the hold­ ing period for that stock does not begin again until the put is sold. Example: Assume the long-term holding period is 6 months. That is, a stock owner must own the stock for 6 months before it can be considered a long-term capital gain. An investor who bought the stock and held it for 5 months and then purchased a put would wipe out his entire holding period of 5 months. Suppose he then held the put and the stock simultaneously for 6 months, liquidating the put at the end of 6 months. His holding period would start all over again for that common stock. Even though he has owned the stock for 11 months - 5 months prior to the put purchase and 6 months more while he simultaneously owned the put - his holding period for tax pur­ poses is considered to be zero! This law could have important tax ramifications, and one should consult a tax advisor if he is in doubt as to the effect that a put purchase might have on the taxability of his common stock holdings. PUT BUYING AS PROTECTION FOR THE COVERED CALL WRITER Since put purchases afford protection to the owner of common stock, some investors naturally feel that the same protective feature could be used to limit their downside risk in the covered call writing strategy. Recall that the covered call writing strategy involves the purchase of stock and the sale of a call option against that stock. The cov­ ered write has limited upside profit potential and offers protection to the downside in the amount of the call premium. The covered writer will make money if the stock falls a little, remains unchanged, or rises by expiration. The covered writer can actually lose money only if the stock falls by more than the call premium received. He has poten­ tially large downside losses. This strategy is known as a protective collar or, more sim­ ply, a "collar." (It is also called a "hedge wrapper," although that is an outdated term.) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:306 SCORE: 45.00 ================================================================================ 276 Part Ill: Put Option Strategies The purchase of an out-of the-money put option can eliminate the risk of large potential losses for the covered write, although the money spent for the put purchase will reduce the overall return from the covered write. One must therefore include the put cost in his initial calculations to determine if it is worthwhile to buy the put. Example: X'YZ is at 39 and there is an XYZ October 40 call selling for 3 points and an XYZ October 35 put selling for ½ point. A covered write could be established by buy­ ing the common at 39 and selling the October 40 call for 3. This covered write would have a maximum profit potential of 4 points if XYZ were anywhere above 40 at expi­ ration. The write would lose money if XYZ were anywhere below 36, the break-even point, at October expiration. By also purchasing the October 35 put at the time the covered write is initiated, the covered writer will limit his profit potential slightly, but will also greatly reduce his risk potential. If the put purchase is added to the covered write, the maximum profit potential is reduced to 3½ points at October expiration. The break-even point moves up to 36½, and the writer will experience some loss if XYZ is below 36½ at expiration. However, the most that the writer could lose would be 1 ¼ points if XYZ were below 35 at expiration. The purchase of the put option produces this loss-limiting effect. Table 17-2 and Figure 17-2 depict the profitability of both the regular covered write and the covered write that is protected by the put purchase. Commissions should be carefully included in the covered writer's return calcula­ tions, as well as the cost of the put. It was demonstrated in Chapter 2 that the covered writer must include all commissions and margin interest expenses as well as all divi­ dends received in order to produce an accurate "total return" picture of the covered write. Figure 17-2 shows that the break-even point is raised slightly and the overall prof­ it potential is reduced by the purchase of the put. However, the maximum risk is quite small and the writer need never be forced to roll down in a disadvantageous situation. Recall that the covered writer who does not have the protective put in place is forced to roll down in order to gain increased downside protection. Rolling down merely means that he buys back the call that is currently written and writes another call, with a lower striking price, in its place. This rolling-down action can be helpful if the stock stabilizes after falling; but if the stock reverses and climbs upward in price again, the covered writer who rolled down would have limited his gains. In fact, he may even have "locked in" a loss. The writer who has the protective put need not be bothered with such things. He never has to roll down, for he has a limited maximum loss. Therefore, he should never get into a "locked-in" loss situation. This can be a great advantage, especially from an emotional viewpoint, because the writer is never forced to make a decision as to the future price of the stock in the middle of the stock's decline. With the put in place, he can feel free to take no action at all, since his overall loss is limited. If the stock should rally upward later, he will still be in a position to make his maximum profit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:307 SCORE: 9.00 ================================================================================ Chapter 17: Put Buying in Conjundion with Common Stock Ownership TABLE 17·2. Comparison of regular and protected covered writes. XYZ Price at Stock October 40 October 35 Expiration Profit Call Profit Put Profit 25 -$1,400 +$300 +$950 30 900 + 300 + 450 35 400 + 300 - 50 36.50 250 + 300 - 50 38 100 + 300 - 50 40 + 100 + 300 - 50 45 + 600 - 200 - 50 50 + 1,100 - 700 - 50 FIGURE 17-2. Covered call write protected by a put purchase. C 0 e ·5. X LU co $0 CJ) CJ) 0 .J 0 ~ -$150 a.. ,, },.,,' ; ,, Regular Covered ,,' Write/ 36 / , , ; ,,' +$400 ,----------➔ ,,,' _____ ...,.. , +$350 ,,,' 40 Stock Price at Expiration 277 Total Profit -$150 - 150 - 150 0 + 150 + 350 + 350 + 350 The longer-term effects of buying puts in combination with covered writes are not easily definable, but it would appear that the writer reduces his overall rate of return slightly by buying the puts. This is because he gives something away if the stock falls slightly, remains unchanged, or rises in price. He only "gains" something if the stock falls heavily. Since the odds of a stock falling heavily are small in compari­ son to the other events (falling slightly, remaining unchanged, or rising), the writer will be gaining something in only a small percentage of cases. However, the put buy­ ing strategy may still prove useful in that it removes the emotional uncertainty of ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:308 SCORE: 34.00 ================================================================================ 278 Part Ill: Put Option Strategies large losses. The covered writer who buys puts may often find it easier to operate in a more rational manner when he has the protective put in place. This strategy is equivalent to one that has been described before, the bull spread. Notice that the profit graph in Figure 17-2 has the same shape as the bull spread profit graph (Figure 7-1). This means that the two strategies are equivalent. In fact, in Chapter 7 it was pointed out that the bull spread could sometimes be con­ sidered a "substitute" for covered writing. Actually, the bull spread is more akin to this strategy - the covered write protected by a put purchase. There are, of course, differences between the strategies. They are equivalent in profit and loss potential, but the covered writer could never lose all his investment in a short period of time, although the spreader could. In order to actually use bull spreads as substitutes for covered writes, one would invest only a small portion of his available funds in the spread and would place the remainder of his funds in fixed-income securities. That strategy was discussed in more depth in Chapter 7. NO-COST COLLARS The "collar" strategy is often arrived at in another manner: a stockholder begins to worry about the downside potential of the stock market and decides to buy puts on his stock as protection. However, he is dismayed by the cost of the puts and so he also considers the sale of calls. If he buys an out-of-the-money put, it is quite possi­ ble that he might be able to sell an out-of-the-money call whose proceeds complete­ ly cover the cost of the put. Thus, he has established a protective collar at no cost - at least no debit. His "cost" is the fact that he has forsaken the upside profit poten­ tial on his stock, above the striking price of the written call. In fact, certain large institutional traders are able to transact collars through large over-the-counter option brokers, such as Goldman Sachs or Morgan Stanley. They might even give the broker instructions such as this: "I own XYZ and I want to buy a put 10 percent out of the money that expires in a year. What would the strik­ ing price of a one-year call have to be in order to create a no-cost collar?" The bro­ ker might then tell him that such a call would have to be struck 30 percent out of the money. The actual strike price of the call would depend on the volatility estimate for the underlying stock, as well as interest rates and dividends. These types of transac­ tions occur with a fair amount of frequency. Some very interesting situations can be created with long-term options. One of the most interesting occurred in 1999, when a company that owned 5 million shares of Cisco ( CSCO) decided it would like to hedge them by creating a no-cost collar over the next three years. At the time, CSCO was trading at about 130, and its volatil­ ity was about 50%. It turns out that a three-year put struck at 130 sells for about the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:309 SCORE: 34.00 ================================================================================ 278 Part Ill: Put Option Strategies large losses. The covered writer who buys puts may often find it easier to operate in a more rational manner when he has the protective put in place. This strategy is equivalent to one that has been described before, the bull spread. Notice that the profit graph in Figure 17-2 has the same shape as the bull spread profit graph (Figure 7-1). This means that the two strategies are equivalent. In fact, in Chapter 7 it was pointed out that the bull spread could sometimes be con­ sidered a "substitute" for covered writing. Actually, the bull spread is more akin to this strategy- the covered write protected by a put purchase. There are, of course, differences between the strategies. They are equivalent in profit and loss potential, but the covered writer could never lose all his investment in a short period of time, although the spreader could. In order to actually use bull spreads as substitutes for covered writes, one would invest only a small portion of his available funds in the spread and would place the remainder of his funds in fixed-income securities. That strategy was discussed in more depth in Chapter 7. NO-COST COLLARS The "collar" strategy is often arrived at in another manner: a stockholder begins to worry about the downside potential of the stock market and decides to buy puts on his stock as protection. However, he is dismayed by the cost of the puts and so he also considers the sale of calls. If he buys an out-of-the-money put, it is quite possi­ ble that he might be able to sell an out-of-the-money call whose proceeds complete­ ly cover the cost of the put. Thus, he has established a protective collar at no cost - at least no debit. His "cost" is the fact that he has forsaken the upside profit poten­ tial on his stock, above the striking price of the written call. In fact, certain large institutional traders are able to transact collars through large over-the-counter option brokers, such as Goldman Sachs or Morgan Stanley. They might even give the broker instructions such as this: "I own XYZ and I want to buy a put 10 percent out of the money that e.:\.J)ires in a year. What would the strik­ ing price of a one-year call have to be in order to create a no-cost collar?" The bro­ ker might then tell him that such a call would have to be struck 30 percent out of the money. The actual strike price of the call would depend on the volatility estimate for the underlying stock, as well as interest rates and dividends. These types of transac­ tions occur with a fair amount of frequency. Some very interesting situations can be created with long-term options. One of the most interesting occurred in 1999, when a company that owned 5 million shares of Cisco (CSCO) decided it would like to hedge them by creating a no-cost collar over the next three years. At the time, CSCO was trading at about 130, and its volatil­ ity was about 50%. It turns out that a three-year put struck at 130 sells for about the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:310 SCORE: 34.00 ================================================================================ 278 Part Ill: Put Option Strategies large losses. The covered writer who buys puts may often find it easier to operate in a more rational manner when he has the protective put in place. This strategy is equivalent to one that has been described before, the bull spread. Notice that the profit graph in Figure 17-2 has the same shape as the bull spread profit graph (Figure 7-1). This means that the two strategies are equivalent. In fact, in Chapter 7 it was pointed out that the bull spread could sometimes be con­ sidered a "substitute" for covered writing. Actually, the bull spread is more akin to this strategy - the covered write protected by a put purchase. There are, of course, differences between the strategies. They are equivalent in profit and loss potential, but the covered writer could never lose all his investment in a short period of time, although the spreader could. In order to actually use bull spreads as substitutes for covered ,vrites, one would invest only a small portion of his available funds in the spread and would place the remainder of his funds in fixed-income securities. That strategy was discussed in more depth in Chapter 7. NO-COST COLLARS The "collar" strategy is often arrived at in another manner: a stockholder begins to worry about the downside potential of the stock market and decides to buy puts on his stock as protection. However, he is dismayed by the cost of the puts and so he also considers the sale of calls. If he buys an out-of-the-money put, it is quite possi­ ble that he might be able to sell an out-of-the-money call whose proceeds complete­ ly cover the cost of the put. Thus, he has established a protective collar at no cost - at least no debit. His "cost" is the fact that he has forsaken the upside profit poten­ tial on his stock, above the striking price of the written call. In fact, certain large institutional traders are able to transact collars through large over-the-counter option brokers, such as Goldman Sachs or Morgan Stanley. They might even give the broker instructions such as this: "I own XYZ and I want to buy a put 10 percent out of the money that expires in a year. What would the strik­ ing p1ice of a one-year call have to be in order to create a no-cost collar?" The bro­ ker might then tell him that such a call would have to be struck 30 percent out of the money. The actual strike price of the call would depend on the volatility estimate for the underlying stock, as well as interest rates and dividends. These types of transac­ tions occur with a fair amount of frequency. Some very interesting situations can be created with long-term options. One of the most interesting occurred in 1999, when a company that owned 5 million shares of Cisco ( CSCO) decided it would like to hedge them by creating a no-cost collar over the next three years. At the time, CSCO was trading at about 130, and its volatil­ ity was about 50%. It turns out that a three-year put struck at 130 sells for about the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:311 SCORE: 33.00 ================================================================================ Cltapter 17: Put Buying in Conjunction with Common Stock Ownership TABLE 17-3. Highest Call Strike That Pays for an At-the-Money Put (Assuming 2.5 years to expiration) Volatility Coll Strike 30% 40% 50% 70% 100% of Underlying 30% out of money 35% out of money 40% out of money 50% out of money 70% out of money 279 same price as a three-year call struck at 200! That may seem illogical, but the figures can be checked out with the aid of an option-pricing model. Thus, this company was able to hedge all of its CSCO stock, with no downside risk ( the striking price of the puts was the same as the current stock price) and still had profit potential of over 50% to the upside over the next three years. Thus, one should consider using LEAPS options when he establishes a collar - even ifhe is not an institutional trader - because the striking price of the calls can be quite high in comparison to that of the put' s strike or in comparison to the price of the underlying stock. Table 17-3 shows how far out-of-the-money a written call could be that still covers the cost of buying an at-the-money put. The time to expiration in this table is 2.5 years - the longest term listed option that currently exists as a LEAPS option. USING LOWER STRIKES AS A PARTIAL COVERED WRITE It should also be pointed out that one does not necessarily have to forsake all of the profit potential from his stock. He might buy the puts, as usual, and then sell calls with a somewhat lower strike than needed for a low-cost collar, but the quantity of calls sold would be less than that of stock owned. In that way, there would be unlim­ ited profit potential on some of the shares of the underlying stock. Example: Suppose that the following prices exist: XYZ:61 Apr 55 put: 1 Apr 65 call: 2 Furthermore, suppose that one owns 1000 shares of XYZ. Thus, the purchase of 10 Apr 55 puts at 1 point apiece would protect the downside. In order to cover the cost of those puts ($1000), one need only sell five of the Apr 65 calls at 2 points ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:312 SCORE: 23.00 ================================================================================ 280 Part Ill: Put Option Strategies apiece. Thus, the protection would have cost nothing and there would still be unlim­ ited profit potential on 500 of the shares of XYZ, since only five calls were sold against the 1000 shares that are owned. In this manner, one could get quite creative in constructing collars - deciding what call strike to use in order to strike a balance between paying for the puts and allowing upside profit potential. The lower the strike he uses for the written calls, the fewer calls he will have to write; the higher the strike of the written calls, the more calls will be necessary to cover the cost of the purchased puts. The tradeoff is that a lower call strike allows for more eventual upside profit potential, but it limits what has been written against to a lower price. Using the above example once again, these facts can be demonstrated: Example (continued): As before, the same prices exist, but now one more call will be brought into the picture: XYZ: 61 Apr55 put: l Apr 65 call: 2 Apr 70 call: l As before one could sell five of the Apr 65 calls to cover the cost of ten puts, or as an alternative he could sell ten of the Apr 70 calls. If he sells the five, he has unlim­ ited profit potential on 500 shares, but the other 500 shares will be called away at 65. In the alternative strategy, he has limited upside profit potential, but nothing will be called away until the stock reaches 70. Which is "better?" It's not easy to say. In the former strategy, if the stock climbs all the way to 75, it results in the same profit as if the stock is called away at 70 in the latter strategy. This is true because 500 shares would be worth 75, but the other 500 would have been called away at 65 - making for an average of 70. Hence, the former strategy only outperforms the latter if the stock actually climbs above 75 - a rather unlikely event, one would have to surmise. Still, many investors prefer the former strategy because it gives them protection with­ out asking them to surrender all of their upside profit potential. In summary, one can often be quite creative with the "collar" strategy. One thing to keep in mind: if one sells options against stock that he has no intention of selling, he is actually writing naked calls in his ovm mind. That is, if one owns stock that "can't" be sold - perhaps the capital gains would be devastating or the stock has been "in the family" for a long time - then he should not sell covered calls against it, because he will be forced into treating the calls as naked (if he refuses to sell the stock). This can cause quite a bit of consternation if the underlying stock rises significantly in price, that could have easily been avoided by not writing calls against the stock in the first place. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:313 SCORE: 29.00 ================================================================================ CHAPCIJER 18 Buying Puts in Conjunction with Call Purchases There are several ways in which the purchases of both puts and calls can be used to the speculator's advantage. One simple method is actually a follow-up strategy for the call buyer. If the stock has advanced and the call buyer has a profit, he might con­ sider buying a put as a means of locking in his call profits while still allowing for more potential upside appreciation. In Chapter 3, four basic alternatives were listed for the call buyer who had a profit: He could liquidate the call and take his profit; he could do nothing; he could "roll up" by selling the call for a profit and using part of the pro­ ceeds to purchase more out-of-the-money calls; or he could create a bull spread by selling the out-of-the-money call against the profitable call that he holds. If the underlying stock has listed puts, he has another alternative: He could buy a put. This put purchase would serve to lock in some of the profits on the call and would still allow room for further appreciation if the stock should continue to rise in price. Example: An investor initially purchased an XYZ October 50 call for 3 points when the stock was at 48. Sometime later, after the stock had risen to 58, the call would be worth about 9 points. If there was an October 60 put, it might be selling for 4 points, and the call holder could buy this put to lock in some of his profits. His position, after purchasing the put, would be: Long l October 50 call at 3 points N t t 7 • t - e cos: pom s Long l October 60 put at 4 points He would own a "strangle" - any position consisting of both a put and a call with dif­ fering terms - that is always worth at least 10 points. The combination will be worth exactly 10 points at expiration if XYZ is anywhere between 50 and 60. For example, 281 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:314 SCORE: 51.00 ================================================================================ 282 Part Ill: Put Option Strategies if xyz is at 52 at expiration, the call will be worth 2 points and the put will be wort Ii 8 points. Alternatively, if the stock is at 58 at expiration, the put will be worth 2 points and the call worth 8 points. Should xyz be above 60 at expiration, the combination's value will be equal to the call's value, since the put will expire worthless with XYZ above 60. The call would have to be worth more than 10 points in that case, since it has a striking price of 50. Similarly, if xyz were below 50 at expiration, the combi­ nation would be worth more than 10 points, since the put would be more than 10 points in-the-money and the call would be worthless. The speculator has thus created a position in which he cannot lose money, because he paid only 7 points for the combination (3 points for the call and 4 points for the put). No matter what happens, the combination will be worth at least 10 points at e:x-piration, and a 3-point profit is thus locked in. If xyz should continue to climb in price, the speculator could make more than 3 points of profit whenever xyz is above 60 at expiration. Moreover, if xyz should suddenly collapse in price, the speculator could make more than 3 points of profit if the stock was below 50 by expi­ ration. The reader must realize that such a position can never be created as an initial position. This desirable situation arose only because the call had built up a substan­ tial profit before the put was purchased. The similar strategy for the put buyer who might buy a call to protect his unrealized put profits was described in Chapter 16. STRADDLE BUYING A straddle purchase consists of buying both a put and a call with the same terms - sarne underlying stock, striking price, and expiration date. The straddle purchase allows the buyer to make large potential profits if the stock moves far enough in either direction. The buyer has a predetermined maximum loss, equal to the amount of his initial investment. Example: The following prices exist: xyz common, 50; XYZ July 50 call, 3; and XYZ July 50 put, 2. If one purchased both the July 50 call and the July 50 put, he would be buying a straddle. This would cost 5 points plus commissions. The investment required to purchase a straddle is the net debit. If the underlying stock is exactly at 50 at expi­ ration, the buyer would lose all his investment, since both the put and the call would expire worthless. If the stock were above .55 at expiration, the call portion of the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:315 SCORE: 73.00 ================================================================================ 18: Buying Puts in Conjundion with Call Purchases 283 dle would be worth more than 5 points and the straddle buyer would make y, even though his put expired worthless. To the downside, a similar situation Mists. If XYZ were below 45 at expiration, the put would be worth more than 5 points and he would have a profit despite the fact that the call expired worthless. Table 18-1 and Figure 18-1 depict the results of this example straddle purchase at expiration. The straddle buyer can immediately determine his break-even points at expiration - 45 and 55 in this example. He will lose money if the underlying stock is between those break-even points at expiration. He has potentially large profits if XYZ should move a great distance away from 50 by expiration. One would normally purchase a straddle on a relatively volatile stock that has the potential to move far enough to make the straddle profitable in the allotted time. This strategy is particularly attractive when option premiums are low, since low pre­ miums will mean a cheaper straddle cost. Although losses may occur in a relatively large percentage of cases that are held all the way until their expiration date, there is actually only a minute probability of losing one's entire investment. Even if XYZ should be at 50 at expiration, there would still be the opportunity to sell the straddle for a small amount on the final day of trading. TABLE 18-1. Results of straddle purchase at expiration. XYZ Price at Total Straddle Expiration Coll Profit Put Profit Profit 30 -$ 300 +$1,800 + $1,500 40 300 + 800 + 500 45 300 + 300 0 50 300 200 500 55 + 200 200 0 60 + 700 200 + 500 70 + 1,700 200 + 1,500 EQUIVALENCES Straddle buying is equivalent to the reverse hedge, a strategy described in Chapter 4 in which one sells the underlying stock short and purchases two calls on the under­ lying stock. Both strategies have similar profit characteristics: a limited loss that would occur at the striking price of the options involved, and potentially large prof­ its if the underlying stock should rise or fall far enough in price. The straddle pur- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:316 SCORE: 44.00 ================================================================================ 284 FIGURE 18-1. Straddle purchase. C: .Q I!! ·a. X w ro $0 en en 0 ..J 0 -e a.. -$500 Part Ill: Put Option Strategies Stock Price at Expiration chase is superior to the reverse hedge, however, and where listed puts exist on a stock, the reverse hedge strategy becomes obsolete. The reasons that the straddle purchase is superior are that dividends are not paid by the holder and that commission costs are much smaller in the straddle situation. REVERSE HEDGE WITH PUTS A third strategy is equivalent to both the straddle purchase and the reverse hedge. It consists of buying the underlying stock and buying two put options. If the stock rises substantially in price, large profits will accrue, for the stock profit will more than offset the fixed loss on the purchase of two put options. If the stock declines in price by a large amount, profits will also be generated. In a decline, the profits gen­ erated by 2 long puts will more than offset the loss on 100 shares of long stock. This form of the straddle purchase has limited risk as well. The worst case would occur if the stock were exactly at the striking price of the puts at their expiration date - the puts would both expire worthless. The risk is limited, percentagevvise and dollar­ wise, since the cost of two put options would normally be a relatively small per­ centage of the total cost of buying the stock. Furthermore, the investor may receive some dividends if the underlying stock is a dividend-paying stock. Buying stock and buying two puts is superior to the reverse hedge strategy, but is still inferior to the straddle purchase. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:317 SCORE: 63.00 ================================================================================ ter 18: Buying Puts in Conjunction with Call Purchases IILECTING A STRADDLE BUY 285 In theory, one could find the best straddle purchases by applying the analyses for best call purchases and best put purchases simultaneously. Then, if both the puts and calls on a particular stock showed attractive opportunity, the straddle could be bought. The straddle should be viewed as an entire position. A similar sort of analysis to that proposed for either put or call purchases could be used for straddles as well. First, one would assume the stock would move up or down in accordance with its volatili­ ty within a fixed time period, such as 60 or 90 days. Then, the prices of both the put and the call could be predicted for this stock movement. The straddles that off er the best reward opportunity under this analysis would be the most attractive ones to buy. To demonstrate this sort of analysis, the previous example can be utilized again. Example: XYZ is at 50 and the July 50 call is selling for 3 while the July 50 put is sell­ ing for 2 points. If the strategist is able to determine that XYZ has a 25% chance of being above 54 in 90 days and also has a 25% chance of being below 46 in 90 days, he can then predict the option prices. A rigorous method for determining what per­ centage chance a stock has of making a predetermined price movement is presented in Chapter 28 on mathematical applications. For now, a general procedure of analy­ sis is more important than its actual implementation. If XYZ were at 54 in 90 days, it might be reasonable to assume that the call would be worth 5½ and the put would be worth 1 point. The straddle would therefore be worth 6½ points. Similarly, if the stock were at 46 in 90 days, the put might be worth 4½ points, and the call worth 1 point, making the entire straddle worth 5½ points. It is fairly common for the strad­ dle to be higher-priced when it is a fixed distance in-the-money on the call side (such as 4 points) than when it is in-the-money on the put side by that same distance. In this example, the strategist has now determined that there is a 25% chance that the straddle will be worth 6½ points in 90 days on an upside movement, and there is a 25% chance that the straddle will be worth 5½ points on a downside movement. The average price of these two expectations is 6 points. Since the straddle is currently sell­ ing for 5 points, this would represent a 20% profit. If all potential straddles are ranked in the same manner - allowing for a 25% chance of upside and downside movement by each underlying stock - the straddle buyer will have a common basis for comparing various straddle opportunities. FOLLOW-UP ACTION It has been mentioned frequently that there is a good chance that a stock will remain relatively unchanged over a short time period. This does not mean that the stock will ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:318 SCORE: 47.00 ================================================================================ 286 Part Ill: Put Option Strategies never move much one way or the other, but that its net movement over the time peri­ od will generally be small. Example: If XYZ is currently at 50, one might say that its chances of being over .5.5 at the end of 90 days are fairly small, perhaps 30%. This may even be supported by mathematical analysis based on the volatility of the underlying stock. This does not imply, however, that the stock has only a 30% chance of ever reaching 55 during the 90-day period. Rather, it implies that it has only a 30% chance of being over 55 at the end of the 90-day period. These are two distinctly different events, with different probabilities of occurrence. Even though the probability of being over 55 at the end of 90 days might be only 30%, the probability of ever being over 55 during the 90- day period could be amazingly high, perhaps as high as 80%. It is important for the straddle buyer to understand the differences between these events occurring, for he might often be able to take follow-up action to improve his position. Many times, after a straddle is bought, the underlying stock will begin to move strongly, making it appear that the straddle is immediately going to become prof­ itable. However, just as things are going well, the stock reverses and begins to change direction, perhaps so quickly that it would now appear that the straddle will become profitable on the other side. These volatile stock movements often result in little net change, however, and at expiration the straddle buyer may have a loss. One might think that he would take profits on the call side when they became available in a quick upward movement, and then hope for a downward reversal so that he could take profits on the put side as well. Taking small profits, however, is a poor strategy. Straddle buying has limited losses and potentially unlimited profits. One might have to suffer through a substantial number of small losses before hitting a big winner, but the magnitude of the gain on that one large stock movement can offset many small losses. By taking small profits, the straddle buyer is immediately cutting off his chances for a substantial gain; that is why it is a poor strategy to limit the profits. This is one of those statements that sounds easier in theory than it is in practice. It is emotionally distressing to watch the straddle gain 2 or 3 points in a short time period, only to lose that and more when the stock fails to follow through. By using a different example, it is possible to demonstrate the types of follow-up action that the straddle buyer might take. Example: One had initially bought an XYZ January 40 straddle for 6 points when the stock was 40. After a fairly short time, the stock jumps up to 45 and the following prices exist: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:319 SCORE: 76.00 ================================================================================ Cl,apter 18: Buying Puts in Conjunction with Call Purchases XYZ common, 45: XYZ January 40 call, 7; XYZ January 40 put, l; and XYZ January 45 put, 3. 287 The straddle itself is now worth 8 points. The January 45 put price is included because it will be part of one of the follow-up strategies. What could the straddle buyer do at this time? First, he might do nothing, preferring to let the straddle run its course, at least for three months or so. Assuming that he is not content to sit tight, however, he might sell the call, taking his profit, and hope for the stock to then drop in price. This is an inferior course of action, since he would be cutting off potential large profits to the upside. In the older, over-the-counter option market, one might have tried a technique known as trading against the straddle. Since there was no secondary market for over-the-counter options, straddle buyers often traded the stock itself against the straddle that they owned. This type of follow-up action dictated that, if the stock rose enough to make the straddle profitable to the upside, one would sell short the underlying stock. This involved no extra risk, since if the stock continued up, the straddle holder could always exercise his call to cover the short sale for a profit. Conversely, if the underlying stock fell at the outset, making the straddle profitable to the downside, one would buy the underlying stock. Again, this involved no extra risk if the stock continued down, since the put could always be exercised to sell the stock at a profit. The idea was to be able to capitalize on large stock price reversals with the addition of the stock position to the straddle. This strategy worked best for the brokers, who made numerous commissions as the trader tried to gauge the whipsaws in the market. In the listed options market, the same strategic effect can be realized ( without as large a commission expense) by merely selling out the long call on an upward move, and using part of the proceeds to buy a second put similar to the one already held. On a downside move, one could sell out the long put for a profit and buy a second call similar to the one he already owns. In the example above, the call would be sold for 7 points and a second January 40 put purchased for 1 point. This would allow the straddle buyer to recover his initial 6-point cost and would allow for large downside profit potential. This strategy is not recommended, however, since the straddle buyer is limiting his profit in the direction that the stock is moving. Once the stock has moved from 40 to 45, as in this example, it would be more reasonable to expect that it could continue up rather than experience a drop of more than 5 points. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:320 SCORE: 56.00 ================================================================================ 288 Part Ill: Put Option Strategies A rrwre desirable sort off allow-up action would be one whereby the straddle buyer could retain much of the profit already built up without limiting further poten­ tial profits if the stock continues to run. In the example above, the straddle buyer could use the January 45 put - the one at the higher price - for this purpose. Example: Suppose that when the stock got to 45, he sold the put that he owned, the January 40, for 1 point, and simultaneously bought the January 45 put for 3 points. This transaction would cost 2 points, and would leave him in the following position: Long 1 January 40 call C b· d t 8 . t - om me cos : porn s Long 1 January 45 put He now owns a combination at a cost of 8 points. However, no matter where the underlying stock is at expiration, this combination will be worth at least 5 points, since the put has a striking price 5 points higher than the call's striking price. In fact, if the stock is above 45 at expiration or is below 40 at expiration, the straddle will be worth more than 5 points. This follow-up action has not limited the potential profits. If the stock continues to rise in price, the call will become more and more valuable. On the other hand, if the stock reverses and falls dramatically, the put will become quite valuable. In either case, the opportunity for large potential profits remains. Moreover, the investor has improved his risk exposure. The most that the new posi­ tion can lose at expiration is 3 points, since the combination cost 8 points originally, and can be sold for 5 points at worst. To summarize, if the underlying stock moves up to the ne:t"t strike, the straddle buyer should consider rolling his put up, selling the one that he is long and buying the one at the next higher striking price. Conversely, if the stock starts out with a downward move, he should consider rolling the call down, selling the one that he is long and buying the one at the next lower strike. In either case, he reduces his risk exposure without limiting his profit potential - exactly the type of follow-up result that the straddle buyer should be aiming for. BUYING A STRANGLE A strangle is a position that consists of both a put and a call, which generally have the same expiration date, but different striking prices. The fallowing example depicts a strangle. Example: One might buy a strangle consisting of an XYZ January 45 put and an XYZ January 50 call. Buying such a strangle is quite similar to buying a straddle, although ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:321 SCORE: 94.00 ================================================================================ O.,,ter 18: Buying Puts in Conjunction with Call Purchases 289 there are some differences, as the following discussion will demonstrate. Suppose the following prices exist: XYZ common, 47; XYZ January 45 put, 2; and XYZ January 50 call, 2. In this example, both options are out-of-the-money when purchased. This, again, is the most normal application of the strangle purchase. If XYZ is still between 45 and 50 at January expiration, both options will expire worthless and the strangle buyer will lose his entire investment. This investment - $400 in the example - is generally smaller than that required to buy a straddle on XYZ. If XYZ moves in either direc­ tion, rising above 50 or falling below 45, the strangle will have some value at expira­ tion. In this example, ifXYZ is above 54 at expiration, the call will be worth more than 4 points (the put will expire worthless) and the buyer will make a profit. In a similar manner, if XYZ is below 41 at expiration, the put will have a value greater than 4 points and the buyer would make a profit in that case as well. The potential profits are quite large if the underlying stock should nwve a great deal before the options expire. Table 18-2 and Figure 18-2 depict the potential profits or losses from this position at January expiration. The maximum loss is possible over a much wider range than that of a straddle. The straddle achieves its maximum loss only if the stock is exactly at the striking price of the options at expiration. However, the strangle has its maximum loss anywhere between the two strikes at expiration. The actual amount of the loss is smaller for the strangle, and that is a compensating factor. The potential profits are large for both strategies. The example above is one in which both options are out-of-the money. It is also possible to construct a very similar position by utilizing in-the-money options. Example: With XYZ at 47 as before, the in-the-money options might have the fol­ lowing prices: XYZ January 45 call, 4; and XYZ January 50 put, 4. If one purchased this in-the-rrwney strangle, he would pay a total cost of 8 points. However, the value of this strangle will always be at least 5 points, since the striking price of the put is 5 points higher than that of the call. The reader has seen this sort of position before, when protective follow-up strategies for straddle buying and for call or put buying were described. Because the strangle will always be worth at least 5 points, the most that the in-the-money strangle buyer can lose is 3 points in this example. His poten­ tial profits are still unlimited should the underlying stock move a large distance. Thus, even though it requires a larger initial investment, the in-the-rrwney strangle may often be a superior strategy to the out-of the-rrwney strangle, from a buyer's ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:322 SCORE: 29.00 ================================================================================ 290 TABLE 18-2. Results at expiration of a strangle purchase. XYZ Price at Expiration 25 35 41 43 45 47 50 54 60 70 FIGURE 18-2. Strangle purchase. C: 0 ~ ·c. X w 1ii (/) $0 (/) 0 ..J 6 il= -$400 e a. Put Call Profit Profit +$1,800 -$ 200 + 800 200 + 200 200 0 200 200 200 200 200 200 200 200 + 200 200 + 800 200 + 1,800 Stock Price at Expiration Part Ill: Put Option Strategies Total Profit +$1,600 + 600 0 200 400 400 400 0 + 600 + 1,600 viewpoint. The in-the-money strangle purchase certainly involves less percentage risk: The buyer can never lose all his investment, since he can always get back 5 points, even in the worst case (when XYZ is behveen 45 and 50 at expiration). His percentage profits are lower with the in-the-money strangle purchase, since he paid more for the strangle to begin with. These observations should come as no surprise, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:323 SCORE: 59.00 ================================================================================ \O.,ter 18: Buying Puts in Conjunction with Call Purchases 291 since when the outright purchase of a call was discussed, it was shown that the purchase of an in-the-money call was more conservative than the purchase of an out­ of-the-money call, in general. The same was true for the outright purchase of puts, perhaps even more so, because of the smaller time value of an in-the-money put. Therefore, the strangle created by the two an in-the-money call and an in-the­ money put - should be more conservative than the out-of-the-money strangle. If the underlying stock moves quickly in either direction, the strangle buyer may sometimes be able to take action to protect some of his profits. He would do so in a manner similar to that described for the straddle buyer. For example, if the stock moved up quickly, he could sell the put that he originally bought and buy the put at the next higher striking price in its place. If he had started from an out-of-the-money strangle position, this would then place him in a straddle. The strategist should not blindly take this sort of follow-up action, however. It may be overly expensive to "roll up" the put in such a manner, depending on the amount of time that has passed and the actual option prices involved. Therefore, it is best to analyze each situation on a case-by-case basis to see whether it is logical to take any follow-up action at all. As a final point, the out-of-the-money strangles may appear deceptively cheap, both options selling for fractions of a point as expiration nears. However, the proba­ bility of realizing the maximum loss equal to one's initial investment is fairly large with strangles. This is distinctly different from straddle purchases, whereby the prob­ ability of losing the entire investment is small. The aggressive speculator should not place a large portion of his funds in out-of-the-money strangle purchases. The per­ centage risk is smaller with the in-the-money strangle, being equal to the amount of time value premium paid for the options initially, but commission costs will be some­ what larger. In either case, the underlying stock still needs to move by a relatively large amount in order for the buyer to profit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:324 SCORE: 27.00 ================================================================================ CH.APTER 19 The Sale of a Put The buyer of a put stands to profit if the underlying stock drops in price. As might then be expected, the seller of a put will make money if the underlying stock increas­ es in price. The uncovered sale of a put is a more common strategy than the covered sale of a put, and is therefore described first. It is a bullishly-oriented strategy. THE UNCOVERED PUT SALE Since the buyer of a put has a right to sell stock at the striking price, the writer of a put is obligating himself to buy that stock at the striking price. For assuming this obli­ gation, he receives the put option premium. If the underlying stock advances and the put expires worthless, the put writer will not be assigned and he could make a maxi­ mum profit equal to the premium received. He has large downside risk, since the stock could fall substantially, thereby increasing the value of the written put and caus­ ing large losses to occur. An example will aid in explaining these general statements about risk and reward. Example: XYZ is at 50 and a 6-month put is selling for 4 points. The naked put writer has a fixed potential profit to the upside - $400 in this example and a large poten­ tial loss to the downside (Table 19-1 and Figure 19-1). This downside loss is limited only by the fact that a stock cannot go below zero. The collateral requirement for writing naked puts is the same as that for writ­ ing naked calls. The requirement is equal to 20% of the current stock price plus the put premium minus any out-of-the-money amount. Example: If XYZ is at 50, the collateral requirement for writing a 4-point put with a striking price of 50 would be $1,000 (20% of 5,000) plus $400 for the put premium 292 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:325 SCORE: 28.00 ================================================================================ Cl,opter 19: The Sale of a Put TABLE 19-1. Results from the sale of an uncovered put. XYZ Price at Put Price at Expiration Expiration (Parity) 30 20 40 10 46 4 50 0 60 0 70 0 f IGURE 19-1. Uncovered sale of a put. $400 C 0 ~ ·5. X w 'lii (/l $0 (/l .3 50 0 ~ a. Stock Price at Expiration 293 Put Sale Profit -$1,600 600 0 + 400 + 400 + 400 for a total of $1,400. If the stock were above the striking price, the striking price dif­ forential would be subtracted from the requirement. The minimum requirement is I 0% of the put' s striking price, plus the put premium, even if the computation above yields a smaller result. The uncovered put writing strategy is similar in many ways to the covered call writing strategy. Note that the profit graphs have the same shape; this means that the two strategies are equivalent. It may be helpful to the reader to describe the aspects of naked put writing by comparing them to similar aspects of covered call writing. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:326 SCORE: 117.00 ================================================================================ 294 Part Ill: Put Option Strategies In either strategy, one needs to be somewhat bullish, or at least neutral, on the underlying stock. If the underlying stock moves upward, the uncovered put writer will make a profit, possibly the entire amount of the premium received. If the under­ lying stock should be unchanged at expiration - a neutral situation - the put writer will profit by the amount of the time value premium received when he initially wrote the put. This could represent the maximum profit if the put was out-of-the-money initially, since that would mean that the entire put premium was composed of time value premium. For an in-the-money put, however, the time value premium would represent something less than the entire value of the option. These are similar qual­ ities to those inherent in covered call writing. If the stock moves up, the covered call writer can make his maximum profit. However, if the stock is unchanged at expira­ tion, he will make his maximum profit only if the stock is above the call's striking price. So, in either strategy, if the position is established with the stock above the striking price, there is a greater probability of achieving the maximum profit. This represents the less aggressive application: writing an out-of-the-money put initially, which is equivalent to the covered write of an in-the-money call. The more aggressive application of naked put writing is to write an in-the­ money put initially. The writer will receive a larger amount of premium dollars for the in-the-money put and, if the underlying stock advances far enough, he will thus make a large profit. By increasing his profit potential in this manner, he assumes more risk. If the underlying stock should fall, the in-the-money put writer will lose money more quickly than one who initially wrote an out-of-the-money put. Again, these facts were demonstrated much earlier with covered call writing. An in-the­ money covered call write affords more downside protection but less profit potential than does an out-of-the-money covered call write. It is fairly easy to summarize all of this by noting that in either the naked put writing strategy or the covered call writing strategy, a less aggressive position is estab­ lished when the stock is higher than the striking price of the written option. If the stock is below the striking price initially, a more aggressive position is created. There are, of course, some basic differences between covered call writing and naked put writing. First, the naked put write will generally require a smaller invest­ ment, since one is only collateralizing 20% of the stock price plus the put premium, as opposed to 50% for the covered call write on margin. Also, the naked put writer is not actually investing cash; collateral is used, so he may finance his naked put writing through the value of his present portfolio, whether it be stocks, bonds, or government securities. However, any losses would create a debit and might therefore cause him to disturb a portion of this portfolio. It should be pointed out that one can, ifhe wish­ es, write naked puts in a cash account by depositing cash or cash equivalents equal to the striking price of the put. This is called "cash-based put writing." The covered call ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:327 SCORE: 79.00 ================================================================================ O.,,ter 19: The Sale of a Put 295 writer receives the dividends on the underlying stock, but the naked put writer does not. In certain cases, this may be a substantial amount, but it should also be pointed out that the puts on a high-yielding stock will have more value and the naked put writer will thus be taking in a higher premium initially. From strictly a rate of return viewpoint, naked put writing is superior to covered call writing. Basically, there is a different psychology involved in writing naked puts than that required for covered call writing. The covered call write is a comfortable strategy for most investors, since it involves common stock ownership. Writing naked options, however, is a more foreign concept to the average investor, even if the strategies are equivalent. Therefore, it is relatively unlikely that the same investor would be a participant in both strategies. FOLLOW-UP ACTION The naked put writer would take protective follow-up action if the underlying stock drops in price. His simplest form of follow-up action is to close the position at a small loss if the stock drops. Since in-the-money puts tend to lose time value premium rap­ idly, he may find that his loss is often quite small if the stock goes against him. In the example above, XYZ was at 50 with the put at 4. If the stock falls to 45, the writer may be able to quite easily repurchase the put for 5½ or 6 points, thereby incurring a fairly small loss. In the covered call writing strategy, it was recommended that the strategist roll down wherever possible. One reason for doing so, rather than closing the covered call position, is that stock commissions are quite large and one cannot generally afford to be moving in and out of stocks all the time. It is more advantageous to try to preserve the stock position and roll the calls down. This commission disadvantage does not exist with naked put writing. When one closes the naked put position, he merely buys in the put. Therefore, rolling down is not as advantageous for the naked put writer. For example, in the paragraph above, the put writer buys in the put for 5½ or 6 points. He could roll down by selling a put with striking price 45 at that time. However, there may be better put writing situations in other stocks, and there should be no reason for him to continue to preserve a position in XYZ stock In fact, this same reasoning can be applied to any sort of rolling action for the naked put writer. It is extremely advantageous for the covered call writer to roll for­ ward; that is, to buy back the call when it has little or no time value premium remain­ ing in it and sell a longer-term call at the same striking price. By doing so, he takes in additional premium without having to disturb his stock position at all. However, the naked put writer has little advantage in rolling forward. He can also take in addition­ al premium, but when he closes the initial uncovered put, he should then evaluate ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:328 SCORE: 43.00 ================================================================================ 296 Part Ill: Put Option Strategies other available put writing positions before deciding to write another put on the sam<' underlying stock. His commission costs are the same if he remains in XYZ stock or if he goes on to a put writing position in a different stock. EVALUATING A NAKED PUT WRITE The computation of potential returns from a naked put write is not as straightforward as were the computations for covered call writing. The reason for this is that the col­ lateral requirement changes as the stock moves up or down, since any naked option position is marked to the market. The most conservative approach is to allow enough collateral in the position in case the underlying stock should fall, thus increasing the requirement. In this way, the naked put writer would not be forced to prematurely close a position because he cannot maintain the margin required. Example: XYZ is at 50 and the October 50 put is selling for 4 points. The initial col­ lateral requirement is 20% of 50 plus $400, or $1,400. There is no additional require­ ment, since the stock is exactly at the striking price of the put. Furthermore, let us assume that the writer is going to close the position should the underlying stock fall to 43. To maintain his put write, he should therefore allow enough margin to collat­ eralize the position if the stock were at 43. The requirement at that stock price would be $1,560 (20% of 43 plus at least 7 points for the in-the-money amount). Thus, the put writer who is establishing this position should allow $1,560 of collateral value for each put written. Of course, this collateral requirement can be reduced by the amount of the proceeds received from the put sale, $400 per put less commissions in this example. If we assume that the writer sells 5 puts, his gross premium inflow would be $2,000 and his commission expense would be about $75, for a net premi­ um of $1,925. Once this information has been determined, it is a simple matter to determine the maximum potential return and also the downside break-even point. To achieve the maximum potential return, the put would expire worthless with the underlying stock above the striking price. Therefore, the maximum potential profit is equal to the net premium received. The return is merely that profit divided by the collateral used. In the example above, the maximum potential profit is $1,925. The collateral required is $1,560 per put (allowing for the stock to drop to 43) or $7,800 for 5 puts, reduced by the $1,925 premium received, for a total requirement of $5,875. The potential return is then $1,925 divided by $5,875, or 32.8%. Table 19-2 summarizes these calculations. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:329 SCORE: 19.00 ================================================================================ t,r 19: The Sale of a Put ILE 19-2. 297 lculation of the potential return of uncovered put writing. 50 4 less commissions Potential maximum profit (premium received) Striking price Less premium per put ($1,925/5) Break-even stock price Collateral required (allowing for stock to drop to 43): 20% of 43 Plus put premium Requirement for 5 puts Less premium received Net collateral Potential return: Premium divided by net collateral $2,000 75 $1,925 $50.00 3.85 46.15 $ 860 + 700 $1,560 X 5 $7,800 - 1,925 $5,875 $1,925/$5,875 = 32.8% There are differences of opinion on how to compute the potential returns from naked put writing. The method presented above is a more conservative one in that it takes into consideration a larger collateral requirement than the initial requirement. Of course, since one is not really investing cash, but is merely using the collateral value of his present portfolio, it may even be correct to claim that one has no invest­ ment at all in such a position. This may be true, but it would be impossible to com­ pare various put writing opportunities without having a return computation available. One other important feature of return computations is the return if unchanged. If the put is initially out-of-the-money, the return if unchanged is the same as the maximum potential return. However, if the put is initially in-the-money, the compu­ tation must take into consideration what the writer would have to pay to buy back the put when it expires. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:330 SCORE: 26.00 ================================================================================ 298 Part Ill: Put Option Strategies Example: XYZ is 48 and the XYZ January 50 put is selling for 5 points. The profit that could be made if the stock were unchanged at expiration would be only 3 points, less commissions, since the put would have to be repurchased for 2 points with XYZ at 48 at expiration. Commissions for the buy-back should be included as well, to make the computation as accurate as possible. As was the case with covered call writing, one can create several rankings of naked put writes. One list might be the highest potential returns. Another list could be the put writes that provide the rrwst downside protection; that is, the ones that have the least chance of losing money. Both lists need some screening applied to them, however. When considering the maximum potential returns, one should take care to ensure at least some room for downside movement. Example: If XYZ were at 50, the XYZ January 100 put would be selling at 50 also and would most assuredly have a tremendously large maximum potential return. However, there is no room for downside movement at all, and one would surely not write such a put. One simple way of allowing for such cases would be to reject any put that did not offer at least 5% downside protection. Alternatively, one could also reject situations in which the return if unchanged is below 5%. The other list, involving maximum downside protection, also must have some screens applied to it. Example: With XYZ at 70, the XYZ January 50 put would be selling for½ at most. Thus, it is extremely unlikely that one would lose money in this situation; the stock would have to fall 20 points for a loss to occur. However, there is practically nothing to be made from this position, and one would most likely not ever write such a deeply out-of-the-money put. A minimum acceptable level of return must accompany the items on this list of put writes. For example, one might decide that the return would have to be at least 12% on an annualized basis in order for the put write to be on the list of positions offering the most downside protection. Such a requirement would preclude an extreme situation like that shown above. Once these screens have been applied, the lists can then be ranked in a normal manner. The put writes offering the highest returns would be at the top of the more aggressive list, and those offering the high­ est percentage of downside protection would be at the top of the more conservative list. In the strictest sense, a more advanced technique to incorporate the volatility of the underlying stock should rightfully be employed. As mentioned previously, that technique is presented in Chapter 28 on mathematical applications. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:331 SCORE: 26.00 ================================================================================ 19: The Sale of a Put 299 YING STOCK BELOW ITS MARKET PRICE addition to viewing naked put writing as a strategy unto itself, as was the case in previous discussion, some investors who actually want to acquire stock will often te naked puts as well. bmple: XYZ is a $60 stock and an investor feels it would be a good buy at 55. He places an open buy order with a limit of 55. Three months later, XYZ has drifted down to 57 but no lower. It then turns and rises heavily, but the buy limit was never reached, and the investor misses out on the advance. This hypothetical investor could have used a naked put to his advantage. Suppose that when XYZ was originally at 60, this investor wrote a naked three-month put for 5 points instead of placing an open buy limit order. Then, if XYZ is anywhere below 60 at expiration, he will have stock put to him at 60. That is, he will have to buy stock at 60. However, since he received 5 points for the put sale, his net cost for the stock is 55. Thus, even ifXYZ is at 57 at expiration and has never been any lower, the investor can still buy XYZ for a net cost of 55. Of course, if XYZ rose right away and was above 60 at expiration, the put would not be assigned and the investor would not own XYZ. However, he would still have made $500 from selling the put, which is now worthless. The put writer thus assumes a more active role in his investments by acting rather than waiting. He receives at least some compensation for his efforts, even though he did not get to buy the stock. If, instead of rising, XYZ fell considerably, say to 40 by expiration, the investor would be forced to purchase stock at a net cost of 55, thereby giving himself an immediate paper loss. He was, however, going to buy stock at 55 in any case, so the put writer and the investor using a buy limit have the same result in this case. Critics may point out that any buy order for common stock may be canceled if one's opinion changes about purchasing the stock. The put writer, of course, may do the same thing by closing out his obligation through a closing purchase of the put. This technique is useful to many types of investors who are oriented toward eventually owning the stock. Large portfolio managers as well as individual investors may find the sale of puts useful for this purpose. It is a method of attempting to accu­ mulate a stock position at prices lower than today's market price. If the stock rises and the stock is not bought, the investor will at least have received the put premium as compensation for his efforts. SOME CAUTION IS REQUIRED Despite the seemingly benign nature of naked put writing, it can be a highly dan­ gerous strategy for two reasons: (1) Large losses are possible if the underlying stock ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:332 SCORE: 49.00 ================================================================================ 300 Part Ill: Put Option Strategies takes a nasty fall, and (2) collateral requirements are small, so it is possible to utilize a great deal of leverage. It may seem like a good idea to write out-of-the-money puts on "quality" stocks that you "wouldn't mind owning." However, any stock is subject to a crushing decline. In almost any year there are serious declines in one or more of the largest stocks in America (IBM in 1991, Procter and Gamble in 1999, and Xerox in 1999, just to name a few). If one happens to be short puts on such stocks - and worse yet, ifhe happens to have overextended himself because he had the initial mar­ gin required to sell a great deal of puts - then he could actually be wiped out on such a decline. Therefore, do not leverage your account heavily in the naked put strategy, regardless of the "quality" of the underlying stock. THE COVERED PUT SALE By definition, a put sale is covered only if the investor also owns a corresponding put with striking price equal to or greater than the strike of the written put. This is a spread. However,formargin purposes, one is covered ifhe sells a put and is also short the underlying stock. The margin required is strictly that for the short sale of the stock; there is none required for the short put. This creates a position with limited profit potential that is obtained if the underlying stock is anywhere below the strik­ ing price of the put at expiration. There is unlimited upside risk, since if the under­ lying stock rises, the short sale of stock will accrue losses, while the profit from the put sale is limited. This is really a position equivalent to a naked call write, except that the covered put writer must pay out the dividend on the underlying stock, if one exists. The naked sale of a call also has an advantage over this strategy in that com­ mission costs are considerably smaller. In addition, the time value premium of a call is generally higher than that of a put, so that the naked call writer is taking in more time premium. The covered put sale is a little-used strategy that appears to be infe­ rior to naked call writing. As a result, the strategy is not described more fully. RATIO PUT WRITING A ratio put write involves the short sale of the underlying stock plus the sale of 2 puts for each 100 shares sold short. This strategy has a profit graph exactly like that of a ratio call write, achieving its maximum profit at the striking price of the written options, and having large potential losses if the underlying stock should move too far in either direction. The ratio call write is a highly superior strategy, however, for the reasons just outlined. The ratio call writer receives dividends while the ratio put ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:334 SCORE: 65.00 ================================================================================ CHAPTER 20 The Sale of a Straddle Selling a straddle involves selling both a put and a call with the same terms. As with any type of option sale, the straddle sale may be either covered or uncovered. Both uses are fairly common. The covered sale of a straddle is very similar to the covered call writing strategy and would generally appeal to the same type of investor. The uncovered straddle write is more similar to ratio call writing, and is attractive to the more aggressive strategist who is interested in selling large amounts of time premi­ um in hopes of collecting larger profits if the underlying stock remains fairly stable. THE COVERED STRADDLE WRITE In this strategy, one owns the underlying stock and simultaneously writes a straddle on that stock. This may be particularly appealing to investors who are already involved in covered call writing. In reality, this position is not totally covered - only the sale of the call is covered by the ownership of the stock. The sale of the put is uncovered. However, the name "covered straddle" is generally used for this type of position in order to distinguish it from the uncovered straddle write. Example: XYZ is at 51 and an XYZ January 50 call is selling for 5 points while an XYZ January 50 put is selling for 4 points. A covered straddle write would be established by buying 100 shares of the underlying stock and simultaneously selling one put and one call. The similarity between this position and a covered call writer's position should be obvious. The covered straddle write is actually a covered write - long 100 shares of XYZ plus short one call - coupled with a naked put write. Since the naked put write has already been shown to be equivalent to a covered call write, this posi­ tion is quite similar to a 200-share covered call write. In fact, all the profit and loss 302 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:335 SCORE: 88.00 ================================================================================ er 20: The Sale of a Straddle 303 aracteristics of a covered call write are the same for the covered straddle write. There is limited upside profit potential and potentially large downside risk. Readers will remember that the sale of a naked put is equivalent to a covered call write. Hence, a covered straddle write can be thought of either as the equivalent of a 200-share covered call write, or as the sale of two uncovered puts. In fact, there •• some merit to the strategy of selling two puts instead of establishing a covered straddle write. Commission costs would be smaller in that case, and so would the ini­ tial investment required (although the introduction of leverage is not always a good tlting). The maximum profit is attained if XYZ is anywhere above the striking price of 50 at expiration. The amount of maximum profit in this example is $800: the premi­ um received from selling the straddle, less the 1-point loss on the stock if it is called 11way at 50. In fact, the maximum profit potential of a covered straddle write is quick­ ly computed using the following formula: Maximum profit = Straddle premium + Striking price - Initial stock price The break-even point in this example is 46. Note that the covered writing por­ tion of this example buying stock at 51 and selling a call for 5 points - has a break­ even point of 46. The naked put portion of the position has a break-even point of 46 as well, since the January 50 put was sold for 4 points. Therefore, the combined posi­ tion - the covered straddle write - must have a break-even point of 46. Again, this observation is easily defined by an equation: B ak . Stock price + Strike price - Straddle premium re -even pnce = 2 Table 20-1 and Figure 20-1 compare the covered straddle write to a 100-share cov­ ered call write of the XYZ January 50 at expiration. The attraction for the covered call writer to become a covered straddle writer is that he may be able to increase his return without substantially altering the parame­ ters of his covered call writing position. Using the prices in Table 20-1, if one had decided to establish a covered write by buying XYZ at 51 and selling the January 50 call at 5 points, he would have a position with its maximum potential return anywhere above 50 and with a break-even point of 46. By adding the naked put to his covered call position, he does not change the price parameters of his position; he still makes his maximum profit anywhere above 50 and he still has a break-even point of 46. Therefore, he does not have to change his outlook on the underlying stock in order to become a covered straddle writer. The investment is increased by the addition of the naked put, as are the poten­ tial dollars of profit if the stock is above 50 and the potential dollars of loss if the stock ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:336 SCORE: 38.00 ================================================================================ 304 Part Ill: Put Option Strategies TABLE 20-1. Results at expiration of covered straddle write. Stock (A) 100-Shore (8) Put Price Covered Write Write 35 40 46 50 60 FIGURE 20-1. -$1, 100 600 0 + 400 + 400 Covered straddle write. +$800 § +$400 e ·5. ~ al en $0 en 0 ...J c5 e a. ~, ,,' ,, ,, ,, ,, ,, ,, ,, -$1, 100 600 0 + 400 + 400 100-Share Covered Call Write ~-----------------► , 46 50 Stock Price at Expiration Covered Straddle Write (A+ 8) -$2,200 - 1,200 0 + 800 + 800 is below 46 at expiration. The covered straddle writer loses money twice as fast on the downside, since his position is similar to a 200-share covered write. Because the commissions are smaller for the naked put write than for the covered call write, the covered call writer who adds a naked put to his position will generally increase his return somewhat. Follow-up action can be implemented in much the same way it would be for a covered call write. Whenever one would normally roll his call in a covered situation, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:337 SCORE: 92.00 ================================================================================ t,r 20: The Sale ol a Straddle 305 now rolls the entire straddle - rolling down for protection, rolling up for an ease in profit potential, and rolling forward when the time value premium of the die dissipates. Rolling up or down would probably involve debits, unless one led to a longer maturity. Some writers might prefer to make a slight adjustment to the covered straddle ting strategy. Instead of selling the put and call at the same price, they prefer to ell an out-of-the-money put against the covered call write. That is, if one is buying XYZ at 50 and selling the call, he might then also sell a put at 45. This would increase his upside profit potential and would allow for the possibility of both options expir­ ing worthless if XYZ were anywhere between 45 and 50 at expiration. Such action would, of course, increase the potential dollars of risk if XYZ fell below 45 by expira­ tion, but the writer could always roll the call down to obtain additional downside pro­ tection. One final point should be made with regard to this strategy. The covered call writer who is writing on margin and is fully utilizing his borrowing power for call writ­ ing will have to add additional collateral in order to write covered straddles. This is because the put write is uncovered. However, the covered call writer who is operat­ ing on a cash basis can switch to the covered straddle writing strategy without put­ ting up additional funds. He merely needs to move his stock to a margin account and use the collateral value of the stock he already owns in order to sell the puts neces­ sary to implement the covered straddle writes. THE UNCOVERED STRADDLE WRITE In an uncovered straddle write, one sells the straddle without owning the underlying stock. In broad terms, this is a neutral strategy with limited profit potential and large risk potential. However, the probability of making a profit is generally quite large, and methods can be implemented to reduce the risks of the strategy. Since one is selling both a put and a call in this strategy, he is initially taking in large amounts of time value premium. If the underlying stock is relatively unchanged at expiration, the straddle writer will be able to buy the straddle back for its intrinsic value, which would normally leave him with a profit. Example: The following prices exist: XYZ common, 45; XYZ January 45 call, 4; and XYZ January 45 put, 3. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:338 SCORE: 54.00 ================================================================================ 306 Part Ill: Put Option Strategies A straddle could be sold for 7 points. If the stock were above 38 and below 52 at expi­ ration, the straddle writer would profit, since the in-the-money option could ht· bought back for less than 7 points in that case, while the out-of-the-money option expires worthless (Table 20-2). TABLE 20-2. The naked straddle write. XYZ Price at Call Put Total Expiration Profit Profit Profit 30 +$ 400 -$1,200 -$800 35 + 400 700 - 300 38 + 400 400 0 40 + 400 200 + 200 45 + 400 + 300 + 700 50 100 + 300 + 200 52 300 + 300 0 55 600 + 300 - 300 60 - 1,100 + 300 - 800 Notice that Figure 20-2 has a shape like a roof. The maximum potential profit point is at the striking price at expiration, and large potential losses exist in either direction if the underlying stock should move too far. The reader may recall that the ratio call writing strategy - buying 100 shares of the underlying stock and selling two calls - has the same profit graph. These two strategies, the naked straddle write and the ratio call write, are equivalent. The two strategies do have some differences, of course, as do all equivalent strategies; but they are similar in that both are highly probabilistic strategies that can be somewhat complex. In addition, both have large potential risks under adverse market conditions or if follow-up strategies are not applied. The investment required for a naked straddle is the greater of the requirement on the call or the put. In general, this means that the margin requirement is equal to the requirement for the in-the-money option in a simple naked write. This require­ ment is 20% of the stock price plus the in-the-money option premium. The straddle writer should allow enough collateral so that he can take whatever follow-up actions he deems necessary without having to incur a margin call. If he is intending to close out the straddle if the stock should reach the upside break-even point - 52 in the example above - then he should allow enough collateral to finance the position with ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:339 SCORE: 40.00 ================================================================================ ler 20: The Sale of a Straddle GURE 20-2. ked straddle sale. 307 Stock Price at Expiration the stock at 52. If, however, he is planning to take other action that might involve staying with the position if the stock goes to 55 or 56, he should allow enough collat­ eral to be able to finance that action. If the stock never gets that high, he will have excess collateral while the position is in place. SELECTING A STRADDLE WRITE Ideally, one would like to receive a premium for the straddle write that produces a profit range that is wide in relation to the volatility of the underlying stock. In the example above, the profit range is 38 to 52. This may or may not be extraordinarily wide, depending on the volatility of XYZ. This is a somewhat subjective measure­ ment, although one could construct a simple straddle writer's index that ranked strad­ dles based on the following simple formula: I d Straddle time value premium n ex= _______ ..._ ___ _ Stock price x Volatility Refinements would have to be made to such a ranking, such as eliminating cases in which either the put or the call sells for less than ¼ point ( or even 1 point, if a more restrictive requirement is desired) or cases in which the in-the-money time premium is small. Furthermore, the index would have to be annualized to be able to compare straddles for different expiration months. More advanced selection criteria, in the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:340 SCORE: 81.00 ================================================================================ 308 Part Ill: Put Option Strategies form of an expected return analysis, will be presented in Chapter 28 on mathemati­ cal applications. More screens can be added to produce a more conservative list of straddl<' writes. For example, one might want to ignore any straddles that are not worth at least a fixed percentage, say 10%, of the underlying stock price. Also, straddles that are too short-term, such as ones with less than 30 days of life remaining, might b<' thrown out as well. The remaining list of straddle writing candidates should be ones that will provide reasonable returns under favorable conditions, and also should be readily adaptable to some of the follow-up strategies discussed later. Finally, one would generally like to have some amount of technical support at or above the lower break-even price and some technical resistance at or below the upper break-even point. Thus, once the computer has generated a list of straddles ranked by an index such as the one listed above, the straddle writer can further pare down the list by looking at the technical pictures of the underlying stocks. FOLLOW-UP ACTION The risks involved in straddle writing can be quite large. When market conditions are favorable, one can make considerable profits, even with restrictive selection require­ ments, and even by allowing considerable extra collateral for adverse stock move­ ments. However, in an extremely volatile market, especially a bullish one, losses can occur rapidly and follow-up action must be taken. Since the time premium of a put tends to shrink when it goes into-the-money, there is actually slightly less risk to the downside than there is to the upside. In an extremely bullish market, the time value premiums of call options will not shrink much at all and might even expand. This may force the straddle writer to pay excessive amounts of time value premium to buy back the written straddle, especially if the movement occurs well in advance of expiration. The simplest form of follow-up action is to buy the straddle back when and if the underlying stock reaches a break-even point. The idea behind doing so is to limit the losses to a small amount, because the straddle should be selling for only slightly more than its original value when the stock has reached a break-even point. In practice, there are several flaws in this theory. If the underlying stock arrives at a break-even point well in advance of expiration, the amount of time value premium remaining in the straddle may be extremely large and the writer will be losing a fairly large amount by repurchasing the straddle. Thus, a break-even point at expiration is probably a loss point prior to expiration. Example: After the straddle is established with the stock at 45, there is a sudden rally in the stock and it climbs quickly to 52. The call might be selling for 9 points, even ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:341 SCORE: 65.00 ================================================================================ 20: The Sale of a Straddle 309 gh it is 7 points in-the-money. This is not unusual in a bullish situation. ver, the put might be worth 1 ½points.This is also not unusual, as out-of-the­ y puts with a large amount of time remaining tend to hold time value premium well. Thus, the straddle writer would have to pay 10½ points to buy back this dle, even though it is at the break-even point, 7 points in-the-money on the call This example is included merely to demonstrate that it is a misconception to ieve that one can always buy the straddle back at the break-even point and hold losses to mere fractions of a point by doing so. This type of buy-back strategy ks best when there is little time remaining in the straddle. In that case, the options will indeed be close to parity and the straddle will be able to be bought back for close to its initial value when the stock reaches the break-even point. Another follow-up strategy that can be employed, similar to the previous one but with certain improvements, is to buy back only the in-the-money option when it reaches a price equal to that of the initial straddle price. ~mple: Again using the same situation, suppose that when XYZ began to climb heavily, the call was worth 7 points when the stock reached 50. The in-the-money option the call - is now worth an amount equal to the initial straddle value. It could then be bought back, leaving the out-of-the-money put naked. As long as the stock then remained above 45, the put would expire worthless. In practice, the put could be bought back for a small fraction after enough time had passed or if the underly­ Ing stock continued to climb in price. This type of follow-up action does not depend on taking action at a fixed stock price, but rather is triggered by the option price itself. It is therefore a dynamic sort of follow-up action, one in which the same action could be applied at various stock prices, depending on the amount of time remaining until expiration. One of the prob­ lems with closing the straddle at the break-even points is that the break-even point is C)nly a valid break-even point at expiration. A long time before expiration, this stock price will not represent much of a break-even point, as was pointed out in the last example. Thus, buying back only the in-the-money option at a fixed price may often be a superior strategy. The drawback is that one does not release much collateral by buying back the in-the-money option, and he is therefore stuck in a position with little potential profit for what could amount to a considerable length of time. The collateral released amounts to the in-the-money amount; the writer still needs to C.'Ollateralize 20% of the stock price. One could adjust this follow-up method to attempt to retain some profit. For example, he might decide to buy the in-the-money option when it has reached a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:342 SCORE: 48.00 ================================================================================ 310 Part Ill: Put Option Strategies value that is 1 point less than the total straddle value initially taken in. This would then allow him the chance to make a I-point profit overall, if the other option expired worthless. In any case, there is always the risk that the stock would suddenly revers(' direction and cause a loss on the remaining option as well. This method of follow-up action is akin to the ratio writing follow-up strategy of using buy and sell stops on th<' underlying stock. Before describing other types of follow-up action that are designed to combat the problems described above, it might be worthwhile to address the method used in ratio writing - rolling up or rolling down. In straddle writing, there is often little to be gained from rolling up or rolling down. This is a much more viable strategy in ratio writing; one does not want to be constantly moving in and out of stock positions, because of the commissions involved. Howeve1~ with straddle writing, once one posi­ tion is closed, there is no need to pursue a similar straddle in that same stock. It may be more desirable to look elsewhere for a new straddle position. There are two other very simple forms of follow-up action that one might con­ sider using, although neither one is for most strategists. First, one might consider doing nothing at all, even if the underlying stock moves by a great deal, figuring that the advantage lies in the probability that the stock will be back near the striking price by the time the options expire. This action should be used only by the most diversi­ fied and well-heeled investors, for in extreme market periods, almost all stocks may move in unison, generating tremendous losses for anyone who does not take some sort of action. A more aggressive type off allow-up action would be to attempt to "leg out" of the straddle, by buying in the profitable side and then hoping for a stock price reversal in order to buy back the remaining side. In the example above, when XYZ ran up to 52, an aggressive trader would buy in the put at 1 ½, taking his profit, and then hope for the stock to fall back in order to buy the call in cheaper. This is a very aggressive type of follow-up action, because the stock could easily continue to rise in price, thereby generating larger losses. This is a trader's sort of action, not that of a disciplined strategist, and it should be avoided. In essence, follow-up action should be designed to do two things: First, to limit the risk in the position, and second, to still allow room for a potential profit to be made. None of the above types of follow-up action accomplish both of these purpos­ es. There is, however, a follow-up strategy that does allow the straddle writer to limit his losses while still allowing for a potential profit. Example: After the straddle was originally sold for 7 points when the stock was at 45, the stock experiences a rally and the following prices exist: XYZ common, 50; XYZ January 45 call, 7; ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:343 SCORE: 84.00 ================================================================================ Cl,opter 20: The Sale of a Straddle XYZ January 45 put, l; and XYZ January 50 call, 3. 311 The January 50 call price is included because it will be part of the follow-up strategy. Notice that this straddle has a considerable amount of time value premium remain­ Ing in it, and thus would be rather expensive to buy back at the current time. Suppose, however, that the straddle writer does not touch the January 45 straddle tliat he is short, but instead buys the January 50 call for protection to the upside. Since this call costs 3 points, he will now have a position with a total credit of 4 points. (The straddle was originally sold for 7 points credit and he is now spending 3 points for the call at 50.) This action of buying a call at a higher strike than the striking price of the straddle has limited the potential loss to the upside, no matter how far the stock might run up. If XYZ is anywhere above 50 at expiration, the put will expire worthless and the writer will have to pay 5 points to close the call spread short January 45, long January 50. This means that his maximum potential loss is 1 point plus commissions if XYZ is anywhere above 50 at expiration. In addition to being able to limit the upside loss, this type of follow-up action still allows room for potential profits. If XYZ is anywhere between 41 and 49 at expi­ ration - that is, less than 4 points away from the striking price of 45 - the writer will he able to buy the straddle back for less than 4 points, thereby making a profit. Thus, the straddle writer has both limited his potential losses to the upside and also allowed room for profit potential should the underlying stock fall back in price toward the original striking price of 45. Only severe price reversal, with the stock falling back below 40, would cause a large loss to be taken. In fact, by the time the stock could reverse its current strong upward momentum and fall all the way back to 40, a significant amount of time should have passed, thereby allowing the writer to purchase the straddle back with only a relatively small amount of time premium left in it. This follow-up strategy has an effect on the margin requirement of the position. When the calls are bought as protection to the upside, the writer has, for margin purposes, a bearish spread in the calls and an uncovered put. The margin for this position would normally be less than that required for the straddle that is 5 points in-the-money. A secondary move is available in this strategy. Example: The stock continues to climb over the short term and the out-of-the­ money put drops to a price of less than ½ point. The straddle writer might now consider buying back the put, thereby leaving himself with a bear spread in the calls. His net credit left in the position, after buying back the put at ½, would be ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:344 SCORE: 59.00 ================================================================================ 312 Part Ill: Put Optian Strategies 3½ points. Thus, if XYZ should reverse direction and be within 3½ points of the striking price - that is, anywhere below 48½ - at expiration, the position will pro­ duce a profit. In fact, if XYZ should be below 45 at expiration, the entire bear spread will expire worthless and the strategist will have made a 3½-point profit. Finally, this repurchase of the put releases the margin requirement for the naked put, and will generally free up excess funds so that a new straddle position can be established in another stock while the low-requirement bear spread remains in place. In summary, this type of follow-up action is broader in purpose than any of the simpler buy-back strategies described earlier. It will limit the writer's loss, but not prevent him from making a profit. Moreover, he may be able to release enough mar­ gin to be able to establish a new position in another stock by buying in the uncov­ ered puts at a fractional price. This would prevent him from tying up his money completely while waiting for the original straddle to reach its expiration date. The same type of strategy also works in a downward market. If the stock falls after the straddle is written, one can buy the put at the next lower strike to limit the down­ side risk, while still allowing for profit potential if the stock rises back to the striking price. EQUIVALENT STOCK POSITION FOLLOW-UP Since there are so many follow-up strategies that can be used with the short straddle, the one method that summarizes the situation best is again the equivalent stock posi­ tion (ESP). Recall that the ESP of an option position is the multiple of the quantity times the delta times the shares per option. The quantity is a negative number if it is referring to a short position. Using the above scenario, an example of the ESP method follows: Example: As before, assume that the straddle was originally sold for 7 points, but the stock rallied. The following prices and deltas exist: XYZ common, 50; XYZ Jan 45 call, 7; delta, .90; XYZ Jan 45 put, l; delta, - .10; and XYZ Jan 50 call, 3; delta, .60. Assume that 8 straddles were sold initially and that each option is for 100 shares of XYZ. The ESP of these 8 short straddles can then be computed: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:345 SCORE: 52.00 ================================================================================ Chapter 20: The Sale of a Straddle Option Jan 45 call Jan 45 put Total ESP Position short 8 short 8 Delta 0.90 -0.10 313 ESP short 720 (-8 x . 9 x 1 00) long 80 (-8 x -. 1 x 100) short 640 shares Obviously, the position is quite short. Unless the trader were extremely bearish on XYZ, he should make an adjustment. The simplest adjustment would be to buy 600 shares of XYZ. Another possibility would be to buy back 7 of the short January 45 calls. Such a purchase would add a delta long of 630 shares to the position (7 x .9 x 100). This would leave the position essentially neutral. As pointed out in the previ­ ous example, however, the strategist may not want to buy that option. If, instead, he decided to try to buy the January 50 call to hedge the short straddle, he would have to buy 10 of those to make the position neutral. He would buy that many because the delta of that January 50 is 0.60; a purchase of 10 would add a delta long of 600 shares to the position. Even though the purchase of 10 is theoretically correct, since one is only short 8 straddles, he would probably buy only 8 January 50 calls as a practical matter. STARTING OUT WITH THE PROTECTION IN PLACE In certain cases, the straddle writer may be able to initially establish a position that has no risk in one direction: He can buy an out-of-the-money put or call at the same time the straddle is written. This accomplishes the same purposes as the follow-up action described in the last few paragraphs, but the protective option will cost less since it is out-of-the-money when it is purchased. There are, of course, both positive and negative aspects involved in adding an out-of-the-money long option to the strad­ dle write at the outset. Example: Given the following prices: XYZ, 45; XYZ January 45 straddle, 7; and XYZ January 50 call, 1 ½, the upside risk will be limited. If one writes the January 45 straddle for 7 points and buys the January 50 call for 1 ½ points, his overall credit will be 5½ points. He has no upside risk in this position, for if XYZ should rise and be over 50 at expiration, he will be able to close the position by buying back the call spread for 5 points. The put will expire worthless. The out-of-the-money call has eliminated any risk above 50 on the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:346 SCORE: 61.00 ================================================================================ 312 Part Ill: Put Option Strategies 3½ points. Thus, if XYZ should reverse direction and be within 3½ points of the striking price - that is, anywhere below 48½ - at expiration, the position will pro­ duce a profit. In fact, if XYZ should be below 45 at expiration, the entire bear spread will expire worthless and the strategist will have made a 3½-point profit. Finally, this repurchase of the put releases the margin requirement for the naked put, and will generally free up excess funds so that a new straddle position can be established in another stock while the low-requirement bear spread remains in place. In summary, this type of follow-up action is broader in purpose than any of the simpler buy-back strategies described earlier. It will limit the writer's loss, but not prevent him from making a profit. Moreover, he may be able to release enough mar­ gin to be able to establish a new position in another stock by buying in the uncov­ ered puts at a fractional price. This would prevent him from tying up his money completely while waiting for the original straddle to reach its expiration date. The same type of strategy also works in a downward market. If the stock falls after the straddle is written, one can buy the put at the next lower strike to limit the down­ side risk, while still allowing for profit potential if the stock rises back to the striking price. EQUIVALENT STOCK POSITION FOLLOW-UP Since there are so many follow-up strategies that can be used with the short straddle, the one method that summarizes the situation best is again the equivalent stock posi­ tion (ESP). Recall that the ESP of an option position is the multiple of the quantity times the delta times the shares per option. The quantity is a negative number if it is referring to a short position. Using the above scenario, an example of the ESP method follows: Example: As before, assume that the straddle was originally sold for 7 points, but the stock rallied. The following prices and deltas exist: XYZ common, 50; XYZ Jan 45 call, 7; delta, .90; XYZ Jan 45 put, l; delta, - .10; and XYZ Jan 50 call, 3; delta, .60. Assume that 8 straddles were sold initially and that each option is for 100 shares of XYZ. The ESP of these 8 short straddles can then be computed: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:347 SCORE: 52.00 ================================================================================ Chapter 20: The Sale of a Straddle Option Jan 45 call Jan 45 put Total ESP Position short 8 short 8 Delta 0.90 -0.10 313 ESP short 720 (-8 x .9 x 100) long 80 (-8 x -. 1 x 1 00) short 640 shares Obviously, the position is quite short. Unless the trader were extremely bearish on XYZ, he should make an adjustment. The simplest adjustment would be to buy 600 shares of XYZ. Another possibility would be to buy back 7 of the short January 45 calls. Such a purchase would add a delta long of 630 shares to the position (7 x .9 x 100). This would leave the position essentially neutral. As pointed out in the previ­ ous example, however, the strategist may not want to buy that option. If, instead, he decided to try to buy the January 50 call to hedge the short straddle, he would have to buy 10 of those to make the position neutral. He would buy that many because the delta of that January 50 is 0.60; a purchase of 10 would add a delta long of 600 shares to the position. Even though the purchase of 10 is theoretically correct, since one is only short 8 straddles, he would probably buy only 8 January 50 calls as a practical matter. STARTING OUT WITH THE PROTECTION IN PLACE In certain cases, the straddle writer may be able to initially establish a position that has no risk in one direction: He can buy an out-of-the-money put or call at the same time the straddle is written. This accomplishes the same purposes as the follow-up action described in the last few paragraphs, but the protective option will cost less since it is out-of-the-money when it is purchased. There are, of course, both positive and negative aspects involved in adding an out-of-the-money long option to the strad­ dle write at the outset. Example: Given the following prices: XYZ, 45; XYZ January 45 straddle, 7; and XYZ January 50 call, 1 ½, the upside risk will be limited. If one writes the January 45 straddle for 7 points and buys the January 50 call for 1 ½ points, his overall credit will be 5½ points. He has no upside risk in this position, for if XYZ should rise and be over 50 at expiration, he will be able to close the position by buying back the call spread for 5 points. The put will expire worthless. The out-of-the-money call has eliminated any risk above 50 on the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:348 SCORE: 69.00 ================================================================================ 314 Part Ill: Put Option Strategies position. Another advantage of buying the protection initially is that one is protected if the stock should experience a gap opening or a trading halt. Ifhe already owns the protection, such stock price movement in the direction of the protection is of little consequence. However, if he was planning to buy the protection as a follow-up action, the sudden surge in the stock price may ruin his strategy. The overall profit potential of this position is smaller than that of the normal straddle write, since the premium paid for the long call will be lost if the stock is below 50 at expiration. However, the automatic risk-limiting feature of the long call may prove to be worth more than the decrease in profit potential. The strategist has peace of mind in a rally and does not have to worry about unlimited losses accruing to the upside. Downside protection for a straddle writer can be achieved in a similar manner by buying an out-of-the-money put at the outset. Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a January 40 put for I point if he is concerned about the stock dropping in price. It should now be fairly easy to see that the straddle writer could limit risk in either direction by initially buying both an out-of-the-money call and an out-of-the­ money put at the same time that the straddle is written. The major benefit in doing this is that risk is limited in either direction. Moreover, the margin requirements are significantly reduced, since the whole position consists of a call spread and a put spread. There are no longer any naked options. The detriment of buying protection on both sides initially is that commission costs increase and the overall profit poten­ tial of the straddle write is reduced, perhaps significantly, by the cost of two long options. Therefore, one must evaluate whether the cost of the protection is too large in comparison to what is received for the straddle write. This completely protected strategy can be very attractive when available, and it is described again in Chapter 23, Spreads Combining Calls and Puts. In summary, any strategy in which the straddle writer also decides to buy pro­ tection presents both advantages and disadvantages. Obviously, the risk-limiting fea­ ture of the purchased options is an advantage. However, the seller of options does not like to purchase pure time value premium as protection at any time. He would gen­ erally prefer to buy intrinsic value. The reader will note that, in each of the protec­ tive buying strategies discussed above, the purchased option has a large amount of time value premium left in it. Therefore, the writer must often try to strike a delicate balance between trying to limit his risk on one hand and trying to hold down the expenses of buying long options on the other hand. In the final analysis, however, the risk must be limited regardless of the cost. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:349 SCORE: 69.00 ================================================================================ 314 Part Ill: Put Option Strategies position. Another advantage of buying the protection initially is that one is protected if the stock should experience a gap opening or a trading halt. If he already owns the protection, such stock price movement in the direction of the protection is of little consequence. However, if he was planning to buy the protection as a follow-up action, the sudden surge in the stock price may ruin his strategy. The overall profit potential of this position is smaller than that of the normal straddle write, since the premium paid for the long call will be lost if the stock is below 50 at expiration. However, the automatic risk-limiting feature of the long call may prove to be worth more than the decrease in profit potential. The strategist has peace of mind in a rally and does not have to worry about unlimited losses accruing to the upside. Downside protection for a straddle writer can be achieved in a similar manner by buying an out-of-the-money put at the outset. Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a January 40 put for l point if he is concerned about the stock dropping in price. It should now be fairly easy to see that the straddle writer could limit risk in either direction by initially buying both an out-of-the-money call and an out-of-the­ money put at the same time that the straddle is written. The major benefit in doing this is that risk is limited in either direction. Moreover, the margin requirements are significantly reduced, since the whole position consists of a call spread and a put spread. There are no longer any naked options. The detriment of buying protection on both sides initially is that commission costs increase and the overall profit poten­ tial of the straddle write is reduced, perhaps significantly, by the cost of two long options. Therefore, one must evaluate whether the cost of the protection is too large in comparison to what is received for the straddle write. This completely protected strategy can be very attractive when available, and it is described again in Chapter 23, Spreads Combining Calls and Puts. In summary, any strategy in which the straddle writer also decides to buy pro­ tection presents both advantages and disadvantages. Obviously, the risk-limiting fea­ ture of the purchased options is an advantage. However, the seller of options does not like to purchase pure time value premium as protection at any time. He would gen­ erally prefer to buy intrinsic value. The reader will note that, in each of the protec­ tive buying strategies discussed above, the purchased option has a large amount of time value premium left in it. Therefore, the ·writer must often try to strike a delicate balance between trying to limit his risk on one hand and trying to hold down the expenses of buying long options on the other hand. In the final analysis, however, the risk must be limited regardless of the cost. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:350 SCORE: 67.00 ================================================================================ 314 Part Ill: Put Option Strategies position. Another advantage of buying the protection initially is that one is protected if the stock should expe1ience a gap opening or a trading halt. If he already owns the protection, such stock price movement in the direction of the protection is of little consequence. However, if he was planning to buy the protection as a follow-up action, the sudden surge in the stock price may ruin his strategy. The overall profit potential of this position is smaller than that of the normal straddle write, since the premium paid for the long call will be lost if the stock is below 50 at ex-piration. However, the automatic risk-limiting feature of the long call may prove to be worth more than the decrease in profit potential. The strategist has peace of mind in a rally and does not have to worry about unlimited losses accruing to the upside. Downside protection for a straddle writer can be achieved in a similar manner by buying an out-of-the-money put at the outset. Example: With XYZ at 45, one might write the January 45 straddle for 7 and buy a January 40 put for l point if he is concerned about the stock dropping in price. It should now be fairly easy to see that the straddle writer could limit risk in either direction by initially buying both an out-of-the-money call and an out-of-the­ money put at the same time that the straddle is written. The major benefit in doing this is that risk is limited in either direction. Moreover, the margin requirements are significantly reduced, since the whole position consists of a call spread and a put spread. There are no longer any naked options. The detriment of buying protection on both sides initially is that commission costs increase and the overall profit poten­ tial of the straddle write is reduced, perhaps significantly, by the cost of two long options. Therefore, one must evaluate whether the cost of the protection is too large in comparison to what is received for the straddle write. This completely protected strategy can be very attractive when available, and it is described again in Chapter 23, Spreads Combining Calls and Puts. In summary, any strategy in which the straddle writer also decides to buy pro­ tection presents both advantages and disadvantages. Obviously, the risk-limiting fea­ ture of the purchased options is an advantage. However, the seller of options does not like to purchase pure time value premium as protection at any time. He would gen­ erally prefer to buy intrinsic value. The reader will note that, in each of the protec­ tive buying strategies discussed above, the purchased option has a large amount of time value premium left in it. Therefore, the writer must often try to strike a delicate balance between trying to limit his risk on one hand and trying to hold down the expenses of buying long options on the other hand. In the final analysis, however, the risk must be limited regardless of the cost. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:351 SCORE: 78.00 ================================================================================ Chapter 20: The Sale of a Straddle 315 STRANGLE (COMBINATION) WRITING Recall that a strangle is any position involving both puts and calls, when there is some difference in the terms of the options. Commonly, the puts and calls will have the same expiration date but differing striking prices. A strangle write is usually estab­ lished by selling both an out-of-the-money put and an out-of-the-money call with the stock approximately centered between the two striking prices. In this way, the naked option writer can remain neutral on the outlook for the underlying stock, even when the stock is not near a striking price. This strategy is quite similar to straddle writing, except that the strangle writer makes his maximum profit over a much wider range than the straddle writer does. In this or any other naked writing strategy, the most money that the strategist can make is the amount of the premium received. The straddle writer has only a minute chance of making a profit of the entire straddle premium, since the stock would have to be exactly at the striking price at expiration in order for both the written put and call to expire worthless. The strangle writer will make his maximum profit potential if the stock is anywhere between the two strikes at expi­ ration, because both options will expire worthless in that case. This strategy is equivalent to the variable ratio write described previously in Chapter 6 on ratio call writing. Example: Given the following prices: XYZ common, 65; XYZ January 70 call, 4; and XYZ January 60 put, 3, a strangle write would be established by selling the January 70 call and the January 60 put. IfXYZ is anywhere between 60 and 70 at January expiration, both options will expire worthless and the strangle writer will make a profit of 7 points, the amount of the original credit taken in. If XYZ is above 70 at expiration, the strategist will have to pay something to buy back the call. For example, if XYZ is at 77 at expiration, the January 70 call will have to be bought back for 7 points, thereby creating a break-even situation. To the downside, if XYZ were at 53 at expiration, the January 60 put would have to be bought back for 7 points, thereby defining that as the downside break­ even point. Table 20-3 and Figure 20-3 outline the potential results of this strangle write. The profit range in this example is quite wide, extending from 53 on the down­ side to 77 on the upside. With the stock presently at 65, this is a relatively neutral position. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:352 SCORE: 14.00 ================================================================================ 316 TABLE 20-3. Results of a combination write. Stock Price at Coll Expiration Profit 40 +$ 400 50 + 400 53 + 400 57 + 400 60 + 400 65 + 400 70 + 400 73 + 100 77 300 80 600 90 - 1,600 FIGURE 20-3. Sale of a combination. C: ~ +$700 ·5. X UJ rn en en 0 ....I ci e a.. $0 Put Profit $1,700 700 400 0 + 300 + 300 + 300 + 300 + 300 + 300 + 300 Stock Price at Expiration Part Ill: Put Option Strategies Total Profit -$1,300 300 0 + 400 + 700 + 700 + 700 + 400 0 300 - 1,300 At first glance, this may seem to be a more conservative strategy than straddle writing, because the profit range is wider and the stock needs to move a great deal to reach the break-even points. In the absence of follow-up action, this is a true obser­ vation. However, if the stock begins to rise quickly or to drop dramatically, the stran­ gle writer often has little recourse but to buy back the in-the-money option in order ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:353 SCORE: 76.00 ================================================================================ Chapter 20: The Sale of a Straddle 317 to limit his losses. This can, as has been shown previously, entail a purchase price involving excess amounts of time value premium, thereby generating a significant loss. The only other alternative that is available to the strangle writer ( outside of attempting to trade out of the position) is to convert the position into a straddle if the stock reaches either break-even point. Example: IfXYZ rose to 70 or 71 in the previous example, the January 70 put would be sold. Depending on the amount of collateral available, the January 60 put may or may not be bought back when the January 70 put is sold. This action of converting the strangle write into a straddle write will work out well if the stock stabilizes. It will also lessen the pain if the stock continues to rise. However, if the stock revers­ es direction, the January 70 put write will prove to be unprofitable. Technical analy­ sis of the underlying stock may prove to be of some help in deciding whether or not to convert the strangle write into a straddle. If there appears to be a relatively large chance that the stock could fall back in price, it is probably not worthwhile to roll the put up. This example of a strangle write is one in which the writer received a large amount of premium for selling the put and the call. Many times, however, an aggres­ sive strangle writer is tempted to sell two out-of-the-money options that have only a short life remaining. These options would generally be sold at fractional prices. This can be an extremely aggressive strategy at times, for if the underlying stock should move quickly in either direction through a striking price, there is little the strangle writer can do. He must buy in the options to limit his loss. Nevertheless, this type of strangle writing - selling short-term, fractionally priced, out-of-the-money options - appeals to many writers. This is a similar philosophy to that of the naked call writer described in Chapter 5, who writes calls that are nearly restricted, figuring there will be a large probability that the option will expire worthless. It also has the same risk: A large price change or gap opening can cause such devastating losses that many profitable trades are wiped away. Selling fractionally priced combinations is a poor strategy and should be avoided. Before leaving the topic of strangle writing, it may be useful to determine how the margin requirements apply to a strangle write. Recall that the margin require­ ment for writing a straddle is 20% of the stock price plus the price of either the put or the call, whichever is in-the-money. In a strangle write, however, both options may be out-of-the-money, as in the example above. When this is the case, the straddle writer is allowed to deduct the smaller out-of-the-money amount from his require­ ment. Thus, if XYZ were at 68 and the January 60 put and the January 70 call had been written, the collateral requirement would be 20% of the stock price, plus the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:354 SCORE: 81.00 ================================================================================ 318 Part Ill: Put Option Strategies call premium, less $200 - the lesser out-of-the-money amount. The call is 2 points out-of-the-money and the put is 8 points out-of-the-money. Actually, the true collat­ eral requirement for any write involving both puts and calls - straddle write or stran­ gle write - is the greater of the requirement on the put or the call, plus the amount by which the other option is in-the-nwney. The last phrase, the amount by which the other option is in-the-money, applies to a situation in which a strangle had been con­ structed by selling two in-the-money options. This is a less popular strategy, since the writer generally receives less time value premium by writing two in-the-money options. An example of an in-the-money strangle is to sell the January 60 call and the January 70 put with the stock at 65. FURTHER COMMENTS ON UNCOVERED STRADDLE AND STRANGLE WRITING When ratio writing was discussed, it was noted that it was a strategy with a high prob­ ability of making a limited profit. Since the straddle write is equivalent to the ratio write and the strangle write is equivalent to the variable ratio write, the same state­ ment applies to these strategies. The practitioner of straddle and strangle writing must realize, however, that protective follow-up action is mandatory in limiting loss­ es in a very volatile market. There are other techniques that the straddle writer can sometimes use to help reduce his risk. It has often been mentioned that puts lose their time value premium more quickly when they become in-the-money options than calls do. One can often con­ struct a neutral position by writing an extra put or two. That is, if one sells 5 or 6 puts and 4 calls 'Ai.th the same terms, he may often have created a more neutral position than a straddle write. If the stock moves up and the call picks up time premium in a bullish market, the extra puts 'Aill help to offset the negative effect of the calls. On the other hand, if the stock drops, the 5 or 6 puts will not hold as much time premi­ um as the 4 calls are losing - again a neutral, standoff position. If the stock begins to drop too much, the writer can always balance out the position by selling another call or two. The advantage of writing an extra put or two is that it counterbalances the straddle writer's most severe enemy: a quick, extremely bullish rise by the underly­ ing stock. USING THE DELTAS This analysis, that adding an extra short put creates a neutral position, can be sub­ stantiated more rigorously. Recall that a ratio writer or ratio spreader can use the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:355 SCORE: 40.00 ================================================================================ Chapter 20: The Sale of a Straddle 319 deltas of the options involved in his position to determine a neutral ratio. The strad­ dle writer can do the same thing, of course. It was stated that the difference between a call's delta and a put' s delta is approximately one. Using the same prices as in the previous straddle writing example, and assuming the call's delta to be .60, a neutral ratio can be determined. Prices XYZ common: XYZ January 45 call: XYZ January 45 put: 45 4 3 Deltas .60 -.40 (.60 - 1) The put has a negative delta, to indicate that the put and the underlying stock are inversely related. A neutral ratio is determined by dividing the call's delta by the put's delta and ignoring the minus sign. The resultant ratio - 1.5:1 (.60/.40) in this case - is the ratio of puts to sell for each call that is sold. Thus, one should sell 3 puts and sell 2 calls to establish a neutral position. The reader may wonder if the assumption that an at-the-money call has a delta of .60 is a fair one. It generally is, although very long-term calls will have higher at-the-money deltas, and very short-term calls will have deltas near .50. Consequently, a 3:2 ratio is often a neutral one. When neutral ratios were discussed with respect to ratio writing, it was mentioned that selling 5 calls and buying 300 shares of stock often results in neutral ratio. The reader should note that a straddle constructed by selling 3 puts and 2 calls is equivalent to the ratio write in which one sells 5 calls and buys 300 shares of stock. If a straddle writer is going to use the deltas to determine his neutral ratio, he should compute each one at the time of his initial investment, of course, rather than relying on a generality such as that 3 puts and 2 calls often result in a neutral posi­ tion. The deltas can be used as a follow-up action, by adjusting the ratio to remain neutral after a move by the underlying stock. AVOID EXCESS TRADING In any of the straddle and strangle writing strategies described above, too much fol­ low-up action can be detrimental because of the commission costs involved. Thus, although it is important to take protective action, the straddle writer should plan in advance to make the minimum number of strategic moves to protect himself. That is why buying protection is often useful; not only does it limit the risk in the direction that the stock is moving, but it also involves only one additional option commission. In fact, if it is feasible, buying protection at the outset is often a better strategy than protecting as a secondary action. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:356 SCORE: 36.00 ================================================================================ 320 Part Ill: Put Option Strategies An extension of this concept of trying to avoid too much follow-up action is that the strategist should not attempt to anticipate movement in an underlying stock. For example, if the straddle writer has planned to take defensive action should the stock reach 50, he should not anticipate by taking action with the stock at 48 or 49. It is possible that the stock could retreat back down; then the writer would have taken a defensive action that not only cost him commissions, but reduced his profit potential. Of course, there is a little trader in everyone, and the temptation to anticipate (or to wait too long) is always there. Unless there are very strong technical reasons for doing so, the strategist should resist the temptation to trade, and should operate his strate­ gy according to his original plan. The ratio writer may actually have an advantage in this respect, because he can use buy and sell stops on the underlying stock to remove the emotion from his follow-up strategy. This technique was described in Chapter 6 on ratio call writing. Unfortunately, no such emotionless technique exists for the straddle or strangle writer. USING THE CREDITS In previous chapters, it was mentioned that the sale of uncovered options does not require any cash investment on the pait of the strategist. He may use the collateral value of his present portfolio to finance the sale of naked options. Moreover, once he sells the uncovered options, he can take the premium dollars that he has brought in from the sales to buy fixed-income securities, such as Treasury bills. The same state­ ments naturally apply to the straddle writing and strangle writing strategies. However, the strategist should not be overly obsessed with continuing to maintain a credit bal­ ance in his positions, nor should he strive to hold onto the Treasury bills at all costs. If one's follow-up actions dictate that he must take a debit to avoid losses or that he should sell out his Treasury bills to keep a credit, he should by all means do so. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:357 SCORE: 17.00 ================================================================================ Synthetic Stock Positions Created by Puts and Calls It is possible for a strategist to establish a position that is essentially the same as a stock position, and he can do this using only options. The option position generally requires a smaller margin investment and may have other residual benefits over sim­ ply buying stock or selling stock short. In brief, the strategies are summarized by: 1. Buy call and sell put instead of buying stock. 2. Buy put and sell call instead of selling stock short. SYNTHETIC LONG STOCK When one buys a call and sells a put at the same strike, he sets up a position that is equivalent to owning the stock. His position is sometimes called "synthetic" long stock. Example: To verify that this option position acts much like a long stock position would, suppose that the following prices exist: XYZ common, 50; XYZ January 50 call, 5; and XYZ January 50 put, 4. If one were bullish on XYZ and wanted to buy stock at 50, he might consider the alternative strategy of buying the January 50 call and selling (uncovered) the January 321 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:358 SCORE: 52.00 ================================================================================ 322 Part Ill: Put Option Strategies 50 put. By using the option strategy, the investor has nearly the same profit and loss potential as the stock buyer, as shown in Table 21-1. The two right-hand columns of the table compare the results of the option strategy with the results that would be obtained by merely owning the stock at .50. The table shows that the result of the option strategy is exactly $100 less than the stock results for any price at expiration. Thus, the "synthetic" long stock and the actual long stock have nearly the same profit and loss potentials. The reason there is a difference in the results of the two equivalent positions lies in the fact that the option strategist had to pay 1 point of time premium in order to set up his position. This time premium represents the $100 by which the "synthetic" position underper­ forms the actual stock position at expiration. Note that, with XYZ at 50, both the put and the call are completely composed of time value premium initially. The synthetic position consists of paying out 5 points of time premium for the call and receiving in 4 points of time premium for the put. The net time premium is thus a 1-point pay­ out. The reason one would consider using the synthetic long stock position rather than the stock position itself is that the synthetic position may require a much small­ er investment than buying the stock would require. The purchase of the stock requires $5,000 in a cash account or $2,500 in a margin account (if the margin rate is 50%). However, the synthetic position requires only a $100 debit plus a collateral requirement - 20% of the stock price, plus the put premium, minus the difference between the striking price and the stock price. The balance, invested in short-term funds, would earn enough money, theoretically, to offset the $100 paid for the syn­ thetic position. In this example, the collateral requirement would be 20% of $5,000, or $1,000, plus the $400 put premium, plus the $100 debit incurred by paying 5 for the call and only receiving 4 for the put. This is a total of $1,500 initially. There is no TABLE 21·1. Synthetic long stock position. XYZ Price at January 50 January 50 Total Option Long Stock Expiration Call Result Put Result Result Result 40 -$500 -$600 -$1, 100 -$1,000 45 - 500 - 100 600 500 50 - 500 + 400 100 0 55 0 + 400 + 400 + 500 60 + 500 + 400 + 900 + 1,000 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:359 SCORE: 56.00 ================================================================================ Chapter 21: Synthetic Stock Positions Created by Puts and Calls 323 initial difference between the stock price and the striking price. Of course, this col­ lateral requirement would increase if the stock fell in price, and would decrease if the stock rose in price, since there is a naked put. Also notice that buying stock creates a $5,000 debit in the account, whereas the option strategy's debit is $100; the rest is a collateral requirement, not a cash requirement. The effect of this reduction in margin required is that some leverage is obtained in the position. If XYZ rose to 60, the stock position profit would be $1,000 for a return of 40% on margin ($1,000/$2,500). With the option strategy, the percentage return would be higher. The profit would be $900 and the return thus 60% ($900/$1,500). Of course, leverage works to the downside as well, so that the percent risk is also greater in the option strategy. The synthetic stock strategy is generally not applied merely as an alternative to buying stock. Besides possibly having a smaller profit potential, the option strategist does not collect dividends, whereas the stock owner does. However, the strategist is able to earn interest on the funds that he did not spend for stock ownership. It is important for the strategist to understand that a long call plus a short put is equiva­ lent to long stock. It thus may be possible for the strategist to substitute the synthet­ ic option position in certain option strategies that normally call for the purchase of stock SYNTHETIC SHORT SALE A position that is equivalent to the short sale of the underlying stock can be estab­ lished by selling a call and simultaneously buying a put. This alternative option strat­ egy, in general, offers significant benefits when compared with selling the stock short. Using the prices above - XYZ at 50, January 50 call at 5, and January 50 put at 4 - Table 21-2 depicts the potential profits and losses at January expiration. Both the option position and the short stock position have similar results: large potential profits if the stock declines and unlimited losses if the underlying stock rises in price. However, the option strategy does better than the stock position, because the option strategist is getting the benefit of the time value premium. Again, this is because the call has more time value premium than the put, which works to the option strategist's advantage in this case, when he is selling the call and buying the put. Two important factors make the option strategy preferable to the short sale of stock: (1) There is no need to borrow stock, and (2) there is no need for an uptick. When one sells stock short, he must first borrow the stock from someone who owns it. This procedure is handled by one's brokerage firm's stock loan department. If, for ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:360 SCORE: 28.00 ================================================================================ 324 Part Ill: Put Option Strategies TABLE 21-2. Synthetic short sale position. XYZ Price at January 50 January 50 Total Option Short Stock Expiration Coll Result Put Result Result Result 40 +$500 +$600 +$1, 100 +$1,000 45 + 500 + 100 + 600 + 500 50 + 500 - 400 + 100 0 55 0 - 400 400 500 60 - 500 - 400 900 - 1,000 some reason, no one who owns the stock wants to loan it out, then a short sale can­ not be executed. In addition, both the NYSE and NASDAQ require that a stock being sold short must be sold on an uptick. That is, the price of the short sale must be higher than the previous sale. This rule was introduced (for the NYSE) years ago in order to prevent traders from slamming the market down in a "bear raid." With the option "synthetic short sale" strategy, however, one does not have to worry about either of these factors. First, calls can be sold short at will; there is no need to borrow anything. Also, calls can be sold short (and puts bought) even though the underlying stock might be trading on a minus tick (a downtick). Many profes­ sional traders use the "synthetic short sale" strategy because it allows them to get equivalently short the stock in a very timely manner. If one wants to short stock, and if he has not previously arranged to borrow it, then some time is wasted while one's broker checks with the stock loan department in order to make sure that the stock can indeed be borrowed. There is a caveat, however. If one sells calls on a stock that cannot be borrowed, then he must be sure to avoid assignment. For if one is assigned a call, then he too will be short the stock. If the stock cannot be borrowed, the broker will buy him in. Thus, in situations in which the stock might be difficult to borrow, one should use a striking price such that the call is out-of-the-money when sold initially. This will decrease, but not eliminate, the possibility of early assignment. Leverage is a factor in this strategy also. The short seller would need $2,500 to collateralize this position, assuming that the margin rate is 50%. The option strategist initially only needs 20% of the stock price, plus the call price, less the credit received, for a $1,400 requirement. Moreover, one of the major disadvantages that was men­ tioned with the synthetic long stock position is not a disadvantage in the synthetic short sale strategy: The option trader does not have to pay out dividends on the options, but the short seller of stock must. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:361 SCORE: 48.00 ================================================================================ Chapter 21: Synthetic Stock Positions Created by Puts and Calls 325 Because of the advantages of the option position in not having to pay out the dividend and also having a slightly larger profit potential from the excess time value premium, it may often be feasible for the trader who is looking to sell stock short to instead sell a call and buy a put. It is also important for the strategist to understand the equivalence between the short stock position and the option position. He might be able to substitute the option position in certain cases when the short sale of stock is normally called for. SPLITTING THE STRIKES The strategist may be able to use a slight variation of the synthetic strategy to set up an aggressive, but attractive, position. Rather than using the same striking price for the put and call, he can use a lower striking price for the put and a higher striking price for the call. This action of splitting apart the striking prices gives him some room for error, while still retaining the potential for large profits. BULLISHLY ORIENTED If an out-of-the-money put is sold naked, and an out-of-the-money call is simultane­ ously purchased, an aggressive bullish position is established - often for a credit. If the underlying stock rises far enough, profits can be generated on both the long call and the short put. If the stock remains relatively unchanged, the call purchase will be a loss, but the put sale will be a profit. The risk occurs if the underlying stock drops in price, producing losses on both the short put and the long call. Example: The following prices exist: XYZ is at 53, a January 50 put is selling for 2, and a January 60 call is selling for 1. An investor who is bullish on XYZ sells the January 50 put naked and simultaneously buys the January 60 call. This position brings in a credit of 1 point, less commissions. There is a collateral requirement necessary for the naked put. If XYZ is anywhere between 50 and 60 at January expiration, both options would expire worthless, and the investor would make a small profit equal to the amount of the initial credit received. If XYZ rallies above 60 by expiration, however, his potential profits are unlimited, since he owns the call at 60. His losses could be very large if XYZ should decline well below 50 before expiration, since he has written the naked put at 50. Table 21-3 and Figure 21-1 depict the results at expiration of this strategy. Essentially, the investor who uses this strategy is bullish on the underlying stock and is attempting to buy an out-of-the-money call for free. If he is moderately wrong ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:362 SCORE: 13.00 ================================================================================ 326 TABLE 21-3. Bullishly split strikes. XYZ Price al January 50 Expirafion 40 45 50 55 60 65 70 FIGURE 21-1. Bullishly split strikes. Pu! Profil -$800 - 300 + 200 + 200 + 200 + 200 + 200 Part Ill: Put Option Strategies January 60 Tolal Call Profil Profif -$100 -$ 900 - 100 400 - 100 + 100 - 100 + 100 - 100 + 100 + 400 + 600 + 900 + 1,100 Stock Price at Expiration and the underlying stock rallies only slightly or even declines slightly, he can still make a small profit. If he is correct, of course, large profits could be generated in a rally. He may lose heavily if he is very wrong and the stock falls by a large amount instead of rising. This strategy is often useful when options are overpriced. Suppose that one has a bullish opinion on the underlying stock, yet is dismayed to find that the calls are quite expensive. If he buys one of these expensive calls, he can mitigate the expen­ siveness somewhat by also selling an out-of-the-money put, which is presumably ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:363 SCORE: 29.00 ================================================================================ Chapter 21: Synthetic Stock Positions Created by Puts and Calls 327 somewhat expensive also. Thus, if he is right about the bullish attitude on the stock, he owns a call that is more "fairly priced" because its cost was reduced by the amount of the put sale. BEARISHLY ORIENTED There is a companion strategy for the investor who is bearish on a stock. He could attempt to buy an out-of-the-money put, giving himself the opportunity for substan­ tial profits in a stock price decline, and could "finance" the purchase of the put by writing an out-of-the-money call naked. The sale of the call would provide profits if the stock stayed below the striking price of the call, but could cost him heavily if the underlying stock rallies too far. Example: With XYZ at 65, the bearish investor buys a February 60 put for 2 points, and simultaneously sells a February 70 call for 3 points. These trades bring in a cred­ it of 1 point, less commissions. The investor must collateralize the sale of the call. If XYZ should decline substantially by February expiration, large profits are possible because the February 60 put is owned. Even if XYZ does not perform as expected, but still ends up anywhere between 60 and 70 at expiration, the profit will be equal to the initial credit because both options will expire worthless. However, if the stock rallies above 70, unlimited losses are possible because there is a naked call at 70. Table 21-4 and Figure 21-2 show the results of this strategy at expiration. This is clearly an aggressively bearish strategy. The investor would like to own an out-of-the-money put for downside potential. In addition, he sells an out-of-the­ money call, normally for a price greater than that of the purchased put. The call sale TABLE 21-4. Bearishly split strikes. XYZ Price at February 60 February 70 Total Expiration Put Profit Call Profit Profit 50 +$800 +$300 +$1, 100 55 + 300 + 300 + 600 60 - 200 + 300 + 100 65 - 200 + 300 + 100 70 - 200 + 300 + 100 75 - 200 - 200 400 80 - 200 - 700 900 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:364 SCORE: 25.00 ================================================================================ 328 FIGURE 21-2. Bearishly split strikes. C 0 e ·15. X w Part Ill: Put Option Strategies 1u +$100 w $0 I-----------'------ ................. ----- ~ 60 ....J 0 ~ a. Stock Price at Expiration essentially lets him own the put for free. In fact, he can still make profits even if the underlying stock rises slightly or only falls slightly. His risk is realized if the stock rises above the striking price of the written call. This strategy of splitting the strikes in a bearish manner is used very frequently in conjunction with the ownership of common stock. That is, a stock owner who is looking to protect his stock will buy an out-of-the-money put and sell an out-of-the­ money call to finance the put purchase. This strategy is called a "protective collar" and was discussed in more detail in the chapter on Put Buying in Conjunction with Common Stock Ownership. A strategy that is similar to these, but modifies the risk, is presented in Chapter 23, Spreads Combining Calls and Puts. SUMMARY In either of these aggressive strategies, the investor must have a definite opinion about the future price movement of the underlying stock. He buys an out-of-the­ money option to provide profit potential for that stock movement. However, an investor can lose the entire purchase proceeds of an out-of-the-money option if the stock does not perform as expected. An aggressive investor, who has sufficient collat­ eral, might attempt to counteract this effect by also writing an out-of-the-money option to cover the cost of the option that he bought. Then, he will not only make money if the stock performs as expected, but he will also make money if the stock remains relatively unchanged. He will lose quite heavily, however, if the underlying stock goes in the opposite direction from his original anticipation. That is why he must have a definite opinion on the stock and also be fairly certain of his timing. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:365 SCORE: 35.00 ================================================================================ Basic Put Spreads Put spreading strategies do not differ substantially in theory from their accompany- ;,,..,,. ,...,,1] v-n..-a<>rl vl-..-al-arriac Rol-h h11llich nnrl hP<>rich nocitionc r>!'.ln hP r>onctn1r>tPrl with .l.J..1.5 V(A,,1.1. .;Jt'.l.'\,.,U'L.L J\...l 1.Vf,A.VoJ• .Jl.,l''\Jl,....t..1. J.J\..1..1..1..1.V.a...._ f.4.1..1..._... ,._,...,_,'-4Ji.A.V..._.,._ ,t'"-"._,..._ ... ...__..._..._...,, .._,.__...,,._ -....,..., _.._,,.._.,....,,...,._ .....,._,_....,,_ , , ,,..._.,._""- put spreads, as was also the case with call spreads. However, because puts are more oriented toward downward stock movement than calls are, some bearish put spread strategies are superior to their equivalent bearish call spread strategies. The three simplest forms of option spreads· are: 1. the bull spread, 2. the bear spread, and 3. the calendar spread. The same types of spreads that were constructed with calls can be established with puts, but there are some differences. BEAR SPREAD In a call bear spread, a call with a lower striking price was sold while a call at a high­ er striking price was bought. Similarly, a put bear spread is established by selling a put at a lower strike while buying a put at a higher strike. The put bear spread is a debit spread. This is true because a put with a higher striking price will sell for more than a put with a lower striking price. Thus, on a stock with both puts and calls trad­ ing, one could set up a bear spread for a credit ( using calls) or alternatively set one up for a debit (using puts): 329 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:366 SCORE: 76.00 ================================================================================ 330 Put Bear Spread Buy XYZ January 60 put Sell XYZ January 50 put (debit spread) Part Ill: Put Option Strategies Call Bear Spread Buy XYZ January 60 call Sell XYZ January 50 call (credit spread) The put bear spread has the same sort of profit potential as the call bear spread. There is a limited maximum potential profit, and this profit would be realized if XYZ were below the lower striking price at expiration. The put spread would widen, in this case, to equal the difference between the striking prices. The maximum risk is also limited, and would be realized if XYZ were anywhere above the higher striking price at expiration. Example: The following prices exist: XYZ common, 55; XYZ January 50 put, 2; and XYZ January 60 put, 7. Buying the January 60 put and selling the January 50 would establish a bear spread for a 5-point debit. Table 22-1 will help verify that this is indeed a bearish position. The reader will note that Figure 22-1 has the same shape as the call bear spread's graph (Figure 8-1). The investment required for this spread is the net debit, and it must be paid in full. Notice that the maximum profit potential is realized any­ where below 50 at expiration, and the maximum risk potential is realized anywhere above 60 at expiration. The maximum risk is always equal to the initial debit required to establish the spread plus commissions. The break-even point is 55 in this example. The following formulae allow one to quickly compute the meaningful statistics regarding a put bear spread. Maximum risk = Initial debit Maximum profit = Difference between strikes - Initial debit Break-even price = Higher striking price - Initial debit Put bear spreads have an advantage over call bear spreads. With puts, one is selling an out-of-the-money option when setting up the spread. Thus, one is not risk­ ing early exercise of his written option before the spread becomes profitable. For the written put to be in-the-money, and thus in danger of being exercised, the spread would have to be profitable, because the stock would have to be below the lower striking price. Such is not the case with call bear spreads. In the call spread, one sells an in-the-money call as part of the bear spread, and thus could be at risk of early exer­ cise before the spread has a chance to become profitable. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:367 SCORE: 47.00 ================================================================================ Chapter 22: Basic Put Spreads 331 TABLE 22-1. Put bear spread. XYZ Price at January 50 January 60 Total Expiration Put Profit Put Profit Profit 40 -$800 +$1,300 +$500 45 - 300 + 800 + 500 50 + 200 + 300 + 500 55 + 200 200 0 60 + 200 700 - 500 70 + 200 700 - 500 80 + 200 700 - 500 FIGURE 22-1. Put bear spread. Stock Price at Expiration Beside this difference in the probability of early exercise, the put bear spread holds another advantage over the call bear spread. In the put spread, if the underly­ ing stock drops quickly, thereby making both options in-the-rrwney, the spread will normally widen quickly as well. This is because, as has been mentioned previously, put options tend to lose time value premium rather quickly when they go into-the­ money. In the example above, if XYZ rapidly dropped to 48, the January 60 put would be near 12, retaining very little time premium. However, the January 50 put that is short would also not retain much time value premium, perhaps selling at 4 points or ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:368 SCORE: 79.00 ================================================================================ 332 Part Ill: Put Option Strategies so. Thus, the spread would have widened to 8 points. Call bear spreads often do not produce a similar result on a short-term downward movement. Since the call spread involves being short a call with a lower striking price, this call may actually pick up time value premium as the stock falls close to the lower strike. Thus, even though the call spread might have a similar profit at expiration, it often will not perform as well on a quick downward movement. For these two reasons - less chance of early exercise and better profits on a short-term movement - the put bear spread is superior to the call bear spread. Some investors still prefer to use the call spread, since it is established for a credit and thus does not require a cash investment. This is a rather weak reason to avoid the superi­ or put spread and should not be an overriding consideration. Note that the margin requirement for a call bear spread will result in a reduction of one's buying power by an amount approximately equal to the debit required for a similar put bear spread. (The margin required for a call bear spread is the difference between the striking prices less the credit received from the spread.) Thus, the only accounts that gain any substantial advantage from a credit spread are those that are near the minimum equi­ ty requirement to begin with. For most brokerage firms, the minimum equity requirement for spreads is $2,000. BULL SPREAD A bull spread can be established with put options by buying a put at a lower striking price and simultaneously selling a put with a higher striking price. This, again, is the same way a bull spread was constructed with calls: selling the higher strike and buy­ ing the lower strike. Example: The same prices can be used: XYZ common, 55; XYZ January 50 put, 2; and XYZ January 60 put, 7. The bull spread is constructed by buying the January 50 put and selling the January 60 put. This is a credit spread. The credit is 5 points in this example. If the underly­ ing stock advances by January expiration and is anywhere above 60 at that time, the maximum profit potential of the spread will be realized. In that case, with XYZ any­ where above 60, both puts would expire worthless and the spreader would make a profit of the entire credit - 5 points in this example. Thus, the maximum profit poten­ tial is limited, and the maximum profit occurs if the underlying stock rises in price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:369 SCORE: 56.00 ================================================================================ Chapter 22: Basic Put Spreads 333 above the higher strike. These are the same qualities that were displayed by a call bull spread (Chapter 7). The name "bull spread" is derived from the fact that this is a bull­ ish position: The strategist wants the underlying stock to rise in price. The risk is limited in this spread. If the underlying stock should decline by expi­ ration, the maximum loss will be realized with XYZ anywhere below 50 at that time. The risk is 5 points in this example. To see this, note that if XYZ were anywhere below 50 at expiration, the differential between the two puts would widen to 10 points, since that is the difference between their striking prices. Thus, the spreader would have to pay 10 points to buy the spread back, or to close out the position. Since he initially took in a 5-point credit, this means his loss is equal to 5 points - the 10-point cost of closing out less the 5 points he received initially. The investment required for a bullish put spread is actually a collateral require­ ment, since the spread is a credit spread. The amount of collateral required is equal -1-r.. f-ha rliffa:rannci, hahuaan tho cfr-il;nrr r\rint::u.:- lace th.-:;). not nrorlit ror-A-iuorl fnr thA \..V l,,J...111._, Ul.J..J..V.lV.l.l.\..,V LIV\..VVVVJ..l '-- J.'L, oJ\..l..l.J.'-l.J.J..o .t'.l.J..\,.,VoJ J.VoJ,J I..J.J.'-' J..1.V\.. \,.,.l.V"-AJ.l.- .LVV'-'..l.Y'-'"'--4 .J..'-.-".I. .__...._.._ ....... spread. In this example, the collateral requirement is $500- the $1,000, or 10-point, differential in the striking prices less the $500 credit received from the spread. Note that the maximum possible loss is always equal to the collateral requirement in a bull­ ish put spread. It is not difficult to calculate the break-even point in a bullish spread. ·In this example, the break-even point before commissions is 55 at expiration. With XYZ at 55 in January, the January 50 put would expire worthless and the January 60 put would have to be bought back for 5 points. It would be 5 points in-the-money with XYZ at 55. Thus, the spreader would break even, since he originally received 5 points credit for the spread and would then pay out 5 points to close the spread. The fol­ lowing formulae allow one to quickly compute the details of a bullish put spread: Maximum potential risk = Initial collateral requirement = Difference in striking prices - Net credit received Maximum potential profit= Net credit Break-even price = Higher striking price - Net credit CALENDAR SPREAD In a calendar spread, a near-term option is sold and a longer-term option is bought, both with the same striking price. This definition applies to either a put or a call cal­ endar spread. In Chapter 9, it was shown that there were two philosophies available for call calendar spreads, either neutral or bullish. Similarly, there are two philoso­ phies available for put calendar spreads: neutral or bearish. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:370 SCORE: 87.00 ================================================================================ 334 Part Ill: Put Option Strategies In a neutral calendar spread, one sets up the spread with the idea of closing the spread when the near-term call or put expires. In this type of spread, the maximum profit will be realized if the stock is exactly at the striking price at expiration. The spreader is merely attempting to capitalize on the fact that the time value premium disappears more rapidly from a near-term option than it does from a longer-term one. Example: XYZ is at 50 and a January 50 put is selling for 2 points while an April 50 put is selling for 3 points. A neutral calendar spread can be established for a 1-point debit by selling the January 50 put and buying the April 50 put. The investment required for this position is the amount of the net debit, and it must be paid for in full. If XYZ is exactly at 50 at January expiration, the January 50 put will expire worth­ less and the April 50 put will be worth about 2 points, assuming other factors are the same. The neutral spreader would then sell the April 50 put for 2 points and take his profit. The spreader's profit in this case would be one point before commissions, because he originally paid a 1-point debit to set up the spread and then liquidates the position by selling the April 50 put for 2 points. Since commission costs can cut into available profits substantially, spreads should be established in a large enough quan­ tity to minimize the percentage cost of commissions. This means that at least 10 spreads should be set up initially. In any type of calendar spread, the risk is limited to the amount of the net debit. This maximum loss would be realized if the underlying stock moved substantially far away from the striking price by the time the near-term option expired. If this hap­ pened, both options would trade at nearly the same price and the differential would shrink to practically nothing, the worst case for the calendar spreader. For example, if the underlying stock drops substantially, say to 20, both the near-term and the long­ term put would trade at nearly 30 points. On the other hand, if the underlying stock rose substantially, say to 80, both puts would trade at a very low price, say 1/15 or 1/s, and again the spread would shrink to nearly zero. Neutral call calendar spreads are generally superior to neutral put calendar spreads. Since the amount of time value premium is usually greater in a call option (unless the underlying stock pays a large dividend), the spreader who is interested in selling time value would be better off utilizing call options. The second philosophy of calendar spreading is a more aggressive one. With put options, a bearish strategy can be constructed using a calendar spread. In this case, one would establish the spread with out-of-the-money puts. Example: With XYZ at 55, one would sell the January 50 put for 1 point and buy the April 50 put for 1 ½ points. He would then like the underlying stock to remain above the striking price until the near-term January put expires. If this happens, he would ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:371 SCORE: 38.00 ================================================================================ Chapter 22: Basic Put Spreads 335 make the I-point profit from the sale of that put, reducing his net cost for the April 50 put to ½ point. Then, he would become bearish, hoping for the underlying stock to decline in price substantially before April expiration in order that he might be able to generate large profits on the April 50 put he holds. Just as the bullish calendar spread with calls can be a relatively attractive strat­ egy, so can the bearish calendar spread with puts. Granted, two criteria have to be fulfilled in order for the position to work to the optimum: The near-term put must expire worthless, and then the underlying stock must drop in order to generate prof­ its on the long side. Although these conditions may not occur frequently, one prof­ itable situation can more than make up for several losing ones. This is true because the initial debit for a bearish calendar spread is small, ½ point in the example above. Thus, the losses will be small and the potential profits could be very large if things work out right. The aggressive spreader must be careful not to "leg out" of his spread, since he could generate a large loss by doing so. The object of the strategy is to accept a rather large number of small losses, with the idea that the infrequent large profits will more than offset the sum of the losses. If one generates a large loss somewhere along the way, this may ruin the overall strategy. Also, if the underlying stock should fall to the striking price before the near-term put expires, the spread will normally have widened enough to produce a small profit; that profit should be taken by closing the spread at that time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:372 SCORE: 55.00 ================================================================================ Spreads Cotnbining Calls and Puts Certain types of spreads can be constructed that utilize both puts and calls. One of these strategies has been discussed before: the butterfly spread. However, other strategies exist that off er potentially large profits to the spreader. These other strate­ gies are all variations of calendar spreads and/or straddles that involve both put and call options. THE BUTTERFLY SPREAD This strategy has been described previously, although its usage in Chapter 10 was restricted to constructing the spread with calls. Recall that the butterfly spread is a neutral position that has limited risk as well as limited profits. The position involves three striking prices, utilizing a bull spread between the lower two strikes and a bear spread between the higher two strikes. The maximum profit is realized at the middle strike at expiration, and the maximum loss is realized if the stock is above the higher strike or below the lower strike at expiration. Since either a bull spread or a bear spread can be constructed with puts or calls, it should be obvious that a butterfly spread ( consisting of both a bull spread and a bear spread) can be constructed in a number of ways. In fact, there are four ways in which the spread can be established. If option prices are fairly balanced - that is, the arbitrageurs are keeping prices in line - any of the four ways will have the same potential profits and losses at expiration of the options. However, because of the ways in which puts and calls behave prior to their expiration, certain advantages or disad- 336 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:373 SCORE: 65.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 331 vantages are connected with some of the methods of establishing the butterfly spread. Example: The following prices exist: Strike: Call: Put: XYZ common: 60 50 12 60 6 5 70 2 1 1 The method using only the calls indicates that one would buy the 50 call, sell two 60 calls, and buy the 70 call. Thus, there would be a bull spread in the calls between the 50 and 60 strikes, and a bear spread in the calls between the 60 and 70 strikes. In a similar manner, one could establish a butterfly spread by combining either type of bull spread between the 50 and 60 strikes with any type of bear spread between the 60 and 70 strikes. Some of these spreads would be credit spreads, while others would be debit spreads. In fact, one's personal choice between two rather equivalent makeups of the butterfly spread might be decided by whether there were a credit or a debit involved. Table 23-1 summarizes the four ways in which the butterfly spread might be constructed. In order to verify the debits and credits listed, the reader should recall that a bull spread consists of buying a lower strike and selling a higher strike, whether puts or calls are used. Similarly, bear spreads with either puts or calls consist of buy­ ing a higher strike and selling a lower strike. Note that the third choice - bull spread with puts and bear spread with calls - is a short straddle protected by buying the out­ of-the-money put and call. In each of the four spreads, the maximum potential profit at expiration is 8 points if the underlying stock is exactly at 60 at that time. The maximum possible loss in any of the four spreads is 2 points, if the stock is at or above 70 at expiration or is at or below 50 at expiration. For example, either the top line in the table, where the spread is set up only with calls; or the bottom line, where the spread is set up only with puts, has a risk equal to the debit involved - 2 points. The large-debit spread (second line of table) will be able to be liquidated for a minimum of 10 points at expi­ ration no matter where the stock is, so the risk is also 2 points. (It cost 12 points to begin with.) Finally, the credit combination (third line) has a maximum buy-back of 10 points, so it also has risk of 2 points. In addition, since the striking prices are 10 points apart, the maximum potential profit is 8 points (maximum profit = striking price differential minus maximum risk) in all the cases. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:374 SCORE: 73.00 ================================================================================ 338 TABLE 23-1. Butterfly spread. Bull Spread (Buy Option at 50, ... plus ... Sell at 60) Calls (6 debit) Calls (6 debit) Puts (4 credit) Puts (4 credit) Bear Spread (Buy Option at 70, Sell at 60) Calls (4 credit) Puts (6 debit) Calls (4 credit) Puts (6 debit) Part Ill: Put Option Strategies Total Money 2 debit 12 debit 8 credit 2 debit The factor that causes all these combinations to be equal in risk and reward is the arbitrageur. If put and call prices get too far out of line, the arbitrageur can take riskless action to force them back. This particular form of arbitrage, known as the box spread, is described later, in Chapter 27, Arbitrage. Even though all four ways of constructing the butterfly spread are equal at expiration, some are superior to others for certain price movements prior to expira­ tion. Recall that it was previously stated that bull spreads are best constructed with calls, and bear spreads are best constructed with puts. Since the butterfly spread is merely the combination of a bull spread and a bear spread, the best way to set up the butterfly spread is to use calls for the bull spread and puts for the bear spread. This combination is the one listed on the second line of Table 23-1. This strategy involves the largest debit of the four combinations and, as a result, many investors shun this approach. However, all the other combinations involve selling an in-the-money put or call at the outset, a situation that could lead to early exercise. The reader may also recall that the credit combination, listed on the third line of Table 23-1, was previ­ ously described as a protected straddle position. That is, one sells a straddle and simultaneously buys both an out-of-the-money put and an out-of-the-money call with the same expiration month, as protection for the straddle. Thus, a butterfly spread is actually the equivalent of a completely protected straddle wiite. A butterfly spread is not an overly attractive strategy, although it may be useful from time to time. The commissions required are extremely high, and there is no chance of making a large profit on the position. The limited risk feature is good to have in a position, but it alone cannot compensate for the less attractive features of the strategy. Essentially, the strategist is looking for the stock to remain in a neutral pattern until the options expire. If the potential profit is at least three times the max­ imum 1isk (and preferably four times) and the underlying stock appears to be in trad­ ing range, the strategy is feasible. Othe:nvise, it is not. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:375 SCORE: 60.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 339 COMBINING AN OPTION PURCHASE AND A SPREAD It is possible to combine the purchase of a call and a credit put spread to produce a position that behaves much like a call buy, although it has less risk over much of the profit range. This strategy is often used when one has a quite bullish opinion regard­ ing the underlying security, yet the call one wishes to purchase is "overpriced." In a similar manner, if one is bearish on the underlying, he can sometimes combine the purchase of a put with the sale of a call credit spread. Both approaches are described in this section. THE BULLISH SCENARIO It sometimes happens that one arrives at a bullish opinion regarding a stock, only to find that the options are very expensive. In fact, they may be so expensive as to pre­ clude thoughts of making an outright call purchase. This might happen, for example, if the stock has suddenly plummeted in price (perhaps during an ongoing, rapid bear­ ish move by the overall stock market). To buy calls at this time would be overly risky. If the underlying began to rally, it would often be the case that the implied volatility of the calls would shrink, thus harming one's long call position. As a counter to this, it might make sense to buy the call, but at the same time to sell a put credit spread. Recall that a put credit spread is a bullish strategy. Moreover, since it is presumed that the options are expensive on this particular stock, the puts being used in the spread would be expensive as well. Thus, the credit received from the spread would be slightly larger than "normal" because the options are expensive. Example: XYZ is selling at 100. One wishes to purchase the December 100 call as an outright bullish speculation. That call is selling for 10. However, one determines that the December 100 call is overpriced at these levels. (In order to make this determi­ nation, one would use an option model whose techniques are described in Chapter 28 on mathematical applications.) Hence, he decides to use the following put spread in addition to buying the December 100 call: Sell December 90 put, 6 Buy December 80 put, 3 The sale of the put spread brings in a 3-point credit. Thus, his total expenditure for the entire position is 7 points ( 10 for the December 100 call, less 3 credit from the sale of the put spread). If one is correct about his bullish outlook for the stock (i.e., the stock goes up), he can in some sense consider that he paid 7 for the call. Another way ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:376 SCORE: 72.00 ================================================================================ 340 Part Ill: Put Option Strategies to look at it is this: The sale of the put spread reduces the call price down to a more moderate level, one that might be in line with its "theoretical value." In other words, the call would not be considered expensive if it were priced at 7 instead of 10. The sale of the put spread can be considered a way to reduce the overall cost of the call. Of course, the sale of the put spread brings some extra risk into the position because, if the stock were to fall dramatically, the put spread could lose 7 points ( the width of the strikes in the spread, 10 points, less the initial credit received, 3 points). This, added to the call's cost of 10 points, means that the entire risk here is 17 points. In fact, that is the margin required for this spread as well. Thus, the overall spread still has limited risk, because both the call purchase and the put credit spread are lim­ ited-risk strategies. However, the total risk of the two combined is larger than for either one separately. Remember that one must be bullish on the underlying in order to employ this strategy. So, if his analysis is correct, the upside is what he wants to maximize. If he is wrong on his outlook for the stock, then he needs to employ some sort of stop-loss measures before the maximum risk of the position is realized. The resulting position is shown in Figure 23-1, along with two other plots. The straight line marked "Spread at expiration" shows how the profitability of the call pur­ chase combined with a bull spread would look at December expiration. In addition, there is a plot with straight lines of the purchase of the December 100 call for 10 points. That plot can be compared with the three-way spread to see where extra risk and reward occur. Note that the three-way spread does better than the outright pur­ chase of the December 100 call as long as the stock is higher than 87 at expiration. Since the stock is initially at 100 and,since one is initially bullish on the stock, one would have to surmise that the odds of it falling to 87 are fairly small. Thus, the three­ way spread outperforms the outright purchase of the call over a large range of stock prices. The final plot in Figure 23-1 is that of the three-way spread's profit and losses halfway to the expiration date. You can see that it looks much like the profitability of merely owning a call: The curve has the same shape as the call pricing curve shown in Chapter 1. Hence, this three-way strategy can often be more attractive and more profitable than merely owning a call option. Remember, though, that it does increase risk and require a larger collateral deposit than the outright purchase of the at-the-money call would. One can experiment with this strategy, too, in that he might consider buying an out-of-the-money call and selling a put spread that brings in enough credit to com­ pletely pay for the call. In that way, he would have no risk as long as the stock remained above the higher striking price used in the put credit spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:377 SCORE: 48.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts FIGURE 23-1. Call buy and put credit (bull) spread. +$2,000 +$1,000 (/J (/J 0 ..J 0 $0 -e a. -$1,000 -$2,000 70 80 .... ,, -----,, -=-----' THE BEARISH SCENARIO ~ Spread at Expiration Call Buy Only, at Expiration 341 Stock In a similar manner, one can construct a position to take advantage of a bearish opin­ ion on a stock. Again, this would be most useful when the options were overpriced and one felt that an at-the-money put was too expensive to purchase by itself. Example: XYZ is trading at 80, and one has a definite bearish opinion on the stock. However, the December 80 put, which is selling for 8, is expensive according to an option analysis. Therefore, one might consider selling a call credit spread (out-of-the­ money) to help reduce the cost of the put. The entire position would thus be: Buy 1 December 80 put: Sell l December 90 call: Buy 1 December 100 call: Total cost: 8 debit 4 credit 2 debit 6 debit ($600) The profitability of this position is shown in Figure 23-2. The straight line on that graph shows how the position would behave at expiration. The introduction of the call credit spread has increased the risk to $1,600 if the stock should rally to 100 or higher by expiration. Note that the risk is limited since both the put purchase and the call credit spread are limited-risk strategies. The margin required would be this max­ imum risk, or $1,600. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:378 SCORE: 35.00 ================================================================================ 342 Part Ill: Put Option Strategies FIGURE 23-2. Put buy and call credit (bear) spread. +$1,000 Halfway to Expiration / Stock 0 60 110 -e a. -$1,000 At Expiration -$2,000 The curved line on Figure 23-2 shows how the three-way spread would behave if one looked at it halfway to its expiration date. In that case, it has a curved appear­ ance much like the outright purchase of a put option. Thus, this strategy could be appealing to bearishly-oriented traders, especially when the options are expensive. It might have certain advantages over an outright put purchase in that case, but it does require a larger margin investment and has theo­ retically larger risk. A SIMPLE FOLLOW-UP ACTION FOR BULL OR BEAR SPREADS Another way of combining puts and calls in a spread can sometimes be used when one has a bull or bear spread already in place. Suppose that one owns a call bull spread and the underlying stock has advanced nicely. In fact, it is above both of the strikes used in the spread. However, as is often the case, the bull spread may not have widened out to its maximum profit potential. One can use the puts for two purposes at this point: (1) to determine whether the call spread is trading at a "reasonable" value, and (2) to try to lock in some profits. First, let's look at an example of the "rea­ sonable value" verification. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:379 SCORE: 53.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 343 Example: A trader buys an XYZ call bull spread for 5 points. The spread uses the January 70 calls and the January 80 calls. Later, XYZ advances to a price of 88, but there is still a good deal of time remaining in the options. Perhaps the spread has widened out only to 7 points at that time. The trader finds it somewhat disappoint­ ing that the spread has not widened out to its maximum profit potential of 10 points. However, this is a fairly common occurrence with bull and bear spreads, and is one of the factors that may make them less attractive than outright call or put purchases. In any case, suppose the following prices exist: January 80 put, 5 January 70 put, 2 We can use these put prices to verify that the call spread is "in line." Notice that the put spread is 3 points and the call spread is 7 points (both are the January 70-January 80 spread). Thus, they add up to 10 points the width of the strikes. When that occurs, we can conclude that the spreads are "in line" and are trading at theoretical­ ly correct prices. Knowing this information doesn't help one make any more profits, but it does provide some verification of the prices. Many times, one feels frustrated when he sees that a call bull spread has not widened out as he expected it to. Using the put spread as verification can help keep the strategist "on track" so that he makes ration­ al, not emotional, decisions. Now let's look at a similar example, in which perhaps the puts can be used to lock in profits on a call bull spread. Example: Using the same bull spread as in the previous example, suppose that one owns an XYZ call bull spread, having bought the January 70 call and sold the January 80 call for a debit of 5 points. Now assume it is approaching expiration, and the stock is once again at 88. At this time, the spread is theoretically nearing its maximum price of 10. However, since both calls are fairly deeply in-the-money, the market-makers are making very wide spreads in the calls. Perhaps these are the markets, with the stock at 88 and only a week or two remaining until expiration: Coll January 70 call January 80 call Bid Price 17.50 8.80 Asked Price 18.50 8.20 If one were to remove this spread at market prices, he would sell his long January 70 call for 17.50 and would buy his short January 80 call back for 8.20, a cred- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:380 SCORE: 71.00 ================================================================================ 344 Part Ill: Put Option Strategies it of 9.30. Since the maximum value of the spread is l 0, one is giving away 70 cents, quite a bit for just such a short time remaining. However, suppose that one looks at the puts and finds these prices: Put January 80 put January 70 put Bid Price 0.20 none Asked Price 0.40 0.10 One could "lock in" his call spread profits by buying the January 80 put for 40 cents. Ignoring commissions for a moment, if he bought that put and then held it along with the call spread until expiration, he would unwind the call spread for a 10 credit at expiration. He paid 40 cents for the put, so his net credit to exit the spread would be 9.60 - considerably better than the 9.30 he could have gotten above for the call spread alone. This put strategy has one big advantage: If the underlying stock should sudden­ ly collapse and tumble beneath 70 - admittedly, a remote possibility - large profits could accrue. The purchase of the January 80 put has protected the bull spread's profits at all prices. But below 70, the put starts to make extra money, and the spread­ er could profit handsomely. Such a drop in price would only occur if some material­ ly damaging news surfaced regarding X'iZ Company, but it does occasionally happen. If one utilizes this strategy, he needs to carefully consider his commission costs and the possibility of early assignment. For a professional trader, these are irrelevant, and so the professional trader should endeavor to exit bull spreads in this manner whenever it makes sense. However, if the public customer allows stock to be assigned at 80 and exercises to buy stock at 70, he will have two stock commissions plus one put option commission. That should be compared to the cost of two in-the-money call option commissions to remove the call spread directly. Furthermore, if the pub­ lic customer receives an early assignment notice on the short January 80 calls, he may need to provide day-trade margin as he exercises his January 70 calls the next day. Without going into as much detail, a bear spread's profits can be locked in via a similar strategy. Suppose that one owns a January 60 put and has sold a January 50 put to create a bear spread. Later, with the stock at 45, the spreader wants to remove the spread, but again finds that the markets for the in-the-money puts are so wide that he cannot realize anywhere near the 10 points that the spread is theoretically worth. He should then see what the January 50 call is selling for. If it is fractionally priced, as it most likely will be if expiration is drawing nigh, then it can be purchased to lock in the profits from the put spread. Again, commission costs should be con­ sidered by the public customer before finalizing his strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:381 SCORE: 50.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 345 THREE USEFUL BUT COMPLEX STRATEGIES The three strategies presented in this section are all designed to limit risk while allowing for large potential profits if correct market conditions develop. Each is a combination strategy - that is, it involves both puts and calls and each is a calendar strategy, in which near-term options are sold and longer-term options are bought. (A fourth strategy that is similar in nature to those about to be discussed is presented in the next chapter.) Although all of these are somewhat complex and are for the most advanced strategist, they do provide attractive risk/reward opportunities. In addition, the strategies can be employed by the public customer; they are not designed strict­ ly for professionals. All three strategies are described conceptually in this section; specific selection criteria are presented in the next section. A TWO-PRONGED ATTACK {THE CALENDAR COMBINATION} A bullish calendar spread was shown to be a rather attractive strategy. A bullish call calendar spread is established with out-of-the-money calls for a relatively small debit. If the near-term call expires worthless and the stock then rises substantially before the longer-term call expires, the profits could potentially be large. In any case, the risk is limited to the small debit required to establish the spread. In a similar man­ ner, the bearish calendar spread that uses put options can be an attractive strategy as well. In this strategy, one would set up the spread with out-of-the-money puts. He would then want the near-term put to expire worthless, followed by a substantial drop in the stock price in order to profit on the longer-term put. Since both strategies are attractive by themselves, the combination of the two should be attractive as well. That is, with a stock midway between two striking prices, one might set up a bullish out-of-the-money call calendar spread and simultaneously establish a bearish out-of-the-money put calendar spread. If the stock remains rela­ tively stable, both near-term options would expire worthless. Then a substantial stock price movement in either direction could produce large profits. With this strategy, the spreader does not care which direction the stock moves after the near options expire worthless; he only hopes that the stock becomes volatile and moves a large dis­ tance in either direction. Example: Suppose that the following prices exist three months before the January options expire: January 70 call: 3 April 70 call: 5 XYZ common: 65 January 60 put: 2 April 60 put: 3 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:382 SCORE: 50.00 ================================================================================ 346 Part Ill: Put Option Strategies The bullish portion of this combination of calendar spreads would be set up by sell­ ing the shorter-term January 70 call for 3 points and simultaneously buying the longer-term April 70 call for 5 points. This portion of the spread requires a 2-point debit. The bearish portion of the spread would be constructed using the puts. The near-term January 60 put would be sold for 2 points, while the longer-term April 60 put would be bought for 3. Thus, the put portion of the spread is a I-point debit. Overall, then, the combination of the calendar spreads requires a 3-point debit, plus commissions. This debit is the required investment; no additional collateral is required. Since there are four options involved, the commission cost will be large. Again, establishing the spreads in quantity can reduce the percentage cost of com­ missions. Note that all the options involved in this position are initially out-of-the-money. The stock is below the striking price of the calls and is above the striking price of the puts. One has sold a near-term put and call combination and purchased a longer-term combination. For nomenclature purposes, this strategy is called a "calendar combi­ nation." There are a variety of possible outcomes from this position. First, it should be understood that the risk is limited to the amount of the initial debit, 3 points in this example. If the underlying stock should rise dramatically or fall dramatically before the near-term options expire, both the call spread and the put spread will shrink to nearly nothing. This would be the least desirable result. In actual practice, the spread would probably have a small positive differential left even after a premature move by the underlying stock, so that the probability of a loss of the entire debit would be small. If the near-term options both expire worthless, a profit will generally exist at that time. Example: IfXYZ were still at 65 at January expiration in the prior example, the posi­ tion should be profitable at that time. The January call and put would expire worth­ less with XYZ at 65, and the April options might be worth a total of 5 points. The spread could thus be closed for a profit with XYZ at 65 in January, since the April options could be sold for 5 points and the initial "cost" of the spread was only 3 points. Although commissions would substantially reduce this 2-point gross profit, there would still be a good percentage profit on the overall position. If the strategist decides to take his profit at this time, he would be operating in a conservative manner. However, the strategist may want to be more aggressive and hold onto the April combination in hopes that the stock might experience a substantial movement before those options expire. Should this occur, the potential profits could be quite large. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:383 SCORE: 40.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 347 Example: If the stock were to undergo a very bullish move and rise to 100 before April expiration, the April 70 call could be sold for 30 points. (The April 60 put would expire worthless in that case.) Alternatively, if the stock plunged to 30 by April expi­ ration, the put at 60 could be sold for 30 points while the call expired worthless. In either case, the strategist would have made a substantial profit on his initial 3-point investment. It may be somewhat difficult for the strategist to decide what he wants to do after the near-term options expire worthless. He may be torn between taking the lim­ ited profit that is at hand or holding onto the combination that he owns in hopes of larger profits. A reasonable approach for the strategist to take is to do nothing imme­ diately after the near-term options expire worthless. He can hold the longer-term options for some time before they will decay enough to produce a loss in the posi­ tion. Referring again to the previous example, when the January options expire worthless, the strategist then owns the April combination, which is worth 5 points at that time. He can continue to hold the April options for perhaps 6 or 8 weeks before they decay to a value of 3 points, even if the stock remains close to 65. At this point, the position could be closed for a net loss of the .commission costs involved in the var­ ious transactions. As a general rule, one should be willing to hold the combination, even if this means that he lets a small profit decay into a loss. The reason for this is that one should give himself the maximum opportunity to realize large profits. He will proba­ bly sustain a number of small losses by doing this, but by giving himself the oppor­ tunity for large profits, he has a reasonable chance of having the profits outdistance the losses. There is a time to take small profits in this strategy. This would be when either the puts or the calls were slightly in-the-money as the near-term options expire. Example: IfXYZ moved to 71 just as the January options were expiring, the call por­ tion of the spread should be closed. The January 70 call could be bought back for 1 point and the April 70 call would probably be worth about 5 points. Thus, the call portion of the spread could be "sold" for 4 points, enough to cover the entire cost of the position. The April 60 put would not have much value with the stock at 71, but it should be held just in case the stock should experience a large price decline. Similar results would occur on the put side of the spread if the underlying stock were slight­ ly in-the-money, say at 58 or 59, at January expiration. At no time does the strategist want to risk being assigned on an option that he is short, so he must always close the portion of the position that is in-the-money at near-term expiration. This is only nec­ essary, of course, if the stock has risen above the striking price of the calls or has fall­ en below the striking price of the puts. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:384 SCORE: 89.00 ================================================================================ 348 Part Ill: Put Option Strategies In summary, this is a reasonable strategy if one operates it over a period of time long enough to encompass several market cycles. The strategist must be careful not to place a large portion of his trading capital in the strategy, however, since even though the losses are limited, they still represent his entire net investment. A varia­ tion of this strategy, whereby one sells more options than he buys, is described in the next chapter. THE CALENDAR STRADDLE Another strategy that combines calendar spreads on both put and call options can be constructed by selling a near-term straddle and simultaneously purchasing a longer­ term straddle. Since the time value premium of the near-term straddle will decrease more rapidly than that of the longer-term straddle, one could make profits on a lim­ ited investment. This strategy is somewhat inferior to the one described in the pre­ vious section, but it is interesting enough to examine. Example: Suppose that three months before January expiration, the following prices exist: XYZ common: 40 January 40 straddle: 5 April 40 straddle: 7 A calendar spread of the straddles could be established by selling the January 40 straddle and simultaneously buying the April 40 straddle. This would involve a cost of 2 points, or the debit of the transaction, plus commissions. The risk is limited to the amount of this debit up until {he time the near-term straddle expires. That is, even if XYZ moves up in price by a substantial amount or declines in price by a substantial amount, the worst that can happen is that the dif­ ference between the straddle prices shrinks to zero. This could cause one to lose an amount equal to his original debit, plus commissions. This limit on the risk applies only until the near-term options expire. If the strategist decides to buy back the near­ term straddle and continue to hold the longer-term one, his risk then increases by the cost of buying back the near-term straddle. Example: XYZ is at 43 when the January options expire. The January 40 call can now be bought back for 3 points. The put expires worthless; so the whole straddle was closed out for 3 points. The April 40 straddle might be selling for 6 points at that time. If the strategist wants to hold on to the April straddle, in hopes that the stock might experience a large price swing, he is free to do so after buying back the January ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:385 SCORE: 100.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 349 40 straddle. However, he has now invested a total of 5 points in the position: the orig­ inal 2-point debit plus the 3 points that he paid to buy back the January 40 straddle. Hence, his risk has increased to 5 points. If XYZ were to be at exactly 40 at April expi­ ration, he would lose the entire 5 points. While the probability of losing the entire 5 points must be considered small, there is a substantial chance that he might lose more than 2 points his original debit. Thus, he has increased his risk by buying back the near-term straddle and continuing to hold the longer-term one. This is actually a neutral strategy. Recall that when calendar spreads were dis­ cussed previously, it was pointed out that one establishes a neutral calendar spread with the stock near the striking price. This is true for either a call calendar spread or a put calendar spread. This strategy - a calendar spread with straddles is merely the combination of a neutral call calendar spread and a neutral put calendar spread. Moreover, recall that the neutral calendar spreader generally establishes the position with the intention of closing it out once the near-term option expires. He is mainly interested in selling time in an attempt to capitalize on the fact that a near-term option loses time value premium more rapidly than a longer-term option does. The straddle calendar spread should be treated in the same manner. It is generally best to close it out at near-term expiration. If the stock is near the striking price at that time, a profit will generally result. To verify this, refer again to the prices in the pre­ ceding paragraph, with XYZ at 43 at January expiration. The January 40 straddle can be bought back for 3 points and the April 40 straddle can be sold for 6. Thus, the dif­ ferential between the two straddles has widened to 3 points. Since the original dif­ ferential was 2 points, this represents a profit to the strategist. The maximum profit would be realized if XYZ were exactly at the striking price at near-term expiration. In this case, the January 40 straddle could be bought back for a very small fraction and the April 40 straddle might be worth about 5 points. The differential would have widened from the original 2 points to nearly 5 points in this case. This strategy is inferior to the one described in the previous section (the "calen­ dar combination"). In order to have a chance for unlimited profits, the investor must increase his net debit by the cost of buying back the near-term straddle. Consequently, this strategy should be used only in cases when the near-term straddle appears to be extremely overpriced. Furthermore, the position should be closed at near-term expiration unless the stock is so close to the striking price at that time that the near-term straddle can be bought back for a fractional price. This fractional buy­ back would then give the strategist the opportunity to make large potential profits with only a small increase in his risk. This situation of being able to buy back the near­ term straddle at a fractional price will occur very infrequently, much more infre- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:386 SCORE: 68.00 ================================================================================ 350 Part Ill: Put Option Strategies quently than the case in which both the out-of-the-money put and call expire worth­ less in the previous strategy. Thus, the "calendar combination" strategy will afford the spreader more opportunities for large profits, and will also never force him to increase his risk. OWNING A ✓,,FREE" COMBINATION (THE ""DIAGONAL BUTTERFLY SPREAD") The strategies described in the previous sections are established for debits. This means that even if the near-term options expire worthless, the strategist still has risk. The long options he then holds could proceed to expire worthless as well, thereby leaving him with an overall loss equal to his original debit. There is another strategy involving both put and call options that gives the strategist the opportunity to own a "free" combination. That is, the profits from the near-term options could equal or exceed the entire cost of his long-term options. This strategy consists of selling a near-term straddle and simultaneously pur­ chasing both a longer-term, out-of the-money call and a longer-term, out-of the­ money put. This differs from the protected straddle write previously described in that the long options have a more distant maturity than do the short options. Example: XYZ common: 40 April 35 put: January 40 straddle: April 45 call: If one were to sell the short-term January 40 straddle for 7 points and simultaneous­ ly purchase the out-of-the-money put and call combination -April 35 put and April 45 call - he would establish a credit spread. The credit for the position is 3 points less commissions, since 7 points are brought in from the straddle sale and 4 points are paid for the out-of-the-money combination. Note that the position technically con­ sists of a bearish spread in the calls - buy the higher strike and sell the lower strike - coupled with a bullish spread in the puts - buy the lower strike and sell the higher strike. The investment required is in the form of collateral since both spreads are credit spreads, and is equal to the differential in the striking prices, less the net cred­ it received. In this example, then, the investment would be 10 points for the striking price differential (5 points for the calls and 5 points for the puts) less the 3-point credit received, for a total collateral requirement of $700, plus commissions. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:387 SCORE: 57.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 351 The potential results from this position may vary widely. However, the risk is limited before near-tenn expiration. If the underlying stock should advance substan­ tially before January expiration, the puts would be nearly worthless and the calls would both be trading near parity. With the calls at parity, the strategist would have to pay, at most, 5 points to close the call spread, since the striking prices of the calls are 5 points apart. In a similar manner, if the underlying stock had declined substan­ tially before the near-term January options expired, the calls would be nearly worth­ less and the puts would be at parity. Again, it would cost a maximum of 5 points to close the put spread, since the difference in the striking prices of the puts is also 5 points. The worst result would be a 2-point loss in this example - 3 points of credit were initially received, and the most that the strategist would have to pay to close the position is 5 points. This is the theoretical risk. In actual practice, it is very unlikely that the calls would trade as much as 5 points apart, even if the underlying stock advanced by a large amount, because the longer-term call should retain some small time value premium even if it is deeply in-the-money. A similar analysis might apply to the puts. The risk can always be quickly computed as being equal to the difference between two contiguous striking prices ( two strikes next to each other), less the net credit received. The strategist's objective with this position is to be able to buy back the near­ tenn straddle for a price less than the original credit received. If he can do this, he will own the longer-term combination for free. Example: Near January expiration, the strategist is able to repurchase the January 40 straddle for 2 points. Since he initially received a 3-point credit and is then able to buy back the written straddle for 2 points, he is left with an overall credit in the posi­ tion of 1 point, less commissions. Once he has done this, the strategist retains the long options, the April 35 put and April 45 call. If the underlying stock should then advance substantially or decline substantially, he could make very large profits. However, even if the long combination expires worthless, the strategist still makes a profit, since he was able to buy the straddle back for less than the amount of the orig­ inal credit. In this example, the strategist's objective is to buy back the January 40 straddle for less than 3 points, since that is the amount of the initial credit. At expiration, this would mean that the stock would have to be between 37 and 43 for the buy-back to be made for 3 points or less. Although it is possible, certainly, that the stock will be in this fairly narrow range at near-term expiration, it is not probable. However, the strategist who is willing to add to his risk slightly can often achieve the same result by "legging out" of the January 40 straddle. It has repeatedly been stated that one should ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:388 SCORE: 67.00 ================================================================================ 352 Part Ill: Put Option Strategies not attempt to leg out of a spread, but this is an exception to that rule, since one owns a long combination and therefore is protected; he is not subjecting himself to large risks by attempting to "leg out" of the straddle he has written. Example: XYZ rallies before January expiration and the January 40 put drops to a price of ½ during the rally. Even though there is time remaining until expiration, the strategist might decide to buy back the put at ½. This could potentially increase his overall risk by ½ point if the stock continues to rise. However, if the stock then reversed itself and fell, he could attempt to buy the call back at 2½ points or less. In this manner, he would still achieve his objective of buying the short-term straddle back for 3 points or less. In fact, he might be able to close both sides of the straddle well before near-term expiration if the underlying stock first moves quickly in one direction and then reverses direction by a large amount. The maximum risk and the optimum potential objectives have been described, but interim results might also be considered in this strategy. Example: XYZ is at 44 at January expiration. The January 40 straddle must be bought back for 4 points. This means that the long combination will not be owned free, but will have a cost of I point plus commissions. The strategist must decide at this time if he wants to hold on to the April options or if he wants to sell them, possibly pro­ ducing a small overall profit on the entire position. There is no ironclad rule in this type of situation. If the decision is made to hold on to the longer-term options, the strategist realizes that he has assumed additional risk by doing so. Nevertheless, he may decide that it is worth owning the long combination at a relatively low cost. The cost in this example would be I point plus commissions, since he paid 4 points to buy back the straddle after only taking in a 3-point credit initially. The more ex.pensive the buy-back of the near-term straddle is, the more the strategist should be readily will­ ing to sell his long options at the same time. For example, if XYZ were at 48 at January expiration and the January 40 straddle had to be bought back for 8 points, there should be no question that he should simultaneously sell his April options as well. The most difficult decisions come when the stock is just outside the optimum buy-back area at near-term expiration. In this example, the strategist would have a fairly difficult decision if XYZ were in the 44 to 45 area or in the 35 to 36 area at January expiration. The reader may recall that, in Chapter 14 on diagonalizing a spread, it was men­ tioned that one is sometimes able to own a call free by entering into a diagonal cred­ it spread. A diagonal bear spread was given as an example. The same thing happens to be true of a diagonal bullish put spread, since that is a credit spread as well. The ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:389 SCORE: 35.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 3S3 strategy discussed in this section is merely a combination of a diagonal bearish call spread and a diagonal bullish put spread and is known as a "diagonal butterfly spread." The same concept that was described in Chapter 14 - being able to make more on the short-term call than one originally paid for the long-term call - applies here as well. One enters into a credit position with the hope of being able to buy back the near-term written options for a profit greater than the cost of the long options. If he is able to do this, he will own options for free and could make large profits if the underlying stock moves substantially in either direction. Even if the stock does not move after the buy-back, he still has no risk. The risk occurs prior to the expiration of the near-term options, but this risk is limited. As a result, this is an attractive strat­ egy that, when operated over a period of market cycles, should produce some large profits. Ideally, these profits would offset any small losses that had to be taken. Since large commission costs are involved in this strategy, the strategist is reminded that establishing the spreads in quantity can help to reduce the percentage effect of the commissions. SELECTING THE SPREADS Now that the concepts of these three strategies have been laid out, let us define selection criteria for them. The "calendar combination" is the easiest of these strate­ gies to spot. One would like to have the stock nearly halfway between two striking prices. The most attractive positions can normally be found when the striking prices are at least 10 points apart and the underlying stock is relatively volatile. The opti­ mum time to establish the "calendar combination" is two or three months before the near-term options expire. Additionally, one would like the sum of the prices of the near-term options to be equal to at least one-half of the cost of the longer-term options. In the example given in the previous section on the "calendar combination," the near-term combination was sold for 5 points, and the longer-term combination was bought for 8 points. Thus, the near-term combination was worth more than one­ half of the cost of the longer-term combination. These five criteria can be summa­ rized as follows: 1. Relatively volatile stock. 2. Stock price nearly midway between two strikes. 3. Striking prices at least 10 points apart. 4. Two or three months remaining until near-term expiration. 5. Price of near-term combination greater than one-half the price of the longer­ term combination. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:390 SCORE: 82.00 ================================================================================ 354 Part Ill: Put Option Strategies Even though five criteria have been stated, it is relatively easy to find a position that satisfies all five conditions. The strategist may also be able to rely upon technical input. If the stock seems to be in a near-term trading range, the position may be more attractive, for that would indicate that the chances of the near-term combination expiring worthless are enhanced. The "calendar straddle" is a strategy that looks deceptively attractive. As the reader should know by now, options do not decay in a linear fashion. Instead, options tend to hold time value premium until they get quite close to expiration, when the time value premium disappears at a fast rate. Consequently, the sale of a near-term straddle and the simultaneous purchase of a longer-term straddle often appear to be attractive because the debit seems small. Again, certain criteria can be set forth that will aid in selecting a reasonably attractive position. The stock should be at or very near the striking price when the position is established. Since this is basically a neu­ tral strategy, one that offers the largest potential profits at near-term expiration, one should want to sell the most time premium possible. This is why the stock must be near the striking price initially. The underlying stock does not have to be a volatile one, although volatile stocks will most easily satisfy the next two criteria. The near­ term credit should be at least two-thirds of the longer-term debit. In the example used to explain this strategy, the near-term straddle was sold for 5, while the longer­ term straddle was bought for 7 points. Thus, the near-term straddle was worth more than two-thirds of the longer-term straddle's price. Finally, the position should be established with two to four months remaining until near-term expiration. If positions with a longer time remaining are used, there is a significant probability that the underlying stock will have moved some distance away from the striking price by the time the near-term options expire. Summarizing, the three criteria for a "calendar straddle" are: 1. Stock near striking price initially. 2. Two to four months remaining until near-term expiration. 3. Near-term straddle price at least two-thirds of longer-term straddle price. The "diagonal butterfly" is the most difficult of these three types of positions to locate. Again, one would like the stock to be near the middle striking price when the position is established. Also, one would like the underlying stock to be somewhat volatile, since there is the possibility that long-term options will be owned for free. If this comes to pass, the strategist wants the stock to be capable of a large move in order to have a chance of generating large profits. The most restrictive criterion -:­ one that will eliminate all but a few possibilities on a daily basis - is that the near­ term straddle price should be at least one and one-half times that of the longer-term, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:391 SCORE: 57.00 ================================================================================ Chapter 23: Spreads Combining Calls and Puts 355 out-of-the-money combination. By adhering to this criterion, one gives himself area­ sonable chance of being able to buy the near-term straddle back for a price low enough to result in owning the longer-term options for free. In the example used to describe this strategy, the near-term straddle was sold for 7 while the out-of-the­ money, longer-term combination cost 4 points. This satisfies the criterion. Finally, one should limit his possible risk before near-term expiration. Recall that the risk is equal to the difference between any two contiguous striking prices, less the net cred­ it received. In the example, the risk would be 5 minus 3, or 2 points. The risk should always be less than the credit taken in. This precludes selling a near-term straddle at 80 for 4 points and buying the put at 60 and the call at 100 for a combined cost of 1 point. Although the credit is substantially more than one and one-half times the cost of the long combination, the risk would be ridiculously high. The risk, in fact, is 20 points ( the difference between two contiguous striking prices) less the 3 points cred­ it, or 17 points - much too high. The criteria can be summarized as follows: 1. Stock near middle striking price initially. 2. Three to four months to near-term expiration. 3. Price of written straddle at least one and one-half times that of the cost of the longer-term, out-of-the-money combination. 4. Risk before near-term expiration less than the net credit received. One way in which the strategist may notice this type of position is when he sees a rel­ atively short-term straddle selling at what seems to be an outrageously high price. Professionals, who often have a good feel for a stock's short-term potential, will some­ times bid up straddles when the stock is about to make a volatile move. This will cause the near-term straddles to be very overpriced. When a straddle seller notices that a particular straddle looks too attractive as a sale, he should consider establish­ ing a diagonal butterfly spread instead. He still sells the overpriced straddle, but also buys a longer-term, out-of-the-money combination as a hedge against a large loss. Both factions can be right. Perhaps the stock will experience a very short-term volatile movement, proving that the professionals were correct. However, this will not worry the strategist holding a diagonal butterfly, for he has limited risk. Once the short-term move is over, the stock may drift back toward the original strike, allowing the near-term straddle to be bought back at a low price - the eventual objective of the strategist utilizing the diagonal butterfly spread. These are admittedly three quite complex strategies and thus are not to be attempted by a novice investor. If one wants to gain experience in how he would operate such a strategy, it would be far better to operate a "paper strategy" for a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:392 SCORE: 60.00 ================================================================================ 356 Part Ill: Put Option Strategies while. That is, one would not actually make investments, but would instead follow prices in the newspaper and make day-to-day decisions without actual risk. This will allow the inexperienced strategist to gain a feel for how these complex strategies per­ form over a particular time period. The astute investor can, of course, obtain price history information and track a number of market cycles in this same way. SUMMARY Puts and call can be combined to make some very attractive positions. The addition of a call or put credit spread to the outright purchase of a put or call can enhance the overall profitability of the position, especially if the options are expensive. In addi­ tion, three advanced strategies were presented that combined puts and calls at vari­ ous expiration dates. These three various types of strategies that involve calendar combinations of puts and calls may all be attractive. One should be especially alert for these types of positions when near-term calls are overpriced. Typically, this would be during, or just after, a bullish period in the stock market. For nomenclature pur­ poses, these three strategies are called the "calendar combination," the "calendar straddle," and the "diagonal butterfly." All three strategies offer the possibility of large potential profits if the underly­ ing stock remains relatively stable until the near-term options expire. In addition, all three strategies have limited risk, even if the underlying stock should move explo­ sively in either direction prior to near-term expiration. If an intermediate result occurs - for example, the stock moves a moderate distance in either direction before near-term expiration - it is still possible to realize a limited profit in any of the strate­ gies, because of the fact that the time premiums decay much more rapidly in the near-term options than they do in the longer-term options. The three strategies have many things in common, but each has its own advan­ tages and disadvantages. The "diagonal butterfly" is the only one of the three strate­ gies whereby the strategist has a possibility of owning free options. Admittedly, the probability of actually being able to own the options completely for free is small. However, there is a relatively large probability that one can substantially reduce the cost of the long options. The "calendar combination," the first of the three strategies discussed, offers the largest probability of capturing the entire near-term premium. This is because both near-term options are out-of-the-money to begin with. The "cal­ endar straddle" offers the largest potential profits at near-term expiration. That is, if the stock is relatively unchanged from the time the position was established until the time the near-term options expire, the "calendar straddle" will show the best profit of the three strategies at that time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:393 SCORE: 17.00 ================================================================================ Chapter 23: Spreads Combining Calls and l'uts 357 Looking at the negative side, the "calendar straddle" is the least attractive of the three strategies, primarily because one is forced to increase his risk after near-term expiration, if he wants to continue to hold the longer-term options. It is often diffi­ cult to find a "diagonal butterfly" that offers enough credit to make the position attractive. Finally, the "calendar combination" has the largest probability oflosing the entire debit eventually, because one may find that the longer-term options expire worthless also. (They are out-of-the-money to begin with, just as the near-term options were.) The strategist will not normally be able to find a large number of these positions available at attractive price levels at any particular time in the market. However, since they are attractive strategies with little or no margin collateral requirements, the strategist should constantly be looking for these types of positions. A certain amount of cash or collateral should be reserved for the specific purpose of utilizing it for these types of positions - perhaps 15 to 20% of one's dollars. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:394 SCORE: 40.00 ================================================================================ Ratio Spreads Using Puts The put option spreader may want to sell more puts than he owns. This creates a ratio spread. Basically, two types of put ratio spreads may prove to be attractive: the stan­ dard ratio put spread and the ratio calendar spread using puts. Both strategies are designed for the more aggressive investor; when operated properly, both can present attractive reward opportunities. THE RATIO PUT SPREAD This strategy is designed for a neutral to slightly bearish outlook on the underlying stock. In a ratio put spread, one buys a number of puts at a higher strike and sells more puts at a lower strike. This position involves naked puts, since one is short more puts than he is long. There is limited upside risk in the position, but the downside risk can be very large. The maximum profit can be obtained if the stock is exactly at the striking price of the written puts at expiration. Example: Given the following: XYZ common, 50; XYZ January 45 put, 2; and XYZ January 50 put, 4. A ratio put spread might be established by buying one January 50 put and simulta­ neously selling two January 45 puts. Since one would be paying $400 for the pur­ chased put and would be collecting $400 from the sale of the two out-of-the-money puts, the spread could be done for even money. There is no upside risk in this posi­ tion. If XYZ should rally and be above 50 at January expiration, all the puts would 358 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:395 SCORE: 34.00 ================================================================================ Cl,apter 24: Ratio Spreads Using Puts 359 expire worthless and the result would be a loss of commissions. However, there is downside risk. If XYZ should fall by a great deal, one would have to pay much more to buy back the two short puts than he would receive from selling out the one long put. The maximum profit would be realized if XYZ were at 45 at expiration, since the short puts would expire worthless, but the long January 50 put would be worth 5 points and could be sold at that price. Table 24-1 and Figure 24-1 summarize the position. Note that there is a range within which the position is profitable - 40 to 50 in this example. If XYZ is above 40 and below 50 at January expiration, there will be some profit, before commissions, from the spread. Below 40 at expiration, losses will be generated and, although these losses are limited by the fact that a stock cannot decline in price below zero, these losses could become very large. There is no upside risk, however, as was pointed out earlier. The following formulae summarize the sit­ uation for any put ratio spread: Maximum upside risk Maximum profit potential = Net debit of spread (no upside risk if done for a credit) = Striking price differential x Number of long puts - Net debit (or plus net credit) Downside break-even price = Lower strike price - Maximum profit potential + Number of naked puts The investment required for the put ratio spread consists of the collateral requirement necessary for a naked put, plus or minus the credit or debit of the entire position. Since the collateral requirement for a naked option is 20% of the stock TABLE 24-1. Ratio put spread. XYZ Price at Long January 50 Short 2 January 45 Total Expiration Put Profit Put Profit Profit 20 +$2,600 -$4,600 -$2,000 30 + 1,600 - 2,600 - 1,000 40 + 600 600 0 42 + 400 200 + 200 45 + 100 + 400 + 500 48 200 + 400 + 200 50 400 + 400 0 60 400 + 400 0 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:396 SCORE: 44.00 ================================================================================ 360 FIGURE 24-1. Ratio put spread. +$500 C: 0 ~ ·5. X w iil (/) $0 (/) 0 ....I 0 e a. Part Ill: Put Option Strategies Stock Price at Expiration price, plus the premium, minus the amount by which the option is out-of-the-money, the actual dollar requirement in this example would be $700 (20% of $5,000, plus the $200 premium, minus the $500 by which the January 45 put is out-of-the-money). As with all types of naked writing positions, the strategist should allow enough collater­ al for an adverse stock move to occur. This will allow enough room for stock move­ ment without forcing early liquidation of the position due to a margin call. If, in this example, the strategist felt that he might stay with the position until the stock declined to 39, he should allow $1,380 in collateral (20% of $3,900 plus the $600 in­ the-money amount). The ratio put spread is generally most attractive when the underlying stock is initially between the two striking prices. That is, if XYZ were somewhere between 45 and 50, one might find the ratio put spread used in the example attractive. If the stock is initially below the lower striking price, a ratio put spread is not as attractive, since the stock is already too close to the downside risk point. Alternatively, if the stock is too far above the striking price of the written calls, one would normally have to pay a large debit to establish the position. Although one could eliminate the debit by writing four or five short options to each put bought, large ratios have extraordi­ narily large downside risk and are therefore very aggressive. Follow-up action is rather simple in the ratio put spread. There is very little that one need do, except for closing the position if the stock breaks below the downside break-even point. Since put options tend to lose time value premium rather quickly after they become in-the-money options, there is not normally an opportunity to roll ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:397 SCORE: 87.00 ================================================================================ Chapter 24: Ratio Spreads Using Puts 361 down. Rather, one should be able to close the position with the puts close to parity if the stock breaks below the downside break-even point. The spreader may want to buy in additional long puts, as was described for call spreads in Chapter 11, but this is not as advantageous in the put spread because of the time value premium shrinkage. This strategy may prove psychologically pleasing to the less experienced investor because he will not lose money on an upward move by the underlying stock. Many of the ratio strategies that involve call options have upside risk, and a large number of investors do not like to lose money when stocks move up. Thus, although these investors might be attracted to ratio strategies because of the possibility of col­ lecting the profits on the sale of multiple out-of-the-money options, they may often prefer ratio put spreads to ratio call spreads because of the small upside risk in the put strategy. USING DELTAS The "delta spread" concept can also be used for establishing and adjusting neutral ratio put spreads. The delta spread was first described in Chapter 11. A neutral put spread can be constructed by using the deltas of the two put options involved in the spread. The neutral ratio is determined by dividing the delta of the put at the higher strike by the delta of the put at the lower strike. Referring to the previous example, suppose the delta of the January 45 put is -.30 and the delta of the January 50 put is -.50. Then a neutral ratio would be 1.67 (-.50 divided by -.30). That is, 1.67 puts would be sold for each put bought. One might thus sell 5 January 45 puts and buy 3 January 50 puts. This type of spread would not change much in price for small fluctuations in the underlying stock price. However, as time passes, the preponderance of time value premium sold via the January 45 puts would begin to tum a profit. As the underlying stock moves up or down by more than a small distance, the neutral ratio between the two puts will change. The spreader can adjust his position back into a neutral one by selling more January 45's or buying more January 50's. THE RATIO PUT CALENDAR SPREAD The ratio put calendar spread consists of buying a longer-term put and selling a larg­ er quantity of shorter-term puts, all with the same striking price. The position is gen­ erally established with out-of-the-money puts that is, the stock is above the striking price - so that there is a greater probability that the near-term puts will expire worth- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:398 SCORE: 31.00 ================================================================================ 362 Part Ill: Put Option Strategies less. Also, the position should be established for a credit, such that the money brought in from the sale of the near-term puts more than covers the cost of the longer-term put. If this is done and the near-term puts expire worthless, the strate­ gist will then own the longer-term put free, and large profits could result if the stock subsequently experiences a sizable downward movement. Example: If XYZ were at 55, and the January 50 put was at 1 ½ with the April 50 at 2, one could establish a ratio put calendar spread by buying the April 50 and selling two January 50 puts. This is a credit position, because the sale of the two January 50 puts would bring in $300 while the cost of the April 50 put is only $200. If the stock remains above 50 until January expiration, the January 50 puts will expire worthless and the April 50 put will be owned for free. In fact, even if the April 50 put should then expire worthless, the strategist will make a small profit on the overall position in the amount of his original credit - $100 - less commissions. However, after the Januarys have expired worthless, if XYZ should drop dramatically to 25 or 20, a very large profit would accrue on the April 50 put that is still owned. The risk in the position could be very large if the stock should drop well below 50 before the January puts expire. For example, if XYZ fell to 30 prior to January expiration, one would have to pay $4,000 to buy back the January 50 puts and would receive only $2,000 from selling out his long April 50 put. This would represent a rather large loss. Of course, this type of tragedy can be avoided by taking appropri­ ate follow-up action. Nomwlly, one would close the position if the stock fell rrwre than 8 to 10% below the striking price before the near-term puts expire. As with any type of ratio position, naked options are involved. This increases the collateral requirement for the position and also means that the strategist should allow enough collateral in order for the follow-up action point to be reached. In this exam­ ple, the initial requirement would be $750 (20% of $5,500, plus the $150 January premium, less the $500 by which the naked January 50 put is out-of-the-money). However, if the strategist decides that he will hold the position until XYZ falls to 46, he should allow $1,320 in collateral (20% of $4,600 plus the $400 in-the-money amount). Of course, the $100 credit, less commissions, generated by the initial posi­ tion can be applied against these collateral requirements. This strategy is a sensible one for the investor who is willing to accept the risk of writing a naked put. Since the position should be established with the stock above the striking price of the put options, there is a reasonable chance that the near-term puts will expire worthless. This means that some profit will be generated, and that the profit could be large if the stock should then experience a large downward move before the longer-term puts expire. One should take care, however, to limit his losses ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:399 SCORE: 50.00 ================================================================================ Chapter 24: Ratio Spreads Using Puts 363 before near-term expiration, since the eventual large profits will be able to overcome a series of small losses, but could not overcome a preponderance oflarge losses. RATIO PUt CALENDARS Using the deltas of the puts in the spread, the strategist can construct a neutral posi­ tion. If the puts are initially out-of-the-money, then the neutral spread generally involves selling more puts than one buys. Another type of ratioed put calendar can be constructed with in-the-money puts. As with the companion in-the-money spread with calls, one would buy more puts than he sells in order to create a neutral ratio. In either case, the delta of the put to be purchased is divided by the delta of the put to be sold. The result is the neutral ratio, which is used to determine how many puts to sell for each one purchased. Example: Consider the out-of-the-money case. XYZ is trading at 59. The January 50 put has a delta of 0.10 and the April 50 put has a delta of -0.17. If a calendar spread is to be established, one would be buying the April 50 and selling the January 50. Thus, the neutral ratio would be calculated as 1.7 to 1 (-0.17/-0.10). Seventeen puts would be sold for every 10 purchased. This spread has naked puts and therefore has large risk if the underlying stock declines too far. However, follow-up action could be taken if the stock dropped in an orderly manner. Such action would be designed to limit the downside risk. Conversely, the calendar spread using in-the-money puts would normally have one buying more options than he is selling. An example using deltas will demonstrate this fact: Example: XYZ is at 59. The January 60 put has a delta of -0.45 and the April 60 put has a delta of -0.40. It is normal for shorter-term, in-the-money options to have a delta that is larger (in absolute terms) than longer-term, in-the-money options. The neutral ratio for this spread would be 0.889 (-0.40/-0.45). That is, one would sell only 0.889 puts for each one he bought. Alternatively stated, he would sell 8 and buy 9. A spread of this type has no naked puts and therefore does have large downside profit potential. If the stock should rise too far, the loss is limited to the initial debit of the spread. The optimum result would occur if the stock were at the strike at expi­ ration because, even though the excess long put would lose money in that case, the spreads involving the other puts would overcome that small loss. Another risk of the in-the-money put spread is that one might be assigned rather quickly if the stock should drop. In fact, one must be careful not to establish ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:400 SCORE: 39.00 ================================================================================ 364 Part Ill: Put Option Strategies the spread with puts that are too deeply in-the-money, for this reason. While being put will not necessarily change the profitability of the spread, it will mean increased commission costs and margin charges for the customer, who must buy the stock upon assignment. A LOGICAL EXTENSION (THE RATIO CALENDAR COMBINATION) The previous section demonstrated that ratio put calendar spreads can be attractive. The ratio call calendar spread was described earlier as a reasonably attractive strate­ gy for the bullish investor. A logical combination of these two types of ratio calendar spreads (put and call) would be the ratio combination - buying a longer-term out-of­ the-money combination and selling several near-term out-of-the-money combina­ tions. Example: The following prices exist: XYZ common: 55 XYZ January 50 put: XYZ January 60 call: XYZ April 50 put: 2 XYZ April 60 call: 5 One could sell the near-term January combination (January 50 put and January 60 call) for 5 points. It would cost 7 points to buy the longer-term April combination (April 50 put and April 60 call). By selling more January combinations than April com­ binations bought, a ratio calendar combination could be established. For example, suppose that a strategist sold two of the near-term January combinations, bringing in 10 points, and simultaneously bought one April combination for 7 points. This would be a credit position, a credit of 3 points in this example. If the near-term, out-of-the­ money combination expires worthless, a guaranteed profit of 3 points will exist, even if the longer-term options proceed to expire totally worthless. If the near-term com­ bination expires worthless, the longer-term combination is owned for free, and a large profit could result on a substantial stock price movement in either direction. Although this is a superbly attractive strategy if the near-term options do, in fact, expire worthless, it must also be monitored closely so that large losses do not occur. These large losses would be possible if the stock broke out in either direction too quickly, before the near-term options expire. In the absence of a technical opin­ ion on the underlying stock, one can generally compute a stock price at which it might be reasonable to take follow-up action. This is a similar analysis to the one ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:401 SCORE: 40.00 ================================================================================ Chapter 24: Ratio Spreads Using Puts 365 described for ratio call calendar spreads in Chapter 12. Suppose the stock in this example began to rally. There would be a point at which the strategist would have to pay 3 points of debit to close the call side of the combination. That would be his break-even point. Example: With XYZ at 65 at January expiration (5 points above the higher strike of the original combination), the near-term January 60 call would be worth 5 points and the longer-term April 60 call might be worth 7 points. If one closed the call side of the combination, he would have to pay 10 points to buy back two January 60 calls, and would receive 7 points from selling out his April 60. This closing transaction would be a 3-point debit. This represents a break-even situation up to this point in time, except for commissions, since a 3-point credit was initially taken in. The strate­ gist would continue to hold the April 50 put (the January 50 put would expire worth­ less) just in case the improbable occurs and the underlying stock plunges below 50 before April expiration. A similar analysis could be performed for the put side of the spread in case of an early downside breakout by the underlying stock. It might be determined that the downside break-even point at January expiration is 46, for exam­ ple. Thus, the strategist has two parameters to work with in attempting to limit loss­ es in case the stock moves by a great deal before near-term expiration: 65 on the upside and 46 on the downside. In practice, if the stock should reach these levels before, rather than at, January expiration, the strategist would incur a small loss by closing the in-the-money side of the combination. This action should still be taken, however, as the objective of risk management of this strategy is to take small losses, if necessary. Eventually, large profits may be generated that could more than compen­ sate for any small losses that were incurred. The foregoing follow-up action was designed to handle a volatile move by the underlying stock prior to near-term expiration. Another, perhaps more common, time when follow-up action is necessary is when the underlying stock is relatively unchanged at near-term expiration. If XYZ in the example above were near 55 at January expiration, a relatively large profit would exist at that time: The near-term combination would expire worthless for a gain of 10 points on that sale, and the longer-term combination would probably still be worth about 5 points, so that the unrealized loss on the April combination would be only 2 points. This represents a total (realized and unrealized) gain of 8 points. In fact, as long as the near-term com­ bination can be bought back for less than the original 3-point credit of the position, the position will show a total unrealized gain at near-term expiration. Should the gain be taken, or should the longer-term combination be held in hopes of a volatile move by the underlying stock? Although the strategist will normally handle each position ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:402 SCORE: 35.00 ================================================================================ 366 Part Ill: Put Option Strategies on a case-by-case basis, the general philosophy should be to hold on to the April com­ bination. A profit is already guaranteed at this time - the worst that can happen is a 3-point profit (the original credit). Consequently, the strategist should allow himself the opportunity to make large profits. The strategist may want to attempt to trade out of his long combination, since he will not risk making the position a losing one by doing so. Technical analysis may be able to provide him with buy or sell zones on the stock, and he would then consider selling out his long options in accordance with these technical levels. In summary, this strategy is very attractive and should be utilized by strategists who have the expertise to trade in positions with naked options. As long as risk man­ agement principles of taking small losses are adhered to, there will be a large proba­ bility of overall profit from this strategy. PUT OPTION SUMMARY This concludes the section on put option strategies. The put option is useful in a vari­ ety of situations. First, it represents a more attractive way to take advantage of a bear­ ish attitude with options. Second, the use of the put options opens up a new set of strategies - straddles and combinations - that can present reasonably high levels of profit potential. Many of the strategies that were described in Part II for call options have been discussed again in this part. Some of these strategies were described more fully in terms of philosophy, selection procedures, and follow-up action when they were first discussed. The second description the one involving put options - was often shortened to a more mechanical description of how puts fit into the strategy. This format is intentional. The reader who is planning to employ a certain strategy that can be established with either puts or calls (a bear spread, for example) should familiarize himself with both applications by a simultaneous review of the call chap­ ter and its analogous put chapter. The combination strategies generally introduced new concepts to the reader. The combination allows the construction of positions that are attractive with either puts or calls (out-of-the-money calendar spreads, for example) to be combined into one position. The four combination strategies that involve selling short-term options and simultaneously buying longer-term options are complex, but are most attractive in that they have the desirable features of limited risk and large potential profits. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:403 SCORE: 32.00 ================================================================================ CHAPTER 25 LEAPS In an attempt to provide customers with a broader range of derivative products, the options exchanges introduced LEAPS. This chapter does a fair amount of reviewing basic option facts in order to explain the concepts behind LEAPS. The reader who has a knowledge of the preceding chapters and therefore does not need the review will be able to quickly skim through this chapter and pick out the strategically impor­ tant points. However, if one encounters concepts here that don't seem familiar, he should review the earlier chapter that discusses the pertinent strategy. The term LEAPS is a name for "long-term option." A LEAPS is nothing more than a listed call or put option that is issued with two or more years of time remain­ ing. It is a longer-term option than we are used to dealing with. Other than that, there is no material difference between LEAPS and the other calls and puts that have been discussed in the previous chapters. LEAPS options were first introduced by the CBOE in October 1990, and were offered on a handful of blue-chip stocks. Their attractiveness spurred listings on many underlying stocks on all option exchanges as well as on several indices. (Index options are covered in a later section of the book.) Strategies involving long-term options are not substantially different from those involving shorter-term options. However, the fact that the option has so much time remaining seems to favor the buyer and be a detriment to the seller. This is one rea­ son why LEAPS have been popular. As a strategist, one knows that the length of time remaining has little to do with whether a certain strategy makes sense or not. Rather, it is the relative value of the option that dictates strategy. If an option is overpriced, it is a viable candidate for selling, whether it has two years of life remaining or two months. Obviously, follow-up action may become much more of a necessity during the life of a two-year option; that matter is discussed later in this chapter. 361 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:404 SCORE: 58.00 ================================================================================ 368 Part Ill: Put Option Strategies THE BASICS Certain facets of LEAPS are the same as for other listed equity options, while others involve slight differences. The amount of standardization is considerably less, which makes the simple process of quoting LEAPS a bit more tedious. LEAPS are listed options that can be traded in a secondary market or can be exercised before expira­ tion. As with other listed equity options, they do not receive the dividend paid by the underlying common stock. Recall that four specifications uniquely describe any option contract: 1. the type (put or call), 2. the underlying stock name (and symbol), 3. the expiration date, and 4. the striking price. Type. LEAPS are puts or calls. The LEAPS owner has the right to buy the stock at the striking price (LEAPS call) or sell it there (LEAPS put). This is exactly the same for LEAPS and for regular equity options. Underlying Stock and Quote Symbol. The underlying stocks are the same for LEAPS as they are for equity options. The base symbol in an option quote is the part that designates the underlying stock. For equity options, the base symbol is the same as the stock symbol. However, until the Option Price Reporting Authority ( OPRA) changes the way that all options are quoted, the base symbols for LEAPS are not the same as the stock symbols. For example, LEAPS options on stock XYZ might trade under the base symbol WXY; so it is possible that one stock might have listed options trading with different base symbols even though all the symbols refer to the same underlying stock. Check with your broker to determine the LEAPS symbol if you need to know it. Expiration Date. LEAPS expire on the Saturday following the third Friday of the expiration month, just as equity options do. One must look in the newspaper, ask his broker, or check the Internet (www.cboe.com) to determine what the expiration months are, however, since they are also not completely standardized. When LEAPS were first listed, there were differing expiration months through December 1993. At the current time, LEAPS are issued to expire in January of each year, so some attempt is being made at standardization. However, there is no guarantee that vary­ ing expiration months won't reappear at some future time. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:405 SCORE: 44.00 ================================================================================ Chapter 25: LEAPS 369 Striking Price. There is no standardized striking price interval for LEAPS as there is for equity options. If XYZ is a 95-dollar stock, there might be LEAPS with striking prices of 80, 95, and 105. Again, one must look in the newspaper, ask his bro­ ker, or check the Internet (www.cboe.com) to determine the actual LEAPS striking prices for any specific underlying stock. New striking prices can be introduced when the underlying stock rises or falls too far. For example, if the lowest strike for XYZ were 80 and the stock fell to 80, a new LEAPS strike of 70 might be introduced. Other Basic Factors. LEAPS may be exercised at any time during their life, just as is the case with equity options. Note that this statement regarding exercise is not necessarily true for Index LEAPS or Index Options. See Part V of this book for discussions of index products. Standard LEAPS contracts are for 100 shares of the underlying stock, just as equity options are. The number of shares would be adjusted for stock splits and stock dividends (leading to even more arcane LEAPS symbol problems). LEAPS are quot­ ed on a per-share basis, as are other listed options. There are position and exercise limits for LEAPS just as there are for other list­ ed options. One must add his LEAPS position and his regular equity option position together in order to determine his entire position quantity. Exemptions may be obtained for bona fide hedgers of common stock. As time passes, LEAPS eventually have less than 9 months remaining until expi­ ration. When such a time is reached, the LEAPS are "renamed" and become ordi­ nary equity options on the underlying security. Example: Assume LEAPS on stock XYZ were initially issued to expire two years hence. Assume that one of these LEAPS is the XYZ January 90; that is, it has a strik­ ing price of 90 and expires in January, two years from now. Its symbol is WXYAR (WXY being the LEAPS base symbol assigned by the exchange where XYZ is traded, A for January, and R for 90). Fifteen months later, the January LEAPS only have 9 months of life remaining. The LEAPS symbol would be changed from WXYAR to XYZAR (a regular equity option), and the quotes would be listed in the regular equity option section of the newspaper instead of in the LEAPS section. PRICING LEAPS Terms such as in-the-money, out-of-the-money, intrinsic value, time value premium, and parity all apply and have the same definitions. The factors influencing the prices of LEAPS are the same as those for any other option: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:406 SCORE: 41.00 ================================================================================ 370 Part Ill: Put Option Strategies 1. underlying stock price, 2. striking price, 3. time remaining, 4. volatility, 5. risk-free interest rate, and 6. dividend rate. The relative influence of these factors may be a little more pronounced for LEAPS than it is for shorter-term equity options. Consequently, the trader may think that a LEAPS is overly expensive or cheap by inspection, when in reality it is not. One should be careful in his evaluation of LEAPS until he has acquired experience in observing how their prices relate to the shorter-tenn equity options with which he is experienced. It might prove useful to reexamine the option pricing curve with some LEAPS included. Please refer to Figure 25-1 for the pricing curves of several options. As always, the solid intrinsic value line is the bottom line; it is the same for any call option. The curves are all drawn with the same values for the pertinent variables: stock price, striking price, volatility, short-term interest rate, and dividends. Thus, they can be compared directly. The most obvious thing to notice about the curves in Figure 25-1 is that the curve depicting the 2-year LEAPS is quite flat. It has the general shape of the shorter-term curves, but there is so much time value at stock prices even 25% in­ or out-of-the-money, that the 2-year curve is much flatter than the others. Other observations can be made as well. Notice the at-the-money options: The 2-year LEAPS sells for a little more than four times the 3-month option. As we shall see, this can change with the effects of interest rates and dividends, but it confirms something that was demonstrated earlier: Time decay is not linear. Thus, the 2-year LEAPS, which has eight times the amount of time remaining as compared to the 3- month call, only sells for about four times as much. This LEAPS might appear cheap to the casual observer, but remember that these graphs depict the fair values for this set of input parameters. Do not be deluded into thinking that a LEAPS looks cheap merely by comparing its price to a nearer-term option; use a model to evaluate it, or at least use the output of someone else's model. The curves in Figure 25-1 depict the relationships between stock price, striking price, and time remaining. The most important remaining determinant of an option's price is the volatility of the underlying stock. Changes in volatility can greatly change the price of any option. This is especially true for LEAPS, since a long-term option's price will fluctuate greatly when volatility changes only a little. Some observations on the differing effects that volatility changes have on short- and long-term options are presented later. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:407 SCORE: 33.00 ================================================================================ Chapter 25: LEAPS FIGURE 25-1. LEAPS call pricing curve. 45 40 35 Q) 30 .g o. 25 'lii U 20 15 10 5 , .... ,, Various Expiration Dates Strike= 80 2 Years (LEAP) , ' ' ,,,,' ,, ,, ,, ,, ,, "' ,, ,, ,, ,, ,,' ,, ,. ,, ,, 0 L----~==--..l.---..J£----1.---L----.I....-- 60 70 80 90 100 110 Stock Price 371 Before that discussion, however, it may be beneficial to examine the effects that interest rates and dividends can have on LEAPS. These effects are much, much greater than those on conventional equity options. Recall that it was stated that inter­ est rates and dividends are minor determinants in the price of an option, unless the dividends were large. That statement pertains mostly to short-term options. For longer-term options such as LEAPS, the cumulative effect of an interest rate or div­ idend over such a long period of time can have a magnified effect in terms of the absolute price of the option. Figure 25-2 presents the option pricing curve again, but the only option depict­ ed is a 2-year LEAPS. The striking price is 100, and the straight line at the right depicts the intrinsic value of the LEAPS. The three curves represent option prices for risk-free interest rates of 3%, 6%, and 9%. All other factors (time to expiration, volatility, and dividends) are fixed. The difference between option prices caused merely by a shift in rates of 3% is very large. The difference in LEAPS prices increases as the LEAPS becomes in-the­ money. Note that in this figure, the distance between the curves gets wider as one scans them from left to right. The price difference for out-of-the-money LEAPS is large enough- nearly a point even for options fairly far out-of-the-money (that is, the points on the left-hand side of the graph). A shift of 3% in rates causes a larger price difference of over 2 points in the at-the-money, 2-year LEAPS. The largest differen­ tial in option prices occurs in-the-rrwney ! This may seem somewhat illogical, but when LEAPS strategies are examined later, the reasons for this will become clear. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:409 SCORE: 8.00 ================================================================================ Chapter 25: LEAPS FIGURE 25-3. LEAPS call pricing curve as dividends increase. 30 25 (I) .g 20 0.. C: :g_ 15 0 10 5 0 70 80 90 100 Stock Price With Current Dividend 110 373 Dividend )> Increases $1 T Increases $2 120 The actual amount that the LEAPS calls lose in price increases slightly as the call is more in-the-money. That is, the curves are closer together on the left-hand (out-of-the-money) side than they are on the right-hand (in-the-money) side. For the in-the-money call, a $1 increase in dividends over two years can cause the LEAPS to be worth about 1 ½ points less in value. Figure 25-3 is to the same scale as Figure 25-2, so they can be compared direct­ ly in terms of magnitude. Notice that the effect of a $1 increase in dividends on the LEAPS call prices is much smaller than that of an increase in interest rates by 3%. Graphically speaking, one can observe this by noting that the spaces between the three curves in the previous figure are much wider than the spaces between the three curves in this figure. Finally, note that dividend increases have the opposite effect on puts. That is, an increase in the dividend payout of the underlying common will cause a put to increase in price. If the put is a long-term LEAPS put, then the effect of the increase will be even larger. Lest one think that LEAPS are too difficult to price objectively, note the follow­ ing. The prior figures of interest rate and dividend effects tend to magnify the effects on LEAPS prices for two reasons. First, they depict the effects on 2-year LEAPS. That is a large amount of life for LEAPS. Many LEAPS have less life remaining, so the effects would be diminished somewhat for LEAPS with 10 to 23 months of life left. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:410 SCORE: 26.00 ================================================================================ 374 Part Ill: Put Option Strategies Second, the figures depict the change in rates or dividends as being instantaneous. This is not completely realistic. If rates change, they will change by a little bit at a time, usually¼% or½% at a time, perhaps as much as 1 %. If dividends are increased, that increase may be instantaneous, but it will not likely occur immediately after the LEAPS are purchased or sold. However, the point that these figures are meant to con­ vey is that interest rates and dividends have a much greater effect on LEAPS than on ordinary shorter-term equity options, and that is certainly a true statement. COMPARING LEAPS AND SHORT-TERM OPTIONS Table 25-1 will help to illustrate the problem in valuing LEAPS, either mentally or with a model. All of the variables - stock price, volatility, interest rates, and dividends - are given in increments and the comparison is shown between 3-month equity options and 2-year LEAPS. There are three sets of comparisons: for options 20% out­ of-the-money, options at-the-money, and options 20% in-the-money. A few words are needed here to explain how volatility is shown in this table. Volatility is normally expressed as a percent. The volatility of the stock market is about 15%. The table shows what would happen if volatility changed by one per­ centage point, to 16%, for example. Of course, the table also shows what would hap­ pen if the other factors changed by a small amount. Most of the discrepancies between the 3-month and the 2-year options are large. For example, if volatility increases by one percentage point, the 3-month out­ of-the-money call will increase in price by only 3 cents (0.03 in the left-hand column) while the 2-year LEAPS call will increase by 43 cents. As another example, look at the bottom right-hand pair of numbers, which show the effect of a dividend increase on the options that are 20% in-the-money. The assumption is that the dividend will increase 25 cents this quarter (and will be 25 cents higher every quarter thereafter). This translates into a loss of 14 cents for the 3-month call, since there is only one ex­ dividend period that affects this call; but it translates into a loss of 1 ½ for the 2-year LEAPS, since the stock will go ex-dividend by an extra $2 over the life of that call. TABLE 25-1. Comparing LEAPS and Short-Term Calls. Change in Price of the Options 20% out at 20% in Variable Increment 3-mo. 2-yr. 3-mo. 2-yr. 3-mo. 2-yr . Stock Pre. + 1 pt . 03 .41 .54 .70 .97 .89 Volatility + 1% .03 .43 .21 .48 .04 .33 Int. Rate + 1/2% .01 .27 .08 .55 .14 .72 Dividend + $.25/qtr 0 -.62 -.08 -1.18 -.14 -1.50 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:411 SCORE: 29.00 ================================================================================ Chapter 25: LEAPS 375 The table also shows that only three of the discrepancies are not large. Two involve the stock price change. If the stock changes in price by 1 point, neither the at­ the-money nor the in-the-money options behave very differently, although the at-the­ money LEAPS do jump by 70 cents. The observant reader will notice that the top line of the table depicts the delta of the options in question; it shows the change in option price for a one-point change in stock price. The only other comparison that is not extremely divergent is that of volatility change for the at-the-money option. The 3- month call changes by 21 cents while the LEAPS changes by nearly ½ point. This is still a factor of two-to-one, but is much less than the other comparisons in the table. Study the other comparisons in the table. The trader who is used to dealing with short-term options might ordinarily ignore the effect of a rise in interest rates of ½ of 1 %, of a 25-cent increase in the quarterly dividend, of the volatility increasing by a mere 1 %, or maybe even of the stock moving by one point (only if his option is out­ of-the-money). The LEAPS option trader will gain or suffer substantially and imme­ diately if any of these occur. In almost every case, his LEAPS call will gain or lose ½ point of value - a significant amount, to be sure. LEAPS STRATEGIES Many of the strategies involving LEAPS are not significantly different from their counterparts that involve short-term options. However, as shown earlier, the long­ term nature of the LEAPS can sometimes cause the strategist to experience a result different from that to which he has become accustomed. As a general rule, one would want to be a buyer of LEAPS when interest rates were low and when the volatilities being implied in the marketplace are low. If the opposite were true (high rates and high volatilities), he would lean toward strategies in which the sale of LEAPS is used. Of course, there are many other specific consid­ erations when it comes to operating a strategy, but since the long-term nature of LEAPS exposes one to interest rate and volatility movements for such a long time, one may as well attempt to position himself favorably with respect to those two ele­ ments when he enters a position. LEAPS AS STOCK SUBSTITUTE Any in-the-money option can be used as a substitute for the underlying stock. Stock owners may be able to substitute a long in-the-money call for their long stock. Short sellers of stock may be able to substitute a long put for their short stock. This is not a new idea; it was discussed briefly in Chapter 3 under reasons why people buy calls. It has been available as a strategy for some time with short-term options. Its attrac­ tiveness seems to have increased somewhat with the introduction of LEAPS, howev- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:412 SCORE: 26.00 ================================================================================ 374 Part Ill: Put Option Strategies Second, the figures depict the change in rates or dividends as being instantaneous. This is not completely realistic. If rates change, they will change by a little bit at a time, usually¼% or ½% at a time, perhaps as much as 1 %. If dividends are increased, that increase may be instantaneous, but it will not likely occur immediately after the LEAPS are purchased or sold. However, the point that these figures are meant to con­ vey is that interest rates and dividends have a much greater effect on LEAPS than on ordinary shorter-term equity options, and that is certainly a true statement. COMPARING LEAPS AND SHORT-TERM OPTIONS Table 25-1 will help to illustrate the problem in valuing LEAPS, either mentally or with a model. All of the variables - stock price, volatility, interest rates, and dividends - are given in increments and the comparison is shown between 3-month equity options and 2-year LEAPS. There are three sets of comparisons: for options 20% out­ of-the-money, options at-the-money, and options 20% in-the-money. A few words are needed here to explain how volatility is shown in this table. Volatility is normally expressed as a percent. The volatility of the stock market is about 15%. The table shows what would happen if volatility changed by one per­ centage point, to 16%, for example. Of course, the table also shows what would hap­ pen if the other factors changed by a small amount. Most of the discrepancies between the 3-month and the 2-year options are large. For example, if volatility increases by one percentage point, the 3-month out­ of-the-money call will increase in price by only 3 cents (0.03 in the left-hand column) while the 2-year LEAPS call will increase by 43 cents. As another example, look at the bottom right-hand pair of numbers, which show the effect of a dividend increase on the options that are 20% in-the-money. The assumption is that the dividend will increase 25 cents this quarter ( and will be 25 cents higher every quarter thereafter). This translates into a loss of 14 cents for the 3-month call, since there is only one ex­ dividend period that affects this call; but it translates into a loss of 1 ½ for the 2-year LEAPS, since the stock will go ex-dividend by an extra $2 over the life of that call. TABLE 25-1. Comparing LEAPS and Short-Term Calls. Change in Price of the Options 20% out al 20% in Variable Increment 3-mo. 2-yr. 3-mo. 2-yr. 3-mo. 2-yr. Stock Pre. + 1 pt .03 .41 .54 .70 .97 .89 Volatility + 1% .03 .43 .21 .48 .04 .33 Int. Rate + 1/2% .01 .27 .08 .55 .14 .72 Dividend + $.25/qtr 0 -.62 -.08 - l.18 -.14 -1.50 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:413 SCORE: 29.00 ================================================================================ Chapter 25: LEAPS 375 The table also shows that only three of the discrepancies are not large. Two involve the stock price change. If the stock changes in price by 1 point, neither the at­ the-money nor the in-the-money options behave very differently, although the at-the­ money LEAPS do jump by 70 cents. The observant reader will notice that the top line of the table depicts the delta of the options in question; it shows the change in option price for a one-point change in stock price. The only other comparison that is not extremely divergent is that of volatility change for the at-the-money option. The 3- month call changes by 21 cents while the LEAPS changes by nearly ½ point. This is still a factor of two-to-one, but is much less than the other comparisons in the table. Study the other comparisons in the table. The trader who is used to dealing with short-term options might ordinarily ignore the effect of a rise in interest rates of½ of 1 %, of a 25-cent increase in the quarterly dividend, of the volatility increasing by a mere 1 %; or maybe even of the stock moving by one point (only if his option is out­ of-the-money). The LEAPS option trader will gain or suffer substantially and imme­ diately if any of these occur. In almost every case, his LEAPS call will gain or lose ½ point of value - a significant amount, to be sure. LEAPS STRATEGIES Many of the strategies involving LEAPS are not significantly different from their counterparts that involve short-term options. However, as shown earlier, the long­ term nature of the LEAPS can sometimes cause the strategist to experience a result different from that to which he has become accustomed. As a general rule, one would want to be a buyer of LEAPS when interest rates were low and when the volatilities being implied in the marketplace are low. If the opposite were true (high rates and high volatilities), he would lean toward strategies in which the sale of LEAPS is used. Of course, there are many other specific consid­ erations when it comes to operating a strategy, but since the long-term nature of LEAPS exposes one to interest rate and volatility movements for such a long time, one may as well attempt to position himself favorably with respect to those two ele­ ments when he enters a position. LEAPS AS STOCK SUBSTITUTE Any in-the-money option can be used as a substitute for the underlying stock. Stock owners may be able to substitute a long in-the-money call for their long stock. Short sellers of stock may be able to substitute a long put for their short stock. This is not a new idea; it was discussed briefly in Chapter 3 under reasons why people buy calls. It has been available as a strategy for some time with short-term options. Its attrac­ tiveness seems to have increased somewhat with the introduction of LEAPS, howev- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:414 SCORE: 31.00 ================================================================================ 376 Part Ill: Put Option Strategies er. More and more people are examining the potential of selling the stock they own and buying long-term calls (LEAPS) as a substitute, or buying LEAPS instead of making an initial purchase in a particular common stock. Substitution for Stock Currently Held Long. Simplistically, this strate­ gy involves this line of thinking: If one owns stock and sells it, an investor could rein­ vest a small portion of the proceeds in a call option, thereby providing continued upside profit potential if the stock rises in price, and invest the rest in a bank to earn interest. The interest earned would act as a substitute for the dividend, if any, to which the investor is no longer entitled. Moreover, he has less downside risk: If the stock should fall dramatically, his loss is limited to the initial cost of the call. In actual practice, one should carefully calculate what he is getting and what he is giving up. For example, is the loss of the dividend too great to be compensated for by the investment of the excess proceeds? How much of the potential gain will be wasted in the form of time value premium paid for the call? The costs to the stock owner who decides to switch into call options as a substitute are commissions, the time value premium of the call, and the loss of dividends. The benefits are the inter­ est that can be earned from freeing up a substantial portion of his funds, plus the fact that there is less downside risk in owning the call than in owning the stock. Example: XYZ is selling at 50. There are one-year LEAPS with a striking price of 40 that sell for $12. XYZ pays an annual dividend of $0.50 and short-term interest rates are 5%. What are the economics that an owner of 100 XYZ common stock must cal­ culate in order to determine whether it is viable to sell his stock and buy the one-year LEAPS as a substitute? The call has time value premium of 2 points (40 + 12 - 50). Moreover, if the stock is sold and the LEAPS purchased, a credit of $3,800 less commissions would be generated. First, calculate the net credit generated: Credit balance generated: Sale of 1 00 XYZ stock Less stock commission Net sale proceeds: Cost of one LEAPS call Plus option commission Net cost of call: Total credit balance: $5,000 25 $4,975 credit $3,760 credit $1,200 15 $1,215 debit Now the costs and benefits of making the switch can be computed: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:415 SCORE: 15.00 ================================================================================ Chapter 25: LEAPS Costs of switching: Time value premium Loss of dividend Stock commissions Option commissions Total cost: Fixed benefit from switching: Interest earned on credit balance of $3,760 at 5% interest for one year= 0.05 x $3,760: Net cost of switching: 317 -$200 -$ 50 -$ 25 - .l__Ll_ -$290 + $188 - $102 The stock owner must now decide if it is worth just over $1 per share in order to have his downside risk limited to a price of 39½ over the next year. The price of 39½ as his downside risk is merely the amount of the net credit he received from doing the switch ($3,760) plus the interest earned ($188), expressed in per-share terms. That is, if XYZ falls dramatically over the next year and the LEAPS expires worthless, this investor will still have $3,948 in a bank account. That is equivalent to limiting his risk to about 39½ on the original 100 shares. If the investor decides to make the substitution, he should invest the proceeds from the sale in a 1-year CD or Treasury bill, for two reasons. First, he locks in the current rate - the one used in his calculations - for the year. Second, he is not tempt­ ed to use the money for something else, an action that might negate the potential benefits of the substitution. The above calculations all assume that the LEAPS call or the stock would have been held for the full year. If that is known not to be the case, the appropriate costs or benefits must be recalculated. Caveats. This ($102) seems like a reasonably small price to pay to make the switch from common stock to call ownership. However, if the investor were planning to sell the stock before it fell to 39½ in any case, he might not feel the need to pay for this protection. (Be aware, however, that he could accomplish essentially the same thing, since he can sell his LEAPS call whenever he wants to.) Moreover, when the year is up, he will have to pay another stock commission to repurchase his XYZ common if he still wants to own it ( or he will have to pay two option commissions to roll his long call out to a later expiration date). One other detriment that might exist, although a relatively unlikely one, is that the underlying common might declare an increased dividend or, even worse, a special cash dividend. The LEAPS call owner would not be entitled to that dividend increase in whatever form, while, obviously, the common ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:416 SCORE: 13.00 ================================================================================ 378 Part Ill: Put Option Strategies stock owner would have been. If the company declared a stock dividend, it would have no effect on this strategy since the call owner is entitled to those. A change in interest rates is not a factor either, since the owner of the LEAPS should invest in a 1-year Treasury bill or a 1-year CD and therefore would not be subject to interim changes in short-term interest rates. There may be other mitigating circumstances. Mostly these would involve tax considerations. If the stock is currently a profitable investment, the sale would gen­ erate a capital gain, and taxes might be owed. If the stock is currently being held at a loss, the purchase of the call would constitute a wash sale and the loss could not be taken at this time. (See Chapter 41 on taxes for a broader discussion of the wash sale rule and option trading.) In tl1eory, the calculations above could produce an overall credit, in which case the stockholder W(?uld normally want to substitute with the call, unless he has overriding tax considerations or suspects that a cash dividend increase is going to be announced. Be very careful about switching if this situation should arise. Normally, arbitrageurs - per­ sons trading for exchange members and paying no commission - would take advantage of such a situation before the general public could. If they are letting the opportunity pass by, there must be a reason (probably the cash dividend), so be extremely certain of your economics and research before venturing into such a situation. In summary, holders of common stock on which there exist in-the-money LEAPS should evaluate the economics of substituting the LEAPS call for the com­ mon stock. Even if arithmetic calculations call for the substitution, the stockholder should consider his tax situation as well as his outlook for the cash dividends to be paid by the common before making the switch. BUYING LEAPS AS THE INITIAL PURCHASE INSTEAD OF BUYING A COMMON STOCK Logic similar to that used earlier to determine whether a stockholder might want to substitute a LEAPS call for his stock can be used by a prospective purchaser of com­ mon stock. In other words, this investor does not already own the common. He is going to buy it. This prospective purchaser might want to buy a LEAPS call and put the rest of the money he had planned to use in the bank, instead of actually buying the stock itself. His costs - real and opportunity - are calculated in a similar manner to those expressed earlier. The only real difference is that he has to spend the stock commis­ sion in this case, whereas he did not in the previous example (since he already owned the stock). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:418 SCORE: 30.00 ================================================================================ 380 Part Ill: Put Option Strategies Using Margin. The same prospective initial purchaser of common stock might have been contemplating the purchase of the stock on margin. If he used the LEAPS instead, he could save the margin interest. Of course, he wouldn't have as much money to put in the bank, but he should also compare his costs against those of buy­ ing the LEAPS call instead. Example: As before, XYZ is selling at 50; there are 1-year LEAPS with a striking price of 40 that sell for $12; XYZ pays an annual dividend of $0.50; and short-term interest rates are 5%. Furthermore, assume the margin rate is 8% on borrowed debit balances. First, calculate the difference in prospective investments: Cost of buying the stock: $5,000 + $25 commission: Amount borrowed (50%) Equity required Cost of buying LEAPS: $1,200 + $15 commission: Difference (available to be placed in bank account) $5,025 -2,512 $2,513 $1,215 $1,298 Now the costs and opportunities can be compared, if it is assumed that he buys the LEAPS: Costs: Time value premium Dividend loss Savings: Interest on $1,298 at 5% Margin interest on $2,512 debit balance at 8% for one year Net Savings: -$200 - 50 +$ 65 + 201 +$ 16 For the prospective margin buyer, there is a real savings in this example. The fact that he does not have to pay the margin interest on his debit balance makes the purchase of the LEAPS call a cost-saving alternative. Finally, it should be noted that current margin rules allow one to purchase a LEAPS option on margin. That can be accounted for in the above calculations as well; merely reduce the investment required and increase the margin charges on the debit balance. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:419 SCORE: 22.00 ================================================================================ Chapter 25: LEAPS 381 In summary, a prospective purchaser of common stock may often find that if there is an in-the-money option available, the purchase of that option is more attrac­ tive than buying the common stock itself. If he were planning to buy on margin, it is even more likely that the LEAPS purchase will be attractive. The main drawback is that he will not participate if cash dividends are increased or a special dividend is declared. Read on, however, because the next strategy may be better than the one above. PROTECTING EXISTING STOCK HOLDINGS WITH LEAPS PUTS What was accomplished in the substitution strategy previously discussed? The stock owner paid some cost ($102 in the actual example) in order to limit the risk of his stock ownership to a price of 39½. What if he had bought a LEAPS put instead? Forgetting the price of the put for a moment, concentrate on what the strategy would accomplish. He would be protected from a large loss on the downside since he owns the put, and he could participate in upside appreciation since he still owns the stock. Isn't this what the substitution strategy was trying to accomplish? Yes, it is. In this strategy, only one commission is paid- that being on a fairly cheap out-of-the-money LEAPS put - and there is no risk of losing out on dividend increases or special divi­ dends. The comparison between substituting a call or buying a put is a relatively sim­ ple one. First, do the calculations as they were performed in the initial example above. That example showed that the stockholder's cost would be $102 to substitute the LEAPS call for the stock, and such a substitution would protect him at a price of 39½. In effect, he is paying $152 for a LEAPS put with a strike of 40- the $102 cost plus the difference between 40 and the 39½ protection price. Now, if an XYZ 1-year LEAPS put with strike 40 were available at 1 ½, he could accomplish everything he had initially wanted merely by buying the put. Moreover, he would save commissions and still be in a position to participate in increased cash dividends. These additional benefits should make the put worth even more to the stockholder, so that he might pay even slightly more than 1 ½ for the put. If the LEAPS put were available at this price, it would clearly be the bet­ ter choice and should be bought instead of substituting the LEAPS call for the com­ mon stock. Thus, any stockholder who is thinking of protecting his position can do it in one of two ways: Sell the stock and substitute a call, or continue to hold his stock and buy a put to protect it. LEAPS calls and puts are amenable to this strategy. Because of the LEAPS' long-term nature, one does not have to keep reestablishing his position and pay numerous commissions, as he would with short-term options. The stock­ holder should perform the simple calculations as shown above in order to decide ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:420 SCORE: 38.00 ================================================================================ 382 Part Ill: Put Option Strategies whether the move is feasible at all, and if it is, whether to use the call substitution strategy or the put protection strategy. LEAPS INSTEAD OF SHORT STOCK Just as in-the-money LEAPS calls may sometimes be a smarter purchase than the stock itself, in-the-money puts may sometimes be a better purchase than shorting the common stock. Recall that either the put purchase or the short sale of stock is a bear­ ish strategy, generally implemented by someone who expects the stock to decline in price. The strategist knows, however, that short stock is a component of many strate­ gies and might reflect other opinions than pure bearishness on the common. In any case, an in-the-money put may prove to be a viable substitute for shorting the stock itself. The two main advantages that the put owner has are that he has limited risk (whereas the short seller of stock has theoretically unlimited risk); and he does not have to pay out any dividends on the underlying stock as the short seller would. Also, the commissions for buying the put would normally be smaller than those required to sell the stock short. There is not much in the way of calculating that needs to be done in order to make the comparison between buying the in-the-money put and shorting the stock. If the time value premium spent is small in comparison \vith the dividend payout that is saved, then the put is probably the better choice. Professional arbitrageurs and other exchange members, as well as some large customers, receive interest on their short sales. For these traders, the put would have to be trading with virtually no time premium at all in order for the comparison to favor the put purchase over the stock short sale. However, the public customer who is going to be shorting stock should be aware of the potential for buying an in-the­ money put instead. SPECULATIVE OPTION BUYING WITH LEAPS Strategists know that buying calls and puts can have various applications; witness the stock substitution strntegies above. However, the most popular reason for buying options is for speculative gain. The leverage inherent in owning options and their lim­ ited risk feature make them attractive for this purpose as well. The risk, of course, can be 100% of the investment, and time decay works against the option owner as well. LEAPS calls and puts fit all of these descriptions; they simply have longer matu­ rities. Time decay is the major enemy of the speculative option holder. Purchasing LEAPS options instead of the shorter-term equity options generally exposes the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:421 SCORE: 43.00 ================================================================================ Chapter 25: LEAPS 383 buyer to less risk of time decay on a daily basis. This is true because the extreme neg­ ative effects of time decay magnify as the option approaches its expiration. Recall that it was shown in Chapter 3 that time decay is not linear: An option decays more rap­ idly at the end of its life than at the beginning. Eventually, a LEAPS put or call will become a normal short-term equity option and time will begin to take a more rapid toll. But in the beginning of the life of LEAPS, there is so much time remaining that the short-term decay is not large in terms of price. Table 25-2 and Figure 25-4 depict the rate of decay of two options: one is at­ the-money (the lower curve) and the other is 20% out-of-the-money (the upper curve). The horizontal axis is months of life remaining until expiration. The vertical axis is the percent of the option price that is lost daily due to time decay. The options that qualify as LEAPS are ones with more than 9 months oflife remaining, and would thus be the ones on the lower right-hand part of the graph. The upward-sloping nature of both curves as time to expiration wanes shows that time decay increases more rapidly as expiration approaches. Notice how much more rapidly the out-of-the-money option decays, percentagewise, than the at-the­ money. LEAPS, however, do not decay much at all compared to normal equity options. Most LEAPS, even the out-of-the-money ones, lose less than¼ of one per­ cent of their value daily. This is a pittance when compared with a 6-month equity option that is 20% out-of-the-money- that option loses well over 1 % of its value daily and it still has 6 months of life remaining. From the accompanying table, observe that the out-of-the-money 2-month option loses over 4% of its value daily! Thus, LEAPS do not decay at a rapid rate. This gives the LEAPS holder a chance to have his opinion about the stock price work for him without having to worry as much about the passage of time as the average equity option holder would. An advantage of owning LEAPS, therefore, is that one's timing of the option pur­ chase does not have to be as exact as that for shorter-term option buying. This can be a great psychological advantage as well as a strategic advantage. The LEAPS option buyer who feels strongly that the stock will move in the desired direction has the lux­ ury of being able to wait calmly for the anticipated move to take place. If it does not, even in perhaps as long as 6 months' time, he may still be able to recoup a reason­ able portion of his initial purchase price because of the slow percentage rate of decay. Do not be deluded into believing that LEAPS don't decay at all. Although the rate of decay is slow (as shown previously), an option that is losing 0.15% of its value daily will still lose about 25% of its value in six months. Example: XYZ is at 60 and there are 18-month LEAPS calls selling for $8, with a striking price of 60. The daily decay of this call with respect to time will be minus- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:423 SCORE: 26.00 ================================================================================ Chapter 25: LEAPS 385 Those familiar with holding equity calls and puts are more accustomed to seeing an option lose 25% of its value in possibly as little as four or five weeks' time. Thus, the advantage of holding the LEAPS is obvious from the viewpoint of slower time decay. This observation leads to the obvious question: "When is the best time to sell my call and repurchase a longer-term one?" Referring again to the figure above may help answer the question. Note that for the at-the-money option, the curve begins to bend dramatically upward soon after the 6-month time barrier is passed. Thus, it seems log­ ical that to minimize the effects of time decay, all other things being equal, one would sell his long at-the-money call when it has about 6 months of life left and simultane­ ously buy a 2-year LEAPS call. This keeps his time decay exposure to a. minimum. The out-of-the-money call is more radical. Figure 25-4 shows that the call that is 20% out-of-the-money begins to decay much more rapidly (percentagewise) at sometime just before it reaches one year until expiration. The same logic would dic­ tate, then, that if one is trading out-of-the-money options, he would sell his option held long when it has about one year to go and reestablish his position by buying a 2- year LEAPS option at the same time. ADVANTAGES OF BUYING HCHEAP" It has been demonstrated that rising interest rates or rising volatility would make the price of a LEAPS call increase. Therefore, if one is attempting to participate in LEAPS speculative call buying strategies, he should be more aggressive when rates and volatilities are low. A few sample prices may help to demonstrate just how powerful the effects of rates and volatilities are, and how they can be a friend to the LEAPS call buyer. Suppose that one buys a 2-year LEAPS call at-the-money when the following situation exists: XYZ: 100 January 2-year LEAPS call with strike of 100: 14 Short-term interest rates: 3% Volatility: below average (historically) For the purposes of demonstration, suppose that the current volatility is low for XYZ (historically) and that 3% is a low level for rates as well. If the stock moves up, there is no problem, because the LEAPS call will increase in price. But what if the stock drops or stays unchanged? Is all hope of a profit lost? Actually, no. If interest rates increase or the volatility that the calls trade at increases, we know the LEAPS call will increase in value as well. Thus, even though the direction in which the stock is mov­ ing may be unfavorable, it might still be possible to salvage one's investment. Table 25-3 shows where volatility would have to be or where short-term rates would have ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:424 SCORE: 12.00 ================================================================================ 386 Part Ill: Put Option Strategies TABLE 25-3. Factors necessary for January 2-year LEAPS to be = 14. Stock price After l month 100 (unchanged) r = 3 .4% or V + 5% 95 90 r = 6% or V + 20% r = 8.5% or V + 45% After 6 months r = 6% or V + 20% r = 9.4% or V + 45% r = 12.6% or V + 70% to go in order to keep the value of the LEAPS call at 14 even after the indicated amount of time had expired. To demonstrate the use of this table, suppose the stock price were 100 (unchanged) after one month. If interest rates had 1isen to 3.4% from their original level of 3% during that time, the call would still be worth 14 even though one month had passed. Alternatively, if rates were the same, but volatility had increased by only 5% from its original level, then the call would also still be worth 14. Note that this means that volatility would have to increase only slightly (by ½oth) from its original level, not by 5 percentage points. Even if the stock were to drop to 90 and six months had passed, the LEAPS call holder would still be even if rates had iisen to 12.6% (highly unlikely) or volatility had risen by 70%. It is often possible for volatilities to fluctuate to that extent in six months, but not likely for interest rates. In fact, as interest rates go, only the top line of the table probably represents realistic interest rates; an increase of 0.4% in one month, or 3% in 6 months, is pos­ sible. The other lines, where the stock drops in price, probably require too large a jump in rates for rates alone to be able to salvage the call price. However, any increase in rates will be helpful. Volatility is another matter. It is often feasible for volatilities to change by as much as 50% from their previous level in a month, and certainly in six months. Hence, as has been stated before, the volatility factor is the more dominant one. This table shows the effect of rising interest rates and volatilities on LEAPS calls. It would be beneficial to the LEAPS call owner and, of course, detrimental to the LEAPS call seller. This is clear evidence that one should be aware of the gener­ al level of rates and volatility before using LEAPS options in a strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:425 SCORE: 77.00 ================================================================================ Chapter 25: LEAPS THE DELTA 387 The delta of an option is the amount by which the option price will change if the underlying stock changes in price by one point. In an earlier section of this chapter, comparing the differences between LEAPS and short-term calls, mention was made of delta. The subject is explored in more depth here because it is such an important concept, not only for option buyers, but for most strategic decisions as well. Figure 25-5 depicts the deltas of two different options: 2-year LEAPS and 3- month equity options. Their terms are the same except for their expiration dates; strik­ ing price is 100, and volatility and interest rate assumptions are equal. The horizontal axis displays the stock price while the vertical axis shows the delta of the options. Several relevant observations can be made. First, notice that the delta of the at­ the-money LEAPS is very large, nearly 0.70. This means that the LEAPS call will move much more in line with the common stock than a comparable short-term equi­ ty option would. Very short-term at-the-money options have deltas of about½, while slightly longer-term ones have deltas ranging up to the 0.55 to 0.60 area. What this implies is that the longer the life of an at-the-nwney option, the greater its delta. In addition, the figure shows that the deltas of the 3-month call and the 2-year LEAPS call are about equal when the options a~e approximately 5% in-the-money. If the options are more in-the-money than that, then the LEAPS call has a lower delta. This means that at- and out-of-the-money LEAPS will move more in line with the common stock than comparable short-term options will. Restated, the LEAPS calls will move faster than the ordinary short-term equity calls unless both options are more than 5% in-the-money. Note that the movement referred to is in absolute terms in change of price, not in percentage terms. The delta of the 2-year LEAPS does not change as dramatically when the stock moves as does the delta of the 3-month option (see Figure 25-5). Notice that the LEAPS curve is relatively flat on the chart, rising only slightly above horizon­ tal. In contrast, the delta of the 3-month call is very low out-of-the-money and very large in-the-money. What this means to the call buyer is that the amount by which he can expect the LEAPS call to increase or decrease in price is somewhat stable. This can affect his choice of whether to buy the in-the-money call or the out-of­ the-money call. With normal short-term options, he can expect the in-the-money call to much more closely mirror the movement in the stock, so he might be tempt­ ed to buy that call if he expects a small movement in the stock. With LEAPS, how­ ever, there is much less discrepancy in the amount of option price movement that will occur. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:426 SCORE: 27.00 ================================================================================ 388 Part Ill: Put Option Strategies FIGURE 25·5. Call delta comparison, 2-year LEAPS versus 3-month equity options. 90 80 70 8 60 ,... X .l!l 50 Q) 0 40 30 t= 3 months 20 10 O 70 80 90 100 110 120 130 Stock Price Example: XYZ is trading at 82. There are 3-month calls with strikes of 80 and 90, and there are 2-year LEAPS calls at those strikes as well. The following table summarizes the available information: XYZ: 82 Date: January, 2002 Option Price Delta April ('02) 80 call 4 s/a April ('02) 90 call i/a January ('04) 80 LEAPS call 14 3/4 January ('04) 90 LEAPS call 7 1/2 Suppose the trader expects a 3-point move by the underlying common stock, from 82 to 85. If he were analyzing short-term calls, he would see his potential as a gain of 17/s in the April 80 call versus a gain of 3/s in the April 90 call. Each of these gains is pro­ jected by multiplying the call's delta times 3 (the expected stock move, in points). Thus, there is a large difference between the expected gains from these two options, particularly after commissions are considered. Now observe the LEAPS. The January 80 would increase by 2¼ while the January 90 would increase by 1 ½ if XYZ moved higher by 3 points. This is not near­ ly as large a discrepancy as the short-term options had. Observe that the January 90 LEAPS sells for half the price of the January 80. These movements projected by the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:427 SCORE: 25.00 ================================================================================ Chapter 25: LEAPS 389 delta indicate that the January 90 LEAPS will move by a larger percentage than the January 80 and therefore would be the better buy. PUT DELTAS Many of the previous observations regarding deltas of LEAPS calls can be applied to LEAPS puts as well. However, Figure 25-5 changes a little when the following for­ mula is applied. Recall that the relationship between put deltas and call deltas, except for deeply in-the-money puts, is: Put delta = Call delta - 1 This has the effect of inverting the relationships that have just been described. In other words, while the short-term calls didn't move as fast as the LEAPS, the short-term puts move Jaster than the LEAPS puts in most cases. Figure 25-6 shows the deltas of these options. The vertical axis shows the puts' delta. Notice that out-of-the-money LEAPS puts and short-term equity puts don't behave very differently in terms of price change (bottom right-hand section of figure). In-the-money puts (when the stock is below the striking price) move faster if they are shorter-term. This fact is accentuated even more when the puts are more deeply in-the-money. The left-hand side of the figure depicts this fact. FIGURE 25-6. Put delta comparison, 2-year LEAPS versus 3-month equity options. 90 80 70 t= 3 months 0 60 0 1 50 X Jg 40 Q) 0 30 20 10 O 70 80 90 100 110 120 130 Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:428 SCORE: 27.00 ================================================================================ 388 Part Ill: Put Option Strategies FIGURE 25-5. Call delta comparison, 2-year LEAPS versus 3-month equity options. 90 80 70 g 60 ; 50 ~ O 40 30 t= 3 months 20 10 O 70 80 90 100 110 120 130 Stock Price Example: XYZ is trading at 82. There are 3-month calls with strikes of 80 and 90, and there are 2-year LEAPS calls at those strikes as well. The following table summarizes the available information: XYZ: 82 Date: January, 2002 Option Price Delta April ('02) 80 call 4 s/a April ('02) 90 call 1 i/s January ('04) 80 LEAPS call 14 3/4 January ('04) 90 LEAPS call 7 1/2 Suppose the trader expects a 3-point move by the underlying common stock, from 82 to 85. Ifhe were analyzing short-term calls, he would see his potential as a gain of F/s in the April 80 call versus a gain of 3/s in the April 90 call. Each of these gains is pro­ jected by multiplying the call's delta times 3 (the expected stock move, in points). Thus, there is a large difference behveen the expected gains from these two options, particularly after commissions are considered. Now observe the LEAPS. The January 80 would increase by 2¼ while the January 90 would increase by 1 ½ if XYZ moved higher by 3 points. This is not near­ ly as large a discrepancy as the short-term options had. Observe that the January 90 LEAPS sells for half the price of the January 80. These movements projected by the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:429 SCORE: 25.00 ================================================================================ Chapter 25: LEAPS 389 delta indicate that the January 90 LEAPS will move by a larger percentage than the January 80 and therefore would be the better buy. PUT DELTAS Many of the previous observations regarding deltas of LEAPS calls can be applied to LEAPS puts as well. However, Figure 25-5 changes a little when the following for­ mula is applied. Recall that the relationship between put deltas and call deltas, except for deeply in-the-money puts, is: Put delta = Call delta - 1 This has the effect of inverting the relationships that have just been described. In other words, while the short-term calls didn't move as fast as the LEAPS, the short-term puts nwve fa,ster than the LEAPS puts in nwst cases. Figure 25-6 shows the deltas of these options. The vertical axis shows the puts' delta. Notice that out-of-the-money LEAPS puts and short-term equity puts don't behave very differently in terms of price change (bottom right-hand section offigure). In-the-money puts (when the stock is below the striking price) move faster if they are shorter-term. This fact is accentuated even more when the puts are more deeply in-the-money. The left-hand side of the figure depicts this fact. FIGURE 25-6. Put delta comparison, 2-year LEAPS versus 3-month equity options. 90 80 70 t= 3 months 0 60 0 1 50 X Jg 40 Q) 0 30 20 10 O 70 80 90 100 110 120 130 Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:430 SCORE: 74.00 ================================================================================ 390 Part Ill: Put Option Strategies The LEAPS put delta curve is flat, just as the call delta curve was. Moreover, the delta is not very large anywhere across the figure. For example, at-the-money 2- year LEAPS puts move only about 30 cents for a one-point move in the underlying stock. LEAPS put buyers who want to speculate on a stock's downward movement must realize that the leverage factor is not large; it takes approximately a 3-point move by the underlying common for an at-the-money LEAPS put to increase in value by one point. Long-term puts don't mirror stock movement nearly as well as shorter-term puts do. In summary, the option buyer who is considering buying LEAPS puts or calls as speculation should be aware of the different price action that LEAPS exhibit when compared to shorter-term options. Due to the large amount of time that LEAPS have remaining in their lives, the time decay of the LEAPS options is smaller. For this rea­ son, the LEAPS option buyer doesn't need to be as precise in his timing. In general, LEAPS calls move faster when the underlying stock moves, and LEAPS puts move more slowly. Other than that, the general reasons for speculative option buying apply to LEAPS as well: leverage and limited risk. SELLING LEAPS Strategies involving selling LEAPS options do not differ substantially from those involving shorter-term options. The discussions in this section concentrate on the two major differences that sellers of LEAPS will notice. First, the slow rate of time decay of LEAPS options means that option writers who are used to sitting back and watch­ ing their written options waste away will not experience the same effect with LEAPS. Second, follow-up action for writing strategies usually depends on being able to buy back the w1itten option when it has little or no time value premium remaining. Since LEAPS retain time value even when substantially in- or out-of-the-money, follow-up action involving LEAPS may involve the repurchase of substantial amounts of time value premium. COVERED WRITING LEAPS options can be sold against underlying stock just as short-term options can. No extra collateral or investment is required to do so. The resulting position is again one with limited profit potential, but enhanced profitability (as compared to stock ownership), if the underlying stock remains unchanged or falls. The maximum prof­ it potential of the covered write is reached whenever the underlying stock is at or above the striking price of the written option at expiration. The LEAPS covered writer takes in substantial premium, in terms of price, when he sells the long-term option. He should compare the return that he could ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:431 SCORE: 20.00 ================================================================================ Chapter 25: LEAPS 391 make from the LEAPS write with returns that can be made from repeatedly writing shorter-term calls. Of course, there is no guarantee that he will actually be able to repeat the short-term writes during the longer life of the LEAPS. As an aside, the strategist who is utilizing the incremental return concept of cov­ ered writing may find LEAPS call writing quite attractive. This is the strategy where­ in he has a higher target price at which he would be willing to sell his common stock, and he writes calls along the way to earn an incremental return (see Chapter 2 for details). Since this type of writer is only concerned with absolute levels of premiums being brought into the account and not with things like return if exercised, he should utilize LEAPS calls if available, since the premiums are the largest available. Moreover, if the incremental return writer is currently in a short-term call and is going to be called away, he might roll into a LEAPS call in order to retain his stock and take in more premium. The rest of this section discusses covered writing from the more normal view­ point of the investor who buys stock and sells a call against it in order to attain a par­ ticular return. Example: XYZ is selling at 50. The investor is considering a 500-share covered write and he is unsure whether to use the 6-month call or the 2-year LEAPS. The July 50 call sells for 4 and has 6 months of life remaining; the January 50 LEAPS call sells for 8½ and has 2 years of life. Further assume that XYZ pays a dividend of $0.25 per quarter. As was done in Chapter 2, the net required investment is calculated, then the return (if exercised) is computed, and finally the downside break-even point is deter­ mined. Stock cost (500 shares @ 50) Plus stock commission Less option premiums received Plus option commissions Net cash investment Net Investment Required July 50 call $25,000 + 300 2,000 + 50 $23,350 January 50 LEAPS $25,000 + 300 4,250 + 100 $21,150 Obviously, the LEAPS covered writer has a smaller cash investment, since he is sell­ ing a more expensive call in his covered write. Note that the option premium is being applied against the net investment in either case, as is the normal custom when doing covered writing. Now, using the net investment required, one can calculate the return (if exer­ cised). That return assumes the stock is above the striking price of the written option ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:432 SCORE: 18.00 ================================================================================ 392 Part Ill: Put Option Strategies at its expiration, and the stock is called away. The short-term writer would have col­ lected two dividends of the common stock, while the LEAPS writer would have col­ lected eight by expiration. Stock sale (500 @ 50) Less stock commission Plus dividends earned until expiration Less net investment Net profit if exercised Return if exercised (net profit/net investment) Return If Exercised + July 50 call $25,000 300 250 - 23,350 $ 1,600 6.9% January 50 LEAPS $25,000 300 + 1,000 - 21,150 $ 4,550 21.5% The LEAPS writer has a much higher net return if exercised, again because he wrote a more expensive option to begin with. However, in order to fairly compare the two writes, one must annualize the returns. That is, the July 50 covered write made 6.9% in six months, so it could make twice that in one year, if it can be duplicated six months from now. In a similar manner, the LEAPS covered writer can make 21.5% in two years if the stock is called away. However, on an annualized basis, he would make only half that amount. Return If Exercised, Annualized July 50 call January 50 LEAPS 13.8% 10.8% Thus, on an annualized basis, the short-term write seems better. The shorter-term call will generally have a higher rate of return, annualized, than the LEAPS call. The problems with annualizing are discussed in the following text. Finally, the downside break-even point can be computed for each write. Downside Break-Even Calculation Net investment Less dividends received Total stock cost to expiration Divided by shares held (500), equals break-even price: July 50 call $23,350 250 $23,100 46.2 January 50 LEAPS $21,150 1 000 $20,150 40.3 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:433 SCORE: 17.00 ================================================================================ Chapter 25: LEAPS 393 The larger premium of the LEAPS call that was written produces this dramatically lower break-even price for the LEAPS covered write. Similar comparisons could be made for a covered write on margin if the investor is using a margin account. The steps above are the mechanical ones that a covered writer should go through in order to see how the short-term write compares to the longer-term LEAPS write. Analyzing them is often a less routine matter. It would seem that the short-term write is better if one uses the annualized rate of return. However, the annualized return is a somewhat subjective number that depends on several assumptions. The first assumption is that one will be able to generate an equivalent return six months from now when the July 50 call expires worthless or the stock is called away. If the stock were relatively unchanged, the covered writer would have to sell a 6- month call for 4 points again six months from now. Or, if the stock were called away, he would have to invest in an equivalent situation elsewhere. Moreover, in order to reach the 2-year horizon offered by the LEAPS write, the 6-month return would have to be regenerated three more times (six months from now, one year from now, and a year and a half from now). The covered writer cannot assume that such returns can be repeated with any certainty every six months. The second assumption that was made when the annualized returns were cal­ culated was that one-half the return if exercised on the LEAPS call would be made when one year had passed. But, as has been demonstrated repeatedly in this chapter, the time decay of an option is not linear. Therefore, one year from now, if XYZ were still at 50, the January 50 LEAPS call would not be selling for half its current price (½ x 8½ = 4¼). It would be selling for something more like 5.00, if all other factors remained unchanged. However, given the variability of LEAPS call premiums when interest rates, volatility, or dividend payouts change, it is extremely difficult to esti­ mate the call price one year from now. Consequently, to say that the 21.5% 2-year return if exercised would be 10.8% after one year may well be a false statement. Thus, the covered writer must make his decision based on what he knows. He knows that with the short-term July 50 write, if the stock is called away in six months, he will make 6.9%, period. If he opts for the longer term, he will make 21.5% if he is called away in two years. Which is better? The question can only be answered by each covered writer individually. One's attitude toward long-term investing will be a major factor in making the decision. If he thinks XYZ has good prospects for the long term, and he feels conservative returns will be below 10% for the next couple of years, then he would probably choose the LEAPS write. However, if he feels that there is a temporary expansion of option premium in the short-term XYZ calls that should be exploited, and he would not really want to be a long-term holder of the stock, then he would choose the short-term covered write. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:434 SCORE: 29.00 ================================================================================ 394 Part Ill: Put Option Strategies Downside Protection. The actual downside break-even point might enter into one's thinking as well. A downside break-even point of 40.3 is available by using the LEAPS write, and that is a known quantity. No matter how far XYZ might fall, as long as it can recover to slightly over 40 by expiration two years from now, the investment will at least break even. A problem arises if XYZ falls to 40 quickly. If that happened, the LEAPS call would still have a significant amount of time value premium remain­ ing on it. Thus, if the investor attempted to sell his stock at that time and buy back his call, he would have a loss, not a break-even situation. The short-term write offers downside protection only to a stock price of 46.2. Of course, repeated writes of 6-month calls over the next 2 years would lower the break-even point below that level. The problem is that if XYZ declines and one is forced to keep selling 6-month calls every 6 months, he may be forced to use a lower striking price, thereby locking in a smaller profit ( or possibly even a loss) if premium levels shrink. The concepts of rolling down are described in detail in Chapter 2. A further word about rolling down may be in order here. Recall that rolling down means buying back the call that is currently written and selling another one with a lower striking price. Such action always reduces the profitability of the over­ all position, although it may be necessary to prevent further downside losses if the common stock keeps declining. Now that LEAPS are available, the short-term writer faced with rolling down may look to the LEAPS as a means of bringing in a healthy premium even though he is rolling down. It is true that a large premium could be brought into the account. But remember that by doing so, one is committing himself to sell the stock at a lower price than he had originally intended. This is why the rolling down reduces the original profit potential. If he rolls down into a LEAPS call, he is reducing his maximum profit potential for a longer period of time. Consequently, one should not always roll dm,vn into an option with a longer maturi­ ty. Instead, he should carefully analyze whether he wants to be committed for an even longer time to a position in which the underlying common stock is declining. To summarize, the large absolute premiums available in LEAPS calls may make a covered write of those calls seem unusually attractive. However, one should calcu­ late the returns available and decide whether a short-term write might not serve his purpose as well. Even though the large LEAPS premium might reduce the initial investment to a mere pittance, be aware that this creates a great amount of leverage, and leverage can be a dangerous thing. The large amount of downside protection offered by the LEAPS call is real, but if the stock falls quickly, there would definitely be a loss at the calculated downside break-even point. Finally, one cannot always roll down into a LEAPS call if trouble develops, because he will be committing himself for an even longer period of time to sell his stock at a lower price than he had originally intended. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:435 SCORE: 47.00 ================================================================================ Chapter 25: LEAPS 39S ✓,,FREE" COVERED CALL WRITES In Chapter 2, a strategy of writing expensive LEAPS options was briefly described. In this section, a more detailed analysis is offered. A certain type of covered call write, one in which the call is quite expensive, sometimes attracts traders looking for a "free ride." To a certain extent, this strategy is something of a free ride. As you might imagine, though, there can be major problems. The investment required for a covered call write on margin is 50% of the stock price, less the proceeds received from selling the call. In theory, it is possible for an option to sell for more than 50% of the stock cost. This is a margin account, a cov­ ered write could be established for "free." Let's discuss this in terms of two types of calls: the in-the-money call write and the out-of-the-money call write. Out-of-the-Money Covered Call Write. This is the simplest way to approach the strategy. One may be able to find LEAPS options that are just slightly out-of-the­ money, which sell for 50% of the stock price. Understandably, such a stock would be quite volatile. Example: GOGO stock is selling for $38 per share. GOGO has listed options, and a 2-year LEAPS call with a striking price of 40 is selling for $19. The requirement for this covered write would be zero, although some commission costs would be involved. The debit balance would be 19 points per share, the amount the broker loans you on margin. Certain brokerage firms might require some sort of minimum margin deposit, but technically there is no further requirement for this position. Of course, the leverage is infinite. Suppose one decided to buy 10,000 shares of GOGO and sell 100 calls, covered. His risk is $190,000 if the stock falls to zero! That also happens to be the debit balance in his account. Thus, for a minimal investment, one could lose a for­ tune. In addition, if the stock begins to fall, one's broker is going to want maintenance margin. He probably wouldn't let the stock slip more than a couple of points before asking for margin. If one owns 10,000 shares and the broker wants two points main­ tenance margin, that means the margin call would be $20,000. The profits wouldn't be as big as they might at first seem. The maximum gross profit potential is $210,000 if the 10,000 shares are called away at 40. The covered write makes 21 points on each share - the $40 sale price less the original cost of $19. However, one will have had to pay interest on the debit balance of $190,000 for two years. At 10%, say, that's a total of $38,000. There would also be commissions on the purchase and the sale. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:436 SCORE: 60.00 ================================================================================ 396 Part Ill: Put Option Strategies In summary, this is a position with tremendous, even dangerous, leverage. In-the-Money Covered Call Write. The situation is slightly different if the option is in-the-money to begin with. The above margin requirements actually don't quite accurately state the case for a margined covered call write. When a covered call is written against the stock, there is a catch: Only 50% of the stock price or the strike price, whichever is less, is available for "release." Thus, one will actually be required to put up more than 50% of the stock price to begin with. Example: XYZ is trading at 50, and there is a 2-year LEAPS call with a strike price of 30, selling for 25 points. One might think that the requirement for a covered call write would be zero, since the call sells for 50% of the stock price. But that's not the case with in-the-money covered calls. Margin requirement: Buy stock: 50 points Less option proceeds -25 Less margin release* -15* Net requirement: 10 points * 50% of the strike price or 50% of stock price, whichever is less. This position still has a lot ofleverage: One invests 10 points in hopes of making 5, if the stock is called away at 30. One also would have to pay interest on the 15-point debit balance, of course, for the two-year duration of the position. Furthermore, should the stock fall below the strike price, the broker would begin to require main­ tenance margin. Note that the above "formula" for the net requirement works equally well for the out-of-the-money covered call write, since 50% of the stock price is always less than 50% of the strike price in that case. To summarize this "free ride" strategy: If one should decide to use this strate­ gy, he must be extremely aware of the dangers of high leverage. One must not risk more money than he can afford to lose, regardless of how small the initial investment might be. Also, he must plan for some method of being able to make the margin pay­ ments along the way. Finally, the in-the-money alternative is probably better, because there is less probability that maintenance margin will be asked for. SELLING UNCOVERED LEAPS Uncovered option selling can be a viable strategy, especially if premiums are over­ priced. LEAPS options may be sold uncovered with the same margin requirements as short-term options. Of course, the particular characteristics of the long-term option may either help or hinder the uncovered writer, depending on his objective. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:437 SCORE: 32.00 ================================================================================ Chapter 25: LEAPS 397 Uncovered Put Selling. Naked put selling is addressed first because, as a strat­ egy, it is equivalent to covered writing, and covered writing was just discussed. Two strategies are equivalent if they have the same profit picture at expiration. Naked put selling and covered call writing are equivalent because they have the profit picture depicted in Graph I, Appendix D. Both have limited upside profit potential and large loss exposure to the downside. In general, when two strategies are equivalent, one of the two has certain advantages over the other. In this case, naked put selling is normally the more advantageous of the two because of the way margin requirements are set. One need not actually invest cash in the sale of a naked put; the margin requirement that is asked for may be satisfied with collateral. This means the naked put writer may use stocks, bonds, T-bills, or money market funds as collateral. Moreover, the actual amount of collateral that is required is less than the cash or margin investment required to buy stock and sell a call. This means that one could operate his portfolio normally - buying stock, then selling it and putting the proceeds in a Treasury bill or perhaps buying another stock - without disturbing his naked put position, as long as he maintained the collateral requirement. Consequently, the strategist who is buying stock and selling calls should probably be selling naked puts instead. This does not apply to covered writers who are writing against existing stock or who are using the incremental return concept of covered writ­ ing, because stock ownership is part of their strategy. However, the strategist who is looking to take in premium to profit if the underlying stock remains relatively unchanged or rises, while having a modicum of downside protection ( which is the definition of both naked put writing and covered writing), should be selling naked puts. As an example of this, consider the LEAPS covered write discussed previously. Example: XYZ is selling at 50. The investor is debating between a 500-share covered write using 2-year LEAPS calls or selling five 2-year LEAPS puts. The January 50 LEAPS call sells for 8½ and has two years of life, while the January 50 LEAPS put sells for 3½. Further assume that XYZ pays a dividend of $0.25 per quarter. The net investment required for the covered write is calculated as it was before. Net Investment Required - Covered Write Stock cost (500 shares @ 50) Plus stock commission Less option premiums received Plus option commissions Net cash investment + $25,000 300 - 4,250 + 100 $21,150 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:438 SCORE: 31.00 ================================================================================ 398 Part Ill: Put Option Strategies The collateral requirement for the naked put write is the same as that for any naked equity option: 20% of the stock price, plus the option price, less any out-of­ the-money amount, with an absolute minimum requirement of 15% of the stock price. Collateral Requirement - Naked Put 20% of stock price (.20 x 500 x $50) Plus option premium Less out-of-the-money amount Total collateral requirement $5,000 1,750 0 $6,750 Note that the actual premium received by the naked put seller is $1,750 less com­ missions of $100, for example, or $1,650. This net premium could be used to reduce the total collateral requirement. Now one can compare the profitability of the two investments: Return If Stock Over 50 at Expiration Stock sale {500 @ 50) Less stock commission Plus dividends earned until expiration Less net investment Net profit if exercised Net put premium received Dividends received Net profit Covered Write $25,000 300 + 1,000 - 21,150 $ 4,55_0 Naked Put Sole $1,650 0 $1,650 Now the returns can be compared, if XYZ is over 50 at expiration of the LEAPS: Return if XYZ over 50 (net profit/net investment) Naked put sale: 24.4% Covered write: 21 .5% The naked put write has a better rate of return, even before the following fact is considered. The strategist who is using the naked put write does not have to spend the $6,750 collateral requirement in the form of cash. That money can be kept in a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:439 SCORE: 56.00 ================================================================================ Chapter 25: LEAPS 399 Treasury bill and earn interest over the two years that the put write is in place. Even if the T-bill were earning only 4% per year, that would increase the overall two-year return for the naked put sale by 8%, to 32.4%. This should make it obvious that naked put selling is rrwre strategically advantageous than covered call writing. Even so, one might rightfully wonder if LEAPS put selling is better than selling shorter-term equity puts. As was the case with covered call writing, the answer depends on what the investor is trying to accomplish. Short-term puts will not bring as much premium into the account, so when they expire, one will be forced to find another suitable put sale to replace it. On the other hand, the LEAPS put sale brings in a larger premium and one does not have to find a replacement until the longer­ term LEAPS put expires. The negative aspect to selling the LEAPS puts is that time decay won't help much right away and, even if the stock moves higher (which is ostensibly good for the position), the put won't decline in price by a large amount, since the delta of the put is relatively small. One other factor might enter in the decision regarding whether to use short­ term puts or LEAPS puts. Some put writers are actually attempting to buy stock below the market price. That is, they would not mind being assigned on the put they sell, meaning that they would buy stock at a net cost of the striking price less the pre­ mium they received from the sale of the put. If they don't get assigned, they get to keep a profit equal to the premium they received when they first sold the put. Generally, a person would only sell puts in this manner on a stock that he had faith in, so that if he was assigned on the put, he would view that as a buying opportunity in the underlying stock. This strategy does not lend itself well to LEAPS. Since the LEAPS puts will carry a significant amount of time premium, there is little (if any) chance that the put writer will actually be assigned until the life of the put shortens substantially. This means that it is unlikely that the put writer will become a stock owner via assignment at any time in the near future. Consequently, if one is attempt­ ing to wTite puts in order to eventually buy the common stock when he is assigned, he would be better served to write shorter-term puts. UNCOVERED CALL SELLING There are very few differences between using LEAPS for naked call selling and using shorter-term calls, except for the ones that have been discussed already with regard to selling uncovered LEAPS: Time value decay occurs more slowly and, if the stock rallies and the naked calls have to be covered, the call writer will normally be paying more time premium than he is used to when he covers the call. Of course, the rea­ son that one is engaged in naked call writing might shed some more light on the use of LEAPS for that purpose. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:440 SCORE: 48.00 ================================================================================ 400 Part Ill: Put Option Strategies The overriding reason that most strategists sell naked calls is to collect the time premium before the stock can rise above the striking price. These strategists gener­ ally have an opinion about the stock's direction, believing that it is perhaps trapped in a trading range or even headed lower over the short term. This strategy does not lend itself well to using LEAPS, since it would be difficult to project that the stock would remain below the strike for so long a period of time. Short LEAPS Instead of Short Stock. Another reason that naked calls are sold is as a strategy akin to shorting the common stock. In this case, in-the-money calls are sold. The advantages are threefold: l. The amount of collateral required to sell the call is less than that required to sell stock short. 2. One does not have to borrow an option in order to sell it short, although one must borrow common stock in order to sell it short. 3. An uptick is not required to sell the option, but one is required in order to sell stock short. For these reasons, one might opt to sell an in-the-money call instead of shorting stock. The profit potentials of the two strategies are different. The short seller of stock has a very large profit potential if the stock declines substantially, while the seller of an in-the-money call can collect only the call premium no matter how far the stock drops. Moreover, the call's price decline will slow as the stock nears the strike. Another way to express this is to say that the delta of the call shrinks from a number close to l (which means the call mirrors stock movements closely) to something more like 0.50 at the strike (which means that the call is only declining half as quickly as the stock). Another problem that may occur for the call seller is early assignment, a topic that is addressed shortly. One should not attempt this strategy if the underlying stock is not borrowable for ordinary short sales. If the underlying stock is not available for borrowing, it generally means that extraneous forces are at work; perhaps there is a tender offer or exchange offer going on, or some form of convertible arbitrage is tak­ ing place. In any case, if the underlying stock is not borrowable, one should not be deluded into thinking that he can sell an in-the-money call instead and have a worry­ free position. In these cases, the call will normally have little or no time premium and may be subject to early assignment. If such assignment does occur, the strategist will become short the stock and, since it is not borrowable, will have to cover the stock. At the least, he will cost himself some commissions by this unprofitable strategy; and at worst, he will have to pay a higher price to buy back the stock as well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:441 SCORE: 119.00 ================================================================================ Chapter 25: LEAPS 401 LEAPS calls may help to alleviate this problem. Since they are such long-term calls, they are likely to have some time value premium in them. In-the-money calls that have time value premium are not normally assigned. As an alternative to shorting a stock that is not borrowable, one might try to sell an in-the-money LEAPS call, but only if it has time value premium remaining. Just because the call has a long time remaining until expiration does not mean that it must have time value premium, as will be seen in the following discussion. Finally, if one does sell the LEAPS call, he must realize that if the stock drops, the LEAPS call will not follow it completely. As the stock nears the strike, the amount of time value premium will build up to an even greater level in the LEAPS. Still, the naked call seller would make some profit in that case, and it presents a better alternative than not being able to sell the stock short at all. Early Assignment. An American-style option is one that can be exercised at any time during its life. All listed equity options, LEAPS included, are of this variety. Thus, any in-the-money option that has been sold may become subject to early assignment. The clue to whether early assignment is imminent is whether there is time value premium in the option. If the option has no time value premium - in other words, it is trading at parity or at a discount then assignment may be close at hand. The option writer who does not want to be assigned would want to cover the option when it no longer carries time premium. LEAPS may be subject to early assignment as well. It is possible, albeit far less likely, that a long-term option would lose all of its time value premium and therefore be subject to early assignment. This would certainly happen if the underlying stock were being taken over and a tender off er were coming to fruition. However, it may also occur because of an impending dividend payment, or more specifically, because the stock is about to go ex-dividend. Recall that the call owner, LEAPS calls includ­ ed, is not entitled to any dividends paid by the underlying stock. So if the call owner wants the dividend, he exercises his call on the day before the stock goes ex-dividend. This makes him an owner of the common stock just in the nick of time to get the div­ idend. What economic factors motivate him to exercise the call? If there is any time value premium at all in the call, the call holder would be better off selling the call in the open market and then purchasing the stock in the open market as well. In this manner, he would still get the dividend, but he would get a better price for his call when he sold it. If, however, there is no time value premium in the call, he does not have to bother with two transactions in the open market; he merely exercises his call in order to buy stock. All well and good, but what makes the call sell at parity before expiration? It has to do with the arbitrage that is available for any call option. In this case, the arbitrage ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:442 SCORE: 53.00 ================================================================================ 402 Part Ill: Put Option Strategies is not the simple discount arbitrage that was discussed in Chapter l when this topic was covered. Rather, it is a more complicated form that is discussed in greater detail in Chapter 28. Suffice it to say that if the dividend is larger than the interest that can be earned from a credit balance equal to the striking price, then the time value pre­ mium will disappear from the call. Example: XYZ is a $30 stock and about to go ex-dividend 50 cents. The prevailing short-term interest rate is 5% and there are LEAPS with a striking price of 20. A 50-cent quarterly dividend on a striking price of 20 is an annual dividend rate (on the strike) of 10%. Since short-term rates are much lower than that, arbitrageurs economically cannot pay out 10% for dividends and earn 5% for their credit balances. In this situation, the LEAPS call would lose its time value premium and would be a candidate for early exercise when the stock goes ex-dividend. In actual practice, the situation is more complicated than this, because the price of the puts comes into play; but this example shows the general reasoning that the arbitrageur must go through. Certain arbitrageurs construct positions that allow them to earn interest on a credit balance equal to the striking price of the call. This position involves being short the underlying stock and being long the call. Thus, when the stock goes ex-dividend, the arbitrageur will owe the dividend. If, however, the amount of the dividend is more than he vvill earn in interest from his credit balance, he will merely exercise his call to cover his short stock. This action will prevent him from having to pay out the dividend. The arbitrageur's exercise of the call means that someone is going to be assigned. If you are a writer of the call, it could be you. It is not important to under­ stand the arbitrage completely; its effect will be reflected in the marketplace in the form of a call trading at parity or a discount. Thus, even a LEAPS call with a sub­ stantial anwunt of time rernaining may be assigned if it is trading at parity. STRADDLE SELLING Straddle selling is equivalent to ratio writing and is a strategy whereby one attempts to sell ( overpriced) options in order to produce a range of stock prices within which the option seller can profit. The strategy often involves follow-up action as the stock moves around, and the strategist feels that he must adjust his position in order to pre­ vent large losses. LEAPS puts and calls might be used for this strategy. However, their long-term nature is often not conducive to the aims of straddle selling. First, consider the effect of time decay. One might normally sell a three-month straddle. If the stock "behaves" and is relatively unchanged after two months have ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:443 SCORE: 60.00 ================================================================================ Chapter 25: LEAPS 403 passed, the straddle seller could reasonably expect to have a profit of about 40% of the original straddle price. However, if one had sold a 2-year LEAPS straddle, and the stock were relatively unchanged after two months, he would only have a profit of about 7% of the original sale price. This should not be surprising in light of what has been demonstrated about the decaying of long-term options. It should make the straddle seller somewhat leery of using LEAPS, however, unless he truly thinks the options are overpriced. Second, consider follow-up action. Recall that in Chapter 20, it was shown that the bane of the straddle seller was the whipsaw. A whipsaw occurs when one makes a follow-up protective action on one side (for instance, he does something bullish because the underlying stock is rising and the short calls are losing money), only to have the stock reverse and come crashing back down. Obviously, the more time left until expiration, the more likely it is that a whipsaw will occur after any follow-up action, and the more expensive it will be, since there will be a lot of time value pre­ mium left in the options that are being repurchased. This makes LEAPS straddle selling less than attractive. LEAPS straddles may look expensive because of their large absolute price, and therefore may appear to be attractive straddle sale candidates. However, the price is often justified, and the seller of LEAPS straddles will be fighting sudden stock move­ ments without getting much benefit from the passage of time. The best time to sell LEAPS straddles is when short-term rates are high and volatilities are high as well (i.e., the options are overpriced). At least, in those cases, the seller will derive some real benefit if rates or volatilities should drop. SPREADS USING LEAPS Any of the spread strategies previously discussed can be implemented with LEAPS as well, if one desires. The margin requirements are the same for LEAPS spreads as they are for ordinary equity option spreads. One general category of spread lends itself well to using LEAPS: that of buying a longer-term option and selling a short­ term one. Calendar spreads, as well as diagonal spreads, fall into that category. The combinations are myriad, but the reasoning is the same. One wants to own the option that is not so subject to time decay, while simultaneously selling the option that is quite subject to time decay. Of course, since LEAPS are long-term and therefore expensive, one is generally taking on a large debit in such a spread and may have substantial risk if the stock performs adversely. Other risks may be pres­ ent as well. As a means of demonstrating these facts, let us consider a simple bull spread using calls. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:444 SCORE: 37.00 ================================================================================ 404 Part Ill: Put Option Strategies Example: The following prices exist in the month of January: XYZ: 105 April 100 call: 10 1/2 April 110 call: 5 1/2 January (2-year) 100 call: 26 January (2-year) 110 call: 21 1/2 An investor is considering a bull spread in XYZ and is unsure about whether to use the short-term calls, the LEAPS calls, or a mixture. These are his choices: Short-term bull spread: Diagonal bull spread: LEAPS bull spread: Buy April 100@ 101/2 Sell April 110@ 51/2 Net Debit: $500 Buy January LEAPS 100 @ 26 Sell April 110@ 51/2 Net Debit: $2,050 Buy January LEAPS 1 00 @ 26 Sell January LEAPS 110@ 21 1/2 Net Debit: $450 Notice that the debit paid for the LEAPS spread is slightly less than that of the short­ term bull spread. This means that they have approximately the same profit potential at their respective expiration dates. However, the strategist is more concerned with how these compare directly with each other. The obvious point in time to make this comparison is when the short-term options expire. Figure 25-7 shows the profitability of these three positions at April expiration. It was assumed that all of the following were the same in April as they had been in January: volatility, short-term rates, and dividend payout. Note that the short-term bull spread has the familiar profit graph from Chapter 7, making its maximum profit over 110 and taking its maximum loss below 100. (See Table 25-4.) The LEAPS spread doesn't generate much of either a profit or a loss in only three months' time. Even if XYZ rises to 120, the LEAPS bull spread will have only a $150 profit. Conversely, if XYZ falls to 80, the spread loses only about $200. This price action is very typical for long-term bull spreads when both options have a sig­ nificant amount of time premium remaining in them. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:445 SCORE: 38.00 ================================================================================ Chapter 25: LEAPS FIGURE 25-7. Bull spread comparison at April expiration. Stock Price 405 The diagonal spread is different, however. Typically, the maximum profit poten­ tial of a bull spread is the difference in the strikes less the initial debit paid. For this diagonal spread, that would be $1,000 minus $2,050, a loss! Obviously, this simple formula is not applicable to diagonal spreads, because the purchased option still has time value premium when the written option expires. The profit graph shows that indeed the diagonal spread is the most bullish of the three. It makes its best profit at the strike of the written option - a standard procedure for any spread - and that prof­ it is greater than either of the other two spreads at April expiration ( under the sig- TABLE 25-4. Bull spread comparison at April expiration. Stock Price Short-Term Diagonal LEAPS 80 -500 -1, 100 -200 90 -500 - 600 -150 100 -500 50 - 25 110 500 750 50 120 500 550 150 140 500 150 250 160 500 50 350 180 500 - 350 450 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:446 SCORE: 112.00 ================================================================================ 406 Part Ill: Put Option Strategies nificant assumption that volatility and interest rates are unchanged). If XYZ trades higher than llO, the diagonal spread will lose some of its profit; in fact, if XYZ were to trade at a very high price, the diagonal spread would actually have a loss (see Table 25-4). Whenever the purchased LEAPS call loses its time value premium, the diag­ onal spread will not perform as well. If the common stock drops in price, the diagonal spread has the greatest risk in dollar terms but not in percentage terms, because it has the largest initial debit. If XYZ falls to 80 in three months, the spread will lose about $1,100, just over half the initial $2,050 debit. Obviously, the short-term spread would have lost 100% of its ini­ tial debit, which is only $500, at that same point in time. The diagonal spread presents an opportunity to earn more money if the under­ lying common is near the strike of the written option when the written option expires. However, if the common moves a great deal in either direction, the diagonal spread is the worst of the three. This means that the diagonal spread strategy is a neutral strategy: One wants the underlying common to remain near the written strike until the near-term option expires. This is a true statement even if the diagonal spread is under the guise of a bullish spread, as in the previous example. Many traders are fond of buying LEAPS and selling an out-of-the-money near­ term call as a hedge. Be careful about doing this. If the underlying common rises too fast and/or interest rates fall and/or volatility decreases, this could be a poor strategy. There is really nothing quite as psychologically damaging as being right about the stock, but being in the wrong option strategy and therefore losing money. Consider the above examples. Ostensibly, the spreader was bullish on XYZ; that's why he chose bull spreads. If XYZ became a wildly bullish stock and rose from 100 to 180 in three months, the diagonal spreader would have lost money. He couldn't have been happy - no one would be. This is something to keep in mind when diagonalizing a LEAPS spread. The deltas of the options involved in the spread will give one a good clue as to how it is going to perform. Recall that a short-term, in-the-money option acquires a rather high delta, especially as expiration draws nigh. However, an in-the-money LEAPS call will not have an extremely high delta, because of the vast amount of time remaining. Thus, one is short an option with a high delta and long an option with a smaller delta. These deltas indicate that one is going to lose money if the underlying stock rises in price. Consider the following situation: XYZ Stock, 120: Call Long 1 January LEAPS 100 call: Short 1 April 110 call: Position Delta 0.70 -0.90 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:447 SCORE: 55.00 ================================================================================ Chapter 25: LEAPS 401 At this point, if XYZ rises in price by 1 point, the spread can be expected to lose 20 cents, since the delta of the short option is 0.20 greater than the delta of the long option. This phenomenon has ramifications for the diagonal spreader of LEAPS. If the two strike prices of the spread are too close together, it may actually be possible to construct a bull spread that loses money on the upside. That would be very difficult for most traders to accept. In the above example, as depicted in Table 25-4, that's what happens. One way around this is to widen the strike prices out so that there is at least some profit potential, even if the stock rises dramatically. That may be diffi­ cult to do and still be able to sell the short-term option for any meaningful amount of premium. Note that a diagonal spread could even be considered as a substitute for a cov­ ered write in some special cases. It was shown that a LEAPS call can sometimes be used as a substitute for the common stock, with the investor placing the difference between the cost of the LEAPS call and the cost of the stock in the bank (or in T­ bills). Suppose that an investor is a covered writer, buying stock and selling relative­ ly short-term calls against it. If that investor were to make a LEAPS call substitution for his stock, he would then have a diagonal bull spread. Such a diagonal spread would probably have less risk than the one described above, since the investor pre­ sumably chose the LEAPS substitution because it was "cheap." Still, the potential pitfalls of the diagonal bull spread would apply to this situation as well. Thus, if one is a covered writer, this does not necessarily mean that he can substitute LEAPS calls for the long stock without taking care. The resulting position may not resemble a cov­ ered write as much as he thought it would. The "bottom line" is that if one pays a debit greater than the difference in the strike prices, he may eventually lose money if the stock rises far enough to virtually eliminate the time value premium of both options. This comes into play also if one rolls his options down if the underlying stock declines. Eventually, by doing so, he may invert the strikes - i.e., the striking price of the written option is lower than the striking price of the option that is owned. In that case, he will have locked in a loss if the overall credit he has received is less than the difference in the strikes - a quite likely event. So, for those who think this strategy is akin to a guaranteed profit, think again. It most certainly is not. Backspreads. LEAPS may be applied to other popular forms of diagonal spreads, such as the one in which in-the-money, near-term options are sold, and a greater quan­ tity of longer-term (LEAPS) at- or out-of-the money calls are bought. (This was referred to as a diagonal backspread in Chapter 14.) This is an excellent strategy, and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:448 SCORE: 51.00 ================================================================================ 408 Part Ill: Put Option Strategies a LEAPS may be used as the long option in the spread. Recall that the object of the spread is for the stock to be volatile, particularly to the upside if calls are used. If that doesn't happen, and the stock declines instead, at least the premium captured from the in-the-money sale will be a gain to offset against the loss suffered on the longer­ term calls that were purchased. The strategy can be established with puts as well, in which case the spreader would want the underlying stock to fall dramatically while the spread was in place. Without going into as much detail as in the examples above, the diagonal back­ spreader should realize that he is going to have a significant debit in the spread and could lose a significant portion of it should the underlying stock fall a great deal in price. To the upside, his LEAPS calls will retain some time value premium and will move quite closely with the underlying common stock. Thus, he does not have to buy as many LEAPS as he might think in order to have a neutral spread. Example: XYZ is at 105 and a spreader wants to establish a backspread. Recall that the quantity of options to use in a neutral strategy is determined by dividing the deltas of the two options. Assume the following prices and deltas exist: Option April 100 call July 110 call January (2-year) LEAPS 100 call XYZ: 105 in January Price 8 5 15 Delta 0.75 0.50 0.60 Two backspreads are available with these options. In the first, one would sell the April 100 calls and buy the July llO calls. He would be selling 3-month calls and buy­ ing 6-month calls. The neutral ratio is 0.75/0.50 or 3 to 2; that is, 3 calls are to be bought for every 2 sold. Thus, a neutral spread would be: Buy 6 July 110 calls Sell 4 April l 00 calls As a second alternative, he might use the LEAPS as the long side of the spread; he would still sell the April 100 calls as the short side of the spread. In this case, his neu­ tral ratio would be 0.75/0.60, or 5 to 4. The resulting neutral spread would be: Buy 5 January LEAPS 110 calls Sell 4 April 100 calls ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:449 SCORE: 53.00 ================================================================================ Chapter 25: LEAPS 409 Thus, a neutral backspread involving LEAPS requires buyingfewer calls than a neu­ tral backspread involving a 6-rnonth option on the long side. This is because the delta of the LEAPS call is larger. The significant point here is that, because of the time value retention of the LEAPS call, even when the stock moves higher, it is not nec­ essary to buy as many. If one does not use the deltas, but merely figures that 3 to 2 is a good ratio for any diagonal backspread, then he will be overly bullish if he uses LEAPS. That could cost him if the underlying stock declines. Calendar Spreads. LEAPS may also be used in calendar spreads - spreads in which the striking price of the longer-term option purchased and the shorter-term option sold are the same. The calendar spread is a neutral strategy, wherein the spreader wants the underlying stock to be as close as possible to the striking price when the near-term option expires. A calendar spread has risk if the stock moves too far away from the striking price (see Chapters 9 and 22). Purchasing a LEAPS call increases that risk in terms of dollars, not percentage, because of the larger debit that one must spend for the spread. Simplistically, calendar spreads are established with equal quantities of options bought and sold. This is often not a neutral strategy in the true sense. As was shown in Chapter 9 on call calendar spreads, one may want to use the deltas of the two options to establish a truly neutral calendar spread, particularly if the stock is not ini­ tially right at the striking price. Out-of-the-money, one would sell more calls than he is buying. Conversely, in-the-money, one would buy more calls than he is selling. Both strategies statistically have merit and are attractive. When using LEAPS deltas to construct the neutral spread, one need generally buy fewer calls than he might think, because of the higher delta of a LEAPS call. This is the same phenomenon described in the previous example of a diagonal backspread. SUMMARY LEAPS are nothing more than long-term options. They are usable in a wide variety of strategies in the same way that any option would be. Their margin and investment requirements are similar to those of the more familiar equity options. Both LEAPS puts and calls are traded, and there is a secondary market for them as well. There are certain differences between the prices of LEAPS and those of short­ er-term options, but the greatest is the relatively large effect that interest rates and dividends have on the price of LEAPS, because LEAPS are long-term options. Increases in interest rates will cause LEAPS to increase in price, while increases in dividend payout will cause LEAPS calls to decrease in price and LEAPS puts to ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:450 SCORE: 27.00 ================================================================================ 410 Part Ill: Put Option Strategies increase in price. As usual, volatility has a major effect on the price of an option, and LEAPS are no exception. Even small changes in the volatility of the underlying com­ mon stock can cause large price differences in a two-year option. The rate of decay due to time is much smaller for LEAPS, since they are long-term options. Finally, the deltas of LEAPS calls are larger than those of short-term calls; conversely, the deltas of LEAPS puts are smaller. Several common strategies lend themselves well to the usage of LEAPS. A LEAPS may be used as a stock substitute if the cash not invested in the stock is instead deposited in a CD or T-bill. LEAPS puts can be bought as protection for common stock. Speculative option buyers will appreciate the low rate of time decay of LEAPS. LEAPS calls can be written against common stock, thereby creating a covered write, although the sale of naked LEAPS puts is probably a better strategy in most cases. Spread strategies with LEAPS may be viable as well, but the spreader should carefully consider the ramifications of buying a long-term option and selling a shorter-term one against it. If the underlying stock moves a great distance quickly, the spread strategy may not perform as expected. Overall, LEAPS are not very different from the shorter-term options to which traders and investors have become accustomed. Once these investors become famil­ iar with the way these long-term options are affected by the various factors that determine the price of an option, they will consider the use of LEAPS as an integral part of a strategic arsenal. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:453 SCORE: 10.00 ================================================================================ Buying Options and Treasury Bills Numerous strategies have been described, ranging from the simple to the complex. Each one has advantages, but there are disadvantages as well. In fact, some of them may be too complex for the average investor to seriously consider implementing. The reader may feel that there should be an easier answer. Isn't there a strategy that might not require such a large investment or so much time spent in monitoring the position, but would still have a chance of returning a reasonable profit? In fact, there is a strategy that has not yet been described, a strategy considered by some experts in the field of mathematical analysis to be the best of them all. Simply stated, the strategy consists of putting 90% of one's money in risk-free investments (such as short-term Treasury bills) and buying options with the remaining 10% of one's funds. It has previously been pointed out that some of the more attractive strategies are those that involve small levels of risk with the potential for large profits. Usually, these types of strategies inherently have a rather large frequency of small losses, and a small probability of realizing large gains. Their advantage lies in the fact that one or two large profits can conceivably more than make up for numerous small losses. This Treasury bill/option strategy is another strategy of this type. HOW THE TREASURY BILL/OPTION STRATEGY OPERATES Although there are certain details involved in operating this strategy, it is basically a simple one to approach. First, the most that one can lose is 10%, less the interest earned on the fixed-income portion of his portfolio (the remaining 90% of his assets), during the life of the purchased options. It is a simple matter to space out one's com- 413 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:454 SCORE: 32.50 ================================================================================ 414 Part IV: Additional Considerations mitments to option purchases so that his overall risk in a one-year period can be kept down to nearly 10%. Example: An investor might decide to put 2½% of his money into three-month option purchases. Thus, in any one year, he would be 1isking 10%. At the same time he would be earning perhaps 6% from the overall interest generated on the fixed­ income securities that make up the remaining 90% of his assets. This would keep his overall risk down to approximately 4.6% per year. There are better ways to monitor this risk, and they are described shortly. The potential profits from this strategy are limited only by time. Since one is owning options - say call options - he could profit handsomely from a large upward move in the stock market. As with any strategy in which one has limited risk and the poten­ tial of large profits, a small number of large profits could offset a large number of small losses. In actual practice, of course, his profits will never be overwhelming, since only approximately 10% of the money is committed to option purchases. In total, this strategy has greatly reduced 1isk with the potential of making above-average profits. Since the 10% of the money that is invested in options gives great leverage, it might be possible for that portion to double or triple in a short time under favorable market conditions. This strategy is something like owning a convert­ ible bond. A convertible bond, since it is convertible into the common stock, moves up and down in price with the price of the underlying stock. However, if the stock should fall a great deal, the bond will not follow it all the way down, because eventu­ ally its yield will provide a "floor" for the price. A strategy that is not used very often is called the "synthetic convertible bond." One buys a debenture and a call option on the same stock. If the stock rises in price, the call does too, and so the combination of the debenture and the call acts much like a convertible bond would to the upside. If, on the other hand, the stock falls, the call will expire worthless; but the investor will retain most of his investment, because he will still have the debenture plus any interest that the bond has paid. The strategy of placing 90% of one's money into risk-free, interest-bearing cer­ tificates and buying options with the remainder is superior to the convertible bond or the "synthetic convertible bond," since there is no risk of price fluctuation in the largest portion of the investment. The Treasury bill/option strategy is fairly easy to operate, although one does have to do some work every time new options are purchased. Also, periodic adjust­ ments need to be made to keep the level of risk approximately the same at all times. As for which options to buy, the reader may recall that specifications were outlined in Chapters 3 and 16 on how to select the best option purchases. These criteria can be summarized briefly as follows: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:455 SCORE: 50.00 ================================================================================ Chapter 26: Buying Options and Treasury Bills 415 1. Assume that each underlying stock can advance or decline in accordance with its volatility over a fixed time period (30, 60, or 90 days). 2. Estimate the call prices after the advance, or put prices after the decline. 3. Rank all potential purchases by the highest reward opportunity. The user of this strategy need only be interested in those option purchases that provide the highest reward opportunity under this ranking method. In the previous chapters on option buying, it was mentioned that one might want to look at the risk/reward ratios of his potential option purchases in order to have a more conser­ vative list. However, that is not necessary in the Treasury bill/option strategy, since the overall risk has already been limited. A ranking of option purchases via the fore­ going criteria will generally give a list of at- or slightly out-of-the-money options. These are not necessarily "underpriced" options; although if an option is truly under­ priced, it will have a better chance of ranking higher on the selection list than one that is "overpriced." A list of potential option purchases that is constructed with criteria similar to those outlined above is available from many data services and brokerage firms. The strategist who is willing to select his option purchases in this manner will find that he does not have to spend a great deal of time on the selection process. The reader should note that this type of option purchase ranking completely ignores the outlook for the underlying stock. If one would rather make his purchases based on an outlook for the underlying stock - preferably a technical outlook - he will be forced to spend more time on his selection process. Although this may be appealing to some investors, it will probably yield worse results in the long run than the previously described unbiased approach to option purchases, unless the strategist is extremely adept at stock selection. KEEPING THE RISK LEVEL EQUAL The second function that the strategist has to perform in this Treasury bill/option strategy is to keep his risk level approximately equal at all times. Example: An investor starts the strategy with $90,000 in Treasury bills (T-bills) and $10,000 in option purchases. After some time has passed, the option purchases may have worked out well and perhaps he now has $90,000 in T-bills plus $30,000 worth of options, plus interest from the T-bills. Obviously, he no longer has 90% of his money in fixed-income securities and 10% in option purchases. The ratio is now 75% in T-bills and 25% in option purchases. This is too risky a ratio, and the strategist must consequently sell some of his options and buy T-bills with the proceeds. Since his total assets are $120,000 currently, he must sell out $18,000 of options to bring his ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:456 SCORE: 36.50 ================================================================================ 416 Part IV: Additional Considerations option investment down from the current $30,000 figure to $12,000, or 10% of his total assets. If one fails to adhere to this readjustment of his funds after profits are made, he may eventually lose those profits. Since options can lose a great percentage of their worth in a short time pe1iod, the investor is always running the risk that the option portion of his investment may be nearly wiped out. If he has kept all his prof­ its in the option portion of his strategy, he is constantly risking nearly all of his accu­ mulated profits, and that is not wise. One must also adjust his ratio of T-bills to options after losses occur. Example: In the first year, the strategist loses all of the $10,000 he originally placed in options. This would leave him with total assets of $90,000 plus interest (possibly $6,000 of interest might be earned). He could readjust to a 90:10 ratio by selling out some of the T-bills and using the proceeds to buy options. If one follows this strate­ gy, he will be risking 10% of his funds each year. Thus, a series of loss years could depreciate the initial assets, although the net losses in one year would be smaller than 10% because of the interest earned on the T-bills. It is recommended that the strate­ gist pursue this method of readjusting his ratios in both up and down markets in order to constantly provide himself with essentially similar risk/reward opportunities at all times. The individual can blend the option selection process and the adjustment of the T-bill/option ratio to fit his individual portfolio. The larger portfolio can be diversi­ fied into options \vith differing holding periods, and the ratio adjustments can be made quite frequently, perhaps once a month. The smaller investor should concen­ trate on somewhat longer holding periods for his options, and would adjust the ratio less often. Some examples might help to illustrate the way in which both the large and small strategist might operate. It should be noted that this T-bill/option strategy is quite adaptable to fairly small sums of money, as long as the 10% that is going to be put into option purchases allows one to be able to participate in a reasonable man­ ner. A tactic for the extremely small investor is also described below. ANNUALIZED RISK Before getting into portfolio size, let us describe the concept of annualized risk. One might want to purchase options with the intent of holding some of them for 30 days, some for 90 days, and some for 180 days. Recall that he does not want his option purchases to represent more than 10% annual risk at any time. In actual practice, if one purchases an option that has 90 days of life, but he is planning to hold the option only 30 days, he will most likely not lose 100% of his investment in ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:457 SCORE: 13.00 ================================================================================ Chapter 26: Buying Options and Treasury Bills 417 the 30-day period. However, for purposes of computing annualized risk easily, the assumption that will be made is that the risk during any holding period is 100%, regardless of the length of time remaining in the life of the option. Thus, a 30-day option purchase represents an annualized risk of 1,200% (100% risk every 30 days times twelve 30-day periods in one year). Ninety-day purchases have 400% annual­ ized risk, and 180-day purchases have 200% annualized risk. There is a multitude of ways to combine purchases in these three holding periods so that the overall risk is 10% annualized. Example: An investor could put 2½% of his total money into 90-day purchases four times a year. That is, 2½% of his total assets are being subjected to a 400% annual­ ized risk; 400% times 2½% equals 10% annualized risk on the total assets. Of course, the remainder of the assets would be placed in risk-free, income-bearing securities. Another of the many combinations might be to place 1 % of the total assets in 90-day purchases and also place 3% of the total assets in 180-day purchases. Thus, 1 % of one's total money would be subjected to a 400% annual risk and 3% would be sub­ jected to a 200% annual risk (.01 times 400 plus .03 times 200 equals 10% annualized risk on the entire assets). If one prefers a formula, annualized risk can be computed as: A al. d • k • r 1. Percent of total 360 nnu 1ze ns on entire portro 10 = d x assets investe Holding period If one is able to diversify into several holding periods, the annualized risk is merely the sum of the risks for each holding period. With this information in mind, the strategist can utilize option purchases of 1 month, 3 months, and 6 months, preferably each generated by a separate computer analysis similar to the one described earlier. He will know how much of his total assets he can place into purchases of each holding period, because he will know his annualized risk. Example: Suppose that a very large investor, or pool of investors, has $1 million com­ mitted to this T-bill/option strategy. Further, suppose ½ of 1 % of the money is to be committed to 30-day option purchases with the idea of reinvesting every 30 days. Similarly, ½ of 1 % is to be placed in 90-day purchases and 1 % in 180-day purchases. The annualized risk is 10%: Total annualized risk = ½% x 360 + ½% x 360 + 1 % x 360 30 90 180 = .06 + .02 + .02 = 10% ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:458 SCORE: 11.50 ================================================================================ 418 Part IV: Additional Considerations With asset.s of $1 million, this means that $.5,000 would be committed to 30-day pur­ chases; $.5,000 to 90-day purchases; and $10,000 to 180-day purchases. This money would be reinvested in similar quantities at the end of each holding period. RISK ADJUSTMENT The subject of adjusting the ratio to constantly reflect 10% risk must be addressed at the end of each holding period. Although it is correct for the investor to keep his per­ centage commitments constant, he must not be deluded into automatically reinvest­ ing the same amount of dollars each time. Example: At the end of 30 days, the value of the entire portfolio, including potential option profits and losses, and interest earned, was down to $990,000. Then only ½ of 1 % of that amount should be invested in the next 30-day purchase ($4,9.50). By operating in this manner - first computing the annualized risk and balanc­ ing it through predetermined percentage commitments to holding periods of various lengths; and second, readjusting the actual dollar commitment at the end of each holding period - the overall risk/reward ratios v,ill be kept close to the levels described in the earlier, simple desciiption of this strategy. This may require a rela­ tively large amount of work on the part of the strategist, but large portfolios usually do require work. The smaller investor does not have the luxury of such complete diversification, but he also does not have to adjust his total position as often. Example: An investor decided to commit $.50,000 to this strategy. Since there is a 1,200% annualized risk in 30-day purchases, it does not make much sense to even consider purchases that are so short-term for assets of this size. Rather, he might decide to commit 1 % of his assets to a 90-day purchase and 3% to a 180-day pur­ chase. In dollar amounts, this would be $.500 in a 90-day option and $1,.500 in 180- day options. Admittedly, this does not leave much room for diversification, but to risk more in the short-term purchases would expose the investor to too much risk. In actual practice, this investor would probably just invest .5% of his assets in 180-day purchases, also a 10% annualized risk. This would mean that he could operate with only one option buyer's analysis (the 180-day one) and could place $2,.500 into selec­ tions from that list. His adjustments of the assets committed to option purchases could not be done as frequently as the large investor, because of the commissions involved. He certain­ ly would have to adjust every 180 days, but might prefer to do so more frequently - perhaps every 90 days - to be able to space his 180-day commitments over different ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:459 SCORE: 18.00 ================================================================================ Chapter 26: Buying Options and Treasury Bills 419 option expiration cycles. It should also be pointed out that T-bills can be bought and sold only in amounts of at least $10,000 and in increments of $5,000 thereafter. That is, one could buy or sell $10,000 or $15,000 or $20,000 or $25,000, and so on, but could not buy or sell $5,000 or $8,000 or $23,000 in T-bills. This is of little concern to the investor with $1 million, since it takes only a fraction of a percentage of his assets to be able to round up to the next $5,000 increment for a T-bill sale or pur­ chase. However, the medium-sized investor with a $50,000 portfolio might run into problems. While short-term T-bills do represent the best risk-free investment, the medium-sized investor might want to utilize one of the no-load, money market funds for at least part of his income-bearing assets. Such funds have only slightly more risk than T-bills and offer the ability to deposit and withdraw in any amount. The truly small investor might be feeling somewhat left out. Could it be possi­ ble to operate this strategy with a very small amount of money, such as $5,000? Yes it could, but there are several disadvantages. Example: It would be extremely difficult to keep the risk level down to 10% annual­ ly with only $5,000. For example, 5% of the money invested every 180 days is only $250 in each investment period. Since the option selection process that is described will tend to select at- or slightly out-of-the-money calls, many of these will cost more than 2½ points for one option. The small investor might decide to raise his risk level slightly, although the risk level should never exceed 20% annually, no matter how small the actual dollar investment. To exceed this risk level would be to completely defeat the purpose of the fixed-income/option purchase strategy. Obviously, this small investor cannot buy T-bills, for his total investable assets are below the mini­ mum $10,000 purchase level. He might consider utilizing one of the money market funds. Clearly, an investor of this small magnitude is operating at a double disadvan­ tage: His small dollar commitment to option purchases may preclude him from buy­ ing some of the more attractive items; and his fixed-income portion will be earning a smaller percentage interest rate than that of the larger investor who is in T-bills or some other form of relatively risk-free, income-bearing security. Consequently, the small investor should carefully consider his financial capability and willingness to adhere strictly to the criteria of this strategy before actually committing his dollars. It may appear to the reader that the actual dollars being placed at risk in each option purchase are quite small in these examples. In fact, they are rather small, but they have been shown to represent 10% annualized risk. An assumption was made in these examples that the risk in each option purchase was 100% for the holding peri­ od. This is a fairly restrictive assumption and, if it were lessened, would allow for a larger dollar commitment in each holding period. It is difficult and dangerous, how- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:460 SCORE: 33.50 ================================================================================ 420 Part IV: Additional Considerations ever, to assume that the risk in holding a call option is less than 100% in a holding period as short as 30 days. The strategist may feel that he is disciplined enough to sell out when losses occur and thereby hold the risk to less than 100%. Alternatively, mathematical analysis will generally show that the expected loss in a fixed time peri­ od is less than 100%. One can also mitigate the probability oflosing all of his money in an option purchase by buying in-the-money options. While they are more expen­ sive, of course, they do have a larger probability of having some residual worth even if the underlying stock doesn't rise to the trader's expectations. Adhering to any of these criteria can lead one to become too aggressive and therefore be too heavily committed to option purchases. It is far safer to stick to the simpler, more restrictive assumption that one is risking all his money, even over a fairly short holding period, when he buys an option. AVOIDING EXCESSIVE RISK One final word of caution must be inserted. The investor should not attempt to become 'Janey" with the income-bearing portion of his assets. T-bills may appear to be too "tame" to some investors, and they consider using GNMA's (Government National Mortgage Association certificates), corporate bonds, convertible bonds, or municipal bonds for the fixed-income portion. Although the latter securities may yield a slightly higher return than do T-bills, they may also prove to be less liquid and they quite clearly involve more risk than a short-term T-bill does. Moreover, some investors might even consider placing the balance of their funds in other places, such as high-yield stock or covered call writing. While high-yield stock purchases and cov­ ered call writing are conservative investments, as most investments go, they would have to be considered very speculative in comparison to the purchase of a 90-day T­ hill. In this strategy, the profit potential is represented by the option purchases. The yield on short-term T-bills will quite adequately offset the risks. One should take great care not to attempt to generate much higher yields on the fixed-income portion of his investment, for he may find that he has assumed risk with the portion of his money that was not intended to have any risk at all. A fair amount of rigorous mathematical work has been done on the evaluation of this strategy. The theoretical papers are quite favorable. Scholars have generally considered only the purchase of call options as the risk portion of the strategy. Obviously, the strategist is quite free to purchase put options without harming the overall intent of the strategy. When only call options are purchased, both static and down markets harm the performance. If some puts are included in the option pur­ chases, only static markets could produce the worst results. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:461 SCORE: 27.00 ================================================================================ Chapter 26: Buying Options and Treasury Bills 421 There are trade-offs involved as well. If, after purchasing the options, the mar­ ket experiences a substantial rally, that portion of the option purchase money that is devoted to put option purchases will be lost. Thus, the combination of both put and call purchases would do better in a down market than a strategy of buying only calls, but would do worse in an up market. In a broad sense, it makes sense to include some put purchases if one has the funds to diversify, since the frequency of market rallies is smaller than the combined frequency of market rallies and declines. The investor who owns both puts and calls will be able to profit from substantial moves in either direction, because the profitable options will be able to overcome the limited losses on the unprofitable ones. SUMMARY In summary, the T-bill/option strategy is attractive from several viewpoints. Its true advantage lies in the fact that it has predefined risk and does not have a limit on potential profits. Some theorists claim it is the best strategy available, if the options are "underpriced" when they are purchased. The strategy is also relatively simple to operate. It is not necessary to have a margin account or to compute collateral require­ ments for uncovered options; the strategy can be operated completely from a cash account. There are no spreads involved, nor is it necessary to worry about details such as early assignment (because there are no short options in this strategy). The investor who is going to employ this strategy, however, must not be delud­ ed into thinking that it is so simple that it does not take any work at all. The concepts and application of annualized risk management are very important to the strategy. So are the mechanics of option buying - particularly a disciplined, rational approach to the selection of which calls and/or puts to buy. Consequently, this strategy is suitable only for the investor who has both the time and the discipline to operate it correctly. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:462 SCORE: 16.00 ================================================================================ Arbitrage Arbitrage in the securities market often connotes that one is buying something in one marketplace and selling it in another marketplace, for a small profit with little or no risk. For example, one might buy XYZ at 55 in New York and sell it at 55¼ in Chicago. Arbitrage, especially option arbitrage, involves a far wider range of tactics than this simple example. Many of the option arbitrage tactics involve buying one side of an equivalent position and simultaneously selling the other side. Since there is a large number of equivalent strategies, many of which have been pointed out in earlier chapters, a full-time option arbitrageur is able to construct a rather large number of positions, most of which have little or no risk. The public customer can­ not generally operate arbitrage-like strategies because of the commission costs involved. Arbitrageurs are firm traders or floor traders who are trading through a seat on the appropriate securities exchange, and therefore have only minimal trans­ action costs. The public customer can benefit from understanding arbitrage techniques, even ifhe does not personally employ them. The arbitrageurs perform a useful function in the option marketplace, often making markets where a market might not otherwise exist (deeply in-the-money options, for example). This chapter is directed at the strategist who is actually going to be participating in arbitrage. This should not be confusing to the public customer, for he will better understand the arbitrage strate­ gies if he temporarily places himself in the arbitrageur's shoes. It is virtually impossible to perform pure arbitrage on dually listed options; that is, to buy an option on the CBOE and sell it on the American exchange in New York for a profit. Such discrepancies occur so infrequently and in such small size that an option arbitrageur could never hope to be fully employed in this type of simple arbi­ trage. Rather, the more complex forms of arbitrage described here are the ones on which he would normally concentrate. 422 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:463 SCORE: 56.00 ================================================================================ Chapter 27: Arbitrage 423 BASIC PUT AND CALL ARBITRAGE ("DISCOUNTING") The basic call and the basic put arbitrages are two of the simpler forms of option arbi­ trage. In these situations, the arbitrageur attempts to buy the option at a discount while simultaneously taking an opposite position in the underlying stock. He can then exercise his option immediately and make a profit equal to the amount of the discount. The basic call arbitrage is described first. This was also outlined in Chapter 1, under the section on anticipating exercise. Example: XYZ is trading at 58 and the XYZ July 50 call is trading at 7¾. The call is actually at a discount from parity of ¼ point. Discount options generally either are quite deeply in-the-money or have only a short time remaining until expiration, or both. The call arbitrage would be constructed by: 1. buying the call at 7¾; 2. selling the stock at 58; 3. exercising the call to buy the stock at 50. The arbitrageur would make 8 points of profit from the stock, having sold it at 58 and bought it back at 50 via the option exercise. He loses the 7¾ points that he paid for the call option, but this still leaves him with an overall profit of¼ point. Since he is a member of the exchange, or is trading the seat of an exchange member, the arbi­ trageur pays only a small charge to transact the trades. In reality, the stock is not sold short per se, even though it is sold before it is bought. Rather, the position is designated, at the time of its inception, as an "irrevo­ cable exercise." The arbitrageur is promising to exercise the call. As a result, no uptick is required to sell the stock. The main goal in the call arbitrage is to be able to buy the call at a discount from the price at which the stock is sold. The differential is the profit potential of the arbi­ trage. The basic put arbitrage is quite similar to the call arbitrage. Again, the arbi­ trageur is looking to buy the put option at a discount from parity. The put arbitrage is completed with a stock purchase and option exercise. Example: XYZ is at 58 and the XYZ July 70 put is at 11 ¾. With the put at ¼ discount from parity, the arbitrageur might take the following action: 1. Buy put at 11 ¾. 2. Buy stock at 58. 3. Exercise put to sell stock at 70. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:464 SCORE: 44.50 ================================================================================ 424 Part IV: Additional Considerations The stock transaction is a 12-point profit, since the stock was bought at 58 and is sold at 70 via the put exercise. The cost of the put - 11 ¾ points - is lost, but the arbi­ trageur still makes ¼-point profit. Again, this profit is equal to the arrwunt of the dis­ count in the option when the position was established. Generally, the arbitrageur would exercise his put option immediately, because he would not want to tie up his capital to carry the long stock. An exception to this would be if the stock were about to go ex-dividend. Dividend arbitrage is discussed in the next section. The basic call and put arbitrages may exist at any time, although they will be more frequent when there is an abundance of deeply in-the-money options or when there is a very short time remaining until expiration. After market rallies, the call arbitrage may be easier to establish; after market declines, the put arbitrage will be easier to find. As an expiration date draws near, an option that is even slightly in-the­ money on the last day or two of trading could be a candidate for discount arbitrage. The reason that this is true is that public buying interest in the option will normally wane. The only public buyers would be those who are short and want to cover. Many covered writers will elect to let the stock be called away, so that will reduce even fur­ ther the buying potential of the public. This leaves it to the arbitrageurs to supply the buying interest. The arbitrageur obviously wants to establish these positions in as large a size as possible, since there is no risk in the position if it is established at a discount. Usually, there will be a larger market for the stock than there will be for the options, so the arbitrageur spends more of his time on the option position. However, there may be occasions when the option markets are larger than the corresponding stock quotes. When this happens, the arbitrageur has an alternative available to him: He might sell an in-the-money option at parity rather than take a stock position. Example: XYZ is at 58 and the XYZ July 50 call is at 7¾. These are the same figures as in the previous example. Furthermore, suppose that the trader is able to buy more options at 7¾ than he is able to sell stock at 58. If there were another in-the-money call that could be sold at parity, it could be used in place of the stock sale. For exam­ ple, if the XYZ July 40 call could be sold at 18 (parity), the arbitrage could still be established. Ifhe is assigned on the July 40 that he is short, he will then be short stock at a net price of 58 - the striking price of 40, plus the 18 points that were brought in from the sale of the July 40 call. Thus, the sale of the in-the-money call at parity is equivalent to shorting the stock for the arbitrage purpose. In a similar manner, an in-the-money put can be used in the basic put arbitrage. Example: With XYZ at 58 and the July 70 put at 11¾, the arbitrage could be estab­ lished. However, if the trader is having trouble buying enough stock at 58, he might ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:465 SCORE: 32.00 ================================================================================ Chapter 27: Arbitrage 425 be able to use another in-the-money put. Suppose the XYZ July 80 put could be sold at 22. This would be the same as buying the stock at 58, because if the put were assigned, the arbitrageur would be forced to buy stock at 80 - the striking price - but his net cost would be 80 minus the 22 points he received from the sale of the put, for a net cost of 58. Again, the arbitrageur is able to use the sale of a deeply in-the-money option as a substitute for the stock trade. The examples above assumed that the arbitrageur sold a deeper in-the-money option at parity. In actual practice, if an in-the-money option is at a discount, an even deeper in-the-money option will generally be at a discount as well. The arbitrageur would normally try to sell, at parity, an option that was less deeply in-the-money than the one he is discounting. In a broader sense, this technique is applicable to any arbitrage that involves a stock trade as part of the arbitrage, except when the dividend in the stock itself is important. Thus, if the arbitrageur is having trouble buying or selling stock as part of his arbitrage, he can always check whether there is an in-the-money option that could be sold to produce a position equivalent to the stock position. DIVIDEND ARBITRAGE Dividend arbitrage is actually quite similar to the basic put arbitrage. The trader can lock in profits by buying both the stock and the put, then waiting to collect the divi­ dend on the underlying stock before exercising his put. In theory, on the day before a stock goes ex-dividend, all puts should have a time value premium at least as large as the dividend amount. This is true even for deeply in-the-money puts. Example: XYZ closes at 45 and is going to go ex-dividend by $1 tomorrow. Then a put with striking price of 50 should sell for at least 6 points ( the in-the-money amount plus the amount of the dividend), because the stock will go ex-dividend and is expect­ ed to open at 44, six points in-the-money. If, however, the put' s time value premium should be less than the amount of the dividend, the arbitrageur can take a riskless position. Suppose the XYZ July 50 put is selling for 5¾, with the stock at 45 and about to go ex-dividend by $1. The arbi­ trageur can take the following steps: 1. Buy the put at 5¼. 2. Buy the stock at 45. 3. Hold the put and stock until the stock goes ex-dividend (1 point in this case). 4. Exercise the put to sell the stock at 50. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:466 SCORE: 28.50 ================================================================================ 426 Part IV: Additional Considerations The trader makes 5 points from the stock trade, buying it at 45 and selling it at 50 via the put exercise, and also collects the I-point dividend, for a total inflow of 6 points. Since he loses the 5¾ points he paid for the put, his net profit is ¼ point. Far in advance of the ex-dividend date, a deeply in-the-money put may trade very close to parity. Thus, it would seem that the arbitrageur could "load up" on these types of positions and merely sit back and wait for the stock to go ex-dividend. There is a flaw in this line of thinking, however, because the arbitrageur has a carrying cost for the rrwney that he must tie up in the long stock. This carrying cost fluctuates with short-term interest rates. Example: If the current rate of carrying charges were 6% annually, this would be equivalent to 1 % every 2 months. If the arbitrageur were to establish this example position 2 months prior to expiration, he would have a carrying cost of .5075 point. (His total outlay is 50¾ points, 45 for the stock and 5¾ for the options, and he would pay 1 % to carry that stock and option for the two months until the ex-dividend date.) This is more than ½ point in costs - clearly more than the ¼-point potential profit. Consequently, the arbitrageur must be aware of his carrying costs if he attempts to establish a dividend arbitrage well in advance of the ex-dividend date. Of course, if the ex-dividend date is only a short time away, the carrying cost has little effect, and the arbitrageur can gauge the profitability of his position mostly by the amount of the dividend and the time value premium in the put option. The arbitrageur should note that this strategy of buying the put and buying the stock to pick up the dividend might have a residual, rather profitable side effect. If the underlying stock should rally up to or above the striking price of the put, there could be rather large profits in this position. Although it is not likely that such a rally could occur, it would be an added benefit if it did. Even a rather small rally might cause the put to pick up some time premium, allowing the arbitrageur to trade out his position for a profit larger than he could have made by the arbitrage discount. This form of arbitrage occasionally lends itself to a limited form of risk arbi­ trage. Risk arbitrage is a strategy that is designed to lock in a profit if a certain event occurs. If that event does not occur, there could be a loss (usually quite limited); hence, the position has risk. This risk element differentiates a risk arbitrage from a standard, no-risk arbitrage. Risk arbitrage is described more fully in a later section, but the following example concerning a special dividend is one form of risk arbitrage. Example: XYZ has been known to declare extra, or special, dividends with a fair amount of regularity. There are several stocks that do so - Eastman Kodak and General Motors, for example. In this case, assume that a hypothetical stock, XYZ, has ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:467 SCORE: 31.00 ================================================================================ Chapter 27: Arbitrage 427 generally declared a special dividend in the fourth quarter of each year, but that its normal quarterly rate is $1.00 per share. Suppose the special dividend in the fourth quarter has ranged from an extra $1.00 to $3.00 over the past five years. If the arbi­ trageur were willing to speculate on the size of the upcoming dividend, he might be able to make a nice profit. Even if he overestimates the size of the special dividend, he has a limited loss. Suppose XYZ is trading at 55 about two weeks before the com­ pany is going to announce the dividend for the fourth quarter. There is no guarantee that there will, in fact, be a special dividend, but assume that XYZ is having a rela­ tively good year profitwise, and that some special dividend seems forthcoming. Furthermore, suppose the January 60 put is trading at 7½. This put has 2½ points of time value premium. If the arbitrageur buys XYZ at 55 and also buys the January 60 put at 7½, he is setting up a risk arbitrage. He will profit regardless of how far the stock falls or how much time value premium the put loses, if the special dividend is larger than $1.50. A special dividend of $1.50 plus the regular dividend of $1.00 would add up to $2.50, or 2½ points, thus covering his risk in the position. Note that $1.50 is in the low end of the $1.00 to $3.00 recent historical range for the special dividends, so the arbitrageur might be tempted to speculate a little by establishing this dividend risk arbitrage. Even if the company unexpectedly decided to declare no special dividend at all, it would most likely still pay out the $1.00 regular dividend. Thus, the most that the arbitrageur would lose would be 1 ½ points (his 2½-point ini­ tial time value premium cost, less the 1-point dividend). In actual practice, the stock would probably not change in price by a great deal over the next two weeks (it is a high-yield stock), and therefore the January 60 put would probably have some time value premium left in it after the stock goes ex-dividend. Thus, the practical risk is even less than 1 ½ points. While these types of dividend risk arbitrage are not frequently available, the arbitrageur who is willing to do some homework and also take some risk may find that he is able to put on a position with a small risk and a profitability quite a bit larger than the normal discount dividend arbitrage. There is really not a direct form of dividend arbitrage involving call options. If a relatively high-yield stock is about to go ex-dividend, holders of the calls will attempt to sell. They do so because the stock will drop in price, thereby generally forcing the call to drop in price as well, because of the dividend. However, the hold­ er of a call does not receive cash dividends and therefore is not willing to hold the call if the stock is going to drop by a relatively large amount (perhaps ¾ point or more). The effect of these call holders attempting to sell their calls may often pro­ duce a discount option, and therefore a basic call arbitrage may be possible. The arbi­ trageur should be careful, however, if he is attempting to arbitrage a stock that is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:468 SCORE: 31.50 ================================================================================ 428 Part IV: Additional Considerations going ex-dividend on the following day. Since he must sell the stock to set up the arbi­ trage, he cannot afford to wind up the day being short any stock, for he will then have to pay out the dividend the following day (the ex-dividend date). Furthermore, his records must be accurate, so that he exercises all his long options on the day before the ex-dividend date. If the arbitrageur is careless and is still short some stock on the ex-date, he may find that the dividend he has to pay out wipes out a large portion of the discount profits he has established. CONVERSIONS AND REVERSALS In the introductory material on puts, it was shown that put and call prices are relat­ ed through a process known as conversion. This is an arbitrage process whereby a trader may sometimes be able to lock in a profit at absolutely no risk. A conversion consists of buying the underlying stock, and also buying a put option and selling a call option such that both options have the same terms. This position will have a locked-in profit if the total cost of the position is less than the striking price of the options. Example: The following prices exist: XYZ common, 55; XYZ January 50 call, 6½; and XYZ January 50 put, 1. The total cost of this conversion is 49½ - 55 for the stock, plus 1 for the put, less 6½ for the call. Since 49½ is less than the striking price of 50, there is a locked-in profit on this position. To see that such a profit exists, suppose the stock is somewhere above 50 at expiration. It makes no difference how far above 50 the stock might be; the result will be the same. With the stock above 50, the call will be assigned and the stock will be sold at a price of 50. The put will expire worthless. Thus, the profit is½ point, since the initial cost of the position was 49½ and it can eventually be liquidat­ ed for a price of 50 at expiration. A similar result occurs if XYZ is below 50 at expi­ ration. In this case, the trader would exercise his put to sell his stock at 50, and the call would expire worthless. Again, the position is liquidated for a price of 50 and, since it only cost 49½ to establish, the same ½-point profit can be made. No matter where the stock is at expiration, this position has a locked-in-profit of½ point. This example is rather simplistic because it does not include two very important factors: the possible dividend paid by the stock and the cost of carrying the position ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:469 SCORE: 22.00 ================================================================================ Chapter 27: Arbitrage 429 until expiration. The inclusion of these factors complicates things somewhat, and its discussion is deferred momentarily while the companion strategy, the reversal, is explained. A reversal (or reverse conversion, as it is sometimes called) is exactly the oppo­ site of a conversion. In a reversal, the trader sells stock short, sells a put, and buys a call. Again, the put and call have the same terms. A reversal will be profitable if the initial credit ( sale price) is greater than the striking price of the options. Example: A different set of prices will be used to describe a reversal: XYZ common, 55; XYZ January 60 call, 2; and XYZ January 60 put, 7½. The total credit of the reversal is 60½ - 55 from the stock sale, plus 7½ from the put sale, less the 2-point cost of the call. Since 60½ is greater than the striking price of the options, 60, there is a locked-in profit equal to the differential of½ point. To ver­ ify this, first assume that XYZ is anywhere below 60 at January expiration. The put will be assigned - stock is bought at 60 - and the call will expire worthless. Thus, the reversal position is liquidated for a cost of 60. A ½-point profit results since the orig­ inal sale value ( credit) of the position was 60½. On the other hand, if XYZ were above 60 at expiration, the trader would exercise his call, thus buying stock at 60, and the put would expire worthless. Again, he would liquidate the position at a cost of 60 and would make a ½-point profit. Dividends and carrying costs are important in reversals, too; these factors are addressed here. The conversion involves buying stock, and the trader will thus receive any dividends paid by the stock during the life of the arbitrage. However, the converter also has to pay out a rather large sum of money to set up his arbitrage, and must therefore deduct the cost of carrying the position from his potential profits. In the example above, the conversion position cost 49½ points to establish. If the trad­ er's cost of money were 6% annually, he would thus lose .06/12 x 49½, or .2475 point per month for each month that he holds the position. This is nearly ¼ of a point per month. Recall that the potential profit in the example is ½ point, so that if one held the position for more than two months, his carrying costs would wipe out his profit. It is extremely important that the arbitrageur compute his carrying costs accurately prior to establishing any conversion arbitrage. If one prefers formulae, the profit potentials of a conversion or a reversal can be stated as: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:470 SCORE: 17.50 ================================================================================ 430 l'art IV: Additional Considerations Conversion profit = Striking price + Call price - Stock price - Put price + Dividends to be received - Carrying cost of position Reversal profit = Stock + Put - Strike - Call + Carrying cost - Dividends Note that during any one trading day, the only items in the formulae that can change are the prices of the securities involved. The other items, dividends and carrying cost, are fixed for the day. Thus, one could have a small computer program prepared that listed the fixed charges on a particular stock for all the strikes on that stock. Example: It is assumed that XYZ stock is going to pay a ½-point dividend during the life of the position, and that the position will have to be held for three months at a carrying cost of 6% per year. If the arbitrageur were interested in a conversion with a striking price of 50, his fixed cost would be: Conversion fixed cost = Carrying rate x Time held x Striking price - Dividend to be received = .06 X 3/12 X 50 - ½ = .75- ½ = .25, or¼ point The arbitrageur would know that if the profit potential, computed in the simplistic manner using only the prices of the securities involved, was greater than ¼ point, he could establish the conversion for an eventual profit, including all costs. Of course, the carrying costs would be different if the striking price were 40 or 60, so a com­ puter printout of all the possible striking prices on each stock would be useful in order for the trader to be able to refer quickly to a table of his fixed costs each day. MORE ON CARRYING COSTS The computation of carrying costs can be made more involved than the simple method used above. Simplistically, the carrying cost is computed by multiplying the debit of the position by the interest rate charged and the time that the position will be held. That is, it could be formulated as: Carrying cost = Strike x r x t where r is the interest rate and t is the time that the position will be held. Relating this formula for the carrying cost to the conversion profit formula given above, one would get: Conversion profit = Call - Stock - Put + Dividend + Strike - Carrying cost = Call - Stock - Put + Dividend + Strike ( 1 - rt) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:471 SCORE: 14.00 ================================================================================ Chapter 27: Arbitrage 431 In an actuarial sense, the carrying cost could be expressed in a slightly more complex manner. The simple formula (strike x r x t) ignores two things: the compounding effect of interest rates and the "present value" concept ( the present value of a future amount). The absolutely correct formula to include both present value and the com­ pounding effect would necessitate replacing the factor strike (1- rt) in the profit for­ mula by the factor Strike (1 + r)f Is this effect large? No, not when rand tare small, as they would be for most option calculations. The interest rate per month would normally be less than 1 %, and the time would be less than 9 months. Thus, it is generally acceptable, and is the com­ mon practice among many arbitrageurs, to use the simple formula for carrying costs. In fact, this is often a matter of convenience for the arbitrageur if he is computing the carrying costs on a hand calculator that does not perform exponentiation. However, in periods of high interest rates when longer-term options are being ana­ lyzed, the arbitrageur who is using the simple formula should double-check his cal­ culations with the correct formula to assure that his error is not too large. For purposes of simplicity, the remaining examples use the simple formula for carrying-cost computations. The reader should remember, however, that it is only a convenient approximation that works best when the interest rate and the holding period are small. This discussion of the compounding effect of interest rates also rais­ es another interesting point: Any investor using margin should, in theory, calculate his potential interest charge using the compounding formula. However, as a matter of practicality, extremely few investors do. An example of this compounding effect on a covered call write is presented in Chapter 2. BACK TO CONVERSIONS AND REVERSALS Profit calculation similar to the conversion profit formula is necessary for the rever­ sal arbitrage. Since the reversal necessitates sho1ting stock, the trader must pay out any dividends on the stock during the time in which the position is held. However, he is now bringing in a credit when the position is established, and this money can be put to work to earn interest. In a reversal, then, the dividend is a cost and the interest earned is a profit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:473 SCORE: 14.00 ================================================================================ Chapter 27: Arbitrage 433 available in the marketplace at a net profit of ½ point, or 50 cents. Such a reversal may not be equally attractive to all arbitrageurs. Those who have "box" stock may be willing to do the reversal for 50 cents; those who have to pay 1 % to borrow stock may want 0.55 for the reversal; and those who pay 2% to borrow stock may need 0.65 for the reversal. Thus, arbitrageurs who do conversions and reversals are in competition with each other not only in the marketplace, but in the stock loan arena as well. Reversals are generally easier positions for the arbitrageur to locate than are conversions. This is because the fixed cost of the conversion has a rather burdensome effect. Only if the stock pays a rather large dividend that outweighs the carrying cost could the fixed portion of the conversion formula ever be a profit as opposed to a cost. In practice, the interest rate paid to carry stock is probably higher than the interest earned from being short stock, but any reasonable computer program should be able to handle two different interest rates. The novice trader may find the term "conversion" somewhat illogical. In the over-the-counter option markets, the dealers create a position similar to the one shown here as a result of actually converting a put to a call. Example: When someone owns a conventional put on XYZ with a striking price of 60 and the stock falls to 50, there is often little chance of being able to sell the put profitably in the secondary market. The over-the-counter option dealer might offer to convert the put into a call. To do this, he would buy the put from the holder, then buy the stock itself, and then offer a call at the original striking price of 60 to the holder of the put. Thus, the dealer would be long the stock, long the put, and short the call - a conversion. The customer would then own a call on XYZ with a striking price of 60, due to expire on the same date that the put was destined to. The put that the customer owned has been converted into a call. To effect this conversion, the dealer pays out to the customer the difference between the current stock price, 50, and the striking price, 60. Thus, the customer receives $1,000 for this conver­ sion. Also, the dealer would charge the customer for costs to carry the stock, so that the dealer had no risk. If the stock rallied back above 60, the customer could make more money, because he owns the call. The dealer has no risk, as he has an arbitrage position to begin with. In a similar manner, the dealer can effect a reverse conver­ sion - converting a call to a put - but will charge the dividends to the customer for doing so. RISKS IN CONVERSIONS AND REVERSALS Conversions and reversals are generally considered to be riskless arbitrage. That is, the profit in the arbitrage is fixed from the start and the subsequent movement of the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:474 SCORE: 15.50 ================================================================================ 434 Part IV: Additional Considerations underlying stock makes no difference in the eventual outcome. This is generally a true statement. However, there are some risks, and they are great enough that one can actually lose money in conversions and reversals if he does not take care. The risks are fourfold in reversal arbitrage: An extra dividend is declared, the interest rate falls while the reversal is in place, an early assignment is received, or the stock is exactly at the striking price at expiration. Converters have similar risks: a dividend cut, an increase in the interest rate, early assignment, or the stock closing at the strike at expiration. These risks are first explored from the viewpoint of the reversal trader. If the company declares an extra dividend, it is highly likely that the reversal will become unprofitable. This is so because most extra dividends are rather large - more than the profit of a reversal. There is little the arbitrageur can do to avoid being caught by the declaration of a truly extra dividend. However, some companies have a track record of declaring extras with annual regularity. The arbitrageur should be aware of which companies these are and of the timing of these extra dividends. A clue sometimes exists in the marketplace. If the reversal appears overly profitable when the arbi­ trageur is first examining it (before he actually establishes it), he should be somewhat skeptical. Perhaps there is a reason why the reversal looks so tempting. An extra div­ idend that is being factored into the opinion of the marketplace may be the answer. The second risk is that of variation in interest rates while the reversal is in progress. Obviously, rates can change over the life of a reversal, normally 3 to 6 months. There are two ways to compensate for this. The simplest way is to leave some room for rates to move. For example, if rates are currently at 12% annually, one might allow for a movement of 2 to 3% in rates, depending on the length of time the reversal is expected to be in place. In order to allow for a 2% move, the arbitrageur would calculate his initial profit based on a rate of 10%, 2% less than the currently prevailing 12%. He would not establish any reversal that did not at least break even with a 10% rate. The rate at which a reversal breaks even is often called the "effec­ tive rate" - 10% in this case. Obviously, if rates average higher than 10% during the life of the reversal, it will make money. Normally, when one has an entire portfolio of reversals in place, he should know the effective rate of each set of reversals expiring at the same time. Thus, he would have an effective rate for his 2-month reversals, his 3-month ones, and so forth. Allowing this room for rates to move does not necessarily mean that there will not be an adverse affect if rates do indeed fall. For example, rates could fall farther than the room allowed. Thus, a further measure is necessary in order to completely protect against a drop in rates: One should invest his credit balances generated by the reversals in interest-bearing paper that expires at approximately the same time the reversals do, and that bears interest at a rate that locks in a profit for the reversal ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:475 SCORE: 52.00 ================================================================================ Chapter 27: Arbitrage 435 account. For example, suppose that an arbitrageur has $5 million in 3-month rever­ sals at an effective rate of 10%. If he can buy $5 million worth of 3-month Certificates of Deposit with a rate of 11 ½%, then he would lock in a profit of 1 ½% on his $5 mil­ lion. This method of using paper to hedge rate fluctuations is not practiced by all arbitrageurs; some think it is not worth it. They believe that by leaving the credit bal­ ances to fluctuate at prevailing rates, they can make more if rates go up, and that will cushion the effect when rates decline. The third risk of reversal arbitrage is reception of an early assignment on the short puts. This forces the arbitrageur to buy stock and incur a debit. Thus, the posi­ tion does not earn as much interest as was originally assumed. If the assignment is received early enough in the life of the reversal (recall that in-the-money puts can be assigned very far in advance of expiration), the reversal could actually incur an overall loss. Such early assignments normally occur during bearish markets. The only advantage of this early assignment is that one is left with unhedged long calls; these calls are well out-of-the-money and normally quite low-priced (¼ or less). If the market should reverse and turn bullish before the expiration of the calls, the arbi­ trageur may make money on them. There is no way to hedge completely against a market decline, but it does help if the arbitrageur tries to establish reversals with the call in-the-money and the put out-of-the-money. That, plus demanding a better overall return for reversals near the strike, should help cushion the effects of the bear market. The final risk is the most common one, that of the stock closing exactly at the strike at expiration. This presents the arbitrageur with a decision to make regarding exercise of his long calls. Since the stock is exactly at the strike, he is not sure whether he will be assigned on his short puts at expiration. The outcome is that he may end up with an unhedged stock position on Monday morning after expiration. If the stock should open on a gap, he could have a substantial loss that wipes out the profits of many reversals. This risk of stock closing at the strike may seem minute, but it is not. In the absence of any real buying or selling in the stock on expiration day, the process of discounting will force a stock that is near the strike virtually right onto the strike. Once it is near the strike, this risk materializes. There are two basic scenarios that could occur to produce this unhedged stock position. First, suppose one decides that he will not get put and he exercises his calls. However, he was wrong and he does get put. He has bought double the amount of stock - once via call exercise and again via put assignment. Thus, he will be long on Monday morning. The other scenario produces the opposite effect. Suppose one decides that he will get put and he decides not to exercise his calls. If he is wrong in this case, he does not buy any stock - he didn't exercise nor did he get put. Consequently, he will be short stock on Monday morning. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:476 SCORE: 59.50 ================================================================================ 436 Part IV: Additional Considerations If one is truly undecided about whether he will be assigned on his short puts, he might look at several clues. First, has any late news come out on Friday evening that might affect the market's opening or the stock's opening on Monday morning? If so, that should be factored into the decision regarding exercising the calls. Another clue arises from the price at which the stock was trading during the Friday expiration day, prior to the close. If the stock was below the strike for most of the day before closing at the strike, then there is a greater chance that the puts will be assigned. This is so because other arbitrageurs (discounters) have probably bought puts and bought stock during the day and will exercise to clean out their positions. If there is still doubt, it may be wisest to exercise only half of the calls, hoping for a partial assignment on the puts (always a possibility). This halfway measure will normally result in some sort of unhedged stock position on Monday morning, but it will be smaller than the maximum exposure by at least half. Another approach that the arbitrageur can take if the stock is near the strike of the reversal during the late trading of the options' life - during the last few days - is to roll the reversal to a later expiration or, failing that, to roll to another strike in the same expiration. First, let us consider rolling to another expiration. The arbitrageur knows the dollar price that equals his effective rate for a 3-month reversal. If the cur­ rent options can be closed out and new options opened at the next expiration for at least the effective rate, then the reversal should be rolled. This is not a likely event, mostly due to the fact that the spread between the bid and asked prices on four sep­ arate options makes it difficult to attain the desired price. Note: This entire four-way order can be entered as a spread order; it is not necessary to attempt to "leg" the spread. The second action - rolling to another strike in the same expiration month - may be more available. Suppose that one has the July 45 reversal in place (long July 45 call and short July 45 put). If the underlying stock is near 45, he might place an order to the exchange floor as a three-way spread: Sell the July 45 call (closing), buy the July 45 put (closing), and sell the July 40 call ( opening) for a net credit of 5 points. This action costs the arbitrageur nothing except a small transaction charge, since he is receiving a 5-point credit for moving the strike by 5 points. Once this is accom­ plished, he will have moved the strike approximately 5 points away and will thus have avoided the problem of the stock closing at the strike. Overall, these four risks are significant, and reversal arbitrageurs should take care that they do not fall prey to them. The careless arbitrageur uses effective rates too close to current market rates, establishes reversals with puts in-the-money, and routinely accepts the risk of acquiring an unhedged stock position on the morning after expiration. He will probably sustain a large loss at some time. Since many rever­ sal arbitrageurs work with small capital and/or have convinced their backers that it is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:477 SCORE: 22.00 ================================================================================ Chapter 27: Arbitrage 437 a riskless strategy, such a loss may have the effect of putting them out of business. That is an unnecessary risk to take. There are countermeasures, as described above, that can reduce the effects of the four risks. Let us consider the risks for conversion traders more briefly. The risk of stock closing near the strike is just as bad for the conversion as it is for the reversal. The same techniques for handling those risks apply equally well to conversions as to reversals. The other risks are similar to reversal risks, but there are slight nuances. The conversion arbitrage suffers if there is a dividend cut. There is little the arbitrageur can do to predict this except to be aware of the fundamentals of the com­ pany before entering into the conversion. Alternatively, he might avoid conversions in which the dividend makes up a major part of the profit of the arbitrage. Another risk occurs if there is an early assignment on the calls before the ex-div­ idend date and the dividend is not received. Moreover, an early assignment leaves the arbitrageur with long puts, albeit fractional ones since they are surely deeply out-of­ the-money. Again, the policy of establishing conversions in which the dividend is not a major factor would help to ease the consequences of early assignment. The final risk is that interest rates increase during the time the conversion is in place. This makes the carrying costs larger than anticipated and might cause a loss. The best way to hedge this initially is to allow a margin for error. Thus, if the pre­ vailing interest rate is 12%, one might only establish reversals that would break even if rates rose to 14%. If rates do not rise that far on average, a profit will result. The arbitrageur can attempt to hedge this risk by shorting interest-bearing paper that matures at approximately the same time as the conversions. For example, if one has $5 million worth of 3-month conversions established at an effective rate of 14% and he shorts 3-month paper at 12½%, he locks in a profit of 1 ½%. This is not common practice for conversion arbitrageurs, but it does hedge the effect of rising interest rates. SUMMARY OF CONVERSION ARBITRAGE The practice of conversion and reversal arbitrage in the listed option markets helps to keep put and call prices in line. If arbitrageurs are active in a particular option, the prices of the put and call will relate to the stock price in line with the formulae given earlier. Note that this is also a valid reason why puts tend to sell at a lower price than calls do. The cost of money is the determining factor in the difference between put and call prices. In essence, the "cost" (although it may sometimes be a credit) is sub­ tracted from the theoretical put price. Refer again to the formula given above for the profit potential of a conversion. Assume that things are in perfect alignment. Then the formula would read: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:478 SCORE: 31.50 ================================================================================ 438 Part IV: Additional Considerations Put price = Striking price + Call price - Stock price - Fixed cost Furthermore, if the stock is at the striking price, the formula reduces to: Put price = Call price - Fixed cost So, whenever the fixed cost, which is equal to the carrying charge less the dividends, is greater than zero (and it usually is), the put will sell for less than the call if a stock is at the striking price. Only in the case of a large-dividend-paying stock, when the fixed cost becomes negative (that is, it is not a cost, but a credit), does the reverse hold true. This is supportive evidence for statements made earlier that at-the-money calls sell for more than at-the-money puts, all other things being equal. The reader can see quite clearly that it has nothing to do with supply and demand for the puts and calls, a fallacy that is sometimes proffered. This same sort of analysis can be used to prove the broader statement that calls have a greater time value premium than puts do, except in the case of a large-dividend-paying stock. One final word of advice should be offered to the public customer. He may sometimes be able to find conversions or reversals, by using the simplistic formula, that appear to have profit potentials that exceed commission costs. Such positions do exist from time to time, but the rate of return to the public customer will almost assuredly be less than the short-term cost of money. If it were not, arbitrageurs would be onto the position very quickly. The public option trader may not actually be think­ ing in terms of comparing the profit potential of a position with what he could get by placing the money into a bank, but he must do so to convince himself that he cannot feasibly attempt conversion or reversal arbitrages. THE "INTEREST PLAY" In the preceding discussion of reversal arbitrage, it is apparent that a substantial por­ tion of the arbitrageur's profits may be due to the interest earned on the credit of the position. Another type of position is used by many arbitrageurs to take advantage of this interest earned. The arbitrageur sells the underlying stock short and simultane­ ously buys an in-the-money call that is trading slightly over parity. The actual amount over parity that the arbitrageur can afford to pay for the call is determined by the interest that he will earn from his short sale and the dividend payout before expira­ tion. He does not use a put in this type of position. In fact, this "interest play" strat­ egy is merely a reversal arbitrage without the short put. This slight variation has a residual benefit for the arbitrageur: If the underlying stock should drop dramatically in price, he could make large profits because he is short the underlying stock. In any case, he will make his interest credit less the amount of time value premium paid for the call less any dividends lost. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:479 SCORE: 46.00 ================================================================================ Chapter 27: Arbitrage 439 Example 1: XYZ is sold short at 60, and a January 50 call is bought for 10¼ points. Assume that the prevailing interest rate is 1 % per month and that the position is established one month prior to expiration. XYZ pays no dividend. The total credit brought in from the trades is $4,975, so the arbitrageur will earn $49.75 in interest over the course of 1 month. If the stock is above 50 at expiration, he will exercise his call to buy stock at 50 and close the position. His loss on the security trades will be $25 the amount of time value premium paid for the call option. (He makes 10 points by selling stock at 60 and buying at 50, but loses 10¼ points on the exercised call.) His overall profit is thus $24.75. Example 2: A real-life example may point out the effect of interest rates even more dramatically. In early 1979, IBM April 240 calls with about six weeks of life remain­ ing were over 60 points in-the-money. IBM was not going to be ex-dividend in that time. Normally, such a deeply in-the-money option would be trading at parity or even a discount when the time remaining to expiration is so short. However, these calls were trading 3½ points over parity because of the prevailing high interest rates at the time. IBM was at 300, the April 240 calls were trading at 63½, and the prevailing interest rate was approximately 1 % per month. The credit from selling the stock and buying the call was $23,700, so the arbitrageur earned $365.50 in interest for 1 ½ months, and lost $350 - the 3½ points of time value premium that he paid for the call. This still left enough room for a profit. In Chapter 1, it was stated that interest rates affect option prices. The above examples of the "interest play" strategy quite clearly show why. As interest rates rise, the arbitrageur can afford to pay more for the long call in this strategy, thus causing the call price to increase in times of high interest rates. If call prices are higher, so will put prices be, as the relationships necessary for conversion and reversal arbitrage are preserved. Similarly, if interest rates decline, the arbitrageur will make lower bids, and call and put prices will be lower. They are active enough to give truth to the theory that option prices are directly related to interest rates. THE BOX SPREAD An arbitrage consists of simultaneously buying and selling the same security or equiv­ alent securities at different prices. For example, the reversal consists of selling a put and simultaneously shorting stock and buying a call. The reader will recall that the short stock/long call position was called a synthetic put. That is, shorting the stock and buying a call is equivalent to buying a put. The reversal arbitrage therefore con­ sists of selling a (listed) put and simultaneously buying a (synthetic) put. In a similar ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:480 SCORE: 46.50 ================================================================================ 440 Part IV: Additional Considerations manner, the conversion is merely the purchase of a (listed) put and the simultaneous sale of a (synthetic) put. Many equivalent strategies can be combined for arbitrage purposes. One of the more common ones is the box spread. Recall that it was shown that a bull spread or a bear spread could be construct­ ed with either puts or calls. Thus, if one were to simultaneously buy a (call) bull spread and buy a (put) bear spread, he could have an arbitrage. In essence, he is merely buying and selling equivalent spreads. If the price differentials work out cor­ rectly, a risk-free arbitrage may be possible. Example: The following prices exist: XYZ common, 55 XYZ January 50 call, 7 XYZ January 50 put, 1 XYZ January 60 call, 2 XYZ January 60 put, 5½ The arbitrageur could establish the box spread in this example by executing the following transactions: Buy a call bull spread: Buy XYZ January 50 call Sell XYZ January 60 call Net call cost Buy a put bear spread: Buy XYZ January 60 put Sell XYZ January 50 put Net put cost Total cost of position 7 debit 2 credit 51/2 debit 1 credit 5 debit No matter where XYZ is at January expiration, this position will be worth 10 points. The arbitrageur has locked in a risk-free profit of½ point, since he "bought" the box spread for 9½ points and will be able to "sell" it for 10 points at expiration. To verify this, evaluate the position at expiration, first with XYZ above 60, then with XYZ between 50 and 60, and finally with XYZ below 50. If XYZ is above 60 at expiration, the puts will expire worthless and the call bull spread will be at its maximum poten­ tial of 10 points, the difference between the striking prices. Thus, the position can be liquidated for 10 points if XYZ is above 60 at expiration. Now assume that XYZ is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:481 SCORE: 63.00 ================================================================================ Chapter 27: Arbitrage 441 between 50 and 60 at expiration. In that case, the out-of-the-money, written options would expire worthless-the January 60 call and the January 50 put. This would leave a long, in-the-money combination consisting of a January 50 call and a January 60 put. These two options must have a total value of 10 points at expiration with XYZ between 50 and 60. (For example, the arbitrageur could exercise his call to buy stock at 50 and exercise his put to sell stock at 60.) Finally, assume that XYZ is below 50 at expiration. The calls would expire worthless if that were true, but the remaining put spread- actually a bear spread in the puts -would be at its maximum potential of 10 points. Again, the box spread could be liquidated for 10 points. The arbitrageur must pay a cost to carry the position, however. In the prior example, if interest rates were 6% and he had to hold the box for 3 months, it would cost him an additional 14 cents (.06 x 9½ x 3112). This still leaves room for a profit. In essence, a bull spread ( using calls) was purchased while a bear spread ( using puts) was bought. The box spread was described in these terms only to illustrate the fact that the arbitrageur is buying and selling equivalent positions. The arbitrageur who is utilizing the box spread should not think in terms of bull or bear spread, how­ ever. Rather, he should be concerned with "buying" the entire box spread at a cost of less than the differential between the two striking prices. By "buying" the box spread, it is meant that both the call spread portion and the put spread portion are debit spreads. Whenever the arbitrageur observes that a call spread and a put spread using the same strikes and that are both debit spreads can be bought for less than the dif­ ference in the strikes plus carrying costs, he should execute the arbitrage. Obviously, there is a companion strategy to the one just described. It might sometimes be possible for the arbitrageur to "sell" both spreads. That is, he would establish a credit call spread and a credit put spread, using the same strikes. If this credit were greater than the difference in the striking prices, a risk-free profit would be locked in. Example: Assume that a different set of prices exists: XYZ common, 75 XYZ April 70 call, 8½ XYZ April 70 put, 1 XYZ April 80 call, 3 XYZ April 80 put, 6 By executing the following transactions, the box spread could be "sold": ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:482 SCORE: 32.50 ================================================================================ 442 Sell a call (bear) spread: Buy April 80 call Sell April 70 call Net credit on calls Sell a put (bull) spread: Buy April 70 put Sell April 80 put Net credit on puts Total credit of position 3 debit 81/2 credit 1 debit 6 credit Part IV: Additional Considerations 5 credit 10 1/2 credit In this case, no matter where XYZ is at expiration, the position can be bought back for 10 points. This means that the arbitrageur has locked in risk-free profit of¼ point. To verify this statement, first assume that XYZ is above 80 at April expiration. The puts will expire worthless, and the call spread will have widened to 10 points - the cost to buy it back. Alternatively, if XYZ were between 70 and 80 at April expira­ tion, the long, out-of-the-money options would expire worthless and the in-the­ money combination would cost 10 points to buy back. (For example, the arbitrageur could let himself be put at 80, buying stock there, and called at 70, selling the stock there - a net "cost" to liquidate of 10 points.) Finally, if XYZ were below 70 at expi­ ration, the calls would expire worthless and the put spread would have widened to 10 points. It could then be closed out at a cost of 10 points. In each case, the arbitrageur is able to liquidate the box spread by buying it back at 10. In this sale of a box spread, he would earn interest on the credit received while he holds the position. There is an additional factor in the profitability of the box spread. Since the sale of a box generates a credit, the arbitrageur who sells a box will earn a small amount of money from that sale. Conversely, the purchaser of a box spread will have a charge for carrying cost. Since profit margins may be small in a box arbitrage, these carrying costs can have a definite effect. As a result, boxes may actually be sold for 5 points, even though the striking prices are 5 points apart, and the arbitrageur can still make money because of the interest earned. These box spreads are not easy to find. If one does appear, the act of doing the arbitrage will soon make the arbitrage impossible. In fact, this is true of any type of arbitrage; it cannot be executed indefinitely because the mere act of arbitraging will force the prices back into line. Occasionally, the arbitrageur will be able to find the option quotes to his liking, especially in volatile markets, and can establish a risk-free ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:483 SCORE: 51.00 ================================================================================ Chapter 27: Arbitrage 443 arbitrage with the box spread. It can be evaluated at a glance. Only two questions need to be answered: 1. If one were to establish a debit call spread and a debit put spread, using the same strikes, would the total cost be less than the difference in the striking prices plus carrying costs? If the answer is yes, an arbitrage exists. 2. Alternatively, if one were to sell both spreads - establishing a credit call spread and a credit put spread - would the total credit received plus interest earned be greater than the difference in the striking prices? If the answer is yes, an arbi­ trage exists. There are some risks to box arbitrage. Many of them are the same as those risks faced by the arbitrageur doing conversions or reversals. First, there is risk that the stock might close at either of the two strikes. This presents the arbitrageur with the same dilemma regarding whether or not to exercise his long options, since he is not sure whether he will be assigned. Additionally, early assignment may change the prof­ itability: Assignment of a short put will incur large carrying costs on the resulting long stock; assignment of a short call will inevitably come just before an ex-dividend date, costing the arbitrageur the amount of the dividend. There are not many opportunities to actually transact box arbitrage, but the fact that such arbitrage exists can help to keep markets in line. For example, if an under­ lying stock begins to move quickly and order flow increases dramatically, the special­ ist or market-markers in that stock's options may be so inundated with orders that they cannot be sure that their markets are correct. They can use the principles of box arbitrage to keep prices in line. The most active options would be the ones at strikes nearest to the current stock price. The specialist can quickly add up the markets of the call and put at the nearest strike above the stock price and add to that the mar­ kets of the options at the strike just below. The sum of the four should add up to a price that surrounds the difference in the strikes. If the strikes are 5 points apart, then the sum of the four markets should be something like 4½ bid, 5½ asked. If, instead, the four markets add up to a price that allows box arbitrage to be established, then the specialist will adjust his markets. VARIATIONS ON EQUIVALENCE ARBITRAGE Other variations of arbitrage on equivalent positions are possible, although they are relatively complicated and probably not worth the arbitrageur's time to analyze. For example, one could buy a butterfly spread with calls and simultaneously sell a but­ terfly spread using puts. A listed straddle could be sold and a synthetic straddle ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:484 SCORE: 44.50 ================================================================================ 444 Part IV: Additional Considerations could be bought - short stock and long 2 calls. Inversely, a listed straddle could be bought against a ratio write - long stock and short 2 calls. The only time the arbi­ trageur should even consider anything like this is when there are more sizable mar­ kets in certain of the puts and calls than there are in others. If this were the case, he might be able to take an ordinary box spread, conversion, or reversal and add to it, keeping the arbitrage intact by ensuring that he is, in fact, buying and selling equiv­ alent positions. THE EFFECTS OF ARBITRAGE The arbitrage process serves a useful purpose in the listed options market, because it may provide a secondary market where one might not otherwise exist. Normally, public interest in an in-the-money option dwindles as the option becomes deeply in­ the-money or when the time remaining until expiration is very short. There would be few public buyers of these options. In fact, public selling pressure might increase, because the public would rather liquidate in-the-money options held long than exer­ cise them. The few public buyers of such options might be writers who are closing out. However, if the writer is covered, especially where call options are concerned, he might decide to be assigned rather than close out his option. This means that the public seller is creating a rather larger supply that is not offset by a public demand. The market created by the arbitrageur, especially in the basic put or call arbitrage, essentially creates the demand. Without these arbitrageurs, there could conceivably be no buyers at all for those options that are short-lived and in-the-money, after pub­ lic writers have finished closing out their positions. Equivalence arbitrage - conversion, reversals, and box spreads - helps to keep the relative prices of puts and calls in line with each other and with the underlying stock price. This creates a more efficient and rational market for the public to oper­ ate in. The arbitrageur would help eliminate, for example, the case in which a public customer buys a call, sees the stock go up, but cannot find anyone to sell his call to at higher prices. If the call were too cheap, arbitrageurs would do reversals, which involve call purchases, and would therefore provide a market to sell into. Questions have been raised as to whether option trading affects stock prices, especially at or just before an expiration. If the amount of arbitrage in a certain issue becomes very large, it could appear to temporarily affect the price of the stock itself. For example, take the call arbitrage. This involves the sale of stock in the market. The corresponding stock purchase, via the call exercise, is not executed on the exchange. Thus, as far as the stock market is concerned, there may appear to be an inordinate amount of selling in the stock. If large numbers of basic call arbitrages are taking place, they might thus hold the price of the stock down until the calls expire. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:485 SCORE: 30.00 ================================================================================ Chapter 27: Arbitrage 445 The put arbitrage has an opposite effect. This arbitrage involves buying stock in the market. The offsetting stock sale via the put exercise takes place off the exchange. If a large amount of put arbitrage is being done, there may appear to be an inordi­ nate amount of buying in the stock. Such action might temporarily hold the stock price up. In a vast majority of cases, however, the arbitrage has no visible effect on the underlying stock price, because the amount of arbitrage being done is very small in comparison to the total number of trades in a given stock. Even if the open interest in a particular option is large, allowing for plenty of option volume by the arbi­ trageurs, the actual act of doing the arbitrage will force the prices of the stock and option back into line, thus destroying the arbitrage. Rather elaborate studies, including doctoral theses, have been written that try to prove or disprove the theory that option trading affects stock prices. Nothing has been proven conclusively, and it may never be, because of the complexity of the task. Logic would seem to dictate that arbitrage could temporarily affect a stock's move­ ment if it has discount, in-the-money options shortly before expiration. However, one would have to reasonably conclude that the size of these arbitrages could almost never be large enough to overcome a directional trend in the underlying stock itself. Thus, in the absence of a definite direction in the stock, arbitrage might help to per­ petuate the inertia; but if there were truly a preponderance of investors wanting to buy or sell the stock, these investors would totally dominate any arbitrage that might be in progress. RISK ARBITRAGE USING OPTIONS Risk arbitrage is a strategy that is well described by its name. It is basically an arbi­ trage - the same or equivalent securities are bought and sold. However, there is gen­ erally risk because the arbitrage usually depends on a future event occurring in order for the arbitrage to be successful. One form of risk arbitrage was described earlier concerning the speculation on the size of a special dividend that an underly­ ing stock might pay. That arbitrage consisted of buying the stock and buying the put, when the put' s time value premium is less than the amount of the projected special dividend. The risk lies in the arbitrageur's speculation on the size of the anticipated special dividend. MERGERS Risk arbitrage is an age-old type of arbitrage in the stock market. Generally, it con­ cerns speculation on whether a proposed merger or acquisition will actually go through as proposed. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:486 SCORE: 14.50 ================================================================================ 446 Part IV: Additional Considerations Example: XYZ, which is selling for $50 per share, offers to buy out LMN and is offer­ ing to swap one share of its (XYZ's) stock for every two shares of LMN. This would mean that LMN should be worth $25 per share if the acquisition goes through as pro­ posed. On the day the takeover is proposed, LMN stock would probably rise to about $22 per share. It would not trade all the way up to 25 until the takeover was approved by the shareholders of LMN stock. The arbitrageur who feels that this takeover will be approved can take action. He would sell short XYZ and, for every share that he is short, he would buy 2 shares of LMN stock. If the merger goes through, he will prof­ it. The reason that he shorts XYZ as well as buying LMN is to protect himself in case the market price of XYZ drops before the acquisition is approved. In essence, he has sold XYZ and also bought the equivalent of XYZ (two shares of LMN will be equal to one share of XYZ if the takeover goes through). This, then, is clearly an arbitrage. However, it is a risk arbitrage because, if the stockholders of LMN reject the offer, he will surely lose money. His profit potential is equal to the remaining differential between the current market price of LMN (22) and the takeover price (25). If the proposed acquisition goes through, the differential disappears, and the arbitrageur has his profit. The greatest risk in a merger is that it is canceled. If that happens, stock being acquired (LMN) will fall in price, returning to its pre-takeover levels. In addition, the acquiring stock (XYZ) will probably rise. Thus, the risk arbitrageur can lose money on both sides of his trade. If either or both of the stocks involved in the proposed takeover have options, the arbitrageur may be able to work options into his strategy. In merger situations, since large moves can occur in both stocks ( they move in concert), option purchases are the preferable option strategy. If the acquiring com­ pany (XYZ) has in-the-money puts, then the purchase of those puts may be used instead of selling XYZ short. The advantage is that if XYZ rallies dramatically during the time it takes for the merger to take effect, then the arbitrageur's profits will be increased. Example: As above, assume that XYZ is at 50 and is acquiring LMN in a 2-for-l stock deal. LMN is at 22. Suppose that XYZ rallies to 60 by the time the deal closes. This would pull LMN up to a price of 30. If one had been short 100 XYZ at 50 and long 200 LMN at 22, then his profit would be $600 - a $1,600 gain on the 200 long LMN minus a $1,000 loss on the XYZ short sale. Compare that result to a similar strategy substituting a long put for the short XYZ stock. Assume that he buys 200 LMN as before, but now buys an XYZ put. If one could buy an XYZ July 55 put with little time premium, say at 5½ points, then he would have nearly the same dollars of profit if the merger should go through with XYZ below 55. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:487 SCORE: 32.00 ================================================================================ Chapter 27: Arbitrage 447 However, when XYZ rallies to 60, his profit increases. He would still make the $1,600 on LMN as it rose from 22 to 30, but now would only lose $550 on the XYZ put - a total profit of $1,050 as compared to $600 with an all-stock position. The disadvantage to substituting long puts for short stock is that the arbitrageur does not receive credit for the short sale and, therefore, does not earn money at the carrying rate. This might not be as large a disadvantage as it initially seems, however, since it is often the case that it is very expensive - even impossible - to borrow the acquiring stock in order to short it. If the stock borrow costs are very large or if no stock can be located for borrowing, the purchase of an in-the-money put is a viable alternative. The purchase of an in-the-money put is preferable to an at- or out-of-the­ money put, because the amount of time value premium paid for the latter would take too much of the profitability away from the arbitrage if XYZ stayed unchanged or declined. This strategy may also save money if the merger falls apart and XYZ rises. The loss on the long put may well be less than the loss would be on short XYZ stock. Note also that one could sell the XYZ July 55 call short as well as buy the put. This would, of course, be synthetic short stock and is a pure substitute for shorting the stock. The use of this synthetic short is recommended only when the arbitrageur cannot borrow the acquiring stock. If this is his purpose, he should use the in-the­ money put and out-of-the-money call, since if he were assigned on the call, he could not borrow the stock to deliver it as a short sale. The use of an out-of-the-money call lessens the chance of eventual assignment. The companion strategy is to buy an in-the-money call instead of buying the company being acquired (LMN). This has advantages if the stock falls too far, either because the merger falls apart or because the stocks in the merger decline too far. Additionally, the cost of carrying the long LMN stock is eliminated, although that is generally built into the cost of the long calls. The larger amount of time value pre­ mium in calls as compared to puts makes this strategy often less attractive than that of buying the puts as a substitute for the short sale. One might also consider selling options instead of buying them. Generally this is an inferior strategy, but in certain instances it makes sense. The reason that option sales are inferior is that they do not limit one's risk in the risk arbitrage, but they cut off the profit. For example, if one sells puts on the company being acquired (LMN), he has a bullish situation. However, if the company being acquired (XYZ) rallies too far, there will be a loss, because the short puts will stop making money as soon as LMN rises through the strike. This is especially disconcerting if a takeover bidding war should develop for LMN. The arbitrageur who is long LMN will participate nice­ ly as LMN rises heavily in price during the bidding war. However, the put seller will not participate to nearly the same extent. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:488 SCORE: 8.50 ================================================================================ 448 Part IV: Additional Considerations The sale of in-the-money calls as a substitute for shorting the acquiring compa­ ny (XYZ) can be beneficial at certain times. It is necessary to have a plus tick in order to sell stock short. When many arbitrageurs are trying to sell a stock short at the same time, it may be difficult to sell such stock short. Morever, natural owners of XYZ may see the arbitrageurs holding the price down and decide to sell their long stock rather than suffer through a possible decline in the stock's price while the merger is in progress. Additionally, buyers of XYZ will become very timid, lowering their bids for the same reasons. All of this may add up to a situation in which it is very difficult to sell the stock short, even if it can be borrowed. The sale of an in-the-money call can overcome this difficulty. The call should be deeply in-the-money and not be too long­ term, for the arbitrageur does not want to see XYZ decline below the strike of the call. If that happened, he would no longer be hedged; the other side of the arbitrage - the long LMN stock - would continue to decline, but he would not have any remaining short against the long LMN. LIMITS ON THE MERGER There is another type of merger for stock that is more difficult to arbitrage, but options may prove useful. In some merger situations, the acquiring company (XYZ) promises to give the shareholders of the company being acquired (LMN) an amount of stock equal to a set dollar price. This amount of stock would be paid even if the acquiring company rose or fell moderately in price. If XYZ falls too far, however, it cannot pay out an extraordinarily increased number of shares to LMN shareholders, so XYZ puts a limit on the maximum number of shares that it will pay for each share of LMN stock. Thus, the shareholders ofXYZ are guaranteed that there will be some downside buffer in terms of dilution of their company in case XYZ declines, as is often the case for an acquiring company. However, ifXYZ declines too far, then LMN shareholders will receive less. In return for getting this downside guarantee, XYZ will usually also stipulate that there is a minimum amount of shares that they will pay to LMN shareholders, even if XYZ stock rises tremendously. Thus, if XYZ should rise tremendously in price, then LMN shareholders will do even better than they had anticipated. An example will demonstrate this type of merger accord. Example: Assume that XYZ is at 50 and it intends to acquire LMN for a stated price of $25 per share, as in the previous example. However, instead of merely saying that it will exchange two shares of LMN for one share of XYZ, the company says that it wants the offer to be worth $25 per share to LMN shareholders as long as XYZ is between 45 and 55. Given this information, we can determine the maximum and minimum number of shares that LMN shareholders will receive: The maximum is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:490 SCORE: 9.50 ================================================================================ 450 Part IV: Additional Considerations Problems arise if XYZ begins to fall below 45 well before the closing of the merger, the lower "hook" in the merger. If it should remain below 45, then one should set up the arbitrage as being short 0.556 shares ofXYZ for each share of LMN that is held long. As long as XYZ remains below 45 until the merger closes, this is the proper ratio. However, if, after establishing that ratio, XYZ rallies back above 45, the arbitrageur can suffer damaging losses. XYZ may continue to rise in price, creating a loss on the short side. However, LMN will not follow it, because the merger is struc­ tured so that LMN is worth 25 unless XYZ rises too far. Thus, the long side stops fol­ lowing as the short side moves higher. On the other hand, no such problem exists if XYZ rises too far from its original price of 50, going above the upper "hook" of 55. In that case, the arbitrageur would already be long the LMN and would not yet have shorted XYZ, since the merger was not yet closing. LMN would merely follow XYZ higher after the latter had crossed 55. This is not an uncommon dilemma. Recall that it was shown that the acquiring stock will often fall in price immediately after a merger is announced. Thus, XYZ may fall close to, or below, the lower "hook." Some arbitrageurs attempt to hedge them­ selves by shorting a little XYZ as it begins to fall near 45 and then completing the short if it drops well below 45. The problem with handling the situation in this way is that one ends up with an inexact ratio. Essentially, he is forcing himself to predict the movements of XYZ. If the acquiring stock drops below the lower "hook," there may be an opportu­ nity to establish a hedge without these risks if that stock has listed options. The idea is to buy puts on the acquiring company, and for those puts to have a striking price nearly equal to the price of the lower "hook." The proper amount of the company being acquired (LMN) is then purchased to complete the arbitrage. If the acquiring company subsequently rallies back into the stated price range, the puts will not lose money past the striking price and the problems described in the preceding paragraph will have been overcome. Example: A merger is announced as described in the preceding example: XYZ is to acquire LMN at a stated value of $25 per share, with the stipulation that each share of LMN will be worth at least 0.455 shares of XYZ and at most 0.556 shares. These share ratios equate to prices of 45 and 55 on XYZ. Suppose that XYZ drops immediately in price after the merger is announced, and it falls to 40. Furthermore, suppose that the merger is expected to close some­ time during July and that there are XYZ August 45 puts trading at 5½. This repre­ sents only ½ point time value premium. The arbitrageur could then set up the arbi­ trage by buying 10,000 LMN and buying 56 of those puts. Smaller investors might buy 1,000 LMN and buy 6 puts. Either of these is in approximately the proper ratio of 1 LMN to 0.556 XYZ. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:491 SCORE: 11.00 ================================================================================ Chapter 27: Arbitrage TENDER OFFERS 451 Another type of corporate takeover that falls under the broad category of risk arbi­ trage is the tender offer. In a tender offer, the acquiring company normally offers to exchange cash for shares of the company to be acquired. Sometimes the off er is for all of the shares of the company being acquired; sometimes it is for a fractional por­ tion of shares. In the latter case, it is important to know what is intended to be done with the remaining shares. These might be exchanged for shares of the acquiring company, or they might be exchanged for other securities (bonds, most likely), or perhaps there is no plan for exchanging them at all. In some cases, a company ten­ ders for part of its own stock, so that it is in effect both the acquirer and the acquiree. Thus, tender offers can be complicated to arbitrage properly. The use of options can lessen the risks. In the case in which the acquiring company is making a cash tender for all the shares (called an "any and all" offer), the main use of options is the purchase of puts as protection. One would buy puts on the company being acquired at the same time that he bought shares of that company. If the deal fell apart for some reason, the puts could prevent a disastrous loss as the acquiring stock dropped. The arbitrageur must be judicious in buying these puts. If they are too expensive or too far out-of-the­ money, or if the acquiring company might not really drop very far if the deal falls apart, then the purchase of puts is a waste. However, if there is substantial downside risk, the put purchase may be useful. Selling options in an "any and all" deal often seems like easy money, but there may be risks. If the deal is completed, the company being acquired will disappear and its options would be delisted. Therefore, it may often seem reasonable to sell out-of­ the-money puts on the acquiring company. If the deal is completed, these expire worthless at the closing of the merger. However, if the deal falls through, these puts will soar in price and cause a large loss. On the other hand, it may also seem like easy money to sell naked calls with a striking price higher than the price being offered for the stock. Again, if the deal goes through, these will be delisted and expire worthless. The risk in this situation is that another company bids a higher price for the compa­ ny on which the calls were written. If this happens, there might suddenly be a large upward jump in price, and the written calls could suffer a large loss. Options can play a more meaningful role in the tender off er that is for only part of the stock, especially when it is expected that the remaining stock might fall sub­ stantially in price after the partial tender offer is completed. An example of a partial tender offer might help to establish the scenario. Example: XYZ proposes to buy back part of its own stock It has offered to pay $70 per share for half the company. There are no plans to do anything further. Based on ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:492 SCORE: 10.50 ================================================================================ 452 Part IV: Additional Considerations the fundamentals of the company, it is expected that the remaining stock will sell for approximately $40 per share. Thus, the average share of XYZ is worth 55 if the ten­ der offer is completed ( one-half can be sold at 70, and the other half will be worth 40). XYZ stock might sell for $52 or $53 per share until the tender is completed. On the day after the tender offer expires, XYZ stock will drop immediately to the $40 per share level. There are two ways to make money in this situation. One is to buy XYZ at the current price, say 52, and tender it. The remaining portion would be sold at the lower price, say 40, when XYZ reopened after the tender expired. This method would yield a profit of $3 per share if exactly 50% of the shares are accepted at 70 in the tender offer. In reality, a slightly higher percentage of shares is usually accepted, because a few people make mistakes and don't tender. Thus, one's average net price tnight be $56 per share, for a $4 profit from this method. The risk in this situation is that XYZ opens substantially below 40 after the tender at 70 is completed. Theoretically, the other way to trade this tender off er might be to sell XYZ short at 52 and cover it at 40 when it reopens after the tender offer expires. Unfortunately, this method cannot be effected because there will not be any XYZ stock to borrow in order to sell it short. All owners will tender the stock rather than loan it to arbi­ trageurs. Arbitrageurs understand this, and they also understand the risk they take if they try to short stock at the last minute: They might be forced to buy back the stock for cash, or they may be forced to give the equivalent of $70 per share for half the stock to the person who bought the stock from them. For some reason, many indi­ vidual investors believe that they can "get away" with this strategy. They short stock, figuring that their brokerage firm will find some way to borrow it for them. Unfortunately, this usually costs the customer a lot of money. The use of calls does not provide a more viable way of attempting to capitalize on the drop of XYZ from 52 to 40. In-the-money call options on XYZ will normally be selling at parity just before the tender offer expires. If one sells the call as a sub­ stitute for the short sale, he will probably receive an assignment notice on the day after the tender offer expires, and therefore find himself with the same problems the short seller has. The only safe way to play for this drop is to buy puts on XYZ. These puts will be very expensive. In fact, with XY"L at 52 before the tender offer expires, if the con­ sensus opinion is that XYZ will trade at 40 after the offer expires, then puts with a 50 strike will sell for at least $10. This large price reflects the expected drop in price of XYZ. Thus, it is not beneficial to buy these puts as downside speculation unless one expects the stock to drop farther than to the $40 level. There is, however, an oppor­ tunity for arbitrage by buying XYZ stock and also buying the expensive puts. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:493 SCORE: 9.00 ================================================================================ Chapter 27: Arbitrage 453 Before giving an example of that arbitrage, a word about short tendering is in order. Short tendering is against the law. It comes about when one tenders stock into a tender offer when he does not really own that stock. There are complex definitions regarding what constitutes ownership of stock during a tender offer. One must be net long all the stock that he tenders on the day the tender offer expires. Thus, he can­ not tender the stock on the day before the offer expires, and then short the stock on the next day ( even if he could borrow the stock). In addition, one must subtract the number of shares covered by certain calls written against his position: Any calls with a strike price less than the tender off er price must be subtracted. Thus, if he is long 1,000 shares and has written 10 in-the-money calls, he cannot tender any shares. The novice and experienced investor alike must be aware of these definitions and should not violate the short tender rules. Let us now look at an arbitrage consisting of buying stock and buying the expen­ sive puts. Example: XYZ is at 52. As before, there is a tender offer for half the stock at 70, with no plans for the remainder. The July 55 puts sell for 15, and the July 50 puts sell for 10. It is common that both puts would be predicting the same price in the after-mar­ ket: 40. If one buys 200 shares ofXYZ at 52 and buys one July 50 put at 10, he has a locked­ in profit as long as the tender offer is completed. He only buys one put because he is assuming that 100 shares will be accepted by the company and only 100 shares will be returned to him. Once the 100 shares have been returned, he can exercise the put to close out his position. The following table summarizes these results: Initial purchase Buy 200 XYZ at 52 Buy 1 July 50 put at 10 Total Cost Closing sale Sell 1 00 XYZ at 70 via tender Sell 1 00 XYZ at 50 via put exercise Total proceeds Total profit: $600 $10,400 debit 1,000 debit $11 ,400 debit 7,000 credit 5,000 credit $12,000 credit This strategy eliminates the risk ofloss ifXYZ opens substantially below 40 after the tender offer. The downside price is locked in by the puts. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:494 SCORE: 16.50 ================================================================================ 454 Part IV: Additional Considerations If more than 50% of XYZ should be accepted in the tender offer, then a larger profit will result. Also, if XYZ should subsequently trade at a high enough price so that the July 50 put has some time value premium, then a larger profit would result as well. (The arbitrageur would not exercise the put, but would sell the stock and the put separately in that case.) Partial tender offers can be quite varied. The type described in the above exam­ ple is called a "two-tier" offer because the tender offer price is substantially different from the remaining price. In some partial tenders, the remainder of the stock is slat­ ed for purchase at substantially the same price, perhaps through a cash merger. The above strategy would not be applicable in that case, since such an offer would more closely resemble the "any and all" offer. In other types of partial tenders, debt secu­ rities of the acquiring company may be issued after the partial cash tender. The net price of these debt securities may be different from the tender offer price. If they are, the above strategy might work. In summary, then, one should look at tender offers carefully. One should be careful not to take extraordinary option risk in an "any and all" tender. Conversely, one should look to take advantage of any "two-tier" situation in a partial tender offer by buying stock and buying puts. PROFITABILITY Since the potential profits in risk arbitrage situations may be quite large, perhaps 3 or 4 points per 100 shares, the public can participate in this strategy. Commission charges will make the risk arbitrage less profitable for a public customer than it would be for an arbitrageur. The profit potential is often large enough, however, to make this type of risk arbitrage viable even for the public customer. In summary, the risk arbitrageur may be able to use options in his strategy, either as a replacement for the actual stock position or as protection for the stock position. Although the public cannot normally participate in arbitrage strategies because of the small profit potential, risk arbitrages may often offer exceptions. The profit potential can be large enough to overcome the commission burden for the public customer. PAIRS TRADING A stock trading strategy that has gained some adherents in recent years is pairs trad­ ing. Simplistically, this strategy involves trading pairs of stocks - one held long, the other short. Thus, it is a hedged strategy. The two stocks' price movements are relat­ ed historically. The pairs trader would establish the position when one stock was ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:495 SCORE: 35.00 ================================================================================ Chapter 27: Arbitrage 455 expensive with respect to the other one, historically. Then, when the stocks return to their historical relationship, a profit would result. In reality, some fairly complicated computer programs search out the appropriate pairs. The interest on the short sale offsets the cost of carry of the stock purchased. Therefore, the pairs trader doesn't have any expense except the possible differential in dividend payout. The bane of pairs trading is a possible escalation of the stock sold short without any corresponding rise in price of the stock held long. A takeover attempt might cause this to happen. Of course, pairs traders will attempt to research the situation to ensure that they don't often sell short stocks that are perceived to be takeover can­ didates. Pairs traders can use options to potentially reduce their risk if there are in-the­ money options on both stocks. One would buy an in-the-money put instead of selling one stock short, and would buy an in-the-money call on the other stock instead of buying the stock itself. In this option combination, traders are paying very little time value premium, so their profit potential is approximately the same as with the pairs trading strategy using stocks. ( One would, however, have a debit, since both options are purchased; so there would be a cost of carry in the option strategy.) If the stocks return to their historical relationship, the option strategy will reflect the same profit as the stock strategy, less any loss of time value premium. One added advantage of the option strategy, however, is that if a takeover occurs, the put has limited liability, and the trader's loss would be less. Another advantage of the option strategy is that if both stocks should experience large moves, it could make money even if the pair doesn't return to historical norms. This would happen, for example, if both stocks dropped a great deal: The call has lim­ ited loss, while the put' s profits would continue to accrue. Similarly, to the upside, a large move by both stocks would make the put worthless, but the call would keep making money. In both cases, the option strategy could profit even if the pair of stocks didn't perform as predicted. This type of strategy- buying in-the-money options as substitutes for both sides of a spread or hedge strategy - is discussed in more detail in Chapter 31 on index spreading and Chapter 35 on futures spreads. FACILITATION (BLOCK POSITIONING) Facilitation is the process whereby a trader seeks to aid in making markets for the purchase or sale of large blocks of stock. This is not really an arbitrage, and its description is thus deferred to Chapter 28. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:496 SCORE: 22.00 ================================================================================ CHAPTER 28 Mathetnatical Applications In previous chapters, many references have been made to the possibility of applying mathematical techniques to option strategies. Those techniques are developed in this chapter. Although the average investor - public, institutional, or floor trader - nor­ mally has a limited grasp of advanced mathematics, the information in this chapter should still prove useful. It will allow the investor to see what sorts of strategy deci­ sions could be aided by the use of mathematics. It will allow the investor to evaluate techniques of an information service. Additionally, if the investor is contemplating hiring someone knowledgeable in mathematics to do work for him, the information to be presented may be useful as a focal point for the work. The investor who does have a knowledge of mathematics and also has access to a computer will be able to directly use the techniques in this chapter. THE BLACK-SCHOLES MODEL Since an option's price is the function of stock price, striking price, volatility, time to expiration, and short-term interest rates, it is logical that a formula could be drawn up to calculate option prices from these variables. Many models have been conceived since listed options began trading in 1973. Many of these have been attempts to improve on one of the first models introduced, the Black-Scholes model. This model was introduced in early 1973, very near the time when listed options began trading. It was made public at that time and, as a result, gained a rather large number of adherents. The formula is rather easy to use in that the equations are short and the number of variables is small. The actual formula is: 456 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:497 SCORE: 23.00 ================================================================================ Chapter 28: Mathematical Applications Theoretical option price= pN(d 1) se-rtN(d2) p v2 ln(8 )+ (r +2 )t where d1 = _ r. V-4 t d2 = d1 - v--ft The variables are: p = stock price s = striking price t = time remaining until expiration, expressed as a percent of a year r = current risk-free interest rate v = volatility measured by annual standard deviation ln = natural logarithm N(x) = cumulative normal density function 457 An important by-product of the model is the exact calculation of the delta - that is, the amount by which the option price can be expected to change for a small change in the stock price. The delta was described in Chapter 3 on call buying, and is more formally known as the hedge ratio. Delta= N(d1) The formula is so simple to use that it can fit quite easily on most programmable cal­ culators. In fact, some of these calculators can be observed on the exchange floors as the more theoretical floor traders attempt to monitor the present value of option pre­ miums. Of course, a computer can handle the calculations easily and with great speed. A large number of Black-Scholes computations can be performed in a very short period of time. The cumulative normal distribution function can be found in tabular form in most statistical books. However, for computation purposes, it would be wasteful to repeatedly look up values in a table. Since the normal curve is a smooth curve (it is the "bell-shaped" curve used most commonly to describe population distributions), the cumulative distribution can be approximated by a formula: x = l-z(l.330274y 5 - l.821256y 4 + l.781478y 3 - .356538y 2 + .3193815y) where y 1 and z = .3989423e- 0 or N(cr) = 1- x if cr < 0 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:498 SCORE: 8.50 ================================================================================ 458 Part IV: Additional Considerations This approximation is quite accurate for option pricing purposes, since one is not really interested in thousandths of a point where option prices are concerned. Example: Suppose that XYZ is trading at 45 and we are interested in evaluating the July 50 call, which has 60 days remaining until expiration. Furthermore, assume that the volatility of XYZ is 30% and that the risk-free interest rate is currently 10%. The theoretical value calculation is shown in detail, in order that those readers who wish to program the model will have something to compare their calculations against. page: Initially, determine t, d1, and d2, by referring to the formulae on the previous t = 60/365 = .16438 years d _ In (45/50) + (.1 + .3 x .3/2) x .16438 1- .3 X ✓.16438 = -.10536 + (.145 X .16438) = __ 67025 .3 X .40544 d2 = -.67025 - .3 ✓.16438 = -.67025 - (.3 x .40544) = -.79189 Now calculate the cumulative normal distribution function for d1 and d2 by referring to the above formulae: dl = -.67025 l 1 y = l + (.2316419 I -.67025 I) = 1.15526 = ·86561 z = .3989423e--(-.67025 X -.67025)/2 = .3989423e-0·22462 = .31868 There are too many calculations involved in the computation of the fifth-order polynomial to display them here. Only the result is given: X = .74865 Since we are determining the cumulative normal distribution of a negative number, the distribution is determined by subtracting x from l. N(d1) = N(-.67O25) = l -x = l - .74865 = .25134 In a similar manner, which requires computing new values for x, y, and z, N(d2) = N(-.79179) = 1- .78579 = .21421 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:499 SCORE: 39.00 ================================================================================ Chapter 28: Mathematical Applications 459 Now, returning to the formula for theoretical option price, we can complete the calculation of the July 50 call's theoretical value, called value here for short: value = 45 x N(d1) - 50 x e-·1 x ·16438 x N(d2) = 45 X .25134 - 50 X .9837 X .21421 = .7746 Thus, the theoretical value of the July 50 call is just slightly over¼ of a point. Note that the delta of the call was calculated along the way as N(d1) and is equal to just over .25. That is, the July 50 call will change price about¼ as fast as the stock for a small price change by the stock. This example should answer many of the questions that readers of the first edi­ tion have posed. The reader interested in a more in-depth description of the model, possibly including the actual derivation, should refer to the article "Fact and Fantasy in the Use of Options." 1 One of the less obvious relationships in the model is that call option prices will increase (and put option prices will decrease) as the risk-free inter­ est rate increases. It may also be observed that the model correctly preserves rela­ tionships such as increased volatility, higher stock prices, or more time to expiration, which all imply higher option prices. CHARACTERISTICS Of THE MODEL Several aspects of this model are worth further discussion. First, the reader will notice that the model does not include dividends paid by the common stock. As has been demonstrated, dividends act as a negative effect on call prices. Thus, direct application of the model will tend to give inflated call prices, especially on stocks that pay relatively large dividends. There are ways of handling this. Fisher Black, one of the coauthors of the model, suggested the following method: Adjust the stock price to be used in the formula by subtracting, from the current stock price, the present worth of the dividends likely to be paid before maturity. Then calculate the option. price. Second, assume that the option expires just prior to the last ex-dividend date preceding actual option expiration. Again adjust the stock price and calculate the option price. Use the higher of the two option prices calculated as the theoretical price. Another, less exact, method is to apply a weighting factor to call prices. The weighting factor would be based on the dividend payment, with a heavier weight being applied to call options on high-yielding stock. It should be pointed out that, in 1Fisher Black, Financial Analysts Journal, July-August 1975, pp. 36-70. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:500 SCORE: 19.50 ================================================================================ 460 Part IV: Additional Considerations many of the applications that are going to be prescribed, it is not necessary to know the exact theoretical price of the call. Therefore, the dividend "correction" might not have to be applied for certain strategy decisions. The model is based on a lognormal distribution of stock prices. Even though the normal distribution is part of the model, the inclusion of the exponential functions makes the distribution lognormal. For those less familiar with statistics, a normal dis­ tribution has a bell-shaped curve. This is the most familiar mathematical distribution. The problem with using a normal distribution is that it allows for negative stock prices, an impossible occurrence. Therefore, the lognormal distribution is generally used for stock prices, because it implies that the stock price can have a range only between zero and infinity. Furthermore, the upward (bullish) bias of the lognormal distribution appears to be logically correct, since a stock can drop only 100% but can rise in price by more than 100%. Many option pricing models that antedate the Black-Scholes model have attempted to use empirical distributions. An empirical distribution has a different shape than either the normal or the lognormal distribu­ tion. Reasonable empirical distributions for stock prices do not differ tremendously from the lognormal distribution, although they often assume that a stock has a greater probability of remaining stable than does the lognormal distribution. Critics of the Black-Scholes model claim that, largely because it uses the lognormal distri­ bution, the model tends to overprice in-the-money calls and underprice out-of-the­ money calls. This criticism is true in some cases, but does not materially subtract from many applications of the model in strategy decisions. True, if one is going to buy or sell calls solely on the basis of their computed value, this would create a large prob­ lem. However, if strategy decisions are to be made based on other factors that out­ weigh the overpriced/underpriced criteria, small differentials will not matter. The computation of volatility is always a difficult problem for mathematical application. In the Black-Scholes model, volatility is defined as the annual standard deviation of the stock price. This is the regular statistical definition of standard devi­ ation: where P = average stock price of all P/s Pi = daily stock price n ~ (Pi -P)2 cr2 = _1=_1 __ _ n-1 v = a!P ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:503 SCORE: 51.00 ================================================================================ Chapter 28: Mathematical Applications 463 This is then the proper way to calculate historical volatility. Obviously, the strategist can calculate 10-, 20-, and 50-day and annual volatilities if he wishes - or any other number for that matter. In certain cases, one can discern valuable infor­ mation about a stock or future and its options by seeing how the various volatilities compare with one another. There is, in fact, a way in which the strategist can let the market compute the volatility for him. This is called using the implied volatility; that is, the volatility that the market itself is implying. This concept makes the assumption that, for options with striking prices close to the current stock price and for options with relatively large trading volume, the market is fairly priced. This is something like an efficient market hypothesis. If there is enough trading interest in an option that is close to the money, that option will generally be fairly priced. Once this assumption has been made, a corollary arises: If the actual price of an option is the fair price, it can be fixed in the Black-Scholes equation while letting volatility be the unknown variable. The volatility can be determined by iteration. In fact, this process of iterating to compute the volatility can be done for each option on a particular underlying stock This might result in several different volatilities for the stock If one weights these various results by volume of trading and by distance in- or out-of-the-money, a single volatility can be derived for the underlying stock This volatility is based on the closing price of all the options on the underlying stock for that given day. Example: XYZ is at 33 and the closing prices are given in Table 28-1. Each option has a different implied volatility, as computed by determining what volatility in the Black-Scholes model would result in the closing price for each option: That is, if .34 were used as the volatility, the model would give 4¼ as the price of the January 30 call. In order to rationally combine these volatilities, weighting factors must be applied before a volatility for XYZ stock itself can be arrived at. The weighting factors for volume are easy to compute. The factor for each option is merely that option's daily volume divided by the total option volume on all XYZ options (Table 28-2). The weighting functions for distance from the striking price should probably not be linear. For example, if one option is 2 points out-of-the­ money and another is 4 points out-of-the-money, the former option should not nec­ essarily get twice as much weight as the latter. Once an option is too far in- or out-of­ the-money, it should not be given much or any weight at all, regardless of its trading volume. Any parabolic function of the following form should suffice: { (x - a)2 if xis less than a Weighting factor = -;;,r- = 0 if x is greater than a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:504 SCORE: 25.50 ================================================================================ 464 Part IV: Additional Considerations TABLE 28-1. Implied volatilities, closing price, and volume. Option Option Price Volume January 30 41/2 January 35 11/2 April 35 21/2 April 40 11/2 TABLE 28-2. Volume weighting factors. Option January 30 January 35 April 35 April 40 Volume 50 90 55 5 50 90 55 ~ 200 Implied Volatility .34 .28 .30 .38 Volume Weighting Factor .25 (50/200) .45 (90/200) .275 (55/200) .025 ( 5/200) where x is the percentage distance between stock price and strike price and a is the maximum percentage distance at which the modeler wants to give any weight at all to the option's implied volatility. Example: An investor decides that he wants to discard options from the weighting criterion that have striking prices more than 25% from the current stock price. The variable, a, would then be equal to .25. The weighting factors, with XYZ at 33, could thus be computed as shown in Table 28-3. To combine the weighting factors for both volume and distance from strike, the two factors are multiplied by the implied volatil­ ity for that option. These products are summed up for all the options in question. This sum is then divided by the products of the weighting factors, summed over all the options in question. As a formula, this would read: Implied _ I,(Volume factor x Distance factor x Implied volatility) volatility - I,(Volume factor x Distance factor) In our example, this would give an implied volatility for XYZ stock of 29.8% (Table 28-4). Note that the implied volatility, .298, is not equal to any of the individ- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:505 SCORE: 17.00 ================================================================================ Chapter 28: Mathematical Applications TABLE 28-3. Distance weighting factors. 465 Option Distonce from Stock Price Distance Weighting Factor January 30 January 35 April 35 April 40 TABLE 28-4. Option's implied volatility. .091 (3/33) .061 (2/33) .061 (2/33) .212 (7 /33) .41 .57 .57 .02 Volume Distance Option's Implied Option Factor Factor Volotility January 30 .25 .41 .34 January 35 .45 .57 .28 April 35 .275 .57 .30 April40 .025 .02 .38 Implied = .25 x .41 x .34 + .45 x .57 x .28 + .275 x .57 x .30 + .025 x .02 x .38 volatility. .25 x .41 + .45 x .57 + .275 x .57 + .025 x .02 = .298 ual option's implied volatilities. Rather, it is a composite figure that gives the most weight to the heavily traded, near-the-money options, and very little weight to the lightly-traded (5 contracts), deeply out-of-the-money April 40 call. This implied volatility is still a form of standard deviation, and can thus be used whenever a stan­ dard deviation volatility is called for. This method of computing volatility is quite accurate and proves to be sensitive to changes in the volatility of a stock. For example, as markets become bullish or bearish (generating large rallies or declines), most stocks will react in a volatile man­ ner as well. Option premiums expand rather quickly, and this method of implied volatility is able to pick up the change quickly. One last bit of fine-tuning needs to be done before the final volatility of the stock is arrived at. On a day-to-day basis, the implied volatility for a stock - especially one whose options are not too active may fluctuate more than the strategist would like. A smoothing effect can be obtained by ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:506 SCORE: 39.50 ================================================================================ 466 Part IV: Additional Considerations taking a moving average of the last 20 or 30 days' implied volatilities. An alternative that does not require the saving of many previous days' worth of data is to use a momentum calculation on the implied volatility. For example, today's final volatility might be computed by adding 5% of today's implied volatility to 95% of yesterday's final volatility. This method requires saving only one previous piece of data - yester­ day's final volatility - and still preserves a "smoothing" effect. Once this implied volatility has been computed, it can then be used in the Black-Scholes model ( or any other model) as the volatility variable. Thus one could compute the theoretical value of each option according to the Black-Scholes formu­ la, utilizing the implied volatility for the stock. Since the implied volatility for the stock will most likely be somewhat different from the implied volatility of this par­ ticular option, there will be a discrepancy between the option's actual closing price and the theoretical price as computed by the model. This differential represents the amount by which the option is theoretically overpriced or underpriced, compared to other options on that same stock. EXPECTED RETURN Certain investors will enter positions only when the historical percentages are on their side. When one enters into a transaction, he normally has a belief as to the pos­ sibility of making a profit. For example, when he buys stock he may think that there is a "good chance" that there will be a rally or that earnings will increase. The investor may consciously or unconsciously evaluate the probabilities, but invariably, an invest­ ment is made based on a positive expectation of profit. Since options have fixed terms, they lend themselves to a more rigorous computation of expected profit than the aforementioned intuitive appraisal. This more rigorous approach consists of com­ puting the expected return. The expected retum is nothing more than the retum that the position should yield over a large number of cases. A simple example may help to explain the concept. The crucial variable in com­ puting expected return is to outline what the chances are of the stock being at a cer­ tain price at some future time. Example: XYZ is selling at 33, and an investor is interested in determining where XYZ will be in 6 months. Assume that there is a 20% chance of XYZ being below 30 in 6 months, and that there is a 40% chance that XYZ will be above 35 in 6 months. Finally, assume that XYZ has an equal 10% chance of being at 31, 32, 33, or 34 in 6 months. All other prices are ignored for simplification. Table 28-5 summarizes these assumptions. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:507 SCORE: 18.00 ================================================================================ Chapter 28: Mathematical Applications TABLE 28-5. Calculation of expected returns. Price of XYZ in 6 Months Below 30 31 32 33 34 Above 35 467 Chance of XYZ Being at That Price · 20% 10% 10% 10% 10% 40% 100% Since the percentages total 100%, all the outcomes have theoretically been allowed for. Now suppose a February 30 call is trading at 4 and a February 35 call is trading at 2 points. A bull spread could be established by buying the February 30 and selling the February 35. This position would cost 2 points - that is, it is a 2-point debit. The spreader could make 3 points if XYZ were above 35 at expiration for a return of 150%, or he could lose 100% if XYZ were below 30 at expiration. The expected return for this spread can be computed by multiplying the outcome at expi­ ration for each price by the probability of being at that price, and then summing the results. For example, if XYZ is below 30 at expiration, the spreader loses $200. It was assumed that there is a 20% chance of XYZ being below 30 at expiration, so the expected loss is 20% times $200, or $40. Table 28-6 shows the computation of the expected results at all the prices. The total expected profit is $100. This means that the expected return (profit divided by investment) is 50% ($100/$200). This appears to be an attractive spread, because the spreader could "expect" to make 50% of his money, less commissions. What has really been calculated in this example is merely the return that one would expect to make in the long run if he invested in the same position many times throughout history. Saying that a particular position has an expected return of 8 or 9% is no different from saying that common stocks return 8 or 9% in the long run. Of course, in bull markets stock would do much better, and in bear markets much worse. In a similar manner, this example bull spread with an expected return of 50% may do as well as the maximum profit or as poorly as losing 100% in any one case. It is the total return on many cases that has the expected return of 50%. Mathematical theory holds that, if one constantly invests in positions with positive expected returns, he should have a better chance of making rrwney. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:508 SCORE: 10.50 ================================================================================ 468 Part IV: Additional Considerations TABLE 28-6. Computation of expected profit. Chance of Being Profit at Expected XYZ Price at at That Price That Price Profit: Expiration (A) (B) (A) x (8) Below 30 20% -$200 -$ 40 31 10% - 100 - 10 32 10% 0 0 33 10% + 100 + 10 34 10% + 200 + 20 Above 35 40% + 300 + 120 Total expected profit $100 As is readily observable, the selection of what percentages to assign to the pos­ sible outcomes in the stock price is a crucial choice. In the example above, if one altered his assumption slightly so that XYZ had a 30% chance of being below 30 and a 30% chance of being above 35 at expiration, the expected return would drop con­ siderably, to 25%. Thus, it is important to have a reasonably accurate and consistent method of assigning these percentages. Furthermore, the example above was too sim­ plistic, in that it did not allow for the stock to close at any fractional prices, such as 32½. A correct expected return computation must take into account all possible out­ comes for the stock. Fortunately, there is a straightforward method of computing the expected per­ centage chance of a given stock being at a certain price at a certain point in time. This computation involves using the distribution of stock prices. As mentioned earlier, the Black-Scholes model assumes a lognormal distribution for stock prices, although many modelers today use nonstandard (empirical or heuristic) distributions. No mat­ ter what the distribution, the area under the distribution curve between any two points gives the probability of being between those two points. Figure 28-1 is a graph of a typical lognormal distribution. The peak always lies at the "mean," or average, of the distribution. For stock price distributions, under the random walk assumption, the "mean" is generally considered to be the current stock price. The graph allows one to visualize the probability of being at any given price. Note that there is a fairly great chance that the stock will be relatively unchanged; there is no chance that the stock will be below zero; and there is a bullish bias to the graph - the stock could rise infinitely, although the chances of it doing so are extremely small. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:510 SCORE: 11.50 ================================================================================ 470 where v = annual volatility t = time, in years vt = volatility for time, t. Part IV: Additional Considerations As an example, a 3-month volatility would be equal to one-half of the annual volatility. In this case, t would equal .25 (one fourth of a year), so v_25 = v65 = .5v. The necessary groundwork has been laid for the computation of the probabili­ ty necessary in the expected return calculation. The following formula gives the prob­ ability of a stock that is currently at price p being below some other price, q, at the end of the time period. The lognormal distribution is assumed. Probability of stock being below price q at end of time period t: P (below) = N (In~)) where N = cumulative normal distribution p = current price of the stock q = price in question In = natural logarithm for the time period in question. If one is interested in computing the probability of the stock being above the given price, the formula is P (above)= 1- P (below) With this formula, the computation of expected return is quickly accomplished with a computer. One merely has to start at some price - the lower strike in a bull spread, for example - and work his way up to a higher price - the high strike for a bull spread. At each price point in between, the outcome of the spread is multiplied by the probability of being at that price, and a running sum is kept. Simplistically, the following iterative equation would be used. P ( of being at price x) = P (below x) - P (below y) where y is close to but less than x in price. As an example: P (of being at 32.4) = P (below 32.4) - P (below 32.3) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:511 SCORE: 14.00 ================================================================================ Chapter 28: Mathematical Applications 471 Thus, once the low starting point is chosen and the probability of being below that price is determined, one can compute the probability of being at prices that are suc­ cessively higher merely by iterating with the preceding formula. In reality, one is using this information to integrate the distribution curve. Any method of approxi­ mating the integral that is used in basic calculus, such as the Trapezoidal Rule or Simpson's Rule, would be applicable here for more accurate results, if they are desired. A partial example of an expected return calculation follows. Example: XYZ is currently at 33 and has an annual volatility of 25%. The previous bull spread is being established- buy the February 30 and sell the February 35 for a 2-point debit - and these are 6-month options. Table 28-7 gives the necessary com­ ponents for computing the expected return. Column (A), the probability of being below price q, is computed according to the previously given formula, where p = 33 and vt = .177 (t = .25-V ½). The first stock price that needs to be looked at is 30, since all results for the bull spread are equal below that price - a 100% loss on the spread. The calculations would be performed for each eighth (or tenth) of a point up through a price of 35. The expected return is computer example, if one index sells for twice the price of the other, and if both indices have similar volatilities, then a one-to-one spread gives too much weight to the higher-priced index. A two-to-one ratio would be better, for that would give equal weighting to the spread between the indices. Example: UVX is an index of stock prices that is currently priced at 100.00. ZYX, another index, is priced at 200.00. The two indices have some similarities and, there­ fore, a spreader might want to trade one against the other. They also display similar volatilities. If one were to buy one UVX future and sell one ZYX future, his spread would be too heavily oriented to ZYX price movement. The following table displays that, showing that if both indices have similar percentage movements, the profit of the one-by-one spread is dominated by the profit or loss in the ZYX future. Assume both fi1tures are worth $500 per point. Market ZYX ZYX uvx uvx Total Direction Price Profit Price Profit Profit up 20% 240 -$20,000 120 +$10,000 -$10,000 up 10% 220 - 10,000 110 + 5,000 - 5,000 down 10% 180 + 10,000 90 - 5,000 + 5,000 down 20% 160 + 20,000 80 - 10,000 + 10,000 This is not much of a hedge. If one wanted a position that reflected the movement of the ZYX index, he could merely trade the ZYX futures and not bother with a spread. If, however, one had used the ratio of the indices to decide how many futures to buy and sell, he would have a more neutral position. In this example, he would buy two UVX futures and sell one ZYX future. Proponents of using the ratio of indices are attempting strictly to capture any performance difference between the two indices. They are not trying to predict the overall direction of the stock market. Technically, the proper ratio should also include the volatility of the two indices, because that is also a factor in determining how fast they move in relationship to each other. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:629 SCORE: 38.00 ================================================================================ Chapter 31: Index Spreading 583 slightly more volatile than these two larger indices, and also has more technology and less basic industry such as steel and chemicals. The OEX movement definitely has good correlation to the S&P 500. The S&P 500 Index (SPX) currently trades at about twice the "speed" of the OEX Index. This has been true since OEX split 2-for-l in November 1997. A one-point move in SPX is approximately equal to a move of 7.5 points in the Dow-Jones Industrial Average, while a one-point move in OEX is approximately equal to 15 Dow points. In general, it is easier to spread the indices by using futures rather than options, although only the S&P 500 Index has liquid futures markets. (There is a mini-Value Line futures market, as well as Dow-Jones futures - both of which are fairly illiq­ uid - but no futures trade on OEX.) One reason for this is liquidity - the index futures markets have large open interest. Another reason is tightness of markets. Futures markets are normally 5 or 10 cents wide, while option markets are 10 cents wide or more. Moreover, an option position that is a full synthetic requires both a put and a call. Thus, the spread in the option quotes comes into play twice. The Japanese stock market can be spread against the U.S. markets by spread­ ing a U.S. index against Nikkei futures or futures options, traded on the Chicago Mere, or against JPN options, traded on the AMEX. INTER-INDEX SPREADS USING OPTIONS As mentioned before, it may not be as efficient to try to use options in lieu of the actual futures spreads since the futures are more liquid. However, there are still many applications of the inter-index strategy using options. OEX versus S&P 500. The OEX cash-based index options are the most liquid option contracts. Thus, any inter-index spread involving the OEX and other indices must include the OEX options. The S&P 100 was first introduced in 1982 by the CBOE. It was originally intended to be an S&P 500 look-alike whose characteristics would allow investors who did not want to trade futures ( S&P 500 futures) the opportunity to be able to trade a broad index by offering options on the OEX. Initially, the index was known as the CBOE 100, but later the CBOE and Standard and Poor's Corp. reached an agreement whereby the index would be added to S&P's array of indices. It was then renamed the S&P 100. Initially, the two indices traded at about the same price. The OEX was the more expensive of the two for a while in the early 1980s. As the bull market of the 1980s matured, the S&P 500 ground its way higher, eventually reaching a price nearly 30 points higher than OEX. As one can see, there is ample room for movement in the spread between the cash indices. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:630 SCORE: 59.00 ================================================================================ 584 Part V: Index Options and Futures The S&P 500 has more stocks, and while both indices are capitalization-weight­ ed, 500 stocks include many smaller stocks than the 100-stock index. Also, the OEX is more heavily weighted by technology issues and is therefore slightly more volatile. Finally, the OEX does not contain several stocks that are heavily weighted in the S&P 500 because those stocks do not have options listed on the CBOE: Procter and Gamble, Philip Morris, and Royal Dutch, to name a few. There are two ways to approach this spread - either from the perspective of the derivative products differ­ ential or by attempting to predict the cash spread. In actual practice, most market-makers in the OEX use the S&P 500 futures to hedge with. Therefore, if the futures have a larger premium - are overpriced - then the OEX calls will be expensive and the puts will be cheap. Thus, there is not as much of an opportunity to establish an inter-index spread in which the derivative products (futures and options in this case) spread differs significantly from the cash spread. That is, the derivative products spread will generally follow the cash spread very closely, because of the number of people trading the spread for hedging purposes. Nevertheless, the application does arise, albeit infrequently, to spread the premium of the derivative products in two indices on strictly a hedged basis with­ out trying to predict the direction of movement of the cash indices. In order to establish such a spread, one would take a position in futures and an opposite posi­ tion in both the puts and calls on OEX. Due to the way that options must be exe­ cuted, one cannot expect the same speed of execution that he can with the futures, unless he is trading from the OEX pit itself. Therefore, there is more of an execu­ tion risk with this spread. Consequently, most of this type of inter-index spreading is done by the market-makers themselves. It is much more difficult for upstairs traders and customers. USING OPTIONS IN INDEX SPREADS Whenever both indices have options, as most do, the strategist may find that he can use the options to his advantage. This does not mean merely that he can use a syn­ thetic option position as a substitute for the futures position (long call, short put at the same strike instead of long futures, for example). There are at least two other alternatives with options. First, he could use an in-the-money option as a substitute for the future. Second, he could use the options' delta to construct a more leveraged spread. These alternatives are best used when one is interested in trading the spread between the cash indices - they are not really amenable to the short-term strategy of spreading the premiums between the futures. Using in-the-money options as a substitute for futures gives one an additional advantage: If the cash indices move far enough in either direction, the spreader could ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:631 SCORE: 57.00 ================================================================================ O,apter 31: Index Spreading 585 still make money, even if he was wrong in his prediction of the relationship of the cash indices. Example: The following prices exist: ZYX: 175.00 UVX: 150.00 ZYX Dec 185 put: 10½ UVX Dec 140 call: 11 Suppose that one wants to buy the UVX index and sell the ZYX index. He expects the spread between the two - currently at 25 points - to narrow. He could buy the UVX futures and sell the ZYX futures. However, suppose that instead he buys the ZYX put and buys the UVX call. The time value of the Dec 185 put is 1/2 point and that of the Dec 140 call is 1 point. This is a relatively small amount of time value premium. Therefore, the com­ bination would have results very nearly the same as the futures spread, as long as both options remain in-the-money; the only difference would be that the futures spread would outperform by the amount of the time premium paid. Even though he pays some time value premium for this long option combina­ tion, the investor has the opportunity to make larger profits than he would with the futures spread. In fact, he could even make a profit if the cash spread widens, if the indices are volatile. To see this, suppose that after a large upward move by the over­ all market, the following prices exist: ZYX: 200.00 UVX: 170.00 ZYX Dec 185 put: 0 ( virtually worthless) UVX Dec 140 call: 30 The combination that was originally purchased for 21 ½ points is now worth 30, so the spread has made money. But observe what has happened to the cash spread: It has widened to 30 points, from the original price of 25. This is a movement in the opposite direction from what was desired, yet the option position still made money. The reason that the option combination in the example was able to make money, even though the cash spread moved unfavorably, is because both indices rose so much in price. The puts that were owned eventually became worthless, but the long call continued to make money as the market rose. This is a situation that is very similar to owning a long strangle (long put and call with different strikes), except that ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:632 SCORE: 61.00 ================================================================================ 586 Part V: Index Options and Futures the put and call are based on different underlying indices. This concept is discussed in more detail in Chapter 35 on futures spreads. The second way to use options in index spreading is to use options that are less deeply in-the-money. In such a case, one must use the deltas of the options in order to accurately compute the proper hedge. He would calculate the number of options to buy and sell by using the formula given previously for the ratio of the indices, which incorporates both price and volatility, and then multiplying by a factor to include delta. where vi is the volatility of index i Pi is the price of index i ui is the unit of trading and di is the delta of the selected option on index i Example: The following data is known: ZYX: 175.00, volatility= 20% UVX: 150.00, volatility = 15% ZYX Dec 175 put: 7, delta= - .45, worth $500/pt. UVX Dec 150 call: 5, delta= .52, worth $100/pt Suppose one decides that he wants to set up a position that will profit if the spread between the two cash indices shrinks. Rather than use the deeply in-the­ money options, he now decides to use the at-the-money options. He would use the option ratio formula to determine how many puts and calls to buy. (Ignore the put's negative delta for the purposes of this formula.) .20 175.00 500 .45 Option Ratio= -x ---x - x - = 6 731 .15 150.00 100 .52 . He would buy nearly 7 UVX calls for every ZYX put purchased. In the previous example, using in-the-money options, one had a very small expense for time value premium and could profit if the indices were volatile, even if the cash spread did not shrink. This position has a great deal of time value premium e:x--pense, but could make profits on smaller moves by the indices. Of course, either one could profit if the cash indices moved favorably. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:633 SCORE: 52.00 ================================================================================ Cl,apter 31: Index Spreading 587 Volatility Differential. A theoretical "edge" that sometimes appears is that of volatility differential. If two indices are supposed to have essentially the same volatil­ ity, or at least a relationship in their volatilities, then one might be able to establish an option spread if that relationship gets out ofline. In such a case, the options might actually show up as fair-valued on both indices, so that the disparity is in the volatili­ ty differential, and not in the pricing of the options. OEX and SPX options trade with essentially the same implied volatility. Thus, if one index's options are trading with a higher implied volatility than the other's, a potential spread might exist. Normally, one would want the differential in implied volatilities to be at least 2% apart before establishing the spread for volatility reasons. In any case, whether establishing the spread because one thinks the cash index relationship is going to change, or because the options on one index are expensive with respect to the options on the other index, or because of the disparity in volatili­ ties, the spreader must use the deltas of the options and the price ratio and volatili­ ties of the indices in setting up the spread. Striking Price Differential. The index relationships can also be used by the option trader in another way. When an option spread is being established with options whose strikes are not near the current index prices - that is, they are rela­ tively deeply in- or out-of-the-money- one can use the ratio between the indices to determine which strikes are equivalent. Example: ZYX is trading at 250 and the ZYX July 270 call is overpriced. An option strategist might want to sell that call and hedge it with a call on another index. Suppose he notices that calls on the UVX Index are trading at approximately fair value with the UVX Index at 175. What UVX strike should he buy to be equivalent to the ZYX 270 strike? One can multiply the ZYX strike, 270, by the ratio of the indices to arrive at the UVX strike to use: UVX strike= 270 x (175/250) = 189.00 So he would buy the UVX July 190 calls to hedge. The exact number of calls to buy would be determined by the formula given previously for option ratio. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:634 SCORE: 17.00 ================================================================================ 588 SUMMARY Part V: Index Options and Futures This concludes the discussion of index spreading. The above examples are intended to be an overview of the most usable strategies in the complex universe of index spreading. The multitude of strategies involving inter-index and intra-index spreads cannot all be fully described. In fact, one's imagination can be put to good use in designing and implementing new strategies as market conditions change and as the emotion in the marketplace drives the premium on the futures contracts. Often one can discern a usable strategy by observation. Watch how two popu­ lar indices trade with respect to each other and observe how the options on the two indices are related. If, at a later time, one notices that the relationship is changing, perhaps a spread between the indices is warranted. One could use the NASDAQ­ based indices, such as the NASDAQ-100 (NDX) or smaller indices based on it (QQQ or MNX). Sector indices can be used as well. This brings into play a fairly large num­ ber of indices with listed options (few, if any, of which have futures), such as the Semiconductor Index (SOX), the Oil & Gas Index (XOI), the Gold and Silver Index (XAU), etc. The key point to remember is that the index option and futures world is more diverse than that of stock options. Stock option strategies, once learned or observed, apply equally well to all stocks. Such is not the case with index spreading strategies. The diversification means that there are more profit opportunities that are recognized by fewer people than is the case with stock options. The reader is thus challenged to build upon the concepts described in this part of the book. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:636 SCORE: 10.00 ================================================================================ 590 Part V: Index Options and Futures The discussion in this chapter concentrates on the structured products that are listed and traded on the major stock exchanges. A broader array of products - typically called exotic options - is traded over-the-counter. These can be very com­ plicated, especially with respect to currency and bond options. It is not our intent to discuss exotic options, although the approaches to valuing the structured products that are presented in this chapter can easily be applied to the overall valuation of many types of exotic products. Also, the comments at the end of the chapter regard­ ing where to find information about these products may prove useful for those seek­ ing further information about either listed structured products or exotic options. Part I: "Riskless" Ownership of a Stock or Index THE "STRUCTURE" OF A STRUCTURED PRODUCT At many of the major institutional banks and brokerages, people are employed who design structured products. They are often called financial engineers because they take existing financial products and build something new with them. The result is packaged as a fund of sorts (or a unit trust, perhaps), and shares are sold to the pub­ lic. Not only that, but the shares are then listed on the American or New York Stock Exchanges and can be traded just like any other stock. These attributes make the structured product a very desirable investment. An example will show how a generic index structured product might look. Example: Let's look at the structured index product to see how it might be designed and then how it might be sold to the public. Suppose that the designers believe there is demand for an index product that has these characteristics: 1. This "index product" will be issued at a low price - say, $10 per share. 2. The product will have a maturity date - say, seven years hence. 3. The owner of these shares can redeem them at their maturity date for the greater of either a) $10 per share orb) the percentage appreciation of the S&P 500 index over that seven-year time period. That is, if the S&P doubles over the seven years, then the shares can be redeemed for double their issue price, or $20. Thus, this product has no price risk! The holder gets his $10 back in the worst case (except for credit risk, which will be addressed in a minute). Moreover, these shares will trade in the open market during the seven years, so that if the holder wants to exit at any time, he can do so. Perhaps the S&P has rallied ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:637 SCORE: 11.00 ================================================================================ O,apter 32: Structured Products 591 dramatically, or perhaps he needs cash for something else - both might be reasons that the holder of the shares would want to sell before maturity. Such a product has appeal to many investors. In fact, if one thought that the stock market was a "long-term" buy, this would be a much safer way to approach it than buying a portfolio of stocks that might conceivably be much lower in value seven years hence. The risk of the structured product is that the underwriter might not be able to pay the $10 obligation at maturity. That is, if the major institutional bank or brokerage firm who underwrote these products were to go out of business over the course of the next seven years, one might not be able to redeem them. In essence, then, structured products are really forms of debt (senior debt) of the brokerage firm that underwrote them. Fortunately, most structured products are underwritten by the largest and best-capitalized institutions, so the chances of a failure to pay at matu­ rity would have to be considered relatively tiny. How does the bank create these items? It might seem that the bank buys stock and buys a put and sells units on the combined package. In reality, the product is not normally structured that way. Actually, it is not a difficult concept to grasp. This example shows how the structure looks from the viewpoint of the bank: Example: Suppose that the bank wants to raise a pool of $1,000,000 from investors to create a structured product based on the appreciation of the S&P 500 index over the next seven years. The bank will use a part of that pool of money to buy U.S. zero­ coupon bonds and will use the rest to buy call options on the S&P 500 index. Suppose that the U.S. government zero-coupon bonds are trading at 60 cents on the dollar. Such bonds would mature in seven years and pay the holder $1.00. Thus, the bank could take $600,000 and buy these bonds, knowing that in seven years, they would mature at a value of $1,000,000. The other $400,000 is spent to buy call options on the S&P 500 index. Thus, the investors would be made whole at the end of seven years even if the options that were bought expired worthless. This is why the bank can "guarantee" that investors will get their initial money back. Meanwhile, if the stock market advances, the $400,000 worth of call options will gain value and that money will be returned to the holders of the structured product as well. In reality, the investment bank uses its own money ($1,000,000) to buy the secu­ rities necessary to structure this product. Then they make the product into a legal entity (often a unit trust) and sell the shares (units) to the public, marking them up slightly as they would do with any new stock brought to market. At the time of the initial offering, the calls are bought at-the-money, meaning the striking price of the calls is equal to the closing price of the S&P 500 index on the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:638 SCORE: 16.00 ================================================================================ 592 Part V: Index Options and Futures day the products were sold to the public. Thus, the structured product itself has a "strike price" equal to that of the calls. It is this price that is used at maturity to deter­ mine whether the S&P has appreciated over the seven-year period - an event that would result in the holders receiving back more than just their initial purchase price. After the initial offering, the shares are then listed on the AMEX or the NYSE and they will begin to rise and fall as the value of the S&P 500 index fluctuates. So, the structured product is not an index fund protected by a put option, but rather it is a combination of zero-coupon government bonds and a call option on an index. These two structures are equivalent, just as the combination of owning stock protected by a put option is equivalent to being long a call option. Structured products of this type are not limited to indices. One could do the same thing with an individual stock, or perhaps a group of stocks, or even create a simulated bull spread. There are many possibilities, and the major ones will be dis­ cussed in the following sections. In theory, one could construct products like this for himself, but the mechanics would be too difficult. For example, where is one going to buy a seven-year option in small quantity? Thus, it is often worthwhile to avail one­ self of the product that is packaged (structured) by the investment banker. In actuality, many of the brokerage firms and investment banks that undetwrite these products give them names - usually acronyms, such as MITTS, TARGETS, BRIDGES, LINKS, DINKS, ELKS, and so on. If one looks at the listing, he may see that they are called notes rather than stocks or index funds. Nevertheless, when the terms are described, they will often match the examples given in this chapter. INCOME TAX CONSEQUENCES There is one point that should be made now: There is "phantom interest" on a struc­ tured product. Phantom interest is what one owes the government when a bond is bought at a discount to maturity. The IRS technically calls the initial purchase price an Original Issue Discount (OID) and requires you to pay taxes annually on a pro­ portionate amount of that OID. For example, if one buys a zero-coupon U.S. gov­ ernment bond at 60 cents on the dollar, and later lets it mature for $1.00, the IRS does not treat the 40-cent profit as capital gains. Rather, the 40 cents is interest income. Moreover, says the IRS, you are collecting that income each year, since you bought the bonds at a discount. (In reality, of course, you aren't collecting a thing; your investment is simply worth a little more each year because the discount decreas­ es as the bonds approach maturity.) However, you must pay income tax on the "phan- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:640 SCORE: 8.00 ================================================================================ 594 Part V: Index Options and Futures Cash Surrender Value = $10 x Final Value/ 1,245.27 This shortened version of the formula only works, though, when the participa­ tion rate is 100% of the increase in the Final Index Value above the striking price. Otherwise, the longer formula should be used. Not all structured products of this type offer the holder 100% of the appreci­ ation of the index over the initial striking price. In some cases, the percentage is smaller ( although in the early days of issuance, some products offered a percentage appreciation that was actually greater than 100%). After 1996, options in general became more expensive as the volatility of the stock market increased tremendous­ ly. Thus, structured products issued after 1997 or 1998 tend to include an "annual adjustment factor." Adjustment factors are discussed later in the chapter. Therefore, a more general formula for Cash Surrender Value - one that applies when the participation rate is a fixed percentage of the striking price - is: Cash Surrender Value = Guarantee + Guarantee x Participation Rate x (Final Index Value/ Striking Price - I) THE COST OF THE IMBEDDED CALL OPTION Few structured products pay dividends. 1 Thus, the "cost" of owning one of these products is the interest lost by not having your money in the bank ( or money market fund), but rather having it tied up in holding the structured product. Continuing with the preceding example, suppose that you had put the $10 in the bank instead of buying a structured product with it. Let's further assume that the money in the bank earns 5% interest, compounded continuously. At the end of seven years, compounded continuously, the $10 would be worth: Money in the bank = Guarantee Price x ert = $10 x e 0-05 x 7 = 14.191, in this case This calculation usually raises some eyebrows. Even compounded annually, the amount is 14.07. You would make roughly 40% (without considering taxes) just by 1Some do pay dividends, though. A structured product existed on a contrived index, called the Dow-Jones Top 10 Yield index (symbol: $XMT). This is a sort of "dogs of the Dow" index. Since part of the reason for owning a "dogs of the Dow" product is that dividends are part of the performance, the creators of the structured product (Merrill Lynch) stated that the minimum price one would receive at maturity would be 12.40, not the 10 that was the initial offering price. Thus, this particular structured product had a "dividend" built into it in the form of an ele­ vated minimum price at maturity. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:641 SCORE: 39.00 ================================================================================ Chapter 32: Structured Products 595 having your money in the bank. Forgetting structured products for a moment, this means that stocks in general would have to increase in value by over 40% during the seven-year period just for your performance to beat that of a bank account. In this sense, the cost of the imbedded call option in the structured product is this lost interest - 4.19 or so. That seems like a fairly expensive option, but if you con­ sider that it's a seven-year option, it doesn't seem quite so expensive. In fact, one could calculate the implied volatility of such a call and compare it to the current options on the index in question. In this case, with the stock at 10, the strike at 10, no dividends, a 5% interest rate, and seven years until expiration, the implied volatility of a call that costs $4.19 is 28.1 %. Call options on the S&P 500 index are rarely that expensive. So you can see that you are paying "something" for this call option, even if it is in the form of lost interest rather than an up-front cost. As an aside, it is also unlikely that the underwriter of the structured product actually paid that high an implied volatility for the call that was purchased; but he is asking you to pay that amount. This is where his underwriting profit comes from. The above example assumed that the holder of the structured product is par­ ticipating in 100% of the upside gain of the underlying index over its striking price. If that is not the case, then an adjustment has to be made when computing the price of the imbedded option. In fact, one must compute what value of the index, at matu­ rity, would result in the cash value being equal to the "money in the bank" calcula­ tion above. Then calculate the imbedded call price, using that value of the index. In that way, the true value of the imbedded call can be found. You might ask, "Why not just divide the 'money in the bank' formula by the par­ ticipation rate?" That would be okay if the participation were always stated as a per­ centage of the striking price, but sometimes it is not, as we will see when we look at the more complicated examples. Further examples of structured products in this chapter demonstrate this method of computing the cost of the imbedded call. PRICE BEHAVIOR PRIOR TO MATURITY The structured product cannot normally be "exercised" by the holder until it matures. That is, the cash surrender value is only applicable at maturity. At any other time during the life of the product, one can compute the cash surrender value, but he cannot actually attain it. What you can attain, prior to maturity, is the market price, since structured products trade freely on the exchange where they are listed. In actu­ al fact, the products generally trade at a slight discount to their theoretical cash sur­ render value. This is akin to a closed-end mutual fund selling at a discount to net ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:642 SCORE: 8.00 ================================================================================ 596 Part V: Index Options and Futures asset value. Eventually, upon maturity, the actual price will be the cash surrender value price; so if you bought the product at a discount, you would benefit, providing you held all the way to maturity. Example: Assume that two years ago, a structured product was issued with an initial offering price of $10 and a strike price of 1,245.27, based upon the S&P 500 index. Since issuance, the S&P 500 index has risen to 1,522.00. That is an increase of 22.22% for the S&P 500, so the structured product has a theoretical cash surrender value of 12.22. I say "theoretical" because that value cannot actually be realized, since the structured product is not exercisable at the current time - five years prior to maturity. In the real marketplace, this particular structured product might be trading at a price of 11. 75 or so. That is, it is trading at a discount to its theoretical cash sur­ render value. This is a fairly common occurrence, both for structured products and for closed-end mutual funds. If the discount were large enough, it should serve to attract buyers, for if they were to hold to maturity, they would make an extra 4 7 cents (the amount of this discount) from their purchase. That's 4% (0.47 divided by 11.75 = 4%) over five years, which is nothing great, but it's something. Why does the product trade at a discount? Because of supply and demand. It is free to trade at any price - premium or discount - because there is nothing to keep it fixed at the theoretical cash surrender value. If there is excess demand or supply in the open market, then the price of the structured product will fluctuate to reflect that excess. Eventually, of course, the discount will disappear, but five years prior to maturity, one will often find that the product differs from its theoretical value by somewhat significant amounts. If the discount is large enough, it will attract buyers; alternatively, if there should be a large premium, that should attract sellers. SIS One of the first structured products of this type that came to my attention was one that traded on the AMEX, entitled "Stock Index return Security" or SIS. It also trad­ ed under the symbol SIS. The product was issued in 1993 and matured in 2000, so we have a complete history of its movements. The terms were as follows: The under­ lying index was the S&P Midcap 400 index (symbol: $MID). Issued in June 1993, the original issue price was $10, and $MID was trading at 166.10 on the day of issuance, so that was the striking price. Moreover, buyers were entitled to 115% of the appre­ ciation of $MID above the strike price. Thus, the cash value formula was: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:643 SCORE: 17.00 ================================================================================ Gopter 32: Structured Products 597 Cash value of SIS $10 + $10 x 1.15 x ($MID - 166.10) / 166.10 where Guarantee price = $10 Underlying index: S&P Midcap 400 ($MID) Striking price: 166.10 Participation rate: 115% of the increase of $MID above 166.10 SIS matured seven years later, on June 2, 2000. At the time of issuance, seven-year interest rates were about 5.5%, so the "money in the bank" formula shows that one could have made about 4.7 points on a $10 investment, just by utilizing risk-free gov­ ernment securities: Money in the bank= 10 x e0-055 x 7 = 14.70 We can't simply say that the cost of the imbedded call was 4. 7 points, though, because the participation rate is not 100% - it's greater. So we need to find out the Final Value of $MID that results in the cash value being equal to the "money in the bank" result. Using the cash value formula and inserting all the terms except the final value of $MID, we have the following equation. Note: $MIDMIB stands for the value of $MID that results in the "money in the bank" cash value, as computed above. 14.70 = 10 + 10 X 1.15 X ($MIDMIB 166.10) I 166.10 Solving for $MIDMIB' we get a value of 233.98. Now, convert this to a percent gain of the striking price: Imbedded call price = 233.98 I 166.10 - 1 = 0.4087 Hence, the imbedded call costs 40.87% of the guarantee price. In this example, where the guarantee price was $10, that means the imbedded call cost $4.087. Thus, a more generalized formula for the value of the imbedded call can be construed from this example. This formula only works, though, where the participa­ tion rate is a fixed percentage of the strike price. Imbedded call value= Guarantee price x (Final Index ValueMIB / Striking Price - 1) Final Index ValueMIB is the final index price that results in the cash value being equal to the "money in the bank" calculation, where Money in the bank = Guarantee Price x ert r = risk-free interest rate t = time to maturity Thus, the calculated value of the imbedded call was approximately 4.087 points, which is an implied volatility of just over 26%. At the time, listed short-term options ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:646 SCORE: 8.00 ================================================================================ 600 Part V: Index Options and Futures Solving the following equation for $MID would give the desired answer: Cash Value = 13 = 10 + 11.5 x ($MID/166.l - 1) 3 = 11.5 x $MID/ 166.1 - 11.5 14.5 x 166.1 / 11.5 = $MID 209.43 = $MID So, if $MID were at 209.43, the cash value would be 13 - the price the investor is currently paying for SIS. This is protection of 12.2% down from the current price of 238.54. That is, $MID could decline 12.2% at maturity, from the current price of 238.54 to a price of 209.43, and the investor who bought SIS would break even because it would still have a cash value of 13. Of course, this discount could have been computed using the SIS prices of 13 and 15.02 as well, but many investors prefer to view it in terms of the underlying index - especially if the underlying is a popular and often-cited index such as the S&P 500 or Dow-Jones Industrials. From Figure 32-1, it is evident that the discount persisted throughout the entire life of the product, shrinking more or less linearly until expiration. SIS TRADING AT A DISCOUNT TO THE GUARANTEE PRICE In the previous example, the investor could have bought SIS at a discount to its cash value computation, but if the stock market had declined considerably, he would still have had exposure from his SIS purchase price of 13 down to the guarantee price of 10. The discount would have mitigated his percentage loss when compared to the $MID index itself, but it would be a loss nevertheless. However, there are sometimes occasions when the structured product is trad­ ing at a discount not only to cash value, but also to the guarantee price. This situation occurred frequently in the early trading life of SIS. From Figure 32-1, you can see that in 1995 the cash value was near 11, but SIS was trading at a discount of more than 2 points. In other words, SIS was trading below its guarantee price, while the cash value was actually above the guarantee price. It is a "double bonus" for an investor when such a situation occurs. Example: In February 1995, the following prices existed: $MID: 177.59 SIS: 8.75 For a moment, set aside considerations of the cash value. If one were to buy SIS at 8. 75 and hold it for the 5.5 years remaining until maturity, he would make 1.25 points on his 8.75 investment- a return of 14.3% for the 5.5-year holding period. As a compounded rate of interest, this is an annual compound return of 2.43%. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:647 SCORE: 13.00 ================================================================================ Cl,apter 32: Structured Produds 601 Now, a rate of return of 2.43% is rather paltry considering that the risk-free T•bill rate was more than twice that amount. However, in this case, you own a call option on the stock market and get to earn 2.43% per year while you own the call. In other words, "they" are paying you to own a call option! That's a situation that doesn't arise too often in the world of listed options. If we introduce cash value into this computation, the discrepancy is even larg­ er. Using the $MID price of 177.59, the cash value can be computed as: Cash Value = 10 + 11.5 x (177.59/166.10 - 1) = 10.80 Thus, with SIS trading at 8. 75 at that time, it was actually trading at a whopping 19% discount to its cash value of 10.80. Even if the stock market declined, the guar­ antee price of 10 was still there to provide a minimal return. In actual practice, a structured product will not normally trade at a discount to its guarantee price while the cash value is higher than the guarantee price. There's only a narrow window in which that occurs. There have been times when the stock market has declined rather substantial­ ly while these products existed. We can observe the discounts at which they then traded to see just how they might actually behave on the downside if the stock mar­ ket declined after the initial offering date. Consider this rather typical example: Example: In 1997, Merrill Lynch offered a structured product whose underlying index was Japan's Nikkei index. At the time, the Nikkei was trading at 20,351, so that was the striking price. The participation rate was 140% of the increase of the Nikkei above 20,351 - a very favorable participation rate. This structured product, trading under the symbol JEM, was designed to mature in five years, on June 14, 2002. As it turned out, that was about the peak of the Japanese market. By October of 1998, when markets worldwide were having difficulty dealing with the Russian debt crisis and the fallout from a major hedge fund in the U.S. going broke, the Nikkei had plummeted to 13,300. Thus, the Nikkei would have had to increase in price by just over 50% merely to get back to the striking price. Hence, it would not appear that JEM was ever going to be worth much more than its guarantee price of 10. Since we have actual price histories of JEM, we can review how the market­ place viewed the situation. In October 1998, JEM was actually trading at 8.75 - only 1.25 points below its guarantee price. That discount equates to an annual com­ pounded rate of 3.64%. In other words, if one were to buy JEM at 8.75 and it matured at 10 about 40 months later, his return would have been 3.64% compound­ ed annually. That by itself is a rather paltry rate of return, but one must keep in mind that he also would own a call option on the Nikkei index, and that option has a 140% participation rate on the upside. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:648 SCORE: 19.00 ================================================================================ 602 Part V: Index Options and Futures COMPUTING THE VALUE OF THE IMBEDDED CALL WHEN THE UNDERLYING IS TRADING AT A DISCOUNT Can we compute the value of the imbedded call when the structured product itself is trading at a discount to its guarantee price? Yes, the formulae presented earlier can always be used to compute the value of the imbedded call. Example: Again using the example of JEM, the structured product on the Nikkei index, recall that it was trading at 8. 75 with a guaranteed price of 10, with maturity 40 months hence. Assume that the risk-free interest rate at the time was 5.5%. Assuming continuous compounding, $8.75 invested today would be worth $10.51 in 40 months. Money in the bank = 8. 75 x ert where r = 0.05 and t = 3.33 years (40 months) Money in the bank= 8.75 x e0-055 x 3-333 = 10.51 Since the structured product will be worth 10 at maturity, the value of the call is 0.51. There is another, nearly equivalent way to determine the value of the call. It involves determining where the structured product would be trading if it were com­ pletely a zero-coupon debt of the underwriting brokerage. The difference between that value and the actual trading price of the structured product is the value of the imbedded call. The credit rating of the underwriter of the structured product is an important factor in how large a discount occurs. Recall that the guarantee price is only as good as the creditworthiness of the underwriter. The underwriter is the one who will pay the cash settlement value at maturity - not the exchange where the product is listed nor any sort of clearinghouse or corporation. THE ADJUSTMENT FACTOR In recent years, some of the structured products have been issued with an adjustment factor. The adjustment factor is generally a negative thing for investors, although the underwriters try to couch it in language that makes it difficult to discern what is going on. Simply put, the adjustment factor is a multiplier (less than 100%) applied to the underlying index value before calculating the Final Cash Value. Adjustment factors seemed to come into being at about the time that index option implied volatility began to trade at much higher levels than it ever had (1997 onward). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:650 SCORE: 13.00 ================================================================================ 604 Part V: Index Options and Futures Or, thinking in the alternative, if the index triples, then the structured produc1 (before adjustment factor) would be triple its initial price, or 30. Then 30 x 91.25o/c == 27.375. This example begins to demonstrate just how onerous the adjustment factor is. Notice that if the underlying doubles, you don't make "double" less 8.75% (the adjustment factor). No, you make "double" times the adjustment factor - 17.5% - less than double. In the case of tripling, you make 3 x 8.75%, or 26.25%, less than triple (i.e., the structured product is worth 27.375, not 30, so the percentage increase was 173. 75%, not 200% - a difference of 26.25%, stated in terms of the initial invest­ ment). How can that be? It is a result of the adjustment factor being applied to the $SPX price before your profit (cash settlement value) is computed. THE BREAK-EVEN FINAL INDEX VALUE Before discussing the adjustment factor in more detail, one more point should be made: The owner of the structured product doesn't get back anything more than the base value unless the underlying has increased by at least a fixed amount at maturi­ ty. In others words, the underlying must appreciate to a price large enough that the final price times the adjustment factor is greater than the striking price of the struc­ tured product. We'll call this price the break-even final index value. An example will demonstrate this concept. Example: As in the preceding example, suppose tl1at the striking price of the struc­ tured product is 1,100 and the adjustment factor is 8.75%. At what price would the final cash settlement value be something greater than the base value of 10? That price can be solved for with the following simple equation: Break-even final index value== Striking price/ (1- Adjustment factor) = 1,100 / (0.9125) == 1,205.48. Generally speaking, the underlying index must increase in value by a specific amount just to break even. In this case that amount is: 1 / (1 -Adjustment factor) = 1 / 0.9175 = 1.0959 In other words, the underlying index must increase in value by more than 9.5% by maturity just to overcome the weight of the adjustment factor. If the index increas­ es by a lesser amount, then the structured product holder will merely receive back his base value ( 10) at maturity. The previous examples all show that the adjustment factor is not a trivial thing. At first glance, one might not realize just how burdensome it is. After all, one might ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:651 SCORE: 23.00 ================================================================================ 605 himself, what does 1.25% per year really matter? However, you can see that it matter. In fact, our above examples did not even factor in the other cost that any Investor has when his money is at risk - the cost of carry, or what he could have made had he just put the money in the bank. MEASURING THE COST OF THE ADJUSTMENT FACTOR The magnitude of the adjustment increases as the price of the underlying increases. lt is an unusual concept. We know that the structured product initially had an imbedded call option. Earlier in this chapter, we endeavored to price that option. However, with the introduction of the concept of an adjustment factor, it turns out that the call option's cost is not a fixed amount. It varies, depending on the final value of the underlying index. In fact, the cost of the option is a percentage of the final value of the index. Thus, we can't really price it at the beginning, because we don't know what the final value of the index will be. In fact, we have to cease thinking of this option's cost as a fixed number. Rather, it is a geometric cost, if you will, for it increases as the underlying does. Perhaps another way to think of this is to visualize what the cost will be in per­ centage terms. Figure 32-2 compares how much of the percent increase in the index is captured by the structured product in the preceding example. The x-axis on the graph is the percent increase by the index. The y-axis is the percent realized by the structured product. The terms are the same as used in the previous examples: The strike price is 1,100, the total adjustment factor is 8. 75%, and the guarantee price of the structured product is 10. The dashed line illustrates the first example that was shown, when a doubling of the index value (an increase of 100%) to 2,200 resulted in a gain of 83.5% in the price of the structured. Thus, the point (100%, 83.5%) is on the line on the chart where the dashed lines meet. Figure 32-2 points out just how little of the percent increase one captures if the underlying index increases only modestly during the life of the structured product. We already know that the index has to increase by 9.59% just to get to the break-even final price. That point is where the curved line meets the x-axis in Figure 32-2. The curved line in Figure 32-2 increases rapidly above the break-even price, and then begins to flatten out as the index appreciation reaches 100% or so. This depicts the fact that, for small percentage increases in the index, the 8.75% adjust­ ment factor - which is a flat-out downward adjustment in the index price - robs one of most of the percentage gain. It is only when the index has doubled in price or so that the curve stops rising so quickly. In other words, the index has increased enough in value that the structured product, while not capturing all of the percentage gain by any means, is now capturing a great deal of it. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:652 SCORE: 13.00 ================================================================================ 604 Part V: Index Options and Futures Or, thinking in the alternative, if the index triples, then the structured product (before adjustment factor) would be triple its initial price, or 30. Then 30 x 91.25% = 27.375. This example begins to demonstrate just how onerous the adjustment factor is. Notice that if the underlying doubles, you don't make "double" less 8.75% (the adjustment factor). No, you make "double" times the adjustment factor - 17.5% - less than double. In the case of tripling, you make 3 x 8.75%, or 26.25%, less than triple (i.e., the structured product is worth 27.375, not 30, so the percentage increase was 173. 75%, not 200% - a difference of 26.25%, stated in terms of the initial invest­ ment). How can that be? It is a result of the adjustment factor being applied to the $SPX price before your profit (cash settlement value) is computed. THE BREAK-EVEN FINAL INDEX VALUE Before discussing the adjustment factor in more detail, one more point should be made: The owner of the structured product doesn't get back anything more than the base value unless the underlying has increased by at least a fixed amount at maturi­ ty. In others words, the underlying must appreciate to a price large enough that the final price times the adjustment factor is greater than the striking price of the struc­ tured product. We'll call this price the break-even final index value. An example will demonstrate this concept. Example: As in the preceding example, suppose that the striking price of the struc­ tured product is 1,100 and the adjustment factor is 8.75%. At what price would the final cash settlement value be something greater than the base value of 10? That price can be solved for with the following simple equation: Break-even final index value = Striking price/ (1- Adjustment factor) = 1,100 / (0.9125) = 1,205.48. Generally speaking, the underlying index must increase in value by a specific amount just to break even. In this case that amount is: 1 / (1 - Adjustment factor) = 1 / 0.9175 = 1.0959 In other words, the underlying index must increase in value by more than 9.5% by maturity just to overcome the weight of the adjustment factor. If the index increas­ es by a lesser amount, then the structured product holder will merely receive back his base value (10) at maturity. The previous examples all show that the adjustment factor is not a trivial thing. At first glance, one might not realize just how burdensome it is. After all, one might ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:653 SCORE: 23.00 ================================================================================ 605 himself, what does 1.25% per year really matter? However, you can see that it matter. In fact, our above examples did not even factor in the other cost that any htvt?stor has when his money is at risk - the cost of carry, or what he could have made he just put the money in the bank. MIASURING THE COST OF THE ADJUSTMENT FACTOR The magnitude of the adjustment increases as the price of the underlying increases. It is an unusual concept. We know that the structured product initially had an hnbedded call option. Earlier in this chapter, we endeavored to price that option. However, with the introduction of the concept of an adjustment factor, it turns out that the call option's cost is not a fixed amount. It varies, depending on the final value of the underlying index. In fact, the cost of the option is a percentage of the final value of the index. Thus, we can't really price it at the beginning, because we don't know what the final value of the index will be. In fact, we have to cease thinking of this option's cost as a fixed number. Rather, it is a geometric cost, if you will, for it increases as the underlying does. Perhaps another way to think of this is t.o visualize what the cost will be in per­ centage terms. Figure 32-2 compares how much of the percent increase in the index is captured by the structured product in the preceding example. The x-axis on the graph is the percent increase by the index. The y-axis is the percent realized by the structured product. The terms are the same as used in the previous examples: The strike price is 1,100, the total adjustment factor is 8.75%, and the guarantee price of the structured product is 10. The dashed line illustrates the first example that was shown, when a doubling of the index value (an increase of 100%) to 2,200 resulted in a gain of 83.5% in the price of the structured. Thus, the point (100%, 83.5%) is on the line on the chart where the dashed lines meet. Figure 32-2 points out just how little of the percent increase one captures if the underlying index increases only modestly during the life of the structured product. We already know that the index has to increase by 9.59% just to get to the break-even final price. That point is where the curved line meets the x-axis in Figure 32-2. The curved line in Figure 32-2 increases rapidly above the break-even price, and then begins to flatten out as the index appreciation reaches 100% or so. This depicts the fact that, for small percentage increases in the index, the 8.75% adjust­ ment factor -which is a flat-out downward adjustment in the index price - robs one of most of the percentage gain. It is only when the index has doubled in price or so that the curve stops rising so quickly. In other words, the index has increased enough in value that the structured product, while not capturing all of the percentage gain by any means, is now capturing a great deal of it. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:656 SCORE: 15.00 ================================================================================ 608 Part V: Index Options and Future; FIGURE 32-4. Comparison of adiusted and unadiusted cash values at maturity. 50 40 20 0 1100 2200 3300 Cost of the Call Option 4400 5500 Index Final Price (Unadjusted) 6600 est. In this section, a couple of different constructs, ones that have been brought to the public marketplace in the past, are discussed. THE BUI.I. SPREAD Several structured products have represented a bull spread, in effect. In some cases, the structured product terms are stated just like those of a call spread in that the final cash value is defined with both a minimum and a maximum value. For example, it might be described something like this: "The final cash value of the (structured) product is equal to a minimum of a base price of 10, plus any appreciation of the underlying index above the striking price, subject to a maximum price of 20" (where the striking price is stated elsewhere). It's fairly simple to see how this resembles a bull spread: The worst you can do is to get back your $10, which is presumably the initial offering price, just as in any of the structured products described previously in this chapter. Then, above that, you'd get some appreciation of the index price above the stated striking price - again ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:657 SCORE: 29.00 ================================================================================ 609 the products discussed earlier. However, in this case, there is a maximum that the c,1.,;h value can be worth: 20. In other words, there is a ceiling on the value of this 1tructured product at maturity. It is exactly like a bull spread with two striking prices, one at 10 and one at 20. In reality, this structured product would have to be evaluat- using both striking prices. We'll get to that in a minute. There is another way that the underwriter sometimes states the terms of the structured product, but it is also a bull spread in effect. The prospectus might say something to the effect that the structured product is defined pretty much in the standard way, but that it is callable at a certain (higher) price on a certain date. In uther words, someone else can call your structured product away on that date. In effect, you have sold a call with a higher striking price against your structured prod­ Ut1:. Thus, you own an imbedded call via the usual purchase of the structured prod­ uct and you have written a call with a higher strike. That, again, is the definition of a bull spread. When analyzing a product such as this, one must be mindful that there are two calls to price, not only in determining the final value, but more importantly in deter­ mining where you might expect the structured product to trade during its life, prior to maturity. An option strategist knows that a bull spread doesn't widen out to its max­ imum profit potential when there is still a lot of time remaining before expiration, unless the underlying rises by a substantial amount in excess of the higher striking price of the spread. Thus, one would expect this type of structured product to behave in a similar manner. The example that will be used in the rest of this section is based on actual "bull spread" structured products of this type that trade in the open marketplace. Example: Suppose that a structured product is linked to the Internet index. The strike price, based on index values, is 150. If the Internet index is below 150 at matu­ rity, seven years hence, then the structured product will be worth a base value of 10. There is no adjustment factor, nor is there a participation rate factor. So far, this is just the same sort of definition that we've seen in the simpler examples presented previously. The final cash value formula would be simply stated as: Final cash value = 10 x (Final Internet index value/150) However, the prospectus also states that this structured product is callable at a price of 25 during the last month of its life. This call feature means that there is, in effect, a cap on the price of the under­ lying. In actual practice, the call feature may be for a longer or shorter period of time, and may be callable well in advance of maturity. Those factors merely determine the expiration date of the imbedded call that has been "written." ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:658 SCORE: 34.00 ================================================================================ 610 Part V: Index Options and Futures The first thing one should do is to convert the striking price into an equivalent price for the underlying index, so that he can see where the higher striking price is in relation to the index price. In this example, the higher striking price when stated in terms of the structured product is 2.5 times the base price. So the higher striking price, in index terms, would be 2.5 times the striking price, or 375: Index call price = ( Call price / Base price) x Striking price = (25 I 10) X 150 = 375 Hence, if the Internet index rose above 375, the call feature would be "in effect" (i.e., the written call would be in-the-money). The value at which we can expect the structured product to trade, at maturity, would be equal to the base price plus the value of the bull spread with strikes of 10 and 25. Valuing the Bull Spread. Just as the single-strike structured products have an imbedded call option in them, whose cost can be inferred, so do double-strike structured products. The same line of analysis leads to the following: "Theoretical" cash value = 10 + Value of bull spread - Cost of carry Cost of carry refers to the cost of carry of the base price (10 in this example). By using an option model and employing knowledge of bull spreads, one can calculate a theoretical value for the structured product at any time during its life. Moreover, one can decide whether it is cheap or expensive - factors that would lead to a decision as to whether or not to buy. Example: Suppose that the Internet index is trading at a price of 210. What price can we expect the structured product to be trading at? The answer depends on how much time has passed. Let's assume that two years have passed since the inception of the structured product (so there are still five years of life remaining in the option). With the Internet index at 210, it is 40% above the structured product's lower striking price of 150. Thus, the equivalent price for the structured product would be 14. Another way to compute this would be to use the cash value formula: Cash value= 10 x (210 / 150) = 14 Now, we could use the Black-Scholes (or some other) model to evaluate the two calls - one with a striking price of 10 and the other with a striking price of 25. Using a volatility estimate of 50%, and assuming the underlying is at 14, the two calls are roughly valued as follows: Underlying price: 14 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:659 SCORE: 40.00 ================================================================================ Cl,opter 32: Structured Products Option 5-year call, strike = 10 5-year call, strike = 25 Theoretical Price 7.30 3.70 611 Thus, the value of the bull spread would be approximately 3.60 (7.30 minus 3.70). The structured product would then be worth 13.60- the base price of 10, plus the value of the spread: "Theoretical" cash value= 10 + 3.60 - Cost of carry= 13.60 - Cost of carry It may seem strange to say that the value of the structured product is actually less than the cash value, but that is what the call feature does: It reduces the worth of the structured product to values below what the cash value formula would indi­ cate. Given this information, we can predict where the structured product would trade at any price or at any time prior to maturity. Let's look at a more extreme example, then, one in which the Internet index has a tremendously big run to the upside. Example: Suppose that the Internet index has risen to 525 with four years of life remaining until maturity of the structured product. This is well above the index­ equivalent call price of 375. Again, it is first necessary to translate the index price back to an equivalent price of the structured product, using either percentage gains or the cash value formula: Cash value = 10 x (525/ 150) = 35 Again, using the Black-Scholes model, we can determine the following theo­ retical values: Underlying price: 35 Option 3-year c~strike = 10 3-year call, strike = 25 Theoretical Price 25.50 14.70 Now, the value of the bull spread is 10.80 (25.50 minus 14.70). The deepest in­ the-money option is trading near parity, but the (written) option is only 10 points in­ the-money and thus has quite a bit of time value premium remaining, since there are three years of life left: "Theoretical" cash value = 10 + 10.80 = 20.80 - Cost of carry ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:660 SCORE: 11.00 ================================================================================ 612 Part V: Index Options and Futures Hence, even though the Internet index is at 525 - far above the equivalent cal price of 375 - the structured product is expected to be trading at a price well belo\\ its maximum price of 25. Figure 32-5 shows the values over a broad spectrum of prices and for various expiration dates. One can clearly see that the structured product will not trade"near its maximum price of 25 until time shrinks to nearly the maturity date, or until the underlying index rises to very high prices. In particular, note where the theoretical values for the bull spread product lie when the index is at the higher striking price of 375 (there is a vertical line on the chart to aid in identifying those values). The struc­ tured product is not worth 20 in any of the cases, and for longer times to maturity, it isn't even worth 15. Thus, the call feature tends to dampen the upside profit poten­ tial of this product in a dramatic manner. The curves in Figure 32-5 were drawn with the assumption that volatility is 50%. Should volatility change materially during the life of the structured product, then the values would change as well. A lower volatility would push the curves up toward the "at maturity" line, while an increase in volatility would push the curves down even further. FIGURE 32-5. Value of bull spread structured product. At Maturity 25 1 Year Left 20 3Years Left 15 5 100 150 200 250 300 350 400 450 500 550 600 Price of Index ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:661 SCORE: 22.00 ================================================================================ Gtpter 32: Structured Products MULTIPLE EXPIRATION DATES 613 In some cases, more than one expiration date is involved when the structured prod­ uct is issued. These products are very similar to the simple ones first discussed in this chapter. However, rather than maturing on a specific date, the final index value - which is used to determine the final cash value of the structured product - is the average of the underlying index price on two or three different dates. For example, one such listed product was issued in 1996 and used the S&P 500 index ($SPX) as the underlying index. The strike price was the price of $SPX on the day of issuance, as usual. However, there were three maturity dates: one each in April 2001, August 2002, and December 2003. The final index value used to determine the cash settlement value was specified as the average of the $SPX closings on the three maturity dates. In effect, this structured product was really the sum of three separate struc­ tured products, each maturing on a different date. Hence, the values of the imbed­ ded calls could each be calculated separately, using the methods presented earlier. Then those three values could be averaged to determine the overall value of the imbedded call in this structured product. OPTION STRATEGIES INVOLVING STRUCTURED PRODUCTS Since the structured products described previously are similar to well-known option strategies (long call, bull spread, etc.), it is possible to use listed options in conjunc­ tion with the structured products to produce other strategies. These strategies are actually quite simple and would follow the same lines as adjustment strategies dis­ cussed in the earlier chapters of this book. Example: Assume that an investor purchased 15,000 shares of a structured product some time ago. It is essentially a call option on the S&P 500 index ($SPX). The prod­ uct was issued at a price of 10, and that is the guarantee price as well. The striking price is 700, which is where $SPX was trading at the time. However, now $SPX is trading at 1,200, well above the striking price. The cash value of the product is: )ox (1,2001100) = 11.14 Furthermore, assume that there are still two years remaining until maturity of the structured product, and the investor is getting a little nervous about the market. He is thinking of selling or hedging his holding in the structured product. However, the structured product itself is trading at 16.50, a discount of 64 cents from its theo- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:662 SCORE: 21.00 ================================================================================ 614 Part V: Index Options and Futurei retical cash value. He is not too eager to sell at such a discount, but he realizes tha he has a lot of exposure between the current price and the guarantee price of 10. He might consider writing a listed call against his position. That would conver it into the equivalent of a bull spread, since he already holds the equivalent of a lonf call via ownership of the structured product. Suppose that he quotes the $SP) options that trade on the CBOE and finds the following prices for 6-month options expiring in December: $SPX: 1,200 Option December 1,200 call December 1,250 call December 1,300 call Price 85 62 43 Suppose that he likes the sale of the December 1,250 call for 62 points. How many should he sell against his position in order to have a proper hedge? First, one must compute a multiplier that indicates how many shares of the structured product are equivalent to one "share" of the $SPX. That is done in the simple case by dividing the striking price by the guarantee price: Multiplier = Striking price/ Base price = 700 / 10 = 70 This means that buying 70 shares of the structured product is equivalent to being long one share of $SPX. To verify this, suppose that one had bought 70 shares of the structured product initially at a price of 10, when $SPX was at 700. Later, assume that $SPX doubles to 1,400. With the simple structure of this product, which has a 100% participation rate and no adjustment factor, it should also double to 20. So 70 shares bought at 10 and sold at 20 would produce a profit of $700. As for $SPX, one "share" bought at 700 and later sold at 1,400 would also yield a profit of $700. This verifies that the 70-to-l ratio is the correct multiplier. This multiplier can then be used to figure out the current equivalent structured product position in terms of $SPX. Recall that the investor had bought 15,000 shares initially. Since the multiplier is 70-to-l, these 15,000 shares are equivalent to: $SPX equivalent shares = Shares of structured product held/ Multiplier = 15,000 / 70 = 214.29 That is, owning this structured product is the equivalent of owning 214+ shares of $SPX at current prices. Since an $SPX call option is an option on 100 "shares" of $SPX, one would write 2 calls (rounding off) against his structured profit position. Since the SPX December 1,250 calls are selling for 62, that would bring in $12,400 less commissions. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:663 SCORE: 34.00 ================================================================================ 615 Note that the sale of these calls effectively puts a cap on the profit potential of investor's overall position until the December expiration of the listed calls. If $SPX were to rise substantially above 1,250, his profits would be "capped" because the two were sold. Thus, he has effectively taken his synthetic long call position and con­ verted it into a bull spread (or a collared index fund, if you prefer that description). In reality, any calls written against the structured product would have to be margined as naked calls. In a virtual sense, the 15,000 shares of the structured prod­ Ut't "cover" the sale of 2 $SPX calls, but margin rules don't allow for that distinction. In essence, the sale of two calls would create a bull spread. Alternatively, if one thinks uf the structured product as a long index fully protected by a put (which is another way to consider it), then the sale of the $SPX listed call produces a "collar." Of course, one could write more than two $SPX calls, if he had the required margin in his account. This would create the equivalent of a call ratio spread, and would have the properties of that strategy: greatest profit potential at the striking price of the written calls, limited downside profit potential, and theoretically unlim­ ited upside risk if $SPX should rise quickly and by a large amount. In any of these option writing strategies, one might want to write out-of-the­ money, short-term calls against his structured product periodically or continuously. Such a strategy would produce good results if the underlying index does not advance quickly while the written calls are in place. However, if the index should rise through the striking price of the written calls, such a strategy would detract from the overall return of the structured product. Changing the Striking Price. Another strategy that the investor could use if he so desired is to establish a vertical call spread in order to effectively change the striking price of the (imbedded) call. For example, if the market had advanced by a great deal since the product was bought, the imbedded call would theoreti­ cally have a nice profit. If one could sell it and buy another, similar call at a high­ er strike, he would effectively ~olling his call up. This would raise the striking price and would reduce downside risk greatly (at the cost of slightly reducing upside profit potential). Example: Using the same product as in the previous example, suppose that the investor who owns the structured product considers another alternative. In the pre­ vious example, he evaluated the possibility of selling a slightly out-of-the-money list­ ed call to effectively produce a collared position, or a bull spread. The problem with that is that it limits upside profit potential. If the market were to continue to rise, he would only participate up to the higher strike (plus the premium received). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:664 SCORE: 20.00 ================================================================================ 616 Part V: Index Options and Futu, A better alternative might be to roll his imbedded call up, thereby taking s01 money out of the position but still retaining upside profit potential. Recall that t structured product had these terms: Guarantee price: 10 Underlying index: S&P 500 index ($SPX) Striking price: 700 As in the earlier example, the investor owns 15,000 shares of the structun product. Furthermore, assume that there are about two years remaining until mat rity of the structured product, and that the current prices are the same as in the pr vious example: Current price of structured product: 16.50 Current price of $SPX: 1,200 For purposes of simplicity, let's assume that there are listed two-year LEAP options available for the S&P index, whose prices are: S&P 2-year LEAPS, striking price 700: 550 S&P 2-year LEAPS, striking price 1,200: 210 In reality, S&P LEAPS options are normally reduced-value options, meanin. that they are for one-tenth the value of the index and thus sell for one-tenth the pricE However, for the purposes of this theoretical example, we will assume that the full value LEAPS shown here exist. It was shown in the previous example that the investor would trade two of thest calls as an equivalent amount to the quantity of calls imbedded in his structurec product. So, this investor could buy two of the 1,200 calls and sell two of the 700 calli and thereby roll his striking price up from 700 to 1,200. This roll would bring in 34( points, two times; or $68,000 less commissions. Since the difference in the striking prices is 500 points, you can see that he is leaving something "on the table" by receiving only 340 points for the roll-up. This is common when rolling up: One loses the time value premium of the vertical spread. However, when viewed from the perspective of what has been accomplished, the investor might still find this roll worthwhile. He has now raised the striking price of his call to 1,200, based on the S&P index, and has taken in $68,000 in doing so. Since he owns 15,000 shares of the structured product, that means he has taken in 4.53 p~r share (68,000 / 15,000). Now, for example, if the S&P crashes during the next two years and plummets below 700 at the maturity date, he will receive $10 as the guar­ antee price plus the $4.53 he got from the roll - a total "guarantee" of $14.53. Thus, he has protected his downside. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:665 SCORE: 36.00 ================================================================================ Otpt,r 32: Structured Products 617 Note that his downside risk is not completely eliminated, though. The current prke of the structured product is 16.50 and the cash value at the current S&P price 11117.14 (see the previous example for this calculation), so he has risk from these lev­ down to a price of $14.53. His upside is still unlimited, because he is net long two calls - the S&P 2-year 1,,EAPS calls, struck at 1,200. The two LEAPS calls that he sold, struck at 700, effec­ tively offsets the call imbedded in the structured product, which is also struck at 700. This example showed how one could effectively roll the striking price of his structured product up to a higher price after the underlying had advanced. The indi­ vidual investor would have to decide if the extra downside protection acquired is worth the profit potential sacrificed. That depends heavily, of course, on the prices of the listed S&P options, which in turn depend on things such as volatility and time remaining until expiration. Of course, one other alternative exists for a holder of a structured product who has built up a good profit, as in the previous two examples: He could sell the prod­ uct he owns and buy another one with a striking price closer to the current market value of the underlying index. This is not always possible, of course, but as long as these products continue to be brought to market every few months or so by the underwriters, there will be a wide variety of striking prices to choose from. A possi­ ble drawback to rolling to another structured product is that one might have to extend his holding's maturity date, but that is not necessarily a bad thing. A different scenario exists when the underlying index drops after the structured product is bought. In that case, one would own a synthetic call option that might be quite far out-of the-rrwney. A listed call spread could be used to theoretically lower the call's striking price, so that upside movement might more readily produce prof­ its. In such a case, one would sell a listed call option with a striking price equal to the striking price of the structured product and would buy a listed call option with a lower striking price - one more in line with current market values. In other words, he would buy a listed call bull spread to go along with his structured product. Whatever debit he pays for this call bull spread will increase his downside risk, of course. However, in return he ~s the ability to make profits more quickly if the underlying index rises above the new, lower striking price. Many other strategies involving listed options and the structured product could be constructed, of course. However, the ones presented here are the primary strate­ gies that an investor should consider. All that is required to analyze any strategy is to remember that this type of structured product is merely a synthetic long call. Once that concept is in mind, then any ensuing strategies involving listed options can easily be analyzed. For example, the purchase of a listed put with a striking price essential- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:666 SCORE: 10.00 ================================================================================ 618 Part V: Index Options and Future ly equal to that of the structured product would produce a position similar to a 101 straddle. The reader is left to interpret and analyze other such strategies on his OWI LISTS OF STRUCTURED PRODUCTS The descriptions provided so far encompass the great majority of listed structure products. There are many similar ones involving individual stocks instead ofJndice (often called equity-linked notes). The concepts are the same; merely substitute stock price for an index price in the previous discussions in this chapter. Some large insurance companies offer similar products in the form of annuities They behave in exactly the same way as the products described above, except tha there is no continuous market for them. However, they still afford one the opportu­ nity to own an index fund with no risk Many of the insurance company products, in fact, pay interest to the annuity holder - something that most of the products listed on the stock exchanges do not. Both the CBOE and American Exchange Web sites (www.cboe.com and www.amex.com) contain details of the structured products listed on their respective exchanges. A sampling at the time of this writing showed the following breakdowns of listed structured products: Underlying Index Percent of Listed Products Broad-based index (S&P 500, e.g.) 23% Sector index Stocks 43% 34% If you browse those lists, an investor may find indices or stocks that are of particular interest to him. In addition, it may be possible to find ones trading at a substantial discount to cash settlement value, something a strategist might find attractive. PERCS Part II: Products Designed to Provide /,/Income" At the beginning of this chapter, it was stated that most listed structured products~ fall into one of two categories. The first category was the type of structured prod­ uct that resembled the ownership of a call option. The second portion, to be dis- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:667 SCORE: 15.00 ================================================================================ 0.,t,r 32: Structured Products 619 t'Ussed in the remainder of this chapter, resembles the covered write of a call option. These often have names involving the term preferreds. Some are called Trust Preferreds; another popular term for them is Preferred Equity Redemption Cumulative Stock (PERCS). We will use the term PERCS in the following exam­ ples, but the reader should understand that it is being used in a generic sense - that any of the similar types of products could be substituted wherever the term PERCS is used. A PERCS is a structured product, issued with a maturity date and tied to an individual stock. At the time of issuance, the PERCS and the common stock are usu­ ally about the same price. The PERCS pays a higher dividend than the common stock, which may pay no dividend at all. If the underlying common should decline in price, the PERCS should decline by a lesser amount because the higher dividend payout will provide a yield floor, as any preferred stock does. There is a limited life span with PERCS that is spelled out in the prospectus at the time it is issued. Typically, that life span is about three years. At the end of that time, the PERCS becomes ordinary common stock. A PERC S may be called at any time by the issuing corporation if the company's common stock exceeds a predetermined call price. In other words, this PERCS stock is callable. The call price is normally higher than the price at which the common is trading when the PERCS is issued. What one has then, if he owns a PERCS, is a position that will eventually become common stock unless it is called away. In order to compensate him for the fact that it might he called away, the owner receives a higher dividend. What if one substitutes the word "premium" for "higher dividend"? Then the last statement reads: In order to compensate him for the fact that it might be called away, the owner receives a premium. This is exactly the definition of a covered call option write. Moreover, it is an out-of-the-money covered write of a long-term call option, since the call price of the PERCS is akin to a striking price and is higher than the initial stock price. Example: XYZ is selling at $35 per share. XYZ common stock pays $1 a year in div­ idends. The company decides to issue a PERCS. The PERCS will have a three~ life and will be callable at $39. Moreover, the PERCS will pay an annual dividend of $2.50. The PERCS annual dividend rate is 7% as compared to 2.8% for the common stock. If XYZ were to rise to 39 in exactly three years, the PERCS would be called. The total return that the PERCS holder would have made over that time would be: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:668 SCORE: 29.00 ================================================================================ 620 Stock price appreciation 139 - 35): Dividends over 3 years: Total gain Total return: Annualized return: Part V: Index Options and Future. 4 7.50 11.50 11.50/35 = 32.9% 32.9%/3 = 11% If the PERCS were called at an earlier time, the annualized return might be ever higher. · CALL FEATURE The company will most likely call the PER CS if the common is above the call price for even a short period of time. The prospectus for the PERCS will describe any requirements regarding the call. A typical one might be that the common must close above the call price for five consecutive trading days. If it does, then the company may call the PERCS, although it does not have to. The decision to call or not is strict­ ly the company's. The PERCS holder has no choice in the matter of when or if his shares are called. This is the same situation in which the writer of a covered call finds himself: He cannot control when the exercise will occur, although there are often clues, including the disappearance of time value premium in the written listed call option. The PERCS holder is more in the dark, because he cannot actually see the separate price of the imbedded call within the PERCS. Still, as will be shown later, he may be able to use several clues to determine whether a call is imminent. Most PERCS may be called for either cash or common stock. This does not change the profitability from the strategist's standpoint. He either receives cash in the amount of the call price, or the same dollar amount of common stock. The only difference between the two is that, in order to completely close his position, he would have to sell out any common stock received via the call feature. If he had received cash instead, he wouldn't have to bother with this final stock transaction. In the case of most PERCS, the call feature is more complicated than that pre­ sented in the preceding example. Recall that the company that issued the PERCS can call it at any time during the three years, as long as the common is above the call price. The holder of the XYZ PERCS in the example would not be pleased to find that the PER CS was called before he had received any of the higher dividends that the PERCS pays. Therefore, in order to give a PERCS holder essentially the same return no matter when the PERCS is called, there is a "sliding scale" of call prices. - At issuance, the call price will be the highest. Then it will drop to a slightly lower level after some of the dividends have been paid (perhaps after the first year). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:669 SCORE: 19.00 ================================================================================ 621 This lowering of the call price continues as more dividends are paid, until it finally reaches the final call price at maturity. The PERCS holder should not be confused this sliding scale of call prices. The sliding call feature is designed to ensure that PERC S holder is compensated for not receiving all his "promised" dividends if the PERCS should be called prior to maturity. Example: As before, XYZ issues a PERCS when the common is at 35. The PERCS pays an annual dividend of $2.50 per share as compared to $1 per share on the com­ mon stock. The PERCS has a final call price of 39 dollars per share in three years. If XYZ stock should undergo a sudden price advance and rise dramatically in a very short period of time, it is possible that the PERCS could be called before any dividends are paid at all. In order to compensate the PERCS holder for such an c>ecurrence, the initial call price would be set at 43.50 per share. That is, the PERCS can't be called unless XYZ trades to a price over 43.50 dollars per share. Notice that the difference between the eventual call price of 39 and the initial call price of 43.50 is 4.50 points, which is also the amount of additional dividends that the PERCS would pay over the three-year period. The PER CS pays $2.50 per year and the com­ mon $1 per year, so the difference is $1.50 per year, or $4.50 over three years. Once the PERCS dividends begin to be paid, the call price will be reduced to reflect that fact. For example, after one year, the call price would be 42, reflecting the fact that if the PERCS were not called until a year had passed, the PERCS hold­ er would be losing $3 of additional dividends as compared to the common stock ($1.50 per year for the remaining two years). Thus, the call price after one year is set at the eventual call price, 39, plus the $3 of potential dividend loss, for a total call price of 42. This example shows how the company uses the sliding call price to compensate the PERCS holder for potential dividend loss if the PERCS is called before the three-year time to maturity has elapsed. Thus, the PER CS holder will make the same dollars of profit - dividends and price appreciation combined - no matter when the PERCS is called. In the case of the XYZ PERCS in the example, that total dollar profit is $11.50 (see the prior example). Notice that the investor's annualized rate of return would be much higher if he were called prior to the eventual maturity date. One final point: The call price §lides on a scale as set forth in the prospectus for the PERCS. It may be every time a dividend is paid, but more likely it will be daily! That is, the present worth of the remaining dividends is added to the final call price to calculate the sliding call price daily. Do not be overwhelmed by this feature. Remember that it is just a means of giving the PERCS holder his entire "dividend premium" if the PERCS is called before maturity. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:670 SCORE: 30.00 ================================================================================ 622 Part V: Index Options and Futures For the remainder of this chapter, the call price of the PERCS will be referrea to as the redemption price. Since much of the rest of this chapter will be concemec with discussing the fact that a PERCS is related to a call option, there could be somE confusion when the word call is used. In some cases, call could refer to the price at which the PER CS can be called; in other cases, it could refer to a call option - either a listed one or one that is imbedded within the PERCS. Hence, the word redemp­ tion will be used to refer to the action and price at which the issuing compa:J)ly may call the PERCS. A PERCS IS A COVERED CALL WRITE It was stated earlier that a PER CS is like a covered write. However, that has not yet been proven. It is known that any two strategies are equivalent if they have the same profit potential. Thus, if one can show that the profitability of owning a PER CS is the same as that of having established a covered call write, then one can conclude that they are equivalent. Example: For the purposes of this example, suppose that there is a three-year listed call option with striking price 39 available to be sold on XYZ common stock. Also, assume that there is a PERCS on XYZ that has a redemption price of 39 in three years. The following prices exist: XYZ common: 35 XYZ PERCS: 35 3-year call on XYZ common with striking price of 39: 4.50 First, examine the XYZ covered call write's profitability from buying 100 XY2 and selling one call. It was initially established at a debit of 30.50 (35 less the 4.50 received from the call sale). The common pays $1 per year in dividends, for a total of $3 over the life of the position. XYZ Price Price of a Profit/loss on Total Profit/loss in 3 Years 3-Year Call Securities Incl. Dividend 25 0 -$550 -$250 30 0 -50 +250 35 0 +450 +750 39 0 +850 + 1,150 45 6 +850 + 1,150 50 11 +850 + 1,150 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:671 SCORE: 38.00 ================================================================================ O.,,ter 32: Structured Products 623 TI1is is the typical picture of the total return from a covered write - potential losses on the downside with profit potential limited above the striking price of the written call. Now look at the profitability of buying the PER CS at 35 and holding it for three (Assume that it is not called prior to maturity.) The PER CS holder will earn a total of $750 in dividends over that time period. XYZ Price Profit/Loss on Total Profit/Loss in 3 Years PERCS Incl. Dividend 25 -$1,000 -$250 30 -500 +250 35 0 +750 >=39 +400 + 1, 150 This is exactly the same profitability as the covered call write. Therefore, it can be concluded with certainty that a PERCS is equivalent to a covered call write. Note that the PER CS potential early redemption feature does not change the truth of this statement. The early redemption possibility merely allows the PERCS holder to receive the same total dollars at an earlier point in time if the PERCS is demanded prior to maturity. The covered call writer could theoretically be facing a similar situ­ ation if the written call option were assigned before expiration: He would make the same total profit, but he would realize it in a shorter period of time. The PERCS is like a covered write of a call option with striking price equal to the redemption price of the PERCS, except that the holder does not receive a call option premium, but rather receives additional dividends. In essence, the PERCS has a call option imbedded within it. The value of the imbedded call is really the value of the additional dividends to be paid between the current date and maturity. The buyer of a PERCS is, in effect, selling a call option and buying common stock. He should have some idea of whether or not he is selling the option at a rea­ sonably fair price. The next section of this chapter addresses the problem of valuing the call option that is imbedded in the PERCS. PRICE BEHAVIOR The way that a PERCS price is often discussed is in relationship to the common stock. One may hear that the PERCS is trading at the same price as the common or at a premium or discount to the common. As an option strategist who understands covered call writing, it should be a simple matter to picture how the PERCS price will relate to the common price. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:673 SCORE: 18.00 ================================================================================ Oapter 32: Structured Products 625 Another observation that can be made from the figure is that the PERCS pric­ ing curves level off at the redemption price. They cannot sell for more than that price. Now look on the left-hand side of the figure. Notice that the more time remain­ Ing until maturity, the higher the PERCS will trade above the common stock. This is because of the extra dividends that the PER CS pay. Obviously, the PERCS with three years until maturity has the potential to pay more dividends than the one with three months remaining, so the three-year PERCS will sell for more than the six-month PERCS when the common is below the issue price. Since either PERCS pays more dividends than the common, they both trade for higher prices than the common. When the common trades above the issue price (point 'T'), the opposite is true. The six-month PERCS trades for a slightly higher price than the three-year PERCS, but both sell for significantly less than the common, which has no limit on its poten­ tial price. One other observation can be made regarding the situation in which the com­ mon trades well below the issue price: After the last additional dividend has been paid by the PERCS, it will trade for approximately the same price as the common in that situation. · Viewed strictly as a security, a PERCS may not appear all that attractive to some investors. It has much, but not all, of the downside risk of the common stock, and not nearly the upside potential. It does provide a better dividend, however, so if the com­ mon is relatively unchanged from the issue price when the PERCS matures, the PERCS holder will have come out ahead. If this description of the PER CS does not appeal to you, then neither should covered call writing, for it is the same strategy; a call option premium is merely substituted for the higher dividend payout. PERCS STRATEGIES Since the PERCS is equivalent to a covered write, strategies that have covered writes as part of their makeup are amenable to having PERCS as part of their makeup as well. Covered writing is part of ratio writing. Other modifications to the covered writ­ ing strategy itself, such as the protected covered write, can also be applied to the PERCS. PROTECTING THE PERCS WITH LISTED OPTIONS ~ The safest way to protect the PERC S holding with listed options is to buy an out-of the-nwney put. The resultant position - long PERCS and long put - is a protected covered write, or a "collar." The long put prevents large losses on the downside, but it costs the PERCS holder something. He won't make as much from his extra divi­ dend payout, because he is spending money for the listed put. Still, he may want the downside comfort. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:674 SCORE: 22.00 ================================================================================ 626 Part V: Index Options and Futures Once one realizes that a PERCS is equivalent to a covered write, he can easily extend that equivalence to other positions as well. For example, it is known that a covered call write is equivalent to the sale of a naked put. Thus, owning a PERCS is equivalent to the sale of a naked put. Obviously, the easiest way to hedge a naked put is to buy another put, preferably out-of-the-money, as protection. Do not be deluded into thinking that selling a listed call against the PERCS is a safe way of hedging. Such a call option sale does add a modicum of downside pro­ tection, but it exposes the upside to large losses and therefore introduces a potential risk into the position. It is really a ratio write. The subject is covered later in this chapter. REMOVING THE REDEMPTION FEATURE At issuance, the imbedded call is a three-year call, so it is not possible to exactly duplicate the PERCS strategy in the listed market. However, as the PERCS nears maturity, there will be listed calls that closely approximate the call that is imbedded in the PERCS. Consequently, one may be able to use the listed call or the underly­ ing stock to his advantage. If one were to buy a listed call with features similar to the imbedded call in a PERCS that he owned, he would essentially be creating long common stock. Not that one would necessarily need to go to all that trouble to create long common stock, but it might provide opportunities for arbitrageurs. In addition, it might appeal to the PERCS holder if the common stock has declined and the imbedded call is now inexpensive. If one covers the equivalent of the imbedded call in the listed market, he would be able to more fully participate in upside participation if the common were to rally later. This is not always a profitable strategy, however. It may be better to just sell out the PERCS and buy the common if one expects a large rally. Example: XYZ issued a PERCS some time ago. It has a redemption price of 39; the common pays a dividend of $1 per year, while the PER CS pays $2.50 per year. XYZ has fallen to a price of 30 and the PERCS holder thinks a rally may be imminent. He knows that the imbedded call in the PERCS must be relatively inex­ pensive, since it is 9 points out-of-the-money (the PERCS is redeemable at 39, while the common is currently 30). Ifhe could buy back this call, he could participate more fully in the upward potential of the stock. Suppose that there is a one-year LEAPS call on XYZ with a striking price of 40. If one were to buy that call, he would essentially be removing the redemption fea-­ ture from his PERCS. Assume the following prices exist: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:675 SCORE: 9.00 ================================================================================ Gapter 32: Structured Products XYZ Common: 30 XYZ PERCS: 31 XYZ January 40 LEAPS call: 2 627 If one buys this LEAPS call and holds it until maturity of the PERCS one year from now, the profit picture of the long PERCS plus long call position will be the fol­ lowing: Total Value XYZ Price in PERCS January 40 of long PERCS January Next Year Price LEAPS + long LEAPS 25 25 0 25 30 30 0 30 35 35 0 35 40 39 0 39 45 39 5 44 50 39 10 49 Thus, the PE RCS + long call position is worth almost exactly what the common stock is after one year. The PERCS holder has regained his upside profit potential. What did it cost the investor to reacquire his upside? He paid out 2 points for the call, thereby more than negating his $1.50 dividend advantage over the course of the year (the common pays a $1 dividend;'the PERCS $2.50). Thus, it may not actu­ ally be worth the bother. In fact, notice that if the PERCS holder really wanted to reacquire his upside profit potential, he would have been better off selling his PERCS at 31 and buying the common at 30. If he had done this, he would have taken in 1 point from the sale and purchase, which is slightly smaller than the $1.50 divi­ dend he is forsaking. In either case, he must relinquish his dividend advantage and then some in order to reacquire his upside profit potential. This seems fair, however, for there must be some cost involved with reacquiring the upside. Remember that an arbitrageur might be able to find a trade involving these sit­ uations. He could buy a PERCS, sell the common short, and buy a listed call. If there were price discrepancies, he could profit. It is actions such as these that are required to keep prices in their proper relationship. 1 CHANGING THE REDEMPTION PRICE OF THE PERCS When covered writing was discussed as a strategy, it was shown that the writer may want to buy back the call that was written and sell another one at a different strike. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:676 SCORE: 23.00 ================================================================================ 628 Part V: Index Options and Futu, If the action results in a lower strike, it is known as rolling down; if it results in a hi§ er strike, it is rolling up. This rolling action changes the profit potential of the position. If one rolls dov; he gets more downside protection, but his upside is even more limited than it prei ously was. Still, if he is worried about the stock falling lower, this may be a prop action to take. Conversely, if the common is rallying, and the covered writer is mo bullish on the stock, he can roll up in order to increase his upside profit potenti~( course, by rolling up, he creates more downside risk if the common stock should sue denly reverse direction and fall. The PERCS holder can achieve the same results as the covered writer. He ca effectively roll his redemption price down or up if he so chooses. His reasons fc doing so would be substantially the same as the covered writer's. For example, if th common were dropping in price, the PERCS holder might become worried that hi extra dividend income would not be enough to protect him in the case of furthe decline. Therefore, he would want to take in even more premium in exchange fo allowing himself to be called away at a lower price. Example: XYZ issued PERCS when both were trading at 35. Now, XYZ has fallen t< 30 with only a year remaining until maturity, and the PERCS holder is nervous abou further declines. He could, of course, merely sell his stock; but suppose that ht: prefers to keep it and attempt to modify his position to more accurately reflect hb attitude about future price movements. Assume the following prices exist: XYZ Common: 30 XYZ PERCS: 31 XYZ January 40 call: 2 XYZ January 35 call: 4 Ifhe buys the January 40 call and sells the January 35 call, he will have accomplished his purpose. This is the same as selling a call bear spread. As shown in the previous example, buying the January 40 call is essentially the same as removing the redemp­ tion feature from the PERCS. Then, selling the January 35 call will reinstate a redemption feature at 35. Thus, the PERCS holder has taken in a premium of 2 points and has lowered the redemption price. If XYZ is below 35 when the options expire, he will have an extra $200 profit from the option trades. If XYZ rallies and is above 35 at expiration, he will be effec­ tively called away at 37 (the striking price of 35 plus the two points from the rollr, instead of at the original demand price of 39. In actual practice, if the January 35 call ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:677 SCORE: 38.00 ================================================================================ 629 were assigned, the trader could then be simultaneously long the PERCS and short common stock, with a long January 40 call in addition. He would have to unwind pieces separately, an action that might include exercising the January 40 call (if It were in-the-money at expiration) to cover the short common stock. The conclusion that can be drawn is that in order to roll down the redemption fiature of a PERCS, one must sell a vertical call spread. In a similar manner, if he wanted to roll the strike up, he would buy a vertical call spread. Using the same example, one would still buy the January 40 call ( this effectively removes the redemp­ tion feature of the PERCS) and would then sell a January 45 call in order to raise the redemption price. Thus, buying a vertical call spread raises the effective redemption price of a PERCS. There is nothing magic about this strategy. Covered writers use it all the time. It merely evolves from thinking of a PERCS as a covered write. SELLING A CALL AGAINST A LONG PERCS IS A RATIO WRITE It is obvious to the strategist that if one owns a PERCS and also sells a call against it, he does not have a covered write. The PERCS is already a covered write. What he has when he sells another call is a ratio write. His equivalent position is long the com­ mon and short two calls. There is nothing inherently wrong with this, as long as the PERCS holder understands that he has exposed himself to potentially large upside losses by selling the extra call. If the common stock were to rally heavily, the PERCS would stop ris­ ing when it reached its redemption price. However, the additional call that was sold would continue to rise in price, possibly inflicting large losses if no defensive action were taken. The same strategies that apply to ratio writing or straddle writing would have to be used by someone who owns a PERCS and sells a call against it. He could buy com­ mon stock if the position were in danger on the upside, or he could roll the call(s) up. A difference between ordinary ratio writing and selling a listed call option against a PERCS is that the imbedded call in the PERCS may be a very long-term call (up to three years). The listed call probably wouldn't be of that duration. So the ratio writer in this case has two different expiration dates for his options. This does not change the overall strategy, but it does mean that the imbedded long-term call will not diminish much in price due to thepssage of time, until the PERCS is near­ er maturity. Neutrality is normally an important consideration for a ratio writer. If one is long a PERCS and short a listed call, he is by definition a ratio writer, so he should ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:678 SCORE: 54.00 ================================================================================ 630 Part V: Index Options and Futures be interested in neutrality. The key to determining one's neutrality, of course, is tc use the delta of the option. In the case of the PERCS stock, one would have to usE the delta of the imbedded call. Example: An investor is long 1,000 shares ofXYZ PERCS maturing in two years. He thinks XYZ is stuck in a trading range and does not expect much volatility in the near future. Thus, a ratio write appeals to him. How many calls should he sell in order to create a neutral position against his 1,000 shares? First, he needs to compute the delta of the imbedded option in the PER CS, and therefore the delta of the PERCS itself. The delta of a PERCS is not 1.00, as is the delta of common stock. Assume the XYZ PERCS matures in two years. It is redeemable at 39 at that time. XYZ common is currently trading at 33. The delta of a two-year call with strik­ ing price 39 and common stock at 33 can be calculated (the dividends, short-term interest rate, and volatility all play a part). Suppose that the delta of such an option is 0.30. Then the delta of the PER CS can be computed: PERCS delta= 1.00- Delta of imbedded call = 1.00 - 0.30 = 0.70 in this example Assume the following data is known: Security XYZ Common XYZ PERCS XYZ October 40 call Price 33 34 2 Delta 1.00 0.70(!) 0.35 Being long 1,000 PER CS shares is the equivalent of being long 700 shares of common (ESP= 1,000 x 0.70 = 700). In order to properly hedge that ESP with the October 40 call, one would need to sell 20 October 40 calls. Quantity to sell = ESP of PER CS/ESP of October 40 call = 700/(100 shares per option x 0.35) = 700/35 = 20 Thus, the position - long 1,000 PER CS, short 20 October 40 calls - is a neutral one and it is a ratio write. One may not want to have such a steep ratio, since the result of this example is the equivalent of being long 1,000 common and short 30 calls in total (10 are imbed­ ded in the long PERCS). Consequently, he could look at other options - perhaps writing in-the-money October calls - that have higher deltas and won't require so many to be sold in order to produce a neutral position. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:679 SCORE: 27.00 ================================================================================ Cl,apter 32: Structured Produds 631 To remain neutral, one would have to keep computing the deltas of the options, both listed and imbedded, as time passes, because stock movements or the passage of time could change the deltas and therefore affect the neutrality of the position. HEDGING PERCS WITH COMMON STOCK Some traders may want to use the common stock to hedge the purchase of PERCS. These would normally be market-makers or block traders who acquire the PERCS in order to provide liquid markets or because they think they are slightly mispriced. The simplest way for these traders to hedge their long PERCS would be with common stock. This strategy might also apply to an individual who holds PERCS, if he wants to hedge them from a potential price decline but does not actually want to sell them (for tax reasons, perhaps). In either case, it is not correct to sell 100 shares of common against each 100 shares of PERCS owned. That is not a true hedge. In fact, what one accomplishes by doing that is to create a naked call option. A PERCS is a covered write; if one sells 100 shares of common stock from a covered write, he is left with a naked call. This could cause large losses if the common rallies. Rather, the proper way to hedge the PERCS with common stock is to calculate the equivalent stock position of the PERC S and hedge with the calculated amount of common stock. The example showed how to calculate the ESP of the PERCS: One must calculate the delta of the imbedded call option, which may be a long-term one. Then the delta of the PERCS can be computed, and the equivalent stock position can be determined. Example: V sing the same prices from the previous example, one can see how much stock he would have to sell in order to properly hedge his PERCS holding of 1,000 shares. Assume XYZ is trading at 33, and the PE RCS has two years until maturity. If the PERCS is redeemable at 39 at maturity, one can determine that the delta of the imbedded option is 0.30 (see previous example). Then: Delta of PE RCS = 1 - Delta of imbedded call = 1- 0.30 = 0.70 Hence, the equivalent stock position of 1,000 PERCS is 700 shares (1,000 x 0.10). 1 Consequently, one would sell short 700 shares of XYZ common in order to hedge this long holding of 1,000 PERCS. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:680 SCORE: 22.00 ================================================================================ 632 Part V: Index Options and Futures This is not a static situation. If XYZ changes in price, the delta of the imbedded option will change as well, so that the proper amount of stock to sell as a hedge will change. The deltas will change with the passage of time as well. A change in volatili­ ty of the common stock can affect the deltas, too. Consequently, one must constant­ ly recalculate the amount of stock needed to hedge the PERCS. What one has actually created by selling some common stock against his long PERCS holding is another ratio write. Consider the fact that being long 1,000 PE RCS shares is the equivalent of being long 1,000 common and short 10 imbedded, long-term calls. If one sells 700 common, he will be left with an equivalent position of long 300 common and short 10 imbedded calls - a ratio write. The person who chooses to hedge his PER CS holding with a partial sale of com­ mon stock, as in the example, would do well to visualize the resulting hedged posi­ tion as a neutral ratio write. Doing so will help him to realize that there is both upside and downside risk if the underlying common stock should become very volatile (ratio writes have risk on both the upside and the downside). If the common remains fair­ ly stable, the value of the imbedded call will decrease and he will profit. However, if it is a long-term imbedded call (that is, if there is a long time until maturity of the PER CS), the rate of time decay will be quite small; the hedger should realize that fact as well. In summary, the sale of some common against a long holding of PERCS is a viable way to hedge the position. When one hedges in this manner, he must contin­ ue to monitor the position and would be best served by viewing it as a ratio write at all times. SELLING PERCS SHORT Can it make sense to sell PER CS short? The payout of the large dividend seems to be a deterrent against such a short sale. However, if one views it as the opposite of a long-term, out-of-the-money covered write, it may make some sense. A covered write is long stock, short call; it is also equivalent to being long a PERCS. The opposite of that is short stock, long call - a synthetic put. Therefore, a long put is the equivalent of being short a PERCS. Profit graph Hin Appendix D shows the profit potential of being short stock and long a call. There is large down­ side profit potential, but the upside risk is limited by the presence of the long call. The amount of premium paid for the long call is a wasting asset. If the stock does not decline in price, the long call premium may be lost, causing an overall loss. Shorting a PERCS would result in a position with those same qualities. The upside risk is limited by the redemption feature of the PERCS. The downside prof­ it potential is large, because the PER CS will trade down in price if the common stoek ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:681 SCORE: 20.00 ================================================================================ Chapter 32: Structured Products 633 does. The problem for the short seller of the PER CS is that he has to pay a lot for the imbedded call that affords him the protection from upside risk. The actual price that he has to pay is the dividends that he, as a short seller, must pay out. But this can also be thought of as having purchased a long-term call out-of-the-money as protec­ tion for a short sale of common stock. The long-term call is bound to be expensive, since it has a great deal of time premium remaining; moreover, the fact that it is out­ of-the-money means that one is also assuming the price risk from the current com­ mon price up to the strike of the call. Hence, this out-of-the-money amount plus the time value premium of the imbedded call can add up to a substantial amount. This discussion mainly pertains to shorting a PERCS near its issuance price and date. However, one is free to short PERCS at any time if they can be borrowed. They may be a more attractive short when they have less time remaining until the maturi­ ty date, or when the underlying common is closer to the redemption price. Overall, one would not normally expect the short sale of a PERCS to be vastly superior to a synthetic put constructed with listed options. Arbitrageurs would be expected to eliminate such a price discrepancy if one exists. However, if such a situ­ ation does present itself, the short seller of the PERCS should realize he has a posi­ tion that is the equivalent of owning a put, and plan his strategy accordingly. DETERMINING THE ISSUE PRICE An investor might wonder how it is always possible for the PERCS and the common to be at the same price at the issue date. In fact, the issuing company has two vari­ ables to work with to ensure that the common price and the PERCS issue price are the same. One variable is the amount of the additional dividend that the PERCS will pay. The other is the redemption price of the PER CS. By altering these two items, the value of the covered write (i.e., the PERCS) can be made to be the same as the common on the issue date. Figure 32-7 shows the values that are significant in determining the issue price of the PE RCS. The line marked Final Value is the shape of the profit graph of a cov­ ered write at expiration. This is the PERCS's final value at its maturity. The curved line is the value of the covered write at the current time, well before expiration. Of course, these two are linked together. The line marked Common Stock is merely the profit or loss of owning stock. The curved line (present PERCS value) crosses the Common Stock line at the issue price. At the time of issuance, the difference between the current stock price and the eventual maturity value of the PER CS is the present value of all the additional divi­ dends to be paid. That amount is marked a1/11e vertical line on the graph. Therefore, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:683 SCORE: 35.00 ================================================================================ G,pter 32: Strudured Products 635 Such discrepancies will be most notable when there is not a listed option that has terms near the terms of the PERCS's imbedded call. If there is such a listed option, then arbitrageurs should be able to use it and the common stock to bring the PERCS into line. However, if there is not any such listed option available, there may be opportunities for theoretical value traders. Models used for pricing call options, such as the Black-Scholes model, are dis­ cussed in Chapter 28 on mathematical applications. These models can be used to value the imbedded call in the PERCS as well. If the strategist determines the implied value of the imbedded call is out of line, he may be able to make a profitable trade. It is a fairly simple matter to determine the implied value of the imbedded call. The formula to be used is: Imbedded call implied value = Current stock price + Present value of dividends - Current PERCS price The validity of this formula can be seen by referring again to Figure 32-7. The difference between the Final Value (that is, the profit of the covered write at expira­ tion) and the Issue Value or current value of the PERCS is the imbedded call price. That is, the difference between the curved line and the line at expiration is merely the present time value of the imbedded call. Since this formula is describing an out­ of-the-money situation, then the time value of the imbedded call is its entire price. It is also known that the Final Value line differs from the current stock price by the present value of all the additional dividends to be paid by the PERCS until maturity. Thus, the four variables are related by the simple formula given above. Example: XYZ has fallen to 32 after the PERCS was issued. The PERCS is current­ ly trading at 34 and, as in previous examples, the PERCS pays an additional $1.50 per year in dividends. If there are two years remaining until maturity of the PERCS, what is the value of the imbedded call option? First, calculate the present value of the additional dividends. One should calcu­ late the present value of each dividend. Since they are paid quarterly, there will be eight of them between now and maturity. Assume the short-term interest rate is 6%. Each additional quarterly dividend is $0.375 ($1.50 divided by 4). Thus, the present value of the dividend to be paid in three months is: pw = 0.375/(1 + .06)114 = $0.3696 The present value of the dividend to be paid two years from now is: pw = 0.375/(1 + .06)2 = $0.338 i ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:684 SCORE: 17.00 ================================================================================ 636 Part V: Index Options and Futures Adding up all eight of these, it is determined that the present worth of all the remaining additional dividends is $2.81. Note that this is less than the actual amount that will eventually be paid over the two years, which is $3.00. Now, using the simple formula given earlier, the value of the imbedded call can be determined: XYZ: 32 PERCS: 34 Present worth of additional dividends: 2.81 Imbedded call = Stock price + pw divs - PERCS price = 32 + 2.81 - 34 = 0.81 Once this call value is determined, the strategist can use a model to see if this call appears to be cheap or expensive. In this case, the call looks cheap for a two-year call option that is 7 points out-of-the-money. Of course, one would need to know how volatile XYZ stock is, in order to draw a definitive conclusion regarding whether the imbedded call is undervalued or not. A basic relationship can be drawn between the PER CS price and the calculated value of the imbedded call: If the imbedded call is undervalued, then the PERCS is too expensive; if the imbedded call is overpriced, then the PERCS is cheap. In this exam­ ple, the value of the imbedded call was only 81 cents. If XYZ is a stock with average or above average volatility, then the call is certainly cheap. Therefore, the PERCS, trading at 34, is too expensive. Once this determination has been made, the strategist must decide how to use the information. A buyer of PER CS will need to know this information to determine if he is paying too much for the PER CS; alternatively stated, he needs to know if he is selling the imbedded call too cheaply. A hedger might establish a true hedge by buying common and selling the PERCS, using the proper hedge ratio. It is possible for a PER CS to remain expensive for quite some time, if investors are buying it for the additional dividend yield alone and are not giving proper consideration to the limited profit potential. Nevertheless, both the outright buyer and the strategist should calculate the correct value of the PER CS in order to make rational decisions. PERCS SUMMARY A PERCS is a preferred stock with a higher dividend yield than the common, and it is demandable at a predetermined series of prices. The decision to demand is strict­ ly at the discretion of the issuing company; the PER CS holder has no say in the deci- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:685 SCORE: 32.00 ================================================================================ Cl,opter 32: Structured Products 637 :don. The PERCS is equivalent to a covered write of a long-term call option, which is imbedded in the PERCS value. Although there are not many PERCS trading at the current time, that number may grow substantially in the future. Any strategies that pertain to covered call writing will pertain to PER CS as well. Conventional listed options can be used to protect the PERCS from downside risk, to remove the limited upside profit potential, or to effectively change the price at which the PERCS is redeemable. Ratio writes can be constructed by selling a listed call. Shorting PERCS creates a security that is similar to a long put, which might be quite expensive if there is a significant amount of time remaining until maturity of the PERCS. Neutral traders and hedgers should be aware that a PERCS has a delta of its own, which is equal to one minus the delta of the imbedded call option. Thus, hedg­ ing PERCS with common stock requires one to calculate the PERCS delta. Finally, the implied value of the call option that is imbedded with the PERCS can be calculated quite easily. That information is used to determine whether the PERCS is fairly priced or not. The serious outright buyer as well as the option strate­ gist should make this calculation, since a PERCS is a security that is option-related. Either of these investors needs to know if he is making an attractive investment, and calculating the valuation of the imbedded call is the only way to do so. OTHER STRUCTURED PRODUCTS EXCHANGE-TRADED FUNDS Other listed products exist that are simpler in nature than those already discussed, but that the exchanges sometimes refer to as structured products. They often take the form of unit trusts and mutual funds. The general term for these products is Exchange-Traded Funds (ETFs). In a unit trust, an underwriter (Merrill Lynch, for example) packages together 10 to 12 stocks that have similar characteristics; perhaps they are in the same industry group or sector. The underwriter forms a unit trust with these stocks. That is, the shares are held in trust and the resulting entity - the unit trust - can actually be traded as shares of its own. The units are listed on an exchange and trade just like stocks. Example: One of the better-known and popular unit trusts is called the Standard & Poor's Depository Receipt{SPDR). It is a unit trust that exactly matches the S&P 500 index, divided by 10. Th&-SPDR unit trust is affectionately called Spiders (or Spyders). It trades on the AMEX under the symbol SPY. If the S&P 500 index itself is at 1,400, for example, then SPY will be trading near 140. Unit trusts are very active, mostly because they allow any investor to buy an index fund, and to move in and out of it at will. The bid-asked spread differential is very tight, due to the liquidity of the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:687 SCORE: 35.00 ================================================================================ Chapter 32: Structured Products 639 Another major segment of ETFs are called Holding Company Depository Receipts (HOLDRS). They were created by Merrill Lynch and are listed on the AMEX. Options on ETFs. Options are listed on many ETFs. QQQ options, for example, are listed on all of the option exchanges and are some of the most liquid contracts in existence. Things can always change, of course: Witness OEX, which at one time traded a million contracts a day and now barely trades one-thirtieth of that on most days. The options on ETFs can be used as substitutes for many expensive indices. This brings index option trading more into the realm of reasonable cost for the small individual investor. Example: The PHLX Semiconductor index ($SOX) has been a popular index since its inception, especially during the time that tech stocks were roaring. The index, whose options are expensive because of its high statistical volatility, traded at prices between 500 and 1,300 for several years. During that time, both implied and histor­ ical volatility was near 70%. So, for example, if $SOX were at 1,000 and one wanted to buy a three-month at-the-money call, it would cost approximately 135 points. That's $13,500 for one call option. For many investors, that's out of the realm of fea­ sibility. However, there are HOLDRS known as Semiconductor HOLDRS (symbol: SMH). The Semiconductor HOLD RS are composed of 20 stocks (in differing quan­ tities, since it is a capitalization-weighted unit trust) that behave in aggregate in much the same manner as the Semiconductor index ($SOX) does. However, SMH has trad­ ed at prices between 40 and 100 over the same period of time that $SOX was trad­ ing between 500 and 1,300. The implied volatility of SMH options is 70% - just like $SOX options - because the same stocks are involved in both indices. However, a three-month at-the-money call on the $100 SMH, say, would cost only 13.50 points ($1,350) - a much more feasible option cost for most investors and traders. Thus, a strategy that most option traders should keep in mind is one in which ETFs are substituted when one has a trading signal or opinion on a high-priced index. Similarities exist among many of them. For example, the Morgan Stanley High-Tech index ($MSH) is well known for the7eliability of its put-call ratio sentiment signals. However, the index is high-priced and volatile, much like $SOX. Upon examination, though, one can discover that QQQ trades almost exactly like $MSH. So QQQ options and "stock" can be used as a substitute when one wants to trade $MSH. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:688 SCORE: 11.00 ================================================================================ 640 Part V: Index Options and Futures STRUCTURED PRODUCT SUMMARY Structured products whether of the simple style of the Exchange-Traded Fund or the more complicated nature of the PERCS, bull spreads, or protected index funds - can and should be utilized by investors looking for unique ways to protect long­ term holdings in indices or individual stocks. The number of these products is constantly evolving and changing. Thus, anyone interested in trading these items should check the Web sites of the exchanges where the shares are listed. Analytical tools are available on the Web as well. For example, the site www.derivativesmodels.com has over 40 different models especially designed for evaluating options and structured products. They range from the simple Black-Scholes model to models that are designed to evaluate extremely complicated exotic options. All of these products have a place, but the most conservative seem to be the structured products that provide upside market potential while limiting downside risk- the products discussed at the beginning of the chapter. As long as the credit­ worthiness of the underwriter is not suspect, such products can be useful longer­ term investments for nearly everyone who bothers to learn about and understand them. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:689 SCORE: 15.00 ================================================================================ CHAPTER 33 Mathetnatical Considerations for Index Products In this chapter, we look at some riskless arbitrage techniques as they apply to index options. Then a summary of mathematical techniques, especially modeling, is pre­ sented. ARBITRAGE Most of the normal arbitrage strategies have been described previously. We will review them here, concentrating on specific techniques not described in previous chapters on hedging (market baskets) and index spreading. DISCOUNTING We saw that discounting in cash-based options is done with in-the-money options as it is with stock options. However, since the discounter cannot exactly hedge the cash­ based options, he will normally do his discounting near the close of the day so that there is as little time as possible between the time the option is bought and the close of the market. This reduces the risk that the underlying index can move too far before the close of trading. Example: OEX is trading at 673.53 7nd an arbitrageur can buy the June 690 puts for 16. That is a discount of 0.47 since,parity is 16.47. Is this enough of a discount? That is, can the discounter buy this put, hold it unhedged until the close of trading, and 641 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:690 SCORE: 39.00 ================================================================================ 642 Part V: Index Options and Futures exercise it; or is there too great a chance that OEX will rally and wipe out his dis­ count? If he buys this put when there is very little time left in the trading day, it might be enough of a discount. Recall that a one-point move in OEX is roughly equivalent to 15 points on the Dow (while a one-point move in SPX is about 7.5 Dow points). Thus, this O EX discount of 0.4 7 is about equal to 7 Dow points. Obviously, this is not a lot of cushion, because the Dow can easily move that far in a short period of time, so it would be sufficient only if there are just a few minutes of trading left and there were not previous indications oflarge orders to buy "market on close." However, if this situation were presented to the discounter at an earlier time in the trading day, he might defer because he would have to hedge his position and that might not be worth the trouble. If there were several hours left in the trading day, even a discount of a full point would not be enough to allow him to remain unhedged (one full OEX point is about 15 Dow points). Rather, he would, for example, buy futures, buy OEX calls, or sell puts on another index. At the end of the day, he could exercise the puts he bought at a discount and reverse the hedge in the open market. CONVERSIONS AND REVERSALS Conversions and reversals in cash-based options are really the market basket hedges (index arbitrage) described in Chapter 30. That is, the underlying security is actually all the stocks in the index. However, the more standard conversions and reversals can be executed with futures and futures options. Since there is no credit to one's account for selling a future and no debit for buy­ ing one, most futures conversions and reversals trade very nearly at a net price equal to the strike. That is, the value of the out-of-the-money futures option is equal to the time premium of the in-the-money option that is its counterpart in the conversion or reversal. Example: An index future is trading at 179.00. If the December 180 call is trading for 5.00, then the December 180 put should be priced near 6.00. The time value pre­ mium of the in-the-money put is 5.00 (6.00 + 179.00 - 180.00), which is equal to the price of the out-of-the-money call at the same strike. If one were to attempt to do a conversion or reversal with these options, he would have a position with no risk of loss but no possibility of gain: A reversal would be established, for example, at a "net price" of 180. Sell the future at 179, add the premium of the put, 6.00, and subtract the cost of the call, 5.00: 179 + 6.00 - 5.00 = 180.00. As we know from Chapter 27 on arbitrage, one unwinds a conversion or reversal for a "net price" equal to the strike. Hence, there would be no gain or loss from this futures reversal. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:691 SCORE: 67.00 ================================================================================ Chapter 33: Mathematical Considerations for Index Products 643 For index futures options, there is no risk when the underlying closes near the strike, since they settle for cash. One is not forced to make a choice as to whether to exercise his calls. (See Chapter 27 on arbitrage for a description of risks at expiration when trading reversals or conversions.) In actual practice, floor traders may attempt to establish conversions in futures options for small increments - perhaps 5 or 10 cents in S&P futures, for example. The arbitrageur should note that futures options do actually create a credit or debit in the account. That is, they are like stock options in that respect, even though the underlying instrument is not. This means that if one is using a deep in-the-money option in the conversion, there will actually be some carrying cost involved. Example: An index future is trading at 179.00 and one is going to price the December 190 conversion, assuming that December expiration is 50 days away. Assume that the current carrying cost of money is 10% annually. Finally, assume that the December 190 call is selling for 1.00, and the December 190 put is selling for 11.85. Note that the put has a time value premium of only 85 cents, less than the pre­ mium of the call. The reason for this is that one would have to pay a carrying cost to do the December 190 conversion. If one established the 190 conversion, he would buy the futures (no credit or debit to the account), buy the put (a debit of 11.85), and sell the call (a credit of 1.00). Thus, the account actually incurs a debit of 10.85 from the options. The carrying cost for 10.85 at 10% for 50 days is 10.85 x 10% x 50/365 = 0.15. This indicates that the converter is willing to pay 15 cents less time premium for the put (or conversely that the reversal trader is willing to sell the put for 15 cents less time premium). Instead of the put trading with a time value premium equal to the call price, the put will trade with a premium of 15 cents less. Thus, the time premium of the put is 85 cents, rather than being equal to the price of the call, 1.00. BOX SPREADS Recall that a "box" consists of a bullish vertical spread involving two striking prices, and a bearish vertical spread using the same two strikes. One spread is constructed with puts and the other with calls. The profitability of the box is the same regardless of the price of the underlying security at expiration. Box arbitrage with equity options involves trying to buy the box for less than the difference in the striking prices, for ~ple, trying to buy a box in which the strikes are 5 points apart for 4. 75. Selling the box for more than 5 points would represent arbitrage as well. In fact, even selling the box at exactly 5 points would produce a profit for the arbitrageur, since he earns interest on the credit from the sale. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:692 SCORE: 45.00 ================================================================================ 644 Part V: Index Options and Futures These same strategies apply to options on futures. However, boxes on cash­ based options involve another consideration. It is often the case with cash-based options that the box sells for more than the difference in the strikes. For example, a box in which the strikes are 10 points apart might sell for 10.50, a substantial premi­ um over the striking price differential. The reason that this happens is because of the possibility of early assignment. The seller of the box assumes that risk and, as a result, demands a higher price for the box. If he sells the box for half a point more than the striking price differential, then he has a built-in cushion of .50 point of index movement if he were to be assigned early. In general, box strategies are not particularly attractive. However, if the pre­ mium being paid for the box is excessively high, then one should consider selling the box. Since there are four commissions involved, this is not normally a retail strategy. MATHEMATICAL APPLICATIONS The following material is intended to be a companion to Chapter 28 on mathemati­ cal applications. Index options have a few unique properties that must be taken into account when trying to predict their value via a model. The Black-Scholes model is still the model of choice for options, even for index options. Other models have been designed, but the Black-Scholes model seems to give accurate results without the extreme complications of most of the other models. FUTURES Modeling the fair value of most futures contracts is a difficult task. The Black-Scholes model is not usable for that task. Recall that we saw earlier that the fair value of a future contract on an index could be calculated by computing the pres­ ent value of the dividend and also knowing the savings in carrying cost of the futures contract versus buying the actual stocks in the index. CASH-BASED INDEX OPTIONS The futures fair value model for a capitalization-weighted index requires knowing the exact dividend, dividend payment date, and capitalization of each stock in the index (for price-weighted indices, the capitalization is unnecessary). This is the only way of getting the accurate dividend for use in the model. The same dividend calculation must be done for any other index before the Black-Scholes formula can be applied. In the actual model, the dividend for cash-based index options is used in much the same way that dividends are used for stock options: The present value of the div- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:693 SCORE: 22.00 ================================================================================ Chapter 33: Mathematical Considerations for Index Products 64S idend is subtracted from the index price and the model is evaluated using that adjust­ ed stock price. With stock options, there was a second alternative - shortening the time to expiration to be equal to the ex-date - but that is not viable with index options since there are numerous ex-dates. Let's look at an example using the same fictional dividend information and index that were used in Chapter 30 on stock index hedging strategies. Example: Assume that we have a capitalization-weighted index composed of three stocks: AAA, BBB, and CCC. The following table gives the pertinent information regarding the dividends and floats of these three stocks: Dividend Days until Stock Amount Dividend Float AAA 1.00 35 50,000,000 BBB 0.25 60 35,000,000 CCC 0.60 8 120,000,000 Divisor: 150,000,000 One first computes the present worth of each stock's dividend, multiplies that amount by the float, and then divides by the index divisor. The sum of these compu­ tations for each stock gives the total dividend for the index. The present worth of the dividend for this index is $0.8667. Assume that the index is currently trading at 175.63 and that we want to evalu­ ate the theoretical value of the July 175 call. Then, using the Black-Scholes model, we would perform the following calculations: 1. Subtract the present worth of the dividend, 0.8667, from the current index price of 175.63, giving an adjusted index price of 174.7633. 2. Evaluate the call's fair value using 17 4. 7633 as the stock price. All other variables are as they are for stocks, including the risk-free interest rate at its actual value (10%, for example). The theoretical value for puts is computed in the same way as for equity options, by using the arbitrage model. This is sufficient for cash-based index options because it is possible - albeit difficult to hedge these options by buying or selling the entire index. Thus, the options should reflect the potential for such arbitrage. The put value should, of course, reflect the potential for dividend arbitrage with the index. The arbitrage valuation model p"resented in Chapter 28 on modeling called for the dividend to be used. For these index puts, one would use the present worth of ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:694 SCORE: 46.00 ================================================================================ 646 Part V: Index Options and Futures the dividend on the index - the same one that was used for the call valuation, as in the last example. THE IMPLIED DIVIDEND If one does not have access to all of the dividend information necessary to make the "present worth of the dividends" calculation (i.e., if he is a private individual or pub­ lic customer who does not subscribe to a computer-based dividend "service"), there is still a way to estimate the present worth of the dividend. All one need do is make the assumption that the market- makers know what the present worth of the dividend is, and are thus pricing the options accordingly. The individual public customer can use this information to deduce what the dividend is. Example: OEX is trading at 700, the June options have 30 days of life remaining, the short-term interest rate is 10%, and the following prices exist: June 700 call: 18.00 June 700 put: 14.50 One can use iterations of the Black-Scholes model to determine what the OEX "dividend" is. In this case, it turns out to be something on the order of $2.10. Briefly, these are the steps that one would need to follow in order to determine this dividend: 1. Assume the dividend is $0.00. 2. Using the assumed dividend, use the Black-Scholes model to determine the implied volatility of the call option, whose price is known (18.00 in the above example). 3. Using the implied volatility determined from step 2 and the assumed dividend, is the arbitrage put value as derived from the Black-Scholes calculations at the end of step 2 roughly equal to the market value of the put (14.50 in the above example)? If yes, you are done. If not, increase the assumed dividend by some nominal amount, say $0.10, and return to step 2. Thus, without having access to complete dividend information, one can use the information provided to him by the marketplace in order to imply the dividend of an index option. The only assumption one makes is that the market-makers know what the dividend is (they most assuredly do). Note that the implied volatility of the options is determined concurrently with the implied dividend (step 2 above). A veiy useful tool, this simple "implied dividend calculator" can be added to any software that employs the Black-Scholes model. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:695 SCORE: 51.00 ================================================================================ O,apter 33: Mathematical Considerations for Index Products EUROPEAN EXERCISE 647 To account for European exercise, one basically ignores the fact that an in-the-money put option's minimum value is its intrinsic value. European exercise puts can trade at a discount to intrinsic value. Consider the situation from the viewpoint of a conver­ sion arbitrage. If one buys stock, buys puts, and sells calls, he has a conversion arbi­ trage. In the case of a European exercise option, he is forced to carry the position to expiration in order to remove it: He cannot exercise early, nor can he be called early. Therefore, his carrying costs will always be the maximum value to expiration. These carrying costs are the amount of the discount of the put value. For a deeply in-the-money put, the discount will be equal to the carrying charges required to carry the striking price to expiration: Carry = s Ji - 1 ] L (1+ r)t Less deeply in-the-money puts, that is, those with deltas less than - 1.00, would not require the full discounting factor. Rather, one could multiply the discounting factor by the absolute value of the put' s delta to arrive at the appropriate discounting factor. FUTURES OPTIONS A modified Black-Scholes model, called the Black Model, can be used to evaluate futures options. See Chapter 29 on futures for a futures discussion. Essentially, the adjustment is as follows: Use 0% as the risk-free rate in the Black-Scholes model and obtain a theoretical call value; then discount that result. Black model: Call value= e-rt x Black-Scholes call value [using r = 0%] where r is the risk-free interest rate and t is the time to expiration in years. The relationship between a futures call theoretical value and that of a put can also be discussed from the model: Call = Put + e-rf(J - s) where f is the futures price ands is the striking price. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:696 SCORE: 54.00 ================================================================================ 648 Part V: Index Options and Futures Example: The following prices exist: ZYX Cash Index: 17 4.49 ZYX December future: 177.00 There are 80 days remaining until expiration, the volatility of ZYX is 15%, and the risk-free interest rate is 6%. In order to evaluate the theoretical value of a ZYX December 185 call, the fol­ lowing steps would be taken: l. Evaluate the regular Black-Scholes model using 185 as the strike, 177.00 as the stock price, 15% as the volatility, 0.22 as the time remaining (80/365), and 0% as the interest rate. Note that the futures price, not the index price, is input to the model as stock price. Suppose that this yields a result of 2.05. 2. Discount the result from step l: Black Model call value = e-(.0 6 x 0-22) x 2.05 = 2.02 In this case, the difference between the Black model and the Black-Scholes model is small (3 cents). However, the discounting factor can be large for longer-term or deeply in-the-money options. The other items of a mathematical nature that were discussed in Chapter 28 on mathematical applications are applicable, without change, to index options. Expected return and implied volatility have the same meaning. Implied volatility can be calcu­ lated by using the Black-Scholes formulas as specified above. Neutral positioning retains its meaning as well. Recall that any of the above the­ oretical value computations gives the delta of the option as a by-product. These deltas can be used for cash-based and futures options just as they are used for stock options to maintain a neutral position. This is done, of course, by calculating the equivalent stock position (or equivalent "index" or "futures" position, in these cases). FOLLOW-UP ACTION The various types of follow-up action that were applicable to stock options are avail­ able for index options as well. In fact, when one has spread options on the same underlying index, these actions are virtually the same. However, when one is doing inter-index spreads, there is another type of follow-up picture that is useful. The rea- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:697 SCORE: 35.00 ================================================================================ Chapter 33: Mathematical Considerations for Index Products 649 son for this is that the spread will have different outcomes not only based on the price of one index, but also based on that index's relationship to the other index. It is possible, for example, that a mildly bullish strategy implemented as an inter-index spread might actually lose money even if one index rose. This could hap­ pen if the other index performed in a manner that was not desirable. If one could have his computer "draw" a picture of several different outcomes, he would have a better idea of the profit potential of his strategy. Example: Assume a put spread between the ZYX and the ABX indices was estab­ lished. An ABX June 180 put was bought at 3.00 and a ZYX June 175 put was sold at 3.00, when the ZYX was at 175.00 and the ABX Index was at 178.00. This spread will obviously have different outcomes if the prices of the ZYX and the ABX move in dra­ matically different patterns. On the surface, this would appear to be a bearish position - long a put at a high­ er strike and short a put at a lower strike. However, the position could make money even in a rising market if the indices move appropriately: If, at expiration, the ZYX and ABX are both at 179.00, for example, then the short option expires worthless and the long option is still worth 1.00. This would mean that a 1-point profit, or $500, was made in the spread ($1,500 profit on the short ZYX puts less a $1,000 loss on the one ABX put). Conversely, a downward movement doesn't guarantee profits either. If the ZYX falls to 170.00 while the ABX declines to 175.00, then both puts would be worth 5 at expiration and there would be no gain or loss in the spread. What the strategist needs in order to better understand his position is a "sliding scale" picture. That is, most follow-up pictures give the outcome (say, at expiration) of the position at various stock or index prices. That is still needed: One would want to see the outcome for ZYX prices of, say, 165 up to 185 in the example. However, in this spread something else is needed: The outcome should also take into account how the ZYX matches up with the ABX. Thus, one might need three (or more) tables of out­ comes, each of which depicts the results as ZYX ranges from 165 up to 185 at expi­ ration. One might first show how the results would look if ZYX were, say, 5 points below ABX; then another table would show ZYX and ABX unchanged from their original relationship (a 3-point differential); finally, another table would show the results if ZYX and ABX were equal at expiration. If the relationship between the two indices were at 3 points at expiration, such a table might look like this: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:698 SCORE: 18.00 ================================================================================ 6S0 Part V: Index Options and Futures Price at Expiration ZYX 165 170 175 180 185 ABX 168 173 178 183 188 ZYX June 175P 10 5 0 0 0 ABX June 1 80P 12 7 2 0 0 Profit +$1,000 +$1,000 +$1,000 0 0 This picture indicates that the position is neutral to bearish, since it makes money even if the indices are unchanged. However, contrast this with the situation in which the ZYX falls to a level 5 points below the ABX by expiration. Price at Expiration ZYX 165 170 175 180 185 ABX 170 175 180 185 190 ZYX June 175P 10 5 0 0 0 ABX June l 80P 10 5 0 0 0 Profit 0 0 0 0 0 In this case, the spread has no potential for profit at all, even if the market col­ lapses. Thus, even a bearish spread like this might not prove profitable if there is an adverse movement in the relationship of the indices. Finally, observe what happens if the ZYX rallies so strongly that it catches up to the ABX. Price at Expiration ZYX 165 170 175 180 185 ABX 165 170 175 180 185 ZYX June 175P 10 5 0 0 0 ABX June 180P 15 10 5 0 0 Profit +$2,500 +$2,500 +$2,500 +$2,500 +$2,500 These tables can be called "sliding scale" tables, because what one is actually doing is showing a different set of results by sliding the ABX scale over slightly each time while keeping the ZYX scale fixed. Note that in the above two tables, the ZYX results are unchanged, but the ABX has been slid over slightly to show a different result. Tables like this are necessary for the strategist who is doing spreads in options with different underlying indices or is trading inter-index spreads. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:699 SCORE: 18.00 ================================================================================ 650 Part V: Index Options and Futures Price at Expiration ZYX 165 170 175 180 185 ABX 168 173 178 183 188 ZYX June 175P 10 5 0 0 0 ABX June 180P 12 7 2 0 0 Profit +$1,000 +$1,000 +$1,000 0 0 This picture indicates that the position is neutral to bearish, since it makes money even if the indices are unchanged. However, contrast this with the situation in which the Z¥X falls to a level 5 points below the ABX by expiration. Price at Expiration ZYX 165 170 175 180 185 ABX 170 175 180 185 190 ZYX June 175P 10 5 0 0 0 ABX June 1 80P 10 5 0 0 0 Profit 0 0 0 0 0 In this case, the spread has no potential for profit at all, even if the market col­ lapses. Thus, even a bearish spread like this might not prove profitable if there is an adverse movement in the relationship of the indices. Finally, observe what happens if the ZYX rallies so strongly that it catches up to the ABX. Price at Expiration ZYX 165 170 175 180 185 ABX 165 170 175 180 185 ZYX June 175P 10 5 0 0 0 ABX June 1 80P 15 10 5 0 0 Profit +$2,500 +$2,500 +$2,500 +$2,500 +$2,500 These tables can be called "sliding scale" tables, because what one is actually doing is showing a different set of results by sliding the ABX scale over slightly each time while keeping the Z¥X scale fixed. Note that in the above two tables, the Z¥X results are unchanged, but the ABX has been slid over slightly to show a different result. Tables like this are necessary for the strategist who is doing spreads in options with different underlying indices or is trading inter-index spreads. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:700 SCORE: 18.00 ================================================================================ 650 ZYX ABX ZYX June 175P ABX June 1 80P Profit 165 168 10 12 +$1,000 170 173 5 7 +$1,000 Part V: Index Options and Futures Price at Expiration 175 180 185 178 183 188 0 0 0 2 0 0 +$1,000 0 0 This picture indicates that the position is neutral to bearish, since it makes money even if the indices are unchanged. However, contrast this with the situation in which the ZYX falls to a level 5 points below the ABX by expiration. Price at Expiration ZYX 165 170 175 180 185 ABX 170 175 180 185 190 ZYX June 175P 10 5 0 0 0 ABX June 1 80P 10 5 0 0 0 Profit 0 0 0 0 0 In this case, the spread has no potential for profit at all, even if the market col­ lapses. Thus, even a bearish spread like this might not prove profitable if there is an adverse movement in the relationship of the indices. Finally, observe what happens if the ZYX rallies so strongly that it catches up to the ABX. Price at Expiration ZYX 165 170 175 180 185 ABX 165 170 175 180 185 ZYX June 175P 10 5 0 0 0 ABX June 1 80P 15 10 5 0 0 Profit +$2,500 +$2,500 +$2,500 +$2,500 +$2,500 These tables can be called "sliding scale" tables, because what one is actually doing is showing a different set of results by sliding the ABX scale over slightly each time while keeping the ZYX scale fixed. Note that in the above two tables, the ZYX results are unchanged, but the ABX has been slid over slightly to show a different result. Tables like this are necessary for the strategist who is doing spreads in options with different underlying indices or is trading inter-index spreads. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:701 SCORE: 18.00 ================================================================================ Cl,apter 33: Mathematical Considerations for Index Products 651 The astute reader will notice that the above example can be generalized by drawing a three-dimensional graph. The X axis would be the price of ZYX; the Y axis would be the dollars of profit in the spread; and instead of "sliding scales," the Z axis would be the price of ABX. There is software that can draw 3-dimensional profit graphs, although they are somewhat difficult to read. The previous tables would then be horizontal planes of the three-dimensional graph. This concludes the chapter on riskless arbitrage and mathematical modeling. Recall that arbitrage in stock options can affect stock prices. The arbitrage techniques outlined here do not affect the indices themselves. That is done by the market basket hedges. It was also known that no new models are necessary for evaluation. For index options, one merely has to properly evaluate the dividend for usage in the standard Black-Scholes model. Future options can be evaluated by set­ ting the risk-free interest rate to 0% in the Black-Scholes model and discounting the result, which is the Black model. ) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:702 SCORE: 59.00 ================================================================================ CHAPTER 34 Futures and Futures Options In the previous chapters on index trading, a particular type of futures option - the index option - was described in some detail. In this chapter, some background infor­ mation on futures themselves is spelled out, and then the broad category of futures options is investigated. In recent years, options have been listed on many types of futures as well as on some physical entities. These include options on things as diverse as gold futures and cattle futures, as well as options on currency and bond futures. Much of the information in this chapter is concerned with describing the ways that futures options are similar to, or different from, ordinary equity and index options. There are certain strategies that can be developed specifically for futures options as well. However, it should be noted that once one understands an option strategy, it is generally applicable no matter what the underlying instrument is. That is, a bull spread in gold options entails the same general risks and rewards as does a bull spread in any stock's options - limited downside risk and limited upside profit potential. The gold bull spread would make its maximum profit if gold futures were above the higher strike of the spread at expiration, just as an equity option bull spread would do if the stock were above the higher strike at expiration. Consequently, it would be a waste of time and space to go over the same strategies again, substituting soybeans or orange juice futures, say, for XYZ stock in all the examples that have been given in the previous chapters of this book. Rather, the concentration will be on areas where there is truly a new or different strategy that futures options provide. Before beginning, it should be pointed out that futures contracts and futures options have far less standardization than equity or index options do. Most futures trade in different units. Most options have different expiration months, expiration times, and striking price intervals. All the different contract specifications are not spelled out here. One should contact his broker or the exchange where the contracts 652 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:703 SCORE: 21.00 ================================================================================ Cl,apter 34: Futures and Futures Options 6S3 are traded in order to receive complete details. However, whenever examples are used, full details of the contracts used in those examples are given. FUTURES CONTRACTS Before getting into options on futures, a few words about futures contracts them­ selves may prove beneficial. Recall that a futures contract is a standardized contract calling for the delivery of a specified quantity of a certain commodity at some future time. Future contracts are listed on a wide variety of commodities and financial instruments. In some cases, one must make or take delivery of a specific quantity of a physical commodity (50,000 bushels of soybeans, for example). These are known as futures on physicals. In others, the futures settle for cash as do the S&P 500 Index futures described in a previous chapter; there are other futures that have this same feature (Eurodollar time deposits, for example). These types of futures are cash­ based, or cash settlement, futures. In terms of total numbers of contracts listed on the various exchanges, the more common type of futures contract is one with a physical commodity underlying it. These are sometimes broken down into subcategories, such as agricultural futures (those on soybeans, oats, coffee, or orange juice) and financial futures (those on U.S. Treasury bonds, bills, and notes). Traders not familiar with futures sometimes get them confused with options. There really is very little resemblance between futures and options. Think of futures as stock with an expiration date. That is, futures contracts can rise dramatically in price and can fall all the way to nearly zero (theoretically), just as the price of a stock can. Thus, there is great potential for risk. Conversely, with ownership of an option, risk is limited. The only real similarity between futures and options is that both have an expiration date. In reality, futures behave much like stock, and the novice should understand that con­ cept before moving on. HEDGING The primary economic function of futures markets is hedging - taking a futures position to offset the risk of actually owning the physical commodity. The physical commodity or financial instrument is known as the "cash." For index futures, this hedging was designed to remove the risk from owning stocks (the "cash market" that underlies index futures). A portfolio manager who owned a large quantity of stocks could sell index futures against the stock to remove much of the price risk of that ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:704 SCORE: 15.00 ================================================================================ 654 Part V: Index Options and Futures stock ownership. Moreover, he is able to establish that hedge at a much smaller com­ mission cost and with much less work than would be required to sell thousands of shares of stock. Similar thinking applies to all the cash markets that underlie futures contracts. The ability to hedge is important for people who must deal in the "cash" market, because it gives them price protection as well as allowing them to be more efficient in their pricing and profitability. A general example may be useful to demon­ strate the hedging concept. Example: An international businessman based in the United States obtains a large contract to supply a Swiss manufacturer. The manufacturer wishes to pay in Swiss francs, but the payment is not due until the goods are delivered six months from now. The U.S. businessman is obviously delighted to have the contract, but perhaps is not so delighted to have the contract paid in francs six months from now. If the U.S. dol­ lar becomes stronger relative to the Swiss franc, the U.S. businessman will be receiv­ ing Swiss francs which will be worth fewer dollars for his contract than he originally thought he would. In fact, if he is working on a narrow profit margin, he might even suffer a loss if the Swiss franc becomes too weak with respect to the dollar. A futures contract on the Swiss franc may be appropriate for the U.S. business­ man. He is "long" Swiss francs via his contract (that is, he will get francs in six months, so he is exposed to their fluctuations during that time). He might sell short a Swiss franc futures contract that expires in six months in order to lock in his current profit margin. Once he sells the future, he locks in a profit no matter what happens. The future's profit and loss are measured in dollars since it trades on a U.S. exchange. If the Swiss franc becomes stronger over the six-month period, he will lose money on the futures sale, but will receive more dollars for the sale of his products. Conversely, if the franc becomes weak, he will receive fewer dollars from the Swiss businessman, but his futures contract sale will show a profit. 111 either case, the futures contract enables him to lock in a future price (hence the name "futures") that is profitable to him at today's level. The reader should note that there are certain specific factors that the hedger must take into consideration. Recall that the hedger of stocks faces possible problems when he sells futures to hedge his stock portfolio. First, there is the problem of sell­ ing futures below their fair value; changes in interest rates or dividend payouts can affect the hedge as well. The U.S. businessman who is attempting to hedge his Swiss francs may face similar problems. Certain items such as short-term interest rates, which affect the cost of carry, and other factors may cause the Swiss franc futures to trade at a premium or discount to the cash price. That is, there is not necessarily a complete one-to-one relationship between the futures price and the cash price. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:705 SCORE: 25.00 ================================================================================ Chapter 34: Futures and Futures Options 655 However, the point is that the businessman is able to substantially reduce the cur­ rency risk, since in six months there could be a large change in the relationship between the U.S. dollar and the Swiss franc. While his hedge might not eliminate every bit of the risk, it will certainly get rid of a very large portion of it. SPECULATING While the hedgers provide the economic function of futures, speculators provide the liquidity. The attraction for speculators is leverage. One is able to trade futures with very little margin. Thus, large percentages of profits and losses are possible. Example: A futures contract on cotton is for 50,000 pounds of cotton. Assume the March cotton future is trading at 60 (that is, 60 cents per pound). Thus, one is con­ trolling $30,000 worth of cotton by owning this contract ($0.60 per pound x 50,000 pounds). However, assume the exchange minimum margin is $1,500. That is, one has to initially have only $1,500 to trade this contract. This means that one can trade cot­ ton on 5% margin ($1,500/$30,000 = 5%). What is the profit or risk potential here? A one-cent move in cotton, from 60 to 61, would generate a profit of $500. One can always determine what a one-cent move is worth as long as he knows the contract size. For cotton, the size is 50,000 pounds, so a one-cent move is 0.01 x 50,000 = $500. Consequently, if cotton were to fall three cents, from 60 to 57, this speculator would lose 3 x $500, or $1,500 - his entire initial investment. Alternatively, a 3-cent move to the upside would generate a profit of $1,500, a 100% profit. This example clearly demonstrates the large risks and rewards facing a specula­ tor in futures contracts. Certain brokerage firms may require the speculator to place more initial margin than the exchange minimum. Usually, the most active customers who have a sufficient net worth are allowed to trade at the exchange minimum mar­ gins; other customers may have to put up two or three times as much initial margin in order to trade. This still allows for a lot of leverage, but not as much as the specu­ lator has who is trading with exchange minimum margins. Initial margin require­ ments can be in the form of cash or Treasury bills. Obviously, if one uses Treasury bills to satisfy his initial margin requirements, he can be earning interest on that money while it serves as collateral for his initial margin requirements. If he uses cash for the initial requirement, he will not earn interest. (Note: Some large customers do earn credit on the cash used for margin requirements in their futures accounts, but most customers do not.) A speculator will also be required to keep his account current daily through the use of maintenance mar~is account is marked to market daily, so unrealized ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:706 SCORE: 16.00 ================================================================================ 656 Part V: Index Options and Futures gains and losses are taken into account as well as are realized ones. If his account loses money, he must add cash into the account or sell out some of his Treasury bills in order to cover the loss, on a daily basis. However, if he makes money, that unreal­ ized profit is available to be withdrawn or used for another investment. Example: The cotton speculator from the previous example sees the price of the March cotton futures contract he owns fall from 60.00 to 59.20 on the first day he owns it. This means there is a $400 unrealized loss in his account, since his holding went down in price by 0.80 cents and a one-cent move is worth $500. He must add $400 to his account, or sell out $400 worth of T-bills. The next day, rumors of a drought in the growing areas send cotton prices much higher. The March future closes at 60.90, up 1.70 from the previous day's close. That represents a gain of $850 on the day. The entire $850 could be withdrawn, or used as initial margin for another futures contract, or transferred to one's stock market account to be used to purchase another investment there. Without speculators, a futures contract would not be successful, for the specu­ lators provide liquidity. Volatility attracts speculators. If the contract is not trading and open interest is small, the contract may be delisted. The various futures exchanges can delist futures just as stocks can be delisted by the New York Stock Exchange. However, when stocks are delisted, they merely trade over-the-counter, since the corporation itself still exists. When futures are delisted, they disappear - there is no over-the-counter futures market. Futures exchanges are generally more aggressive in listing new products, and delisting them if necessary, than are stock exchanges. TERMS Futures contracts have certain standardized terms associated with them. However, trading in each separate commodity is like trading an entirely different product. The standardized terms for soybeans are completely different from those for cocoa, for example, as might well be expected. The size of the contract (50,000 pounds in the cotton example) is often based on the historical size of a commodity delivered to market; at other times it is merely a contrived number ($100,000 face amount of U.S. Treasury bonds, for example). Also, futures contracts have expiration dates. For some commodities (for exam­ ple, crude oil and its products, heating oil and unleaded gasoline), there is a futures contract for every month of the year. Other commodities may have expirations in only 5 or 6 calendar months of the year. These items are listed along with the quotes in a good financial newspaper, so they are not difficult to discover. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:707 SCORE: 21.00 ================================================================================ Gapter 34: Futures and Futures Options 657 The number of expiration months listed at any one time varies from one mar­ ket to another. Eurodollars, for example, have futures contracts with expiration dates that extend up to ten years in the future. T-bond and 10-year note contracts have expiration dates for only about the next year or so. Soybean futures, on the other hand, have expirations going out about two years, as do S&P futures. The day of the expiration month on which trading ceases is different for each commodity as well. It is not standardized, as the third Friday is for stock and index options. Trading hours are different, even for different commodities listed on the same futures exchange. For example, U.S. Treasury bond futures, which are listed on the Chicago Board of Trade, have very long trading hours (currently 8:20 A.M. to 3 P.M. and also 7 P.M. to 10:30 P.M. every day, Eastern time). But, on the same exchange, soy­ bean futures trade a very short day (10:30 A.M. to 2:15 P.M., Eastern time). Some mar­ kets alter their trading hours occasionally, while others have been fixed for years. For example, as the foreign demand for U.S. Treasury bond futures increases, the trad­ ing hours might expand even further. However, the grain markets have been using these trading hours for decades, and there is little reason to expect them to change in the future. · Units of trading vary for different futures contracts as well. Grain futures trade in eighths of a point, 30-year bond futures trade in thirty-seconds of a point, while the S&P 500 futures trade in 10-cent increments (0.10). Again, it is the responsibili­ ty of the trader to familiarize himself with the units of trading in the futures market if he is going to be trading there. Each futures contract has its own margin requirements as well. These conform to the type of margin that was described with respect to the cotton example above: An initial margin may be advanced in the form of collateral, and then daily mark-to­ market price movements are paid for in cash or by selling some of the collateral. Recall that maintenance margin is the term for the daily mark to market. Finally, futures are subject to position limits. This is to prevent any one entity from attempting to comer the market in a particular delivery month of a commodi­ ty. Different futures have different position limits. This is normally only of interest to hedgers or very large speculators. The exchange where the futures trade establishes the position limit. TRADING LIMITS Most futures contracts have some limit on their maximum daily price change. For index futures, it was shown that the limits are designed to act like circuit breakers to prevent the stock market from crashing. Trading limits exist in many futures con- ( ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:708 SCORE: 19.00 ================================================================================ 658 Part V: Index Options and Futures tracts in order to help ensure that the market cannot be manipulated by someone forcing the price to move tremendously in one direction or the other. Another rea­ son for having trading limits is ostensibly to allow only a fixed move, approximately equal to or slightly less than the amount covered by the initial margin requirement, so that maintenance margin can be collected if need be. However, limits have been applied to all futures, some of which don't really seem to warrant a limit - U.S. Treasury bonds, for example. The bond issue is too large to manipulate, and there is a liquid "cash" bond market to hedge with. Regardless, limits are a fact of life in futures trading. Each individual commod­ ity has its own limits, and those limits may change depending on how the exchange views the volatility of that commodity. For example, when gold was trading wildly at a price of more than $700 per ounce, gold futures had a larger daily trading limit than they do at more stable levels of $300 to $400 an ounce (the current limit is a $15 move per day). If a commodity reaches its limit repeatedly for two or three days in a row, the exchange will usually increase the limit to allow for more price movement. The Chicago Board of Trade automatically increases limits by 50% if a futures con­ tract trades at the limit three days in a row. Whenever limits exist there is always the possibility that they can totally destroy the liquidity of a market. The actual commodity underlying the futures contract is called the "spot" and trades at the "spot price." The spot trades without a limit, of course. Thus, it is possible that the spot commodity can increase in price tremen­ dously while the futures contract can only advance the daily limit each day. This sce­ nario means that the futures could trade "up or down the limit" for a number of days in a row. As a consequence, no one would want to sell the futures if they were trad­ ing up the limit, since the spot was much higher. In those cases there is no trading in the futures - they are merely quoted as bid up the limit and no trades take place. This is disastrous for short sellers. They may be wiped out without ever naving the chance to close out their positions. This sometimes happens to orange juice futures when an unexpected severe freeze hits Florida. Options can help alleviate the illiquidity caused by limit moves. That topic is covered later in this chapter. DELIVERY Futures on physical commodities can be assigned, much like stock options can be assigned. When a futures contract is assigned, the buyer of the contract is called upon to receive the full contract. Delivery is at the seller's option, meaning that the owner of the contract is informed that he must take delivery. Thus, if a corn contract is assigned, one is forced to receive 5,000 bushels of corn. The old adage about this being dumped in your yard is untrue. One merely receives a warehouse receipt and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:709 SCORE: 14.00 ================================================================================ Chapter 34: Futures and Futures Options 659 is charged for storage. His broker makes the actual arrangements. Futures contracts cannot be assigned at any time during their life, as options can. Rather, there is a short period of time before they expire during which one can take delivery. This is generally a 4- to 6-week period and is called the "notice period" - the time during which one can be notified to accept delivery. The first day upon which the futures contract may be assigned is called the "first notice day," for logical reasons. Speculators close out their positions before the first notice day, leaving the rest of the trading up to the hedgers. Such considerations are not necessary for cash-based futures contracts (the index futures), since there is no physical commodity involved. It is always possible to make a mistake, of course, and receive an assignment when you didn't intend to. Your broker will normally be able to reverse the trade for you, but it will cost you the warehouse fees and generally at least one commission. The terms of the futures contract specify exactly what quantity of the commod­ ity must be delivered, and also specify what form it must be in. Normally this is straightforward, as is the case with gold futures: That contract calls for delivery of 100 troy ounces of gold that is at least 0.995 fine, cast either in one bar or in three one­ kilogram bars. However, in some cases, the commodity necessary for delivery is more compli­ cated, as is the case with Treasury bond futures. The futures contract is stated in terms of a nominal 8% interest rate. However, at any time, it is likely that the pre­ vailing interest rate for long-term Treasury bonds will not be 8%. Therefore, the delivery terms of the futures contract allow for delivery of bonds with other interest rates. Notice that the delivery is at the seller's option. Thus, if one is short the futures and doesn't realize that first notice day has passed, he has no problem, for delivery is under his control. It is only those traders holding long futures who may receive a sur­ prise delivery notice. One must be familiar with the specific terms of the contract and its methods of delivery if he expects to deal in the physical commodity. Such details on each futures contract are readily available from both the exchange and one's broker. However, most futures traders never receive or deliver the physical commodity; they close out their futures contracts before the time at which they can be called upon to make delivery. PRICING OF FUTURES It is beyond the scope of this book to describe futures arbitrage versus the cash com­ modity. Suffice it to say that this arbitrage is done, more in some markets (U.S. Treasury bonds, for example) than others (soybeans). Therefore, futures can be over- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:710 SCORE: 51.00 ================================================================================ 660 Part V: Index Options and Futures priced or underpriced as well. The arbitrage possibilities would be calculated in a manner similar to that described for index futures, the futures premium versus cash being the determining factor. OPTIONS ON FUTURES The reader is somewhat familiar with options on futures, having seen many examples of index futures options. The commercial use of the option is to lock in a worst-case price as opposed to a future price. The U.S. businessman from the earlier example sold Swiss franc futures to lock in a future price. However, he might decide instead to buy Swiss franc futures put options to hedge his downside risk, but still leave room for upside profits if the currency markets move in his favor. DESCRIPTION A futures option is an option on the futures contract, not on the cash commodity. Thus, if one exercises or assigns a futures option, he buys or sells the futures contract. The options are always for one contract of the underlying commodity. Splits and adjustments do not apply in the futures markets as they do for stock options. Futures options generally trade in the same denominations as the future itself ( there are a few exceptions to this rule, such as the T-bond options, which trade in sixty-fourths while the futures trade in thirty-seconds). Example: Soybean options will be used to illustrate the above features of futures options. Suppose that March soybeans are selling at 575. Soybean quotes are in cents. Thus, 575 is $5.75 - soybeans cost $5.75 per bushel. A soybean contract is for 5,000 bushels of soybeans, so a one-cent move is worth $50 (5,000 x .01). - Suppose the following option prices exist. The dollar cost of the options is also shown (one cent is worth $50). Option Price Dollar Cost March 525 put 5 $ 250 March 550 call 35 1/2 $1,775 March 600 call 81/4 $ 412.50 The actual dollar cost is not necessary for the option strategist to determine the profitability of a certain strategy. For example, if one buys the March 600 call, he ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:711 SCORE: 54.00 ================================================================================ Chapter 34: Futures and Futures Options 661 needs March soybean futures to be trading at 608.25 or higher at expiration in order to have a profit at that time. This is the normal way in which a call buyer views his break-even point at expiration: strike price plus cost of the call. It is not necessary to know that soybean options are worth $50 per point in order to know that 608.25 is the break-even price at expiration. If the future is a cash settlement future (Eurodollar, S&P 500, and other indices), then the options and futures generally expire simultaneously at the end of trading on the last trading day. (Actually, the S&P's expire on the next morning's opening.) However, options on physical futures will expire before the first notice day of the actual futures contract, in order to give traders time to close out their positions before receiving a delivery notice. The fact that the option expires in advance of the expiration of the underlying future has a slightly odd effect: The option often expires in the month preceding the month used to describe it. Example: Options on March soybean futures are referred to as "March options." They do not actually expire in March - however, the soybean futures do. The rather arcane definition of the last trading day for soybean options is "the last Friday preceding the last business day of the month prior to the contract month by at least 5 business days"! Thus, the March soybean options actually expire in February. Assume that the last Friday of February is the 23rd. If there is no holiday during the business week of February 19th to 23rd, then the soybean options will expire on Friday, February 16th, which is 5 business days before the last Friday of February. However, if President's Day happened to fall on Monday, February 19th, then there would only be four business days during the week of the 19th to the 23rd, so the options would have to expire one Friday earlier, on February 9th. Not too simple, right? The best thing to do is to have a futures and options expi­ ration calendar that one can refer to. Futures Magazine publishes a yearly calendar in its December issue, annually, as well as monthly calendars which are published each month of the year. Alternatively, your broker should be able to provide you with the information. In any case, the March soybean futures options expire in February, well in advance of the first notice day for March soybeans, which is the last business day of the month preceding the expiration month (February 28th in this case). The futures option trader must be careful not to assume that there is a long time between option expiration and first notice day of the futures contract. In certain commodities, the futures first notice day is the day after the options expire (live cattle futures, for example). \ ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:712 SCORE: 37.00 ================================================================================ 662 Part V: Index Options and Futures Thus, if one is long calls or short puts and, therefore, acquires a long futures contract via exercise or assignment, respectively, he should be aware of when the first notice day of the futures is; he could receive a delivery notice on his longfutures posi­ tion unexpectedly if he is not paying attention. OTHER TERMS Striking Price Intervals. Just as futures on differing physical commodities have differing terms, so do options on those futures. Striking price intervals are a prime example. Some options have striking prices 5 points apart, while others have strikes only 1 point apart, reflecting the volatility of the futures contract. Specifically, S&P 500 options have striking prices 5 points apart, while soybean options striking prices are 25 points (25 cents) apart, and gold options are 10 points ($10) apart. Moreover, as is often the case ,vith stocks, the striking price differential for a particular com­ modity may change if the price of the commodity itself is vastly different. Example: Gold is quoted in dollars per ounce. Depending on the price of the futures contract, the striking price interval may be changed. The current rules are: Striking Price Interval $10 $20 $50 Price of Futures below $500/oz. between $500 and $1,000/oz. above $1,000/oz. Thus, when gold futures are more expensive, the striking prices are further apart. Note that gold has never traded above $1,000/oz., but the option exchanges are all set if it does. This variability in the striking prices is common for many commodities. In fact, some commodities alter the striking price interval depending on how much time is remaining until expiration, possibly in addition to the actual prices of the futures themselves. Realizing that the striking price intervals may change - that is, that new strikes will be added when the contract nears maturity - may help to plan some strategies, as it will give more choices to the strategist as to which options he can use to hedge or adjust his position. Automatic Exercise. All futures options are subject to automatic exercise as are stock options. In general, a futures option will be exercised automatically, even if it is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:713 SCORE: 81.00 ================================================================================ Chapter 34: Futures and Futures Options 663 one tick in the money. You can give instructions to not have a futures option auto­ matically exercised if you wish. SERIAL OPTIONS Serial options are futures options whose expiration month is not the same as the expi­ ration month of their corresponding underlying futures. Example: Gold futures expire in February, April, June, August, October, and December. There are options that expire in those months as well. Notice that these expirations are spaced two months apart. Thus, when one gold contract expires, there are two months remaining until the next one expires. Most option traders recognize that the heaviest activity in an option series is in the nearest-term option. If the nearest-term option has two months remaining until expiration, it will not draw the trading interest that a shorter-term option would. Recognizing this fact, the exchange has decided that in addition to the regular expiration, there will be an option contract that expires in the nearest non-cycle rrwnth, that is, in the nearest month that does not have an actual gold future expir­ ing. So, if it were currently January 1, there might be gold options expiring in February, March, April, etc. Thus, the March option would be a serial option. There is no actual March gold future. Rather, the March options would be exercisable into Arpl futures. Serial options are exercisable into the nearest actual futures contract that exists after the options' expiration date. The number of serial option expirations depends on the underlying commodity. For example, gold will always have at least one serial option trading, per the definition highlighted in the example above. Certain futures whose expirations are three months apart (S&P 500 and all currency options) have serial options for the nearest two months that are not represented by an actual futures contract. Sugar, on the other hand, has only one serial option expiration per year - in December - to span the gap that exists between the normal October and March sugar futures expirations. Strategists trading in options that may have serial expirations should be careful in how they evaluate their strategies. For example, June S&P 500 futures options strategies can be planned with respect to where the underlying S&P 500 Index of stocks will be at expiration, for the June options are exercisable into the June futures, which settle at the same price as the Index itself on the last day of trading. However, if one is trading April S&P 500 options, he must plan his strategy on where the June futures contract is going to be trading at April expiration. The April options are exer- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:714 SCORE: 46.00 ================================================================================ 664 Part V: Index Options and Futures cisable into the June futures at April expiration. Since the June futures contract will still have some time premium in it in April, the strategist cannot plan his strategy with respect to where the actual S&P 500 Index will be in April. Example: The S&P 500 Stock Index (symbol SPX) is trading at 410.50. The follow­ ing prices exist: Cash (SPX): 410.50 June futures: 415.00 Options April 415 coll: 5.00 June 415 coll: 10.00 If one buys the June 415 call for 10.00, he knows that the SPX Index will have to rise to 425.00 in order for his call purchase to break even at June expiration. Since the SPX is currently at 410.50, a rise of 14.50 by the cash index itself will be neces­ sary for break-even at June expiration. However, a similar analysis will not work for calculating the break-even price for the April 415 call at April expiration. Since 5.00 points are being paid for the 415 call, the break-even at April expiration is 420. But exactly what needs to be at 420? The June future, since that is what the April calls are exercisable into. Currently, the June futures are trading at a premium of 4.50 to the cash index (415.00 - 410.50). However, by April expiration, the fair value of that premium will have shrunk. Suppose that fair .value is projected to be 3.50 premium at April expi­ ration. Then the SPX would have to be at 416.50 in order for the June futures to be fairly valued at 420.00 (416.50 + 3.50 = 420.00). Consequently, the SPX cash index would have to rise 6 points, from 410.50 to 416.50, in order for the June futures to trade at 420 at April expiration. If this hap­ pened, the April 415 call purchase would break even at expiration. Quote symbols for futures options have improved greatly over the years. Most vendors use the convenient method of stating the striking price as a numeric num­ ber. The only "code" that is required is that of the expiration month. The codes for futures and futures options expiration months are shown in Table 34-1. Thus, a March (2002) soybean 600 call would use a symbol that is something like SH2C600, where S is the symbol for soybeans, H is the symbol for March, 2 means 2002, C stands for call option, and 600 is the striking price. This is a lot simpler and more flex­ ible than stock options. There is no need for assigning striking prices to letters of the alphabet, as stocks do, to everyone's great consternation and confusion. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:715 SCORE: 29.00 ================================================================================ Chapter 34: Futures and Futures Options TABLE 34-1. Month symbols for futures or futures options. Futures or Futures Options Expiration Month Month Symbol January F February G March H April J May K June M July N August Q September u October V November X December z 665 Bid-Offer Spread. The actual markets - bids and offers - for most futures options are not generally available from quote vendors ( options traded on the Chicago Mere are usually a pleasant exception). The same is true for futures con­ tracts themselves. One can always request a ~rket from the trading floor, but that is a time-consuming process and is impractic!al if one is attempting to analyze a large number of options. Strategists who are used to dealing in stock or index options will find this to be a major inconvenience. The situation has persisted for years and shows no sign of improving. Commissions. Futures traders generally pay a commission only on the closing side of a trade. If a speculator first buys gold futures, he pays no commission at that time. Later, when he sells what he is long - closes his position - he is charged a com­ mission. This is referred to as a "round-tum" commission, for obvious reasons. Many futures brokerage firms treat future options the same way - with a round-tum com­ mission. Stock option traders are used to paying a commission on every buy and sell, and there are still a few futures option brokers who treat futures options that way, too. This is an important difference. Consider the following example. Example: A futures option trader has been paying a commission of $15 per side - that is, he pays a commission of $15 per contract each time he buys and sells. His bro- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:716 SCORE: 54.00 ================================================================================ 666 Part V: Index Options and Futures ker informs him one day that they are going to charge him $30 per round tum, payable up front, rather than $15 per side. That is the way most futures option bro­ kerage firms charge their commissions these days. Is this the same thing, $15 per side or $30 round turn, paid up front? No, it is not! What happens if you buy an option and it expires worthless? You have already paid the commission for a trade that, in effect, never took place. Nevertheless, there is little you can do about it, for it has become the industry standard to charge round-turn commission on futures options. In either case, commissions are negotiated to a flat rate by many traders. Discount futures commission merchants (i.e., brokerage houses) often attract business this way. In general, this method of paying commissions is to the customer's benefit. However, it does have a hidden effect that the option trader should pay attention to. This effect makes it potentially more profitable to trade options on some futures than on others. Example: A customer who buys com futures pays $30 per round turn in option com­ missions. Since corn options are worth $50 per one point (one cent), he is paying 0.60 of a point every time he trades a corn option (30/50 = 0.60). Now, consider the same customer trading options on the S&P 500 futures. The S&P 500 futures and options are worth $250 per point. So, he is paying only 0.12 of a point to trade S&P 500 options (30/250 = .12). He clearly stands a much better chance of making money in an S&P 500 option than he does in a corn option. He could buy an S&P option at 5.00 and sell it at 5.20 and make .08 points profit. However, with com options, if he buys an option at 5, he needs to sell it at 55/s to make money- a substantial difference between the two con­ tracts. In fact, if he is participating in spread strategies and trading many options, the differential is even more important. Position limits exist for futures options. While the limits for financial futures are generally large, other futures - especially agricultural ones - may have small limits. A large speculator who is doing spreads might inadvertently exceed a smaller limit. Therefore, one should check with his broker for exact limits in the various futures options before acquiring a large position. ) OPTION MARGINS Futures option margin requirements are generally more logical than equity or index option requirements. For example, if one has a conversion or reversal arbitrage in place, his requirement would be nearly zero for futures options, while it could be quite large for equity options. Moreover, futures exchanges have introduced a better way of margining futures and futures option portfolios. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:717 SCORE: 61.00 ================================================================================ Chapter 34: Futures and Futures Options 667 SPAN Margin. The SPAN margin system (Standard Portfolio ANalysis of Risk) is used by nearly all of the exchanges. SPAN is designed to determine the entire risk of a portfolio, including all futures and options. It is a unique system in that it bases the option requirements on projected movements in the futures contracts as well as on potential changes in implied volatility of the options in one's portfolio. This cre­ ates a more realistic measure of the risk than the somewhat arbitrary requirements that were previously used (called the "customer margin" system) or than those used for stock and index options. Not all futures clearing firms automatically put their customers on SPAN mar­ gin. Some use the older customer margin system for most of their option accounts. As a strategist, it would be beneficial to be under SPAN margin. Thus, one should deal with a broker who will grant SPAN margin. The main advantages of SPAN margin to the strategist are twofold. First, naked option margin requirements are generally less; second, certain long option requirements are reduced as well. This second point may seem somewhat unusual - margin on long options? SPAN calculates the amount of a long option's value that is at risk for the current day. Obviously, if there is time remaining until expiration, a call option will still have some value even if the underlying futures trade down the limit. SPAN attempts to calculate this remaining value. If that value is less than the market price of the option, the excess can be applied toward any other requirement in the portfoliol Obviously, in-the-money options would have a greater excess value under this system. ~ How SPAN Works. Certain basic requirements are determined by the futures exchange, such as the amount of movement by the futures contract that must be mar­ gined (maintenance margin). Once that is known, the exchange's computers gener­ ate an array of potential gains and losses for the next day's trading, based on futures movement within a range of prices and based on volatility changes. These results are stored in a "risk array." There is a different risk array generated for each futures con­ tract and each option contract. The clearing member (your broker) or you do not have to do any calculations other than to see how the quantities of futures and options in your portfolio are affected under the gains or losses in the SPAN risk array. The exchange does all the mathematical calculations needed to project the potential gains or losses. The results of those calculations are presented in the risk array. There are 16 items in the risk array: For seven different futures prices, SPAN projects a gain or loss for both increased and decreased volatility; that makes 14 items. SPAN also projects a profit or loss for an "extreme" upward move and an "extreme" downward move. The futures exchange determines the exact definition of "extreme," and defines "increased" or "decreased" volatility. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:718 SCORE: 15.00 ================================================================================ 668 Part V: Index Options and Futures SPAN "margin" applies to futures contracts as well, although volatility consid­ erations don't mean anything in terms of evaluating the actual futures risk As a first example, consider how SPAN would evaluate the risk of a futures contract. Example: The S&P 500 futures will be used for this example. Suppose that the Chicago Mercantile Exchange determines that the required maintenance margin for the futures is $10,000, which represents a 20-point move by the futures (recall that S&P futures are worth $500 per point). Moreover, the exchange determines that an "extreme" move is 14 points, or $7,000 of risk Scenario Futures unchanged; volatility up Futures unchanged; volatility down Futures up one-third of range; volatility up Futures up one-third of range; volatility down Futures down one-third of range; volatility up Futures down one-third of range; volatility down Futures up two-thirds of range; volatility up Futures up two-thirds of range; volatility down Futures down two-thirds of range; volatility up Futures down two-thirds of range; volatility down Futures up three-thirds of range; volatility up Futures up three-thirds of range; volatility down Futures down three-thirds of range; volatility up Futures down three-thirds of range; volatility down Futures up "extreme" move Futures down "extreme" move Long 1 Future Potential Pit/Loss 0 0 + 3,330 + 3,330 - 3,330 - 3,330 + 6,670 + 6,670 - 6,670 - 6,670 + 10,000 + l 0,000 -10,000 - 10,000 + 7,000 - 7,000 The 16 array items are always displayed in this order. Note that since this array is for a futures contract, the "volatility up" and "volatility down" scenarios are always the same, since the volatility that is referred to is the one that is used as the input to an option pricing model. Notice that the actual price of the futures contract is not needed in order to generate the risk array. The SPAN requirement is always the largest potential loss from the array. Thus, if one were long one S&P 500 futures contract, his SPAN mar­ gin requirement would be $10,000, which occurs under the "futures down three­ thirds" scenarios. This will always be the maintenance margin for a futures contract. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:719 SCORE: 20.00 ================================================================================ Cl,apter 34: Futures and Futures Options 669 Now let us consider an option example. In this type of calculation, the exchange uses the same moves by the underlying futures contract and calculates the option theoretical values as they would exist on the next trading day. One calculation is per­ formed for volatility increasing and one for volatility decreasing. Example: Using the same S&P 500 futures contract, the following array might depict the risk array for a long December 410 call. One does not need to know the option or futures price in order to use the array; the exchange incorporates that information into the model used to generate the potential gains and losses. Scenario Futures unchanged; volatility up Futures unchanged; volatility down Futures up one-third of range; volatility up Futures up one-third of range; volatility down Futures down one-third of range; volatility up Futures down one-third of range; volatility down Futures up two-thirds of range; volatility up Futures up two-thirds of range; volatility down Futures down two-thirds of range; volatility ur Futures down two-thirds of range; volatility /o:n Futures up three-thirds of range; volatility up Futures up three-thirds of range; volatility down Futures down three-thirds of range; volatility up Futures down three-thirds of range; volatility down Futures up "extreme" move Futures down "extreme" move Long 1 Dec 410 call Potential Ph/Loss + 460 610 + 2,640 + 1,730 - 1,270 - 2,340 + 5,210 + 4,540 - 2,540 - 3,430 + 8,060 + 7,640 - 3,380 - 3,990 + 3,130 - 1,500 The items in the risk array are all quite logical: Upward futures movements pro­ duce profits and downward futures movements produce losses in the long call posi­ tion. Moreover, worse results are always obtained by using the lower volatility as opposed to the higher one. In this particular example, the SPAN requirement would be $3,990 ("futures down three-thirds; volatility down"). That is, the SPAN system predicts that you could lose $3,990 of your call value if futures fell by their entire range and volatility decreased - a worst-case scenario. Therefore, that is the amount of margin one is required to keep for this long option position. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:720 SCORE: 14.00 ================================================================================ 670 Part V: Index Options and Futures While the exchange does not tell us how much of an increase or decrease it uses in terms of volatility, one can get something of a feel for the magnitude by looking at the first two lines of the table. The exchange is saying that if the futures are unchanged tomorrow, but volatility "increases," then the call will increase in value by $460 (92 cents); if it "decreases," however, the call will lose $610 (1.22 points) of value. These are large piice changes, so one can assume that the volatility assump­ tions are significant. The real ease of use of the SPAN iisk array is when it comes to evaluating the iisk of a more complicated position, or even a portfolio of options. All one needs to do is to combine the risk array factors for each option or future in the position in order to arrive at the total requirement. Example: Using the above two examples, one can see what the SPAN requirements would be for a covered wiite: long the S&P future and short the Dec 410 call. Short 1 Long Dec 410 call 1 S&P Potential Covered Scenario Future Pft/Loss Write Futures unchanged; vol. up 0 460 - 460 Futures unchanged; vol. down 0 + 610 + 610 Futures up 1 /3 of range; vol. up + 3,330 - 2,640 + 690 Futures up 1 /3 of range; vol. down + 3,330 - 1,730 + 1,600 Futures down 1 /3 of range; vol. up - 3,330 + 1,270 -2,060 Futures down 1 /3 of range; vol. down 3,330 + 2,340 - 990 Futures up 2/3 of range; vol. up + 6,670 - 5,210 + 1,460 Futures up 2/3 of range; vol. down + 6,670 - 4,540 +2, 130 Futures down 2/3 of range; vol. up 6,670 + 2,540 -4, 130 Futures down 2/3 of range; vol. down - 6,670 + 3,430 -3,240 Futures up 3/3 of range; vol. up + 10,000 - 8,060 + 1,940 Futures up 3/3 of range; vol. down + 10,000 - 7,640 +2,360 Futures down 3/3 of range; vol. up -10,000 + 3,380 -6,620 Futures down 3/3 of range; vol. down -10,000 + 3,990 -6,010 Futures up ,, extreme" move + 7,000 - 3,130 +3\870 Futures down "extreme" move - 7,000 + 1,500 -5,500 As might be expected, the worst-case projection for a covered wiite is for the stock to drop, but for the implied volatility to increase. The SPAN system projects that this covered wiiter would lose $6,620 if that happened. Thus, "futures down 3/3 of range; volatility up" is the SPAN requirement, $6,620. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:721 SCORE: 51.00 ================================================================================ Chapter 34: Futures and Futures Options 671 As a means of comparison, under the older "customer margin" option require­ ments, the requirement for a covered write was the futures margin, plus the option premium, less one-half the out-of-the-money amount. In the above example, assume the futures were at 408 and the call was trading at 8. The customer covered write margin would then be more than twice the SPAN requirement: Futures margin Option premium 1/2 out-of-money amount $10,000 + 4,000 - 1,000 $13,000 Obviously, one can alter the quantities in the use of the risk array quite easily. For example, ifhe had a ratio write oflong 3 futures and short 5 December 410 calls, he could easily calculate the SPAN requirement by multiplying the projected futures gains and losses by 3, multiplying the projected option gains and losses by 5, and adding the two together to obtain the total requirement. Once he had completed this calculation, his SPAN requirement would be the worst expected loss as projected by SPAN for the next trading day. In actual practice, the SPAN calculations are even more sophisticated: They take into account a certain minimum option margin (for deeply out-of-the-money options); they account for spreads between futures contracts on the same commodi­ ty (different expiration months); they add a delivery month charge (if you are hold­ ing a position past the first notice day); ~ they even allow for slightly reduced requirements for related, but different, futures spreads (T-bills versus T-bonds, for example). If you are interested in calculating SPAN margin yourself, your broker may be able to provide you with the software to do so. More likely, though, he will provide the service of calculating the SPAN margin on a position prior to your establishing it. The details for obtaining the SPAN margin requirements should thus be requested from your broker. PHYSICAL CURRENCY OPTIONS Another group oflisted options on a physical is the currency options that trade on the Philadelphia Stock Exchange (PHLX). In addition, there is an even larger over-the­ counter market in foreign currency options. Since the physical commodity underly­ ing the option is currency, in some sense of the word, these are cash-based options as well. However, the cash that the options are based in is not dollars, but rather may be deutsche marks, Swiss francs, British pounds, Canadian dollars, French francs, or ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:722 SCORE: 50.00 ================================================================================ 672 Part V: Index Options and Futures Japanese yen. Futures trade in these same currencies on the Chicago Mercantile Exchange. Hence, many traders of the physical options use the Chicago-based futures as a hedge for their positions. Unlike stock options, currency options do not have standardized terms - the amount of currency underlying the option contract is not the same in each of the cases. The striking price intervals and units of trading are not the same either. However, since there are only the six different contracts and since their terms corre­ spond to the details of the futures contracts, these options have had much success. The foreign currency markets are some of the largest in the world, and that size is reflected in the liquidity of the futures on these currencies. The Swiss franc contract will be used to illustrate the workings of the foreign currency options. The other types of foreign currency options work in a similar man­ ner, although they are for differing amounts of foreign currency. The amount of for­ eign currency controlled by the foreign currency contract is the unit of trading, just as 100 shares of stock is the unit of trading for stock options. The unit of trading for the Swiss franc option on the PHLX is 62,500 Swiss francs. Normally, the currency itself is quoted in terms of U.S. dollars. For example, a Swiss franc quote of 0.50 would mean that one Swiss franc is worth 50 cents in U.S. currency. Note that when one takes a position in foreign currency options (or futures), he is simultaneously taking an opposite position in U.S. dollars. That is, if one owns a Swiss franc call, he is long the franc (at least delta long) and is by implication there­ fore short U.S. dollars. Striking prices in Swiss options are assigned in one-cent increments and are stated in cents, not dollars. That is, if the Swiss franc is trading at 50 cents, then there might be striking prices of 48, 49, 50, 51, and 52. Given the unit of trading and the striking price in U.S. dollars, one can compute the total dollars involved in a foreign currency exercise or assignment. Example: Suppose the Swiss franc is trading at 0.50 and there are striking prices of 48, 50, and 52, representing U.S. cents per Swiss franc. If one were to exercise a call with a strike of 48, then the dollars involved in the exercise would be 125,000 (the unit of trading) times 0.48 (the strike in U.S. dollars), or $60,000. Option premiums are stated in U.S. cents. That is, if a Swiss franc option is quoted at 0. 75, its cost is $.0075 times the unit of trading, 125,000, for a total of $937.50. Premiums are quoted in hundredths of a point. That is, the next "tick" from 0.75 would be 0.76. Thus, for the Swiss franc options, each tick or hundredth of a point is equal to $12.50 (.0001 x 125,000). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:723 SCORE: 63.00 ================================================================================ Chapter 34: Futures and Futures Options 673 Actual delivery of the security to satisfy an assignment notice must occur with­ in the country of origin. That is, the seller of the currency must make arrangements to deliver the currency in its country of origin. On exercise or assignment, sellers of currency would be put holders who exercise or call writers who are assigned. Thus, if one were short Swiss franc calls and he were assigned, he would have to deliver Swiss francs into a bank in Switzerland. This essentially means that there have to be agreements between your firm or your broker and foreign banks if you expect to exercise or be assigned. The actual payment for the exercise or assignment takes place between the broker and the Options Clearing Corporation (OCC) in U.S. dol­ lars. The OCC then can receive or deliver the currency in its country of origin, since OCC has arrangements with banks in each country. EXERCISE AND ASSIGNMENT The currency options that trade on the PHLX (Philadelphia Exchange) have exercise privileges similar to those for all other options that we have studied: They can be exercised at any time during their life. Even though PHLX currency options are "cash" options in the most literal sense of the word, they do not expose the writer to the same risks of early assignment that cash-based index options do. Example: Suppose that a currency trader has established the following spread on the PHLX: long Swiss franc December 50 puts, short Swiss franc December 52 puts - a bullish spread. As in any one-to-one spread, there is limited risk. However, the dol­ lar rallies and the Swiss franc falls, pushing the exchange rate down to 48 cents (U.S.) per Swiss franc. Now the puts that were wri,tten - the December 52 contracts - are deeply in-the-money and might be subject to early assignment, as would any deeply in-the-money put if it were trading at a discount. Suppose the trader learns that he has indeed been assigned on his short puts. He still has a hedge, for he is long the December 50 puts and he is now long Swiss francs. This is still a hedged position, and he still has the same limited risk as he did when he started (plus possibly some costs involved in taking physical delivery of the francs). This situation is essentially the same as that of a spreader in stock or futures options, who would still be hedged after an assignment because he would have acquired the stock or future. Contrast this to the cash-based index option, in which there is no longer a hedge after an assignment. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:724 SCORE: 53.00 ================================================================================ 674 Part V: Index Options and Futures FUTURES OPTION TRADING STRATEGIES The strategies described here are those that are unique to futures option trading. Although there may be some general relationships to stock and index option strate­ gies, for the most part these strategies apply only to futures options. It will also be shown - in the backspread and ratio spread examples - that one can compute the profitability of an option spread in the same manner, no matter what the underlying instrument is (stocks, futures, etc.) by breaking everything down into "points" and not "dollars." Before getting into specific strategies, it might prove useful to observe some relationships about futures options and their price relationships to each other and to the futures contract itself. Carrying cost and dividends are built into the price of stock and index options, because the underlying instrument pays dividends and one has to pay cash to buy or sell the stock. Such is not the case with futures. The "investment" required to buy a futures contract is not initially a cash outlay. Note that the cost of carry associated with futures generally refers to the carrying cost of owning the cash commodity itself. That carrying cost has no bearing on the price of a futures option other than to determine the futures price itself. Moreover, the future has no divi­ dends or similar payout. This is even true for something like U.S. Treasury bond options, because the interest rate payout of the cash bond is built into the futures price; thus, the option, which is based on the futures price and not directly on the cash price, does not have to allow for carry, since the future itself has no initial car­ rying costs associated with it. Simplistically, it can be stated that: Futures Call = Futures Put + Futures Price - Strike Price Example: April crude oil futures closed at 18.74 ($18.74 per barrel). The following prices exist: Strike April Call April Put Put + Futures Price Price Price - Strike 17 1.80 0.06 1.80 18 0.96 0.22 0.96 19 0.35 0.61 \ 0.35 20 0.10 1.36 0.10 Note that, at every strike, the above formula is true (Call = Put + Futures - Strike). These are not theoretical prices; they were taken from actual settlement prices on a particular trading day. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:725 SCORE: 40.00 ================================================================================ Chapter 34: Futures and Futures Options 675 In reality, where deeply in-the-money or longer-term options are involved, this simple formula is not correct. However, for most options on a particular nearby futures contract, it will suffice quite well. Examine the quotes in today's newspaper to verify that this is a true statement. A subcase of this observation is that when the futures contract is exactly at the striking price, the call and put with that strike will both trade at the same price. Note that in the above formula, if one sets the futures price equal to the striking price, the last two terms cancel out and one is left with: Call price = Put price. One final observation before getting into strategies: For a put and a call with the same strike, Net change call - Net change put = Net change futures This is a true statement for stock and index options as well, and is a useful rule to remember. Since futures options bid and offer quotes are not always disseminat­ ed by quote vendors, one is forced to use last sales. If the last sales don't conform to the rule above, then at least one of the last sales is probably not representative of the true market in the options. Example: April crude oil is up 50 cents to 19.24. A trader punches up the following quotes on his machine and sees the following prices: Option April 19 call: April 19 put: Last Sale 0.55 0.31 These options conform to the abo~rule: Net change futures = Net change call - Net change put = +0.20 - (-0.30) = +0.50 Net Change + 0.20 - 0.30 The net changes of the call and put indicate the April future should be up 50 cents, which it is. Suppose that one also priced a less active option on his quote machine and saw the following: Option April 17 call: April 17 put: Last Sale 2.10 0.04 Net Change + 0.30 - 0.02 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:726 SCORE: 92.00 ================================================================================ 676 Part V: Index Options and Futures In this case, the formula yields an incorrect result: Net change futures= +0.30 - (-0.02) = +0.32 Since the futures are really up 50 cents, one can assume that one of the last sales is out of date. It is obviously the April 17 call, since that is the in-the-money option; if one were to ask for a quote from the trading floor, that option would probably be indicated up about 48 cents on the day. DELTA While we are on the subject of pricing, a word about delta may be in order as well. The delta of a futures option has the same meaning as the delta of a stock option: It is the amount by which the option is expected to increase in price for a one-point move in the underlying futures contract. As we also know, it is an instantaneous meas­ urement that is obtained by taking the first derivative of the option pricing model. In any case, the delta of an at-the-money stock or index option is greater than 0.50; the more time remaining to expiration, the higher the delta is. In a simplified sense, this has to do with the cost of carrying the value of the striking price until the option expires. But part of it is also due to the distribution of stock price movements - there is an upward bias, and with a long time remaining until expiration, that bias makes call movements more pronounced than put movements. Options on futures do not have the carrying cost feature to deal with, but they do have the positive bias in their price distribution. A futures contract, just like a stock, can increase by more than 100%, but cannot fall more than 100%. Consequently, deltas of at-the-money futures calls will be slightly larger than 0.50. The more time remaining until expiration of the futures option, the higher the at-the­ money call delta will be. Many traders erroneously believe that the delta of an at-the-money futures option is 0.50, since there is no carrying cost involved in the futures conversion or reversal arbitrage. That is not a true statement, since the distribution of futures prices affects the delta as well. As always, for futures options as well as for stock and index options, the delta of a put is related to the delta of a call with the same striking price and expiration date: Delta of put = 1 - Delta of call Finally, the concept of equivalent stock position applies to futures optin strate­ gies, except, of course, it is called the equivalent futures position (EFP). The EFP is calculated by the simple formula: EFP = Delta of option x Option quantity ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:727 SCORE: 64.00 ================================================================================ Chapter 34: Futures and Futures Options 677 Thus, if one is long 8 calls with a delta of 0. 75, then that position has an EFP of 6 (8 x 0.75). This means that being long those 8 calls is the same as being long 6 futures contracts. Note that in the case of stocks, the equivalent stock position formula has anoth­ er factor shares per option. That concept does not apply to futures options, since they are always options on one futures contract. MATHEMATICAL CONSIDERATIONS This brief section discusses modeling considerations for futures options and options on physicals. Futures Options. The Black model (see Chapter 33 on mathematical consider­ ations for index options) is used to price futures options. Recall that futures don't pay dividends, so there is no dividend adjustment necessary for the model. In addition, there is no carrying cost involved with futures, so the only adjustment that one needs to make is to use 0% as the interest rate input to the Black-Scholes model. This is an oversimplification, especially for deeply in-the-money options. One is tying up some money in order to buy an option. Hence, the Black model will discount the price from the Black-Scholes model price. Therefore, the actual pricing model to be used for theoretical evaluation of futures options is the Black model, which is merely the Black-Scholes model, using 0% as the interest rate, and then discounted: Call Theoretical Price = e-rt x Black-Scholes formula [r = O] Recall that it was stated above that: Futures call = Futures put + Future price - Strike price The actual relationship is: ~ Futures call= Futures put+ e-rt (Futures price - Strike price) where r = the short-term interest rate, t = the time to expiration in years, and e-rt = the discounting factor. The short-term interest rate has to be used here because when one pays a debit for an option, he is theoretically losing the interest that he could earn if he had that money in the bank instead, earning money at the short-term interest rate. The difference between these two formulae is so small for nearby options that are not deeply in-the-money that it is normally less than the bid-asked spread in the options, and the first equation can be used. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:728 SCORE: 52.00 ================================================================================ 678 Part V: Index Options and Futures Example: The table below compares the theoretical values computed with the two formulae, where r = 6% and t = 0.25 (1/4 of a year). Furthermore, assume the futures price is 100. The strike price is given in the first column, and the put price is given in the second column. The predicted call prices according to each formula are then shown in the next two columns. Put Formula l Formula 2 Strike Price (Simple) ( Using e-rf) 70 0.25 30.25 29.80 80 1.00 21.00 20.70 90 3.25 13.25 13.10 95 5.35 10.35 10.28 100 7.50 7.50 7.50 105 10.70 5.70 5.77 110 13.90 3.90 4.05 120 21.80 1.80 2.10 For options that are 20 or 30 points in- or out-of-the-money, there is a notice­ able differential in these three-month options. However, for options closer to the strike, the differential is small. If the time remaining to expiration is shorter than that used in the example above, the differences are smaller; if the time is longer, the differences are magnified. Options on Physicals. Determining the fair value of options on physicals such as currencies is more complicated. The proper way to calculate the fair value of an option on a physical is quite similar to that used for stock options. Recall that in the case of stock options, one first subtracts the present worth of the dividend from the current stock price before calculating the option value. A similar process is used for determining the fair value of currency or any other options on physicals. In any of these cases, the underlying security bears interest continuously, instead of quarterly as stocks do. Therefore, all one needs to do is to subtract from the underlying price the amount of interest to be paid until option expiration and then add the amount of accrued interest to be paid. All other inputs into the Black-Scholes model would remain the same, including the risk-free interest rate being equal to the 90-day T-bill rate. Again, the practical option strategist has a shortcut available to him. If one assumes that the various factors necessary to price currencies have been assimilated into the futures markets in Chicago, then one can merely use the futures price as the price of the underlying for evaluating the physical delivery options in Philadelphia. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:729 SCORE: 44.00 ================================================================================ Chapter 34: Futures and Futures Options 679 This will not work well near expiration, since the future expires one week prior to the PHLX option. In addition, it ignores the early exercise value of the PHLX options. However, except for these small differentials, the shortcut will give theoretical values that can be used in strategy-making decisions. Example: It is sometime in April and one desires to calculate the theoretical values of the June deutsche mark physical delivery options in Philadelphia. Assume that one knows four of the basic items necessary for input to the Black-Scholes formula: 60 days to expiration, strike price of 68, interest rate of 10%, and volatility of 18%. But what should be used as the price of the underlying deutsche mark? Merely use the price of the June deutsche mark futures contract in Chicago. STRATEGIES REGARDING TRADING LIMITS The fact that trading limits exist in most futures contracts could be detrimental to both option buyers and option writers. At other times, however, the trading limit may present a unique opportunity. The following section focuses on who might benefit from trading limits in futures and who would not.. Recall that a trading limit in a futures contract limits the absolute number of points that the contract can trade up or down from the previous close. Thus, if the trading limit in T-bonds is 3 points and they closed last night at 7 421132, then the high­ est they can trade on the next day is 7721132, regardless of what might be happening in the cash bond market. Trading limits exist in many futures contracts in order to help ensure that the market cannot be manipulated by someone forcing the price to move tremendously in one direction or the other. Another reason for having trading limits is ostensibly to allow only a fixed move, approximately equal to the amount cov­ ered by the initial margin, so that maintenance margin can be collected if need be. However, limits have been applied in case~which they are unnecessary. For exam­ ple, in T-bonds, there is too much liquidity for anyone to be able to manipulate the market. Moreover, it is relatively easy to arbitrage the T-bond futures contract against cash bonds. This also increases liquidity and would keep the future from trading at a price substantially different from its theoretical value. Sometimes the markets actually need to move far quickly and cannot because of the trading limit. Perhaps cash bonds have rallied 4 points, when the limit is 3 points. This makes no difference when a futures contract has risen as high as it can go for the day, it is bid there (a situation called "limit bid") and usually doesn't trade again as long as the underlying commodity moves higher. It is, of course, possible for a future to be limit bid, only to find that later in the day, the underlying commodity becomes weaker, and traders begin to sell the future, driving it down off the limit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:730 SCORE: 29.00 ================================================================================ 680 Part V: Index Options and Futures Similar situations can also occur on the downside, where, if the future has traded as low as it can go, it is said to be "limit offered." As was pointed out earlier, futures options sometimes have trading limits imposed on them as well. This limit is of the same magnitude as the futures limit. Most of these are on the Chicago Board of Trade (all grains, U.S. Treasury bonds, Municipal Bond Index, Nikkei stock index, and silver), although currency options on the Chicago Mere are included as well. In other markets, options are free to trade, even though futures have effectively halted because they are up or down the limit. However, even in the situations in which futures options themselves have a trading limit, there may be out-of-the-money options available for trading that have not reached their trading limit. When options are still trading, one can use them to imply the price at which the futures would be trading, were they not at their trading limit. Example: August soybeans have been inflated in price due to drought fears, having closed on Friday at 650 ($6.50 per bushel). However, over the weekend it rains heav­ ily in the Midwest, and it appears that the drought fears were overblown. Soybeans open down 30 cents, to 620, down the allowable 30-cent limit. Furthermore, there are no buyers at that level and the August bean contract is locked limit down. No fur­ ther trading ensues. One may be able to use the August soybean options as a price discovery mech­ anism to see where August soybeans would be trading if they were open. Suppose that the following prices exist, even though August soybeans are not trading because they are locked limit down: Lost Sole Net Change Option Price for the Day August 625 call 19 - 21 August 625 put 31 +16 An option strategist knows that synthetic long futures can be created by buying a call and selling a put, or vice versa for short futures. Knowing this, one can tell what price futures are projected to be trading at: Implied Futures Price = Strike Price + Call Price - Put Price = 625 + 19 - 31 = 613 With these options at the prices shown, one can create a synthetic futures posi­ tion at a price of 613. Therefore, the implied price for August soybean futures in this example is 613. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:731 SCORE: 37.00 ================================================================================ Chapter 34: Futures and Futures Options 681 Note that this formula is merely another version of the one previously present­ ed in this chapter. In the example above, neither of the options in question had moved the 30- point limit, which applies to soybean options as well as to soybean futures. If they had, they would not be useable in the formula for implying the price of the future. Only options that are freely trading - not limit up or down - can be used in the above formula. A more complete look at soybean futures options on the day they opened and stayed down the limit would reveal that some of them are not tradeable either: Example: Continuing the above example, August soybeans are locked limit down 30 cents on the day. The following list shows a wider array of option prices. Any option that is either up or down 30 cents on the day has also reached its trading limit, and therefore could not be used in the process necessary to discover the implied price of the August futures contract. last Sale Net Change Option Price for the Day August 550 call 71 - 30 August 575 call 48 30 August 600 call 31 - 26 August 625 call 19 - 21 August 650 call 11 - 15 August 675 call 6 - 10 August 550 put 4 + 3 August 575 put 9 + 6 August 600 put 18 + 11 August 625 put -----------31 + 16 August 650 put 48 + 22 August 675 put 67 + 30 The deeply in-the-money calls, August 550's and August 575's, and the deeply in­ the-money August 675 puts are all at the trading limit. All other options are freely trad­ ing and could be used for the above computation of the August future's implied price. One may ask how the market-makers are able to create markets for the options when the future is not freely trading. They are pricing the options off cash quotes. Knowing the cash quote, they can imply the price of the future (613 in this case), and they can then make option markets as well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:732 SCORE: 26.00 ================================================================================ 682 Part V: Index Options and Futures The real value in being able to use the options when a future is locked limit up or limit down, of course, is to be able to hedge one's position. Simplistically, if a trad­ er came in long the August soybean futures and they were locked limit down as in the example above, he could use the puts and calls to effectively close out his posi­ tion. Example: As before, August soybeans are at 620, locked down the limit of 30 cents. A trader has come into this trading day long the futures and he is very worried. He cannot liquidate his long position, and if soybeans should open down the limit again tomorrow, his account will be wiped out. He can use the August options to close out his position. Recall that it has been shown that the following is true: Long put + Short call is equivalent to short stock. It is also equivalent to short futures, of course. So if this trader were to buy a put and short a call at the same strike, then he would have the equivalent of a short futures position to offset his long futures position. Using the following prices, which are the same as before, one can see how his risk is limited to the effective futures price of 613. That is, buying the put and selling the call is the same as selling his futures out at 613, down 37 cents on the trading day. Current prices: Option August 625 call August 625 put Position: Buy August 625 put for 19 Sell August 625 call for 31 August Futures at Option Expiration Put Price 575 50 600 25 613 12 625 0 650 0 Put P/L + $1,900 600 - 1,900 - 3,100 3,100 Last Sale Price 19 31 Call Price 0 0 0 0 25 Call P/L +$1,900 + 1,900 + 1,900 + 1,900 600 Net Change for the Day -21 +16 Net Profit or loss on Position +$3,800 + 1,300 0 - 1,200 - 3,700 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:733 SCORE: 34.00 ================================================================================ Otapter 34: Futures and Futures Options 683 This profit table shows that selling the August 625 call at 19 and buying the August 625 put at 31 is equivalent to - that is, it has the same profit potential as - selling the August future at 613. So, if one buys the put and sells the call, he will effectively have sold his future at 613 and taken his loss. His resultant position after buying the put and selling the call would be a con­ version (long futures, long put, and short call). The margin required for a conversion or reversal is zero in the futures market. The margin rules recognize the riskless nature of such a strategy. Thus, any excess money that he has after paying for the unrealized loss in the futures will be freed up for new trades. The futures trader does not have to completely hedge off his position ifhe does not want to. He might decide to just buy a put to limit the downside risk. Unfortunately, to do so after the futures are already locked limit down may be too lit­ tle, too late. There are many kinds of partial hedges that he could establish - buy some puts, sell some calls, utilize different strikes, etc. The same or similar strategies could be used by a naked option seller who can­ not hedge his position because it is up the limit. He could also utilize options that are still in free trading to create a synthetic futures position. Futures options generally have enough out-of-the-money striking prices listed that some of them will still be free trading, even if the futures are up or down the limit. This fact is a boon to anyone who has a losing position that has moved the daily trading limit. Knowing how to use just this one option trading strategy should be a worthwhile benefit to many futures traders. COMMONPLACE MISPRICING STRATEGIES Futures options are sometimes prone to severe mispricing. Of course, any product's options may be subject to mispricing from time to time. However, it seems to appear in futures options more often than it does in stock options. The following discussion of strategies concentrates on a specific pattern of futures options mispricing that occurs with relative frequency. It generally m{inifests itself in that out-of-the-money puts are too cheap, and out-of-the-money calls are too expensive. The proper term for this phenomenon is "volatility skewing" and it is discussed further in Chapter 36 on advanced concepts. In this chapter, we concentrate on how to spot it and how to attempt to profit from it. Occasionally, stock options exhibit this trait to a certain extent. Generally, it occurs in stocks when speculators have it in their minds that a stock is going to expe­ rience a sudden, substantial rise in price. They then bid up the out-of-the-money calls, particularly the near-term ones, as they attempt to capitalize on their bullish expectations. When takeover rumors abound, stock options display this mispricing ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:734 SCORE: 20.00 ================================================================================ 684 Part V: Index Options and Futures pattern. Mispricing is, of course, a statistically related term; it does not infer anything about the possible validity of takeover rumors. A significant amount of discussion is going to be spent on this topic, because the futures option trader will have ample opportunities to see and capitalize on this mis­ pricing pattern; it is not something that just comes along rarely. He should therefore be prepared to make it work to his advantage. Example: January soybeans are trading at 583 ($5.83 per bushel). The following prices exist: Strike 525 550 575 600 625 650 675 January beans: 583 Call Price 191/2 11 51/4 31/2 21/4 Put Price Suppose one knows that, according to historic patterns, the "fair values" of these options are the prices listed in the following table. Strike 525 550 575 600 625 650 675 Call Price 191/2 11 53/4 31/2 21/4 Call Theo. Value 21.5 10.4 4.3 1.5 0.7 Put Put Theo. Price Value 1/2 1.6 31/4 5.4 12 13.7 28 27.6 Notice that the out-of-the-money puts are priced well below their theoretical value, while the out-of-the-money calls are priced above. The options at the 575 and 600 strikes are much closer in price to their theoretical values than are the out-of­ the-money options. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:735 SCORE: 43.00 ================================================================================ Chapter 34: Futures and Futures Options 685 There is another way to look at this data, and that is to view the options' implied volatility. Implied volatility was discussed in Chapter 28 on mathematical applica­ tions. It is basically the volatility that one would have to plug into his option pricing model in order for the model's theoretical price to agree with the actual market price. Alternatively, it is the volatility that is being implied by the actual marketplace. The options in this example each have different implied volatilities, since their mispricing is so distorted. Table 34-2 gives those implied volatilities. The deltas of the options involved are shown as well, for they will be used in later examples. These implied volatilities tell the same story: The out-of-the-money puts have the lowest implied volatilities, and therefore are the cheapest options; the out-of-the­ money calls have the highest implied volatilities, and are therefore the most expen­ sive options. So, no matter which way one prefers to look at it - through comparison of the option price to theoretical price or by comparing implied volatilities - it is obvious that these soybean options are out of line with one another. This sort of pricing distortion is prevalent in many commodity options. Soybeans, sugar, coffee, gold, and silver are all subject to this distortion from time to time. The distortion is endemic to some - soybeans, for example - or may be pres­ ent only when the speculators tum extremely bullish. This precise mispricing pattern is so prevalent in futures options that strategists should constantly be looking for it. There are two major ways to attempt to profit from this pattern. Both are attractive strategies, since one is buying options that are relatively less expensive than the options that are being sold. Such strategies, if implemented when the options are mispriced, tilt the odds in the strategist's favor, creating a positive expected return for the position. TABLE 34-2. Volatility skewing of soybean options. Strike 525 550 575 600 625 650 675 Call Price 19 1/2 11 53/4 31/2 21/4 Put Price 1/2 31/4 ; 12 28 Implied Delta Volatility Call/Put 12% /-0.02 13% /-0.16 15% 0.59/-0.41 17% 0.37 /-0.63 19% 0.21 21% 0.13 23% 0.09 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:736 SCORE: 31.00 ================================================================================ 686 Part V: Index Options and Futures The two theoretically attractive strategies are: 1. Buy out-of-the-money puts and sell at-the-money puts; or 2. Buy at-the-money calls and sell out-of-the-money calls. One might just buy one cheap and sell one expensive option - a bear spread with the puts, or a bull spread with the calls. However, it is better to implement these spreads with a ratio between the number of options bought and the number sold. That is, the first strategy involving puts would be a backspread, while the second strategy involving calls would be a ratio spread. By doing the ratio, each strategy is a more neutral one. Each strategy is examined separately. BACKSPREAD/NG THE PUTS The backspread strategy works best when one expects a large degree of volatility. Implementing the strategy with puts means that a large drop in price by the under­ lying futures would be most profitable, although a limited profit could be made if futures rose. Note that a moderate drop in price by expiration would be the worst result for this spread. Example: Using prices from the above example, suppose that one decides to estab­ lish a backspread in the puts. Assume that a neutral ratio is obtained in the following spread: Buy 4 January bean 550 puts 31/4 Sell 1 January bean 600 put at 28 Net position: 13 DB 28 CR 15 Credit The deltas (see Table 34-2) of the options are used to compute this neutral ratio. Figure 34-1 shows the profit potential of this spread. It is the typical picture for a put backspread - limited upside potential with a great deal of profit potential for large downward moves. Note that the spread is initially established for a credit of 15 cents. If January soybeans have volatile movements in either direction, the position should profit. Obviously, the profit potential is larger to the downside, where there are extra long puts. However, if beans should rally instead, the spreader could still make up to 15 cents ($750), the initial credit of the position. Note that one can treat the prices of soybean options in the same manner as he would treat the prices of stock options in order to determine such things as break­ even points and maximum profit potential. The fact that soybean options are worth ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:737 SCORE: 10.00 ================================================================================ Chapter 34: Futures and Futures Options 687 FIGURE 34-1. January soybean, backspread. 60 50 40 30 ..... e 20 a.. 0 10 ~ r::: ~ 550 600 625 -20 -30 Futures Price $50 per point ( which is cents when referring to soybeans) and stock options are worth $100 per point do not alter these calculations for a put backspread. Maximum upside profit potential= Initial debit or credit of position = 15 points Maximum risk = Maximum upside Distance between strikes x Number of puts sold short = 15-50 X 1 = -35 points Downside break-even point = Lower strike - Points of risk/Number of excess puts = 550- 35/3 = 538.3 Thus, one is able to analyze a futures option p~tion or a stock option position in the same manner - by reducing everything to be in terms of points, not dollars. Obviously, one will eventually have to convert to dollars in order to calculate his prof­ its or losses. However, note that referring to everything in "points" works very well. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:738 SCORE: 40.00 ================================================================================ 688 Part V: Index Options and Futures Later, one can use the dollars per point to obtain actual dollar cost. Dollars per point would be $50 for soybeans options, $100 for stock or index options, $400 for live cat­ tle options, $375 for coffee options, $1,120 for sugar options, etc. In this way, one does not have to get hung up in the nomenclature of the futures contract; he can approach everything in the same fashion for purposes of analyzing the position. He will, of course, have to use proper nomenclature to enter the order, but that comes after the analysis is done. RATIO SPREADING THE CALLS Returning to the subject at hand - spreads that capture this particular mispricing phenomenon of futures options - recall that the other strategy that is attractive in such situations is the ratio call spread. It is established with the maximum profit potential being somewhat above the current futures price, since the calls that are being sold are out-of-the-money. Example: Again using the January soybean options of the previous few examples, suppose that one establishes the following ratio call spread. Using the calls' deltas (see Table 34-2), the following ratio is approximately neutral to begin with: Buy 2 January bean 600 calls at 11 Sell 5 January bean 650 calls at 31/2 Net position: 22 DB 171/2 CR 41/2 Debit Figure 34-2 shows the profit potential of the ratio call spread. It looks fairly typ­ ical for a ratio spread: limited downside exposure, maximum profit potential at the strike of the written calls, and unlimited upside exposure. Since this spread is established with both options out-of-the-money, one needs some upward movement by January soybean futures in order to be profitable. However, too much movement would not be welcomed (although follow-up strate­ gies could be used to deal with that). Consequently, this is a moderately bullish strat­ egy; one should feel that the underlying futures have a chance to move somewhat higher before expiration. Again, the analyst should treat this position in terms of points, not dollars or cents of soybean movement, in order to calculate the significant profit and loss points. Refer to Chapter 11 on ratio call spreads for the original explanation of these formulae for ratio call spreads: Maximum downside loss = Initial debit or credit = -4½ (it is a debit) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:739 SCORE: 16.00 ================================================================================ Chapter 34: Futures and Futures Options FIGURE 34-2. January soybean, ratio spread. 90 80 70 60 50 :!:: 40 0 ... a.. 30 0 20 .le C 10 ~ 0 -10 -20 -30 575 625 650 At Expiration Futures Price Points of maximum profit = Maximum downside loss + Difference in strikes x Number of calls owned =-4½ + 50 X 2 =95½ Upside break-even price = Higher striking price 700 + Maximum profit/Net number of naked calls = 650 + 95½/3 = 681.8 689 These are the significant points of profitability at expiration. One does not care what the unit of trading is (for example, cents for soybeans) or how many dollars are involved in one unit of trading ($50 for soybeans and soybean options). He can con­ duct his analysis strictly in terms of points, and he should do so. Before proceeding into the comparisons beleen the backspread and the ratio spread as they apply to mispriced futures options, it should be pointed out that the seri­ ous strategist should analyze how his position will perform over the short term as well as at expiration. These analyses are presented in Chapter 36 on advanced concepts. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:740 SCORE: 50.00 ================================================================================ 690 Part V: Index Options and Futures WHICH STRATEGY TO USE The profit potential of the put backspread is obviously far different from that of the call ratio spread. They are similar in that they both offer the strategist the opportu­ nity to benefit from spreading mispriced options. Choosing which one to implement (assuming liquidity in both the puts and calls) may be helped by examining the tech­ nical picture ( chart) of the futures contract. Recall that futures traders are often more technically oriented than stock traders, so it pays to be aware of basic chart patterns, because others are watching them as well. If enough people see the same thing and act on it, the chart pattern will be correct, if only from a "self-fulfilling prophecy" viewpoint if nothing else. Consequently, if the futures are locked in a (smooth) downtrend, the put strat­ egy is the strategy of choice because it offers the best downside profit. Conversely, if the futures are in a smooth uptrend, the call strategy is best. The worst result will be achieved if the strategist has established the call ratio spread, and the futures have an explosive rally. In certain cases, very bullish rumors - weather predictions such as drought or El Nifio, foreign labor unrest in the fields or mines, Russian buying of grain - will produce this mispricing phenomenon. The strategist should be leery of using the call ratio spread strategy in such situations, even though the out-of-the-money calls look and are ridiculously expensive. If the rumors prove true, or if there are too many shorts being squeezed, the futures can move too far, too fast and seriously hurt the spreader who has the ratio call spread in place. His margin requirements will escalate quickly as tl1e futures price moves high­ er. The option premiums will remain high or possibly even expand if the futures rally quickly, thereby overriding the potential benefit of time decay. Moreover, if the fun­ damentals change immediately - it rains; the strike is settled; no grain credits are offered to the Russians - or rumors prove false, the futures can come crashing back down in a hurry. Consequently, if rumors of fundamentals have introduced volatility in the futures rnarket, implement the strategy with the put backspread. The put backspread is geared to taking advantage of volatility, and this fundamental situation as described is certainly volatile. It may seem that because the market is exploding to the upside, it is a waste of time to establish the put spread. Still, it is the wisest choice in a volatile market, and there is always the chance that an explosive advance can turn into a quick decline, especially when the advance is based on rumors or fundamentals that could change overnight. There are a few "don'ts" associated with the ratio call spread. Do not be tempt­ ed to use the ratio spread strategy in volatile situations such as those just described; it works best in a slowly rising market. Also, do not implement the ratio spread with ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:741 SCORE: 28.00 ================================================================================ Chapter 34: Futures and Futures Options 691 ridiculously far out-of-the-money options, as one is wasting his theoretical advantage if the futures do not have a realistic chance to climb to the striking price of the writ­ ten options. Finally, do not attempt to use overly large ratios in order to gain the most theoretical advantage. This is an important concept, and the next example illustrates it well. Example: Assume the same pricing pattern for January soybean options that has been the basis for this discussion. January beans are trading at 583. The (novice) strategist sees that the slightly in-the-money January 575 call is the cheapest and the deeply out-of-the-money January 675 call is the most expensive. This can be verified from either of two previous tables: the one showing the actual price as compared to the "theoretical" price, or Table 34-2 showing the implied volatilities. Again, one would use the deltas (see Table 34-2) to create a neutral spread. A neutral ratio of these two would involve selling approximately six calls for each one purchased. Buy 1 January bean 575 call at 191/z Sell 6 January bean 675 calls at 21/4 Net position: 191/z DB 131/z CR 6 Debit Figure 34-3 shows the possible detrimental effects of using this large ratio. While one could make 94 points of profit if beans were at 675 at January expiration, he could lose that profit quickly if beans shot on through the upside break-even point, which is only 693.8. The previous formulae can be used to verify these maxi­ mum profit and upside break-even point calculations. The upside break-even point is too close to the striking price to allow for reasonable follow-up action. Therefore, this would not be an attractive position from a practical viewpoint, even though at first glance it looks attractive theoretically. It would seem that neutral spreading could get one into trouble if it "recom­ mends" positions like the 6-to-l ratio spread. In reality, it is the strategist who is get­ ting into trouble if he doesn't look at the whole picture. The statistics are just an aid - a tool. The strategist must use the tools to his advantage. It should be pointed out as well that there is a tool missing from the toolkit at this point. There are statistics that will clearly show the risk of this type of high-rati<,Yspread. In this case, that tool is the gamma of the option. Chapter 40 covers the -Lise of gamma and other more advanced statistical tools. This same example is expanded in that chapter to include the gamma concept. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:742 SCORE: 18.00 ================================================================================ 692 Part V: Index Options and Futures FIGURE 34-3. January soybean, heavily ratioed spread. 90 60 30 - 0 e 575 625 650 675 725 a. -30 0 .1!l -60 C ~ -90 -120 At Expiration -150 -180 Futures Price FOLLOW-UP ACTION The same follow-up strategies apply to these futures options as did for stock options. They will not be rehashed in detail here; refer to earlier chapters for broader expla­ nations. This is a summary of the normal follow-up strategies: Ratio call spread: Follow-up action in strategies with naked options, such as this, generally involves taking or limiting losses. A rising market will produce a negative EFP. Neutralize a negative EFP by: Buying futures Buying some calls Limit upside losses by placing buy stop orders for futures at or near the upside break-even point. Put backspread: Follow-up action in strategies with an excess of long options generally involves taking or protecting profits. A falling market will produce a negative EFP. Neutralize a negative EFP by: Buying futures Selling some puts ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:743 SCORE: 41.00 ================================================================================ Chapter 34: Futures and Futures Options 693 The reader has seen these follow-up strategies earlier in the book. However, there is one new concept that is important: The mispricing continues to propagate itself no matter what the price of the underlying futures contract. The at-the-money options will always be about fairly priced; they will have the average implied volatility. Example: In the previous examples, January soybeans were trading at 583 and the implied volatility of the options with striking price 575 was 15%, while those with a 600 strike were 17%. One could, therefore, conclude that the at-the-money January soybean options would exhibit an implied volatility of about 16%. This would still be true if beans were at 525 or 675. The mispricing of the other options would extend out from what is now the at-the-money strike. Table 34-3 shows what one might expect to see if January soybeans rose 75 cents in price, from 583 to 658. Nate that the same mispricing properties exist in both the old and new situa­ tions: The puts that are 58 points out-of-the-money have an implied volatility of only 12%, while the calls that are 92 points out-of-the-money have an implied volatility of 23%. TABLE 34-3. Propagation of volatility skewing. Original Situation January beans: 583 Implied Strike Volatility 525 12% 550 13% 575 15% 600 17% 625 19% 650 21% 675 23% New Situation January beans: 658 Strike 600 625 650 675 700 725 750 This example is not meant to infer that the volatility of an at-the-money soybean futures option will always be 16%. It could be anything, depending on the historical and implied volatility of the futures contract itself. However, the volatility skewing will still persist even if the futures rally or decline. This fact will affect how these strategies behave as the(linderlying futures con­ tract moves. It is a benefit to both strategies. First, look at the put backspread when the stock falls to the striking price of the purchased puts. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:744 SCORE: 47.00 ================================================================================ 694 Part V: Index Options and Futures Example: The put backspread was established under the following conditions: Strike 550 600 Put Price Theoretical Put Price 5.4 27.6 Implied Volatility 13% 17% If January soybean futures should fall to 550, one would expect the implied volatility of the January 550 puts that are owned to be about 16% or 17%, since they would be at-the-money at that time. This makes the assumption that the at-the­ money puts will have about a 17% implied volatility, which is what they had when the position was established. Since the strategy involves being long a large quantity of January 550 puts, this increase in implied volatility as the futures drop in price will be of benefit to the spread. Note that the implied volatility of the January 600 puts would increase as well, which would be a small negative aspect for the spread. However, since there is only one put short and it is quite deeply in the money with the futures at 550, this nega­ tive cannot outweigh the positive effect of the expansion of volatility on the long January 550 puts. In a similar manner, the call spread would benefit. The implied volatility of the written options would actually drop as the futures rallied, since they would be less far out-of-the-money than they originally were when the spread was established. While the same can be said of the long options in the spread, the fact that there are extra, naked, options means the spread will benefit overall. In summary, the futures option strategist should be alert to mispricing situations like those described above. They occur frequently in a few commodities and occa­ sionally in others. The put backspread strategy has limited risk and might therefore be attractive to more individuals; it is best used in downtrending and/or volatile mar­ kets. However, if the futures are in a smooth uptrend, not a volatile one, a ratio call spread would be better. In either case, the strategist has established a spread that is statistically attractive because he has sold options that are expensive in relation to the ones that he has bought. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:745 SCORE: 40.00 ================================================================================ Chapter 34: Futures and Futures Options 695 SUMMARY This chapter presented the basics of futures and futures options trading. The basic differences between futures options and stock or index options were laid out. In a certain sense, a futures option is easier to utilize than is a stock option because the effects of dividends, interest rates, stock splits, and so forth do not apply to futures options. However, the fact that each underlying physical commodity is completely different from most other ones means that the strategist is forced to familiarize him­ self with a vast array of details involving striking prices, trading units, expiration dates, first notice days, etc. More details mean there could be more opportunities for mistakes, most of which can be avoided by visualizing and analyzing all positions in terms of points and not in dollars. Futures options do not create new option strategies. However, they may afford one the opportunity to trade when the futures are locked limit up. Moreover, the volatility skewing that is present in futures options will offer opportunities for put backspreads and call ratio spreads that are not normally present in stock options. Chapter 35 discusses futures spreads and how one can use futures options with those spreads. Calendar spreads are discussed as well. Calendar spreads with futures options are different from calendar spreads using stock or index options. These are important concepts in the futures markets - distinctly different from an option spread - and are therefore significant for the futures option trader. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:746 SCORE: 23.00 ================================================================================ Futures Option Strategies for Futures Spreads A spread with futures is not the same as a spread with options, except that one item is bought while another is simultaneously sold. In this manner, one side of the spread hedges the risk of the other. This chapter describes futures spreading and offers ways to use options as an adjunct to those spreads. The concept of calendar spreading with futures options is covered in this chap­ ter as well. This is the one strategy that is very different when using futures options, as opposed to using stock or index options. FUTURES SPREADS Before getting into option strategies, it is necessary to define futures spreads and to examine some common futures spreading strategies. FUTURES PRICING DIFFERENTIALS It has already been shown that, for any paiticular physical commodity, there are, at any one time, several futures that expire in different months. Oil futures have month­ ly expirations; sugar futures expire in only five months of any one calendar year. The frequency of expiration months depends on which futures contract one is discussing. Futures on the same underlying commodity will trade at different prices. The differential is due to several factors, not just time, as is the case with stock options. A major factor is carrying costs - how much one would spend to buy and hold the phys- 696 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:747 SCORE: 22.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 697 ical commodity until futures expiration. However, other factors may enter in as well, including supply and demand considerations. In a normal carrying cost market, futures that expire later in time are more expensive than those that are nearer-term. Example: Gold is a commodity whose futures exhibit forward or normal carry. Suppose it is March 1st and spot gold is trading at 351. Then, the futures contracts on gold and their respective prices might be as follows: Expiration Month Price April 352.50 June 354.70 August 356.90 December 361.00 June 366.90 Notice that each successive contract is more expensive than the previous one. There is a 2.20 differential between each of the first three expirations, equal to 1.10 per month of additional expiration time. However, the differential is not quite that great for the December, which expires in 9 months, or for the June contract, which expires in 15 months. The reason for this might be that longer-term interest rates are slightly lower than the short-term rates, and so the cost of carry is slightly less. However, prices in all futures don't line up this nicely. In some cases, different months may actually represent different products, even though both are on the same underlying physical commodity. For example, wheat is not always wheat. There is a summer crop and a winter crop. While the two may be related in general, there could be a substantial difference between the July wheat futures contract and the December contract, for example, that has very little to do with what interest rates are. Sometimes short-term demand can dominate the interest rate effect, and a series of futures contracts can be aligned such that the short-term futures are more expensive. This is known as a reverse carrying charge market, or contango. INTRAMARKET FUTURES SPREADS Some futures traders attempt to predict the relationships between various expiration months on the same underlying physical commodity. That is, one might buy July soybean futures and sell September soybean futures. When one both buys and sells differing futures contracts, he has a spread. When both contracts are on the same underlying physical commodity, he has an intramarket spread. ~ ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:748 SCORE: 10.00 ================================================================================ 698 Part V: Index Options and Futures The spreader is not attempting to predict the overall direction of prices. Rather, he is trying to predict the differential in prices between the July and September con­ tracts. He doesn't care if beans go up or down, as long as the spread between July and September goes his way. Example: A spread trader notices that historic price charts show that if September soybeans get too expensive with respect to July soybeans, the differential usually dis­ appears in a month or two. The opportunity for establishing this trade usually occurs early in the year - February or March. Assume it is February 1st, and the following prices exist: July soybean futures: 600 ($6.00/bushel) September soybean futures: 606 The price differential is 6 cents. It rarely gets worse than 12 cents, and often revers­ es to the point that July futures are more expensive than soybean futures - some years as much as 100 cents more expensive. If one were to trade this spread from a historical perspective, he would thus be risking approximately 6 cents, with possibilities of making over 100 cents. That is certainly a good risk/reward ratio, if historic price patterns hold up in the current environment. Suppose that one establishes the spread: Buy one July future @ 600 Sell one September future @ 606 At some later date, the following prices and, hence, profits and losses, exist. Futures Price July: 650 September: 630 Total Profit: Profit/Loss +50 cents -24 cents 26 cents ($1,300) The spread has inverted, going from an initial state in which September was 6 cents more expensive than July, to a situation in which July is 20 cents more expen­ sive. The spreader would thus make 26 cents, or $1,300, since 1 cent in beans is worth $50. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:749 SCORE: 27.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 699 Notice that the same profit would have been made at any of the following pairs of prices, because the price differential between July and September is 20 cents in all cases (with July being the more expensive of the two). July Futures September Futures July Profit September Profit 420 400 -180 +206 470 450 -130 +156 550 530 -50 +76 600 580 0 +26 650 630 +50 -24 700 680 +100 -74 800 780 +200 -174 Therefore, the same 26-cent profit can be made whether soybeans are in a severe bear market, in a rousing bull market, or even somewhat unchanged. The spreader is only concerned with whether the spread widens from a 6-cent differen­ tial or not. Charts, some going back years, are kept of the various relationships between one expiration month and another. Spread traders often use these historical charts to determine when to enter and exit intramarket spreads. These charts display the sea­ sonal tendencies that make the relationships between various contracts widen or shrink. Analysis of the fundamentals that cause the seasonal tendencies could also be motivation for establishing intramarket spreads. The margin required for intramarket spread trading (and some other types of futures spreads) is smaller than that required for speculative trading in the futures themselves. The reason for this is that spreads are considered less risky than outright positions in the futures. However, one can still make or lose a good deal of money in a spread - percentage-wise as well as in dollars - so it cannot be considered conser­ vative; it's just less risky than outright futures speculation. Example: Using the soybean spread from the example above, assume the speculative initial margin requirement is $1,700. Then, the spread margin requirement might be $500. That is considerably less than one would have to put up as initial margin if each side of the spread had to be margined separately, a situation that would require $3,400. In the previous example, it was shown that the soybean spread had the poten­ tial to widen as much as 100 points ($1.00), a move that would be worth $5,000 if it ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:750 SCORE: 18.00 ================================================================================ 700 Part V: Index Options and Futures occurred. While it is unlikely that the spread would actually widen to historic highs, it is certainly possible that it could widen 25 or 30 cents, a profit of $1,250 to $1,500. That is certainly high leverage on a $500 investment over a short time period, so one must classify spreading as a risk strategy. INTERMARKET FUTURES SPREADS Another type of futures spread is one in which one buys futures contracts in one mar­ ket and sells futures contracts in another, probably related, market. When the futures spread is transacted in two different markets, it is known as an intermarket spread. Intermarket spreads are just as popular as intramarket spreads. One type of intermarket spread involves directly related markets. Examples include spreads between currency futures on two different international currencies; between financial futures on two different bond, note, or bill contracts; or between a commodity and its products - oil, unleaded gasoline, and heating oil, for example. Example: Interest rates have been low in both the United States and Japan. As a result, both currencies are depressed with respect to the European currencies, where interest rates remain high. A trader believes that interest rates will become more uni­ form worldwide, causing the Japanese yen to appreciate with respect to the German mark. However, since he is not sure whether Japanese rates will move up or German rates will move down, he is reluctant to take an outright position in either currency. Rather, he decides to utilize an intermarket spread to implement his trading idea. Assume he establishes the spread at the following prices: Buy I June yen future: 77.00 Sell I June mark future: 60.00 This is an initial differential of 17.00 between the two currency futures. He is hoping for the differential to get larger. The dollar trading terms are the same for both futures: One point of movement (from 60.00 to 61.00, for example) is worth $1,250. His profit and loss potential would therefore be: Spread Differential al a Later Date Profit/Loss 14.00 $3,750 16.00 - $1,250 18.00 + 1,250 20.00 + 3,750 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:751 SCORE: 60.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 701 In some cases, the exchanges recognize frequently traded intermarket spreads as being eligible for reduced margin requirements. That is, the exchange recognizes that the two futures are hedges against one another if one is sold and the other is bought. These spreads between currencies, called cross-currency spreads, are so heavi­ ly traded that there are other specific vehicles - both futures and warrants - that allow the speculator to trade them as a single entity. Regardless, they serve as a prime example of an intermarket spread when the two futures are used. In the example above, assume the outright speculative margin for a position in either currency future is $1,700 per contract. Then, the margin for this spread would probably be nearly $1,700 as well, equal to the speculative margin for one side of the spread. This position is thus recognized as a spread position for margin purposes. The margin treatment isn't as favorable as for the intramarket spread (see the earlier soy­ bean example), but the spread margin is still only one-half of what one would have to advance as initial margin if both sides of the spread had to be margined separately. Other intermarket spreads are also eligible for reduced margin requirements, although at first glance they might not seem to be as direct a hedge as the two cur­ rencies above were. Example: A common intermarket spread is the TED spread, which consists of Treasury bill futures on one side and Eurodollar futures on the other. Treasury bills represent the safest investment there is; they are guaranteed. Eurodollars, however, are not insured, and therefore represent a less safe investment. Consequently, Eurodollars yield more than Treasury bills. How much more is the key, because as the yield differential expands or shrinks, the spread between the prices of T-bill futures and Eurodollar futures expands or shrinks as well. In essence, the yield dif­ ferential is small when there is stability and confidence in the financial markets, because uninsured deposits and insured deposits are not that much different in times of financial certainty. However, in times of financial uncertainty and instability, the spread widens because the uninsured depositors require a comparatively higher yield for the higher risk they are taking. Assume the outright initial margin for either the T-bill future or the Eurodollar future is $800 per contract. The margin for the TED spread, however, is only $400. Thus, one is able to trade this spread for only one-fourth of the amount of margin that would be required to margin both sides separately. The reason that the margin is more favorable is that there is not a lot of volatil­ ity in this spread. Historically, it has ranged between about 0.30 and 1.70. In both futures contracts, one cent (0.01) of movement is worth $25. Thus, the entire 140- cent historic range of the spread only represents $3,500 (140 x $25). ( ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:752 SCORE: 34.00 ================================================================================ 702 Part V: Index Options and Futures More will be said later about the TED spread when the application of futures options to intermarket spreads is discussed. Since there is a liquid option market on both futures, it is sometimes more logical to establish the spread using options instead of futures. One other comment should be made regarding the TED spread: It has carry­ ing cost. That is, if one buys the spread and holds it, the spread will shrink as time passes, causing a small loss to the holder. When interest rates are low, the carrying cost is small (about 0.05 for 3 months). It would be larger if short-term rates rose. The prices in Table 35-1 show that the spread is more costly for longer-term con­ tracts. TABLE 35-1. Carrying costs of the TED spread. Month T-Bill Future March 96.27 June 96.15 September 95.90 Eurodollar Future 95.86 95.69 95.39 TED Spread 0.41 0.46 0.51 Many intermarket spreads have some sort of carrying cost built into them; the spreader should be aware of that fact, for it may figure into his profitability. One final, and more complex, example of an intermarket spread is the crack spread. There are two major areas in which a basic commodity is traded, as well as two of its products: crude oil, unleaded gasoline, and heating oil; or soybeans, soy­ bean oil, and soybean meal. A crack spread involves trading all three - the base com­ modity and both byproducts. Example: The crack spread in oil consists of buying two futures contracts for crude oil and selling one contract each for heating oil and unleaded gasoline. The units of trading are not the same for all three. The crude oil future is a con­ tract for 1,000 barrels of oil; it is traded in units of dollars per barrel, so a $1 increase in oil prices from $18.00 to $19.00, say - is worth $1,000 to the futures contract. Heating oil and unleaded gasoline futures contracts have similar terms, but they are different from crude oil. Each of these futures is for 42,000 gallons of the product, and they are traded in cents. So, a one-cent move - gasoline going from 60 cents a gallon to 61 cents a gallon - is worth $420. This information is summarized in Table 35-2 by showing how much a unit change in price is worth. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:753 SCORE: 12.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads TABLE 35-2. Terms of oil production contract. Contract Crude Oil Unleaded Gasoline Heating Oil Initial Price 18.00 .6000 .5500 Subsequent Price 19.00 .6100 .5600 The following formula is generally used for the oil crack spread: Crack= (Unleaded gasoline + Heating oil) x 42 - 2 x Crude 2 (.6000 + .5500) X 42 - 2 X 18.00 = 2 = (48.3 - 36)/2 = 6.15 703 Gain in Dollars $1,000 $ 420 $ 420 Some traders don't use the divisor of 2 and, therefore, would arrive at a value of 12.30 with the above data. In either case, the spreader can track the history of this spread and will attempt to buy oil and sell the other two, or vice versa, in order to attempt to make an over­ all profit as the three products move. Suppose a spreader felt that the products were too expensive with respect to crude oil prices. He would then implement the spread in the following manner: Buy 2 March crude oil futures @ 18.00 Sell 1 March heating oil future @ 0.5500 Sell l March unleaded gasoline future @ 0.6000 Thus, the crack spread was at 6.15 when he entered the position. Suppose that he was right, and the futures prices subsequently changed to the following: March crude oil futures: 18.50 March unleaded gas futures: .6075 March heating oil futures: .5575 The profit is shown in Table 35-3. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:754 SCORE: 59.00 ================================================================================ 704 TABLE 35-3. Profit and loss of crack spread. Contract 2 March Crude 1 March Unleaded 1 March Heating Oil Net Profit (before commissions) Initial Price 18.00 .6000 .5500 Part V: Index Options and Futures Subsequent Price 18.50 .6075 .5575 Gain in Dollars + $1,000 - $ 315 - $ 315 + $ 370 One can calculate that the crack spread at the new prices has shrunk to 5.965. Thus, the spreader was correct in predicting that the spread would narrow, and he profited. Margin requirements are also favorable for this type of spread, generally being slightly less than the speculative requirement for two contracts of crude oil. The above examples demonstrate some of the various intermarket spreads that are heavily watched and traded by futures spreaders. They often provide some of the most reliable profit situations without requiring one to predict the actual direction of the market itself. Only the differential of the spread is important. One should not assume that all intermarket spreads receive favorable margin treatment. Only those that have traditional relationships do. USING FUTURES OPTIONS IN FUTURES SPREADS After viewing the above examples, one can see that futures spreads are not the same as what we typically know as option spreads. However, option contracts may be use­ ful in futures spreading strategies. They can often provide an additional measure of profit potential for very little additional risk. This is true for both intramarket and intermarket spreads. The futures option calendar spread is discussed first. The calendar spread with futures options is not the same as the calendar spread with stock or index options. In fact, it may best be viewed as an alternative to the intramarket futures spread rather than as an option spread strategy. CALENDAR SPREADS A calendar spread with futures options would still be constructed in the familiar manner - buy the May call, sell the March call with the same striking price. However, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:755 SCORE: 96.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 705 there is a major difference between the futures option calendar spread and the stock option calendar spread. That difference is that a calendar spread using futures options involves two separate underlying instruments, while a calendar spread using stock options does not. When one buys the May soybean 600 call and sells the March soybean 600 call, he is buying a call on the May soybean futures contract and selling a call on the March soybean futures contract. Thus, the futures option calendar spread involves two separate, but related, underlying futures contracts. However, if one buys the IBM May 100 call and sells the IBM March 100 call, both calls are on the same underlying instrument, IBM. This is a major difference between the two strategies, although both are called "calendar spreads." To the stock option trader who is used to visualizing calendar spreads, the futures option variety may confound him at first. For example, a stock option trader may conclude that if he can buy a four-month call for 5 points and sell a two-month call for 2 points, he has a good calendar spread possibility. Such an analysis is mean­ ingless with futures options. If one can buy the May soybean 600 call for 5 and sell the March soybean 600 call for 3, is that a good spread or not? It's impossible to tell, unless you know the relationship between May and March soybean futures contracts. Thus, in order to analyze the futures option calendar spread, one must not only ana­ lyze the options' relationship, but the two futures contracts' relationship as well. Simply stated, when one establishes a futures option calendar spread, he is not only spreading time, as he does with stock options, he is also spreading the relationship between the underlying futures. Example: A trader notices that near-term options in soybeans are relatively more expensive than longer-term options. He thinks a calendar spread might make sense, as he can sell the overpriced near-term calls and buy the relatively cheaper longer­ term calls. This is a good situation, considering the theoretical value of the options involved. He establishes the spread at the following prices: Soybean Trading Contract Initial Price Position March 600 call 14 Sell 1 May 600 call 21 Buy 1 March future 594 none May future 598 none The May/March 600 call calendar spread is established for 7 points debit. March expiration is two months away. At the current time, the May futures are trad­ ing at a 4-point premium to March futures. The spreader figures that if March ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:756 SCORE: 74.00 ================================================================================ 706 Part V: Index Options and Futures futures are approximately unchanged at expiration of the March options, he should profit handsomely, because the March calls are slightly overpriced at the current time, plus they will decay at a faster rate than the May calls over the next two months. Suppose that he is correct and March futures are unchanged at expiration of the March options. This is still no guarantee of profit, because one must also determine where May futures are trading. If the spread between May and March futures behaves poorly (May declines with respect to March), then he might still lose money. Look at the following table to see how the futures spread between March and May futures affects the profitability of the calendar spread. The calendar spread cost 7 debit when the futures spread was +4 initially. Futures Calendar Futures Prices Spread May 600 Call Spread March/May Price Price Profit/Loss 594/570 -24 4 -3 cents 594/580 -14 61/2 _1/2 594/590 -4 10 +3 594/600 +6 141/2 +71/2 Thus, the calendar spread could lose money even with March futures unchanged, as in the top two lines of the table. It also could do better than expected if the futures spread widens, as in the bottom line of the table. The profitability of the calendar spread is heavily linked to the futures spread price. In the above example, it was possible to lose money even though the March futures contract was unchanged in price from the time the calendar spread was initially established. This would never happen with stock options. If one placed a calendar spread on IBM and the stock were unchanged at the expiration of the near­ term option, the spread would make money virtually all of the time ( unless implied volatility had shrunk dramatically). The futures option calendar spreader is therefore trading two spreads at once. The first one has to do with the relative pricing differentials (implied volatilities, for example) of the two options in question, as well as the passage of time. The second one is the relationship between the two underlying futures contracts. As a result, it is difficult to draw the ordinary profit picture. Rather, one must approach the problem in this manner: 1. Use the horizontal axis to represent the futures spread price at the expiration of the near-term option. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:757 SCORE: 28.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 707 2. Draw several profit curves, one for each price of the near-term future at near­ term expiration. Example: Expanding on the above example, this method is demonstrated here. Figure 35-1 shows how to approach the problem. The horizontal axis depicts the spread between March and May soybean futures at the expiration of the March futures options. The vertical axis represents the profit and loss to be expected from the calendar spread, as it always does. The major difference between this profit graph and standard ones is that there are now several sets of profit curves. A separate one is drawn for each price of the March futures that one wants to consider in his analysis. The previous example showed the profitability for only one price of the March futures - unchanged at 594. However, one cannot rely on the March futures to remain unchanged, so he must view the profitability of the calendar spread at various March futures prices. The data that is plotted in the figure is summarized in Table 35-4. Several things are readily apparent. First, if the futures spread improves in price, the calendar spread will generally make money. These are the points on the far right of the figure and on the bottom line of Table 35-4. Second, if the futures spread behaves miser- FIGURE 35-1. Soybean futures calendar spreads, at March expiration. gj 20 16 12 .3 8 ::.: 0 ct 4 0 -8 March/May Spread March =604 March =594 March= 614 March =584 March= 574 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:758 SCORE: 77.00 ================================================================================ 708 Part V: Index Options and Futures ably, the calendar spread will almost certainly lose money (points on the left-hand side of the figure, or top line of the table). Third, if March futures rise in price too far, the calendar spread could do poor­ ly. In fact, if March futures rally and the futures spread worsens, one could lose more than his initial debit (bottom left-hand point on figure). This is partly due to the fact that one is buying the March options back at a loss if March futures rally, and may also be forced to sell his May options out at a loss if May futures have fallen at the same time. Fourth, as might be expected, the best results are obtained if March futures rally slightly or remain unchanged and the futures spread also remains relatively unchanged (points in the upper right-hand quadrant of the figure). In Table 35-4, the far right-hand column shows how a futures spreader would have fared if he had bought May and sold March at 4 points May over March, not using any options at all. TABLE 35-4. Profit and loss from soybean call calendar. All Prices at March Option Expiration Futures Future Spread Calendar Spread Profit Spread (May-March) March Future Price: 574 584 594 604 614 Profit -24 -5.5 - 4.5 -3 -4.5 -11.5 -28 -14 -4.5 3 -0.5 -1 -7 -18 -4 -2.5 0 +3 +3.5 -1 - 8 6 0 + 3 +7.5 +9 +5.5 + 2 16 +7 + 11 +17 +19 +13 +12 This example demonstrates just how powerful the influence of the futures spread is. The calendar spread profit is predominantly a function of the futures spread price. Thus, even though the calendar spread was attractive from the theo­ retical viewpoint of the option's prices, its result does not seem to reflect that theo­ retical advantage, due to the influence of the futures spread. Another important point for the calendar spreader used to dealing with stock options to remember is that one can lose more than his initial debit in a futures calendar spread if the spread between the underlying futures inverts. There is another way to view a calendar spread in futures options, however, and that is as a substitute or alternative to an intramarket spread in the futures contracts themselves. Look at Table 35-4 again and notice the far right-hand column. This is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:759 SCORE: 86.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 709 the profit or loss that would be made by an intramarket soybean spreader who bought May and sold March at the initial prices of 598 and 594, respectively. The calendar spread generally outperforms the intramarket spread for the prices shown in this example. This is where the true theoretical advantage of the calendar spread comes in. So, if one is thinking of establishing an intrarnarket spread, he should check out the calendar spread in the futures options first. If the options have a theoretical pric­ ing advantage, the calendar spread may clearly outperform the standard intramarket spread. Study Table 35-4 for a moment. Note that the intramarket spread is only better when prices drop but the spread widens (lower left comer of table). In all other cases, the calendar spread strategy is better. One could not always expect this to be true, of course; the results in the example are partly due to the fact that the March options that were sold were relatively expensive when compared with the May options that were bought. In summary, the futures option calendar spread is more complicated when compared to the simpler stock or index option calendar spread. As a result, calendar spreading with futures options is a less popular strategy than its stock option coun­ terpart. However, this does not mean that the strategist should overlook this strate­ gy. As the strategist knows, he can often find the best opportunities in seemingly complex situations, because there may be pricing inefficiencies present. This strate­ gy's main application may be for the intramarket spreader who also understands the usage of options. LONG COMBINATIONS Another attractive use of options is as a substitute for two instruments that are being traded one against the other. Since intermarket and intramarket futures spreads involve two instruments being traded against each other, futures options may be able to work well in these types of spreads. You may recall that a similar idea was pre­ sented with respect to pairs trading, as well as certain risk arbitrage strategies and index futures spreading. In any type of futures spread, one might be able to substitute options for the actual futures. He might buy calls for the long side of the spread instead of actually buying futures. Likewise, he could sell calls or buy puts instead of selling futures for the other side of the spread. In using options, however, he wants to avoid two prob­ lems. First, he does not want to increase his risk. Second, he does not want to pay a lot of time value premium that could waste away, costing him the profits from his spread. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:760 SCORE: 36.00 ================================================================================ 710 Part V: Index Options and Futures Let's spend a short time discussing these two points. First, he does not want to increase his risk. In general, selling options instead of utilizing futures increases one's risk. If he sells calls instead of selling futures, and sells puts instead of buying futures, he could be increasing his risk tremendously if the futures prices moved a lot. If the futures rose tremendously, the short calls would lose money, but the short puts would cease to make money once the futures rose through the striking price of the puts. Therefore, it is not a recommended strategy to sell options in place of the futures in an intramarket or intennarket spread. The next example will show why not. Example: A spreader wants to trade an intramarket spread in live cattle. The con­ tract is for 40,000 pounds, so a one-cent move is worth $400. He is going to sell April and buy June futures, hoping for the spread to narrow between the two contracts. The following prices exist for live cattle futures and options: April future: 78.00 June future: 74.00 April 78 call: 1.25 June 74 put: 2.00 He decides to use the options instead of futures to implement this spread. He sells the April 78 call as an alternative to selling the April future; he also sells the June 74 put as an alternative to buying the June future. Sometime later, the following prices exist: April future: 68.00 June future: 66.00 April 78 call: 0.00 June 74 put: 8.05 The futures spread has indeed narrowed as expected - from 4.00 points to 2.00. However, this spreader has no profit to show for it; in fact he has a loss. The call that he sold is now virtually worthless and has therefore earned a profit of 1.25 points; however, the put that was sold for 2.00 is now worth 8.05 - a loss of 6.05 points. Overall, the spreader has a net loss of 4.80 points since he used short options, instead of the 2.00-point gain he could have had if he had used futures instead. The second thing that the futures spreader wants to ensure is that he does not pay for a lot of time value premium that is wasted, costing him his potential profits. If he buys at- or out-of-the-money calls instead of buying futures, and if he buys at- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:761 SCORE: 60.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 711 or out-of-the-money puts instead of selling futures, he could be exposing his spread profits to the ravages of time decay. Do not substitute at- or out-of-the-rrwney options for the futures in intramarket or intennarket spreads. The next example will show why not. Example: A futures spreader notices that a favorable situation exists in wheat. He wants to buy July and sell May. The following prices exist for the futures and options: May futures: 410 July futures: 390 May 410 put: 20 July 390 call: 25 This trader decides to buy the May 410 put instead of selling May futures; he also buys the July 390 call instead of buying July futures. Later, the following prices exist: May futures: 400 July futures: 400 May 410 put: 25 July 390 call: 30 The futures spread would have made 20 points, since they are now the same price. At least this time, he has made money in the option spread. He has made 5 points on each option for a total of 10 points overall - only half the money that could have been made with the futures themselves. Nate that these sample option prices still show a good deal of time value premium remaining. If more time had passed and these options were trading closer to parity, the result of the option spread would be worse. It might be pointed out that the option strategy in the above example would work better if futures prices were volatile and rallied or declined substantially. This is true to a certain extent. If the market had moved a lot, one option would be very deeply in-the-money and the other deeply out-of-the-money. Neither one would have much time value premium, and the trader would therefore have wasted all the money spent for the initial time premium. So, unless the futures moved so far as to outdistance that loss of time value premium, the futures strategy would still outrank the option strategy. However, this last point of volatile futures movement helping an option position is a valid one. It leads to the reason for the only favorable option strategy that is a sub- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:762 SCORE: 54.00 ================================================================================ 712 Part V: Index Options and Futures stitute for futures spreads - that is, using in-the-money options. If one buys in-the­ rnoney calls instead of buying futures, and buys in-the-money puts instead of selling futures, he can often create a position that has an advantage over the intramarket or intermarket futures spread. In-the-money options avoid most of the problems described in the two previous examples. There is no increase of risk, since the options are being bought, not sold. In addition, the amount of money spent on time value premium is small, since both options are in-the-money. In fact, one could buy them so far in the money as to virtually eliminate any expense for time value premium. However, that is not recommended, for it would negate the possible advantage of using moderately in-the-money options: If the underlyingfutures behave in a volatile manner, it might be possible for the option spread to make money, even if the futures spread does not behave as expected. In order to illustrate these points, the TED spread, an intermarket spread, will be used. Recall that in order to buy the TED spread, one would buy T-bill futures and sell an equal quantity of Eurodollar futures. Options exist on both T-bill futures and Eurodollar futures. If T-bill calls were bought instead of T-bill futures, and if Eurodollar puts were bought instead of sell­ ing Eurodollar futures, a similar position could be created that might have some advantages over buying the TED spread using futures. The advantage is that if T-bills and/or Eurodollars change in price by a large enough amount, the option strategist can make money, even if the TED spread itself does not cooperate. One might not think that short-term rates could be volatile enough to make this a worthwhile strategy. However, they can move substantially in a short period of time, especially if the Federal Reserve is active in lowering or raising rates. For example, suppose the Fed continues to lower rates and both T-bills and Eurodollars substan­ tially rise in price. Eventually, the puts that were purchased on the Eurodollars will become worthless, but the T-bill calls that are owned will continue to grow in value. Thus, one could make money, even if the TED spread was unchanged or shrunk, as long as short-term rates dropped far enough. Similarly, if rates were to rise instead, the option spread could make money as the puts gained in value (rising rates mean T-bills and Eurodollars will fall in price) and the calls eventually became worthless. Example: The following prices for June T-bill and Eurodollar futures and options exist in January. All of these products trade in units of 0.01, which is worth $25. So a whole point is worth $2,500. June T-bill futures: 94.75 June Euro$ futures: 94.15 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:763 SCORE: 54.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads June T-bill 9450 calls: 0.32 June Euro$ 9450 puts: 0.40 713 The TED spread, basis June, is currently at 0.60 (the difference in price of the two futures). Both futures have in-the-money options with only a small amount of time value premium in them. The June T-bill calls with a striking price of 94.50 are 0.25 in the money and are selling for 0.32. Their time value premium is only 0.07 points. Similarly, the June Eurodollar puts with a striking price of 94.50 are 0.35 in the money and are selling for 0.40. Hence, their time value premium is 0.05. Since the total time value premium - 0.12 ($300) - is small, the strategist decides that the option spread may have an advantage over the futures intermarket spread, so he establishes the following position: Buy one June T-bill call @ 0.40 Buy one June Euro$ put @ 0.32 Total cost: Cost $1,000 $ 800 $1,800 Later, financial conditions in the world are very stable and the TED spread begins to shrink. However, at the same time, rates are being lowered in the United States, and T-bill and Eurodollar prices begin to rally substantially. In May, when the June T-bill options expire, the following prices exist: June T-bill futures: 95.50 June Euro$ futures: 95.10 June T-bill 9450 calls: 1.00 June Euro$ 9450 puts: 0.01 The TED spread has shrunk from 0.60 to only 0.40. Thus, any trader attempt­ ing to buy the TED spread using only futures would have lost $500 as the spread moved against him by 0.20. However, look at the option position. The options are now worth a combined value of 1.01 points ($2,525), and they were bought for 0.72 points ($1,800). Thus, the option strategy has turned a profit of $725, while the futures strategy would have lost money. Any traders who used this option strategy instead of using futures would have enjoyed profits, because as the Federal Reserve lowered rates time after time, the prices of both T-bills and Eurodollars rose far enough to make the option strategist's ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:764 SCORE: 56.00 ================================================================================ 714 Part V: Index Options and Futures calls more profitable than the loss in his puts. This is the advantage of using in-the­ money options instead of futures in futures spreading strategies. In fairness, it should be pointed out that if the futures prices had remained rel­ atively unchanged, the 0.12 points of time value premium ($300) could have been lost, while the futures spread may have been relatively unchanged. However, this does not alter the reasoning behind wanting to use this option strategy. Another consideration that might come into play is the margin required. Recall that the initial margin for implementing the TED spread was $400. However, if one uses the option strategy, he must pay for the options in full - $1,800 in the above example. This could conceivably be a deterrent to using the option strategy. Of course, if by investing $1,800, one can make money instead of losing money with the smaller investment, then the initial margin requirement is irrelevant. Therefore, the profit potential must be considered the more important factor. FOLLOW-UP CONSIDERATIONS When one uses long option combinations to implement a futures spread strategy, he may find that his position changes from a spread to more of an outright position. This would occur if the markets were volatile and one option became deeply in-the­ money, while the other one was nearly worthless. The TED spread example above showed how this could occur as the call wound up being worth 1.00, while the put was virtually worthless. As one side of the option spread goes out-of-the-money, the spread nature begins to disappear and a more outright position takes its place. One can use the deltas of the options in order to calculate just how much exposure he has at any one time. The following examples go through a series of analyses and trades that a strate­ gist might have to face. The first example concerns establishing an intermarket spread in oil products. Example: In late summer, a spreader decides to implement an intermarket spread. He projects that the coming winter may be severely cold; furthermore, he believes that gasoline prices are too high, being artificially buoyed by the summer tourist sea­ son, and the high prices are being carried into the future months by inefficient mar­ ket pricing. Therefore, he wants to buy heating oil futures or options and sell unleaded gasoline futures or options. He plans to be out of the trade, if possible, by early December, when the market should have discounted the facts about the winter. Therefore, he decides to look at January futures and options. The following prices exist: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:765 SCORE: 42.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads Future or Option January heating oil futures: January unleaded gasoline futures: January heating oil 60 call: January unleaded gas 62 put: Price .6550 .5850 6.40 4.25 715 Time Value Premium 0.90 0.75 The differential in futures prices is .07, or 7 cents per gallon. He thinks it could grow to 12 cents or so by early winter. However, he also thinks that oil and oil prod­ ucts have the potential to be very volatile, so he considers using the options. One cent is worth $420 for each of these items. The time value premium of the options is 1.65 for the put and call combined. If he pays this amount ($693) per combination, he can still make money if the futures widen by 5.00 points, as he expects. Moreover, the option spread gives him the potential for profits if oil products are volatile, even if he is wrong about the futures relationship. Therefore, he decides to buy five combinations: Position Buy 5 January heating oil 60 calls @ 6.40 Buy 5 January unleaded 62 puts @ 4.25 Total cost: Cost $13,440 8,925 $22,365 This initial cost is substantially larger than the initial margin requirement for five futures spreads, which would be about $7,000. Moreover, the option cost must be paid for in cash, while the futures requirement could be taken care of with Treasury bills, which continue to earn money for the spreader. Still, the strategist believes that the option position has more potential, so he establishes it. Notice that in this analysis, the strategist compared his time value premium cost to the profit potential he expected from the futures spread itself This is often a good way to evaluate whether or not to use options or futures. In this example, he thought that, even if futures prices remained relatively unchanged, thereby wasting away his time premium, he could still make money - as long as he was correct about heating oil outperforming unleaded gasoline. Some follow-up actions will now be examined. If the futures rally, the position becomes long. Some profit might have accrued, but the whole position is subject to losses if the futures fall in price. The strategist can calculate the extent to which his ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:766 SCORE: 57.00 ================================================================================ 716 Part V: Index Options and Futures position has become long by using the delta of the options in the strategy. He can then use futures or other options in order to make the position more neutral, if he wants to. Example: Suppose that both unleaded gasoline and heating oil have rallied some and that the futures spread has widened slightly. The following information is known: Future or Option January heating oil futures: January unleaded gasoline futures: January heating oil 60 call: January unleaded gas 62 put: Total profit: Price .7100 .6300 11.05 1.50 Net Change + .055 + .045 + 4.65 - 2.75 Profit/loss +$9,765 - 5,775 +$3,990 The futures spread has widened to 8 cents. If the strategist had established the spread with futures, he would now have a one-cent ( $420) profit on five contracts, or a $2,100 profit. The profit is larger in the option strategy. The futures have rallied as well. Heating oil is up 5½ cents from its initial price, while unleaded is up 4½ cents. This rally has been large enough to drive the puts out­ of-the-money. When one has established the intermarket spread with options, and the futures rally this much, the profit is usually greater from the option spread. Such is the case in this example, as the option spread is ahead by almost $4,000. This example shows the most desirable situation for the strategist who has implemented the option spread. The futures rally enough to force the puts out-of­ the-money, or alternatively fall far enough to force the calls to be out-of-the-money. If this happens in advance of option expiration, one option will generally have almost all of its time value premium disappear (the calls in the above example). The other option, however, will still have some time value ( the puts in the example). This represents an attractive situation. However, there is a potential negative, and that is that the position is too long now. It is not really a spread anymore. If futures should drop in price, the calls will lose value quickly. The puts will not gain much, though, because they are out-of-the-money and will not adequately protect the calls. At this juncture, the strategist has the choice of taking his profit - closing the position - or making an adjustment to make the spread more neutral once again. He could also do nothing, of course, but a strategist would normally want to protect a profit to some extent. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:767 SCORE: 30.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 717 Example: The strategist decides that, since his goal was for the futures spread to widen to 12 cents, he will not remove the position when the spread is only 8 cents, as it is now. However, he wants to take some action to protect his current profit, while still retaining the possibility to have the profit expand. As a first step, the equivalent futures position (EFP) is calculated. The pertinent data is shown in Table 35-5. TABLE 35-5. EFP of long combination. Future or Option January heating oil futures: January unleaded gasoline futures: January heating oil 60 call: Long 5 January unleaded gas 62 put: Long 5 Price .7100 .6300 11.05 1.50 Delta 0.99 -0.40 EFP +4.95 -2.00 Total EFP: +2.95 Overall, the position is long the equivalent of about three futures contracts. The position's profitability is mostly related to whether the futures rise or fall in price, not to how the spread between heating oil futures and unleaded gas futures behaves. The strategist could easily neutralize the long delta by selling three contracts. This would leave room for more profits if prices continue to rise ( there are still two extra long calls). It would also provide downside protection if prices suddenly drop, since the 5 long puts plus the 3 short futures would offset any loss in the 5 in-the­ money calls. Which futures should the strategist short? That depends on how confident he is in his original analysis of the intermarket spread widening. If he still thinks it will widen further, then he should sell unleaded gasoline futures against the deeply in­ the-money heating oil calls. This would give him an additional profit or loss opportu­ nity based on the relationship of the two oil products. However, ifhe decides that the intermarket spread should have widened more than this by now, perhaps he will just sell 3 heating oil futures as a direct hedge against the heating oil calls. Once one finds himself in a profitable situation, as in the above example, the rrwst conservative course is to hedge the in-the-rrwney option with its own underly­ ing future. This action lessens the further dependency of the profits on the inter­ market spread. There is still profit potential remaining from futures price action. Furthermore, if the futures should fall so far that both options return to in-the­ money status, then the intermarket spread comes back into play. Thus, in the above ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:768 SCORE: 29.00 ================================================================================ 718 Part V: Index Options and Futures example, the conservative action would be to sell three heating oil futures against the heating oil calls. The more aggressive course is to hedge the in-the-money option with the future underlying the other side of the intermarket spread. In the above example, that would entail selling the unleaded gasoline futures against the heating oil calls. Suppose that the strategist in the previous example decides to take the conser­ vative action, and he therefore shorts three heating oil futures at .7100, the current price. This action preserves large profit potential in either direction. It is better than selling out-of-the-money options against his current position. He would consider removing the hedge if futures prices dropped, perhaps when the puts returned to an in-the-money status with a put delta of at least -0. 75 or so. At that point, the position would be at its original status, more or less, except for the fact that he would have taken a nice profit in the three futures that were sold and covered. Epilogue. The above examples are taken from actual price movements. In reality, the futures fell back, not only to their original price, but far below it. The funda­ mental reason for this reversal was that the weather was warm, hurting demand for heating oil, and gasoline supplies were low. By the option expiration in December, the following prices existed: January heating oil futures: .5200 January unleaded gas futures: .5200 Not only had the futures prices virtually crashed, but the intermarket spread had been decimated as well. The spread had fallen to zero! It had never reached any­ thing near the 12-cent potential that was envisioned. Any spreader who had estab­ lished this spread with futures would almost certainly have lost money; he probably would not have held it until it reached this lowly level, but there was never much opportunity to get out at a profit. The strategist who established the spread with options, however, most certain­ ly would have made money. One could safely assume that he covered the three futures sold in the previous example at a nice profit, possibly 7 points or so. One could also assume that as the puts became in-the-money options, he established a similar hedge and bought three unleaded gasoline futures when the EFP reached -3.00. This probably occurred with unleaded gasoline futures around .5700-5 cents in the money. Assuming that these were the trades, the following table shows the profits and losses. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:769 SCORE: 45.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 719 Initial Final Net Profit/ Position Price Price Loss Bought 5 calls 6.40 0 -$13,440 Bought 5 puts 4.25 10.00 + 12,075 Sold 3 heating oil futures .7100 .6400 + 8,820 Bought 3 unleaded gas futures .5700 .5200 - 6,300 Total profit: +$ 1,155 In the final analysis, the fact that the intermarket spread collapsed to zero actu­ ally aided the option strategy, since the puts were the in-the-money option at expira­ tion. This was not planned, of course, but by being long the options, the strategist was able to make money when volatility appeared. INTRAMARKET SPREAD STRATEGY It should be obvious that the same strategy could be applied to an intramarket spread as well. If one is thinking of spreading two different soybean futures, for example, he could substitute in-the-money options for futures in the position. He would have the same attributes as shown for the intermarket spread: large potential profits if volatil­ ity occurs. Of course, he could still make money if the intramarket spread widens, but he would lose the time value premium paid for the options. SPREADING FUTURES AGAINST STOCK SECTOR INDICES This concept can be carried one step further. Many futures contracts are related to stocks - usually to a sector of stocks dealing in a particular commodity. For example, there are crude oil futures and there is an Oil & Gas Sector Index (XOI). There are gold futures and there is a Gold & Silver Index (XAU). If one charts the history of the commodity versus the price of the stock sector, he can often find tradeable pat­ terns in terms of the relationship between the two. That relationship can be traded via an intermarket spread using options. For example, if one thought crude oil was cheap with respect to the price of oil stocks in general, he could buy calls on crude oil futures and buy puts on the Oil & Gas (XOI) Index. One would have to be certain to determine the number of options to trade on each side of the spread, by using the ratio that was presented in Chapter 31 on inter-index spreading. (In fact, this formula should be used for futures inter­ market spreading if the two underlying futures don't have the same terms.) Only now, there is an extra component to add if options are used - the delta of the options: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:770 SCORE: 31.00 ================================================================================ 720 Part V: Index Options and Futures where vi = volatility Pi = price of the underlying ui = unit of trading of the option Lli = delta of the option Example: Suppose that one indeed wants to buy crude oil calls and also buy puts on the XOI Index because he thinks that crude oil is cheap with respect to oil stocks. The following prices exist: July crude futures: 16.35 Crude July 1550 call: 1.10 Volatility: 25% Call delta: O. 7 4 $XOI: 256.50 June 265 put: 14½ Volatility: 17% Put delta: 0. 73 The unit of trading for XOI options is $100 per point, as it is with nearly all stock and index options. The unit of trading for crude oil futures and options is $1,000 per point. With all of this information, the ratio can be computed: Crude= 1,000 x 0.25 x 16.35 x 0.74 XOI = 100 x 0.17 x 256.50 x 0.73 Ratio = Crude/ XOI = 0.91 Therefore, one would buy 0.91 XOI put for every 1 crude oil call that he bought. For small accounts, this is essentially a 1-to-l ratio, but for large accounts, the exact ratio could be used (for example, buy 91 XOI puts and 100 crude oil calls). The resultant quantities encompass the various differences in these two markets - mainly the price and volatility of the underlyings, plus the large differential in their units of trading (100 vs. 1,000). SUMMARY Futures spreading is a very important and potentially profitable endeavor. Utilizing options in these spreads can often improve profitability to the point that an originally mistaken assumption can be overcome by volatility of price movement. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:771 SCORE: 26.00 ================================================================================ Chapter 35: Futures Option Strategies for Futures Spreads 721 Futures spreads fall into two categories - intermarket and intramarket. They are important strategies because many futures exhibit historic and/or seasonal ten­ dencies that can be traded without regard to the overall movement of futures prices. Options can be used to enhance these futures spreading strategies. The futures calendar spread is closely related to the intramarket spread. It is distinctly different from the stock or index option calendar spread. Using in-the-money long option combinations in lieu of futures can be a very attractive strategy for either intermarket or intramarket spreads. The option strategy gives the spreader two ways to make money: ( 1) from the movement of the underly­ ing futures in the spread; or (2) if the futures prices experience a big move, from the fact that one option can continually increase in value while the other can drop only to zero. The option strategy also affords the strategist the opportunity for follow-up action based on the equivalent futures position that accumulates as prices rise or fall. The concepts introduced in this chapter apply not only to futures spreads, but to intermarket spreads between any two entities. An example was given of an inter­ market spread between futures and a stock sector index, but the concept can be gen­ eralized to apply to any two related markets of any sort. Traders who utilize futures spreads as part of their trading strategy should give serious consideration to substituting options when applicable. Such an alternative strategy will often improve the chances for profit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:774 SCORE: 16.00 ================================================================================ 724 Part VI: Measuring and Trading Volatility Even though a myriad of strategies and concepts have been presented so far, a com­ mon thread among them is lacking. The one thing that ties all option strategies together and allows one to make comparative decisions is volatility. In fact, volatility is the most important concept in option trading. Oh, sure, if you're a great picker of stocks, then you might be able to get by without considering volatility. Even then, though, you'd be operating without full consideration of the main factor influencing option prices and strategy. For the rest of us, it is mandatory that we consider volatil­ ity carefully before deciding what strategy to use. In this section of the book, an extensive treatment of volatility and volatility trading is presented. The first part defines the terms and discusses some general concepts about how volatility can - and should - be used. Then, a number of the more popular strategies, described earlier in the book, are discussed from the vantage point of how they perform when implied volatilities change. After that, volatility trading strategies are discussed - and these are some of the most important concepts for option traders. A discussion is present­ ed of how stock prices actually behave, as opposed to how investors perceive them to behave, and then specific criteria and methodology for both buying and selling volatility are introduced. The information to be presented here is not overly theoretical. All of the con­ cepts should be understandable by most option traders. Whether or not one chooses to actually "trade volatility," it is nevertheless important for an option trader to under­ stand the concepts that underlie the basic principles of volatility trading. WHY TRADE 11 THE MARKET"? The "game" of stock market predicting holds appeal for many because one who can do it seems powerful and intelligent. Everyone has his favorite indicators, analysis techniques, or "black box" trading systems. But can the market really be predicted? And if it can't, what does that say about the time spent trying to predict it? The answers to these questions are not clear, and even if one were to prove that the mar­ ket can't be predicted, most traders would refuse to believe it anyway. In fact, there may be more than one way to "predict" the market, so in a certain sense one has to qualify exactly what he is talking about before it can be determined if the market can be predicted or not. The astute option trader knows that market prediction falls into two categories: (1) the prediction of the short-term movement of prices, and (2) the prediction of volatility of the underlying. These are not independent predictions. For example, anyone who is using a "target" is trying to predict both. That's pretty hard. Not only do you have to be right about the direction of prices, but you also have to be able to ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:777 SCORE: 26.00 ================================================================================ CHAPTER 36 The Basics of Volatility Trading Volatility trading first attracted mathematically oriented traders who noticed that the market's prediction of forthcoming volatility - for example, implied volatility - was substantially out of line with what one might reasonably expect should happen. Moreover, many of these traders (market-makers, arbitrageurs, and others) had found great difficulties with keeping a "delta neutral" position neutral. Seeking a bet­ ter way to trade without having a market opinion on the underlying security, they turned to volatility trading. This is not to suggest that volatility trading eliminates all market risk, turning it all into volatility risk, for example. But it does suggest that a certain segment of the option trading population can handle the risk of volatility with more deference and aplomb than they can handle price risk Simply stated, it seems like a much easier task to predict volatility than to pre­ dict prices. That is said notwithstanding the great bull market of the 1990s, in which every investor who strongly participated certainly feels that he understands how to predict prices. Remember not to confuse brains with a bull market. Consider the chart in Figure 36-1. This seems as if it might be a good stock to trade: Buy it near the lows and sell it near the highs, perhaps even selling it short near the highs and covering when it later declines. It appears to have been in a trading range for a long time, so that after each purchase or sale, it returns at least to the midpoint of its trading range and sometimes even continues on to the other side of the range. There is no scale on the chart, but that doesn't change the fact that it appears to be a tradable entity. In fact, this is a chart of implied volatility of the options on a major U.S. corporation. It really doesn't matter which one (it's IBM), because the implied volatility chart of near­ ly every stock, index, or futures contract has a similar pattern - a trading range. The only time that implied volatility will totally break out of its "normal" range is if some­ thing material happens to change the fundamentals of the way the stock moves - a takeover bid, for example, or perhaps a major acquisition or other dilution of the stock 727 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:778 SCORE: 8.00 ================================================================================ 728 Part VI: Measuring and Trading Volatility FIGURE 36-1. A sample chart. Buy at these points. So, many traders observed this pattern and have become adherents of trying to predict volatility. Notice that if one is able to isolate volatility, he doesn't care where the stock price goes he is just concerned with buying volatility near the bottom of the range and selling it when it gets back to the middle or high end of the range, or vice versa. In real life, it is nearly impossible for a public customer to be able to iso­ late volatility so specifically. He will have to pay some attention to the stock price, but he still is able to establish positions in which the direction of the stock price is irrel­ evant to the outcome of the position. This quality is appealing to many investors, who have repeatedly found it difficult to predict stock prices. Moreover, an approach such as this should work in both bull and bear markets. Thus, volatility trading appeals to a great number of individuals. Just remember that, for you personally to operate a strategy properly, you must find that it appeals to your own philosophy of trading. Trying to use a strategy that you find uncomfortable will only lead to losses and frus­ tration. So, if this somewhat neutral approach to option trading sounds interesting to you, then read on. DEFINITIONS OF VOLATILITY Volatility is merely the term that is used to describe how fast a stock, future, or index changes in price. When one speaks of volatility in connection with options, there are two types of volatility that are important. The first is historical volatility, which is a measure of how fast the underlying instrument has been changing in price. The other is implied volatility, which is the option market's prediction of the volatility of the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:779 SCORE: 13.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 729 underlying over the life of the option. The computation and comparison of these two measures can aid immensely in predicting the forthcoming volatility of the underly­ ing instrument - a crucial matter in determining today's option prices. Historical volatility can be measured with a specific formula, as shown in the · chapter on mathematical applications. It is merely the formula for standard deviation as contained in most elementary books on statistics. The important point to under­ stand is that it is an exact calculation, and there is little debate over how to compute historical volatility. It is not important to know what the actual measurement means. That is, if one says that a certain stock has a historical volatility of 20%, that by itself is a relatively meaningless number to anyone but an ardent statistician. However, it can be used for comparative purposes. The standard deviation is expressed as a percent. One can determine that the historical volatility of the broad stock market has usually been in the range of 15% to 20%. A very volatile stock might have an historical volatility in excess of 100%. These numbers can be compared to each other, so that one might say that a stock with the latter historical volatility is five times more volatile that the "stock market." So, the historical volatility of one instrument can be compared with that of another instru­ ment in order to determine which one is more volatile. That in itself is a useful func­ tion of historical volatility, but its uses go much farther than that. Historical volatility can be measured over different time periods to give one a sense of how volatile the underlying has been over varying lengths of time. For exam­ ple, it is common to compute a 10-day historical volatility, as well as a 20-day, 50-day, and even 100-day. In each case, the results are annualized so that one can compare the figures directly. Consider the chart in Figure 36-2. It shows a stock (although it could be a futures contract or index, too) that was meandering in a rather tight range for quite some time. At the point marked "A" on the chart, it was probably at its least volatile. At that time, the 10-dayvolatility might have been something quite low, say 20%. The price movements directly preceding point A had been very small. However, prior to that time the stock had been more volatile, so longer-term measures of the historical volatility would shown higher numbers. The possible measures of historical volatility, then at point A, might have been something like: 10-day historical volatility: 20% 20-day historical volatility: 23% 50-day historical volatility: 35% 100-day historical volatility: 45% A pattern of historical volatilities of this sort describes a stock that has been slowing down lately. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:780 SCORE: 8.00 ================================================================================ 730 FIGURE 36-2. Sample stock chart. :::::::::r;~.w· r I , .. ~ n I ll•• ~N IT Part VI: Measuring and Trading Volatllity : I I j j ~ JI • I' 'Vn ~- A Its price movements have been less extreme in the near term. Again referring to Figure 36-2, note that shortly after point A, the stock jumped much higher over a short period of time. Price action like this increases the implied volatility dramatically. And, at the far right edge of the chart, the stock had stopped rising but was swinging back and forth in far more rapid fashion than it had been at most other points on the chart. Violent action in a back-and-forth manner can often produce a higher historical volatility reading that straight-line move can; it's just the way the numbers work out. So, by the far right edge of the chart, the 10-day histori­ cal volatility would have increased rather dramatically, while the longer-term meas­ ures wouldn't be so high because they would still contain the price action that occurred prior to point A. At the far right edge of Figure 36-2, these figures might apply: l 0-day historical volatility: 80% 20-day historical volatility: 75% 50-day historical volatility: 60% l 00-day historical volatility: 55% With this alignment of historical volatilities, one can see that the stock has been more volatile recently than in the more distant past. In Chapter 38 on the distribu­ tion of stock prices, we will discuss in some detail just which one, if any, of these his­ torical volatilities one should use as "the" historical volatility input into option and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:781 SCORE: 26.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 731 probability models. We need to be able to make volatility estimates in order to deter­ mine whether or not a strategy might be successful, and to determine whether the current option price is a relatively cheap one or a relatively expensive one. For exam­ ple, one can't just say, "I think XYZ is going to rise at least 18 points by February expi­ ration." There needs to be some basis in fact for such a statement and, lacking inside information about what the company might announce between now and February, that basis should be statistics in the form of volatility projections. Historical volatility is, of course, useful as an input to the (Black-Scholes) option model. In fact, the volatility input to any model is crucial because the volatility com­ ponent is such a major factor in determining the price of an option. Furthermore, historical volatility is useful for more than just estimating option prices. It is neces­ sary for making stock price projections and calculating distributions, too, as will be shown when those topics are discussed later. Any time one asks the question, "What is the probability of the stock moving from here to there, or of exceeding a particu­ lar target price?" the answer is heavily dependent on the volatility of the underlying stock (or index or futures). It is obvious from the above example that historical volatility can change dra­ matically for any particular instrument. Even if one were to stick with just one measure of historical volatility ( the 20-day historical is commonly the most popular measure), it changes with great frequency. Thus, one can never be certain that bas­ ing option price predictions or stock price distributions on the current historical volatility will yield the "correct" results. Statistical volatility may change as time goes forward, in which case your projections would be incorrect. Thus, it is impor­ tant to make projections that are on the conservative side. ANOTHER APPROACH: GARCH GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity, which is why it's shortened to GARCH. It is a technique for forecasting volatility that some analysts say produces better projections than using historical volatility alone or implied volatility alone. GARCH was created in the 1980s by specialists in the field of econometrics. It incorporates both historical and implied volatility, plus one can throw in a constant ("fudge factor"). In essence, though, the user of GARCH volatility mod­ els has to make some predictions or decisions about the weighting of the factors used for the estimate. By its very nature, then, it can be just as vague as the situations described in the previous section. The model can "learn," though, if applied correctly. That is, if one makes a volatility prediction for today (using GARCH, let's say), but it turns out that the actu- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:782 SCORE: 25.00 ================================================================================ 732 Part VI: Measuring and Trading Volatility al volatility was lower, then when you make the volatility prediction for tomorrow, you'll probably want to adjust it downward, using the experience of the real world, where you see volatility declining. This also incorporates the common-sense notion that volatility tends to remain the same; that is, tomorrow's volatility is likely to be much like today's. Of course, that's a little bit like saying tomorrow's weather is likely to be the same as today's (which it is, two-thirds of the time, according to statistics). It's just that when a tornado hits, you have to realize that your forecast could be wrong. The same thing applies to GAR CH volatility projections. They can be wrong, too. So, GARCH does not do a perfect job of estimating and forecasting volatility. In fact, it might not even be superior, from a strategist's viewpoint, to using the simple minimum/maximum techniques outlined in the previous section. It is really best geared to predicting short-term volatility and is favored most heavily by dealers in currency options who must adjust their markets constantly. For longer-term volatility projections, which is what a position trader of volatility is interested in, GARCH may not be all that useful. However, it is considered state-of-the-art as far as volatility pre­ dicting goes, so it has a following among theoretically oriented traders and analysts. MOVING AVERAGES Some traders try to use moving averages of daily composite implied volatility read­ ings, or use a smoothing of recent past historical volatility readings to make volatility estimates. As mentioned in the chapter on mathematical applications, once the com­ posite daily implied volatility has been computed, it was recommended that a smoothing effect be obtained by taking a moving average of the 20 or 30 days' implied volatilities. In fact, an exponential moving average was recommended, because it does not require one to keep accessing the last 20 or 30 days' worth of data in order to compute the moving average. Rather, the most recent exponential mov­ ing average is all that's needed in order to compute the next one. IMPLIED VOLATILITY Implied volatility has been mentioned many times already, but we want to expand on its concept before getting deeper into its measure and uses later in this section. Implied volatility pertains only to options, although one can aggregate the implied volatilities of the various options trading on a particular underlying instrument to produce a single number, which is often referred to as the implied volatility of the underlying. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:783 SCORE: 25.00 ================================================================================ 732 Part VI: Measuring and Trading Volatility al volatility was lower, then when you make the volatility prediction for tomorrow, you'll probably want to adjust it downward, using the experience of the real world, where you see volatility declining. This also incorporates the common-sense notion that volatility tends to remain the same; that is, tomorrow's volatility is likely to be much like today's. Of course, that's a little bit like saying tomorrow's weather is likely to be the same as today's (which it is, two-thirds of the time, according to statistics). It's just that when a tornado hits, you have to realize that your forecast could be wrong. The same thing applies to GARCH volatility projections. They can be wrong, too. So, GARCH does not do a perfect job of estimating and forecasting volatility. In fact, it might not even be superior, from a strategist's viewpoint, to using the simple minimum/maximum techniques outlined in the previous section. It is really best geared to predicting short-term volatility and is favored most heavily by dealers in currency options who must adjust their markets constantly. For longer-term volatility projections, which is what a position trader of volatility is interested in, GAR CH may not be all that useful. However, it is considered state-of-the-art as far as volatility pre­ dicting goes, so it has a following among theoretically oriented traders and analysts. MOVING AVERAGES Some traders try to use moving averages of daily composite implied volatility read­ ings, or use a smoothing of recent past historical volatility readings to make volatility estimates. As mentioned in the chapter on mathematical applications, once the com­ posite daily implied volatility has been computed, it was recommended that a smoothing effect be obtained by taking a moving average of the 20 or 30 days' implied volatilities. In fact, an exponential moving average was recommended, because it does not require one to keep accessing the last 20 or 30 days' worth of data in order to compute the moving average. Rather, the most recent exponential mov­ ing average is all that's needed in order to compute the next one. IMPLIED VOLATILITY Implied volatility has been mentioned many times already, but we want to expand on its concept before getting deeper into its measure and uses later in this section. Implied volatility pertains only to options, although one can aggregate the implied volatilities of the various options trading on a particular underlying instrument to produce a single number, which is often referred to as the implied volatility of the underlying. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:784 SCORE: 25.00 ================================================================================ 732 Part VI: Measuring and Trading Volatility al volatility was lower, then when you make the volatility prediction for tomorrow, you'll probably want to adjust it downward, using the experience of the real world, where you see volatility declining. This also incorporates the common-sense notion that volatility tends to remain the same; that is, tomorrow's volatility is likely to be much like today's. Of course, that's a little bit like saying tomorrow's weather is likely to be the same as today's (which it is, two-thirds of the time, according to statistics). It's just that when a tornado hits, you have to realize that your forecast could be wrong. The same thing applies to GARCH volatility projections. They can be wrong, too. So, GAR CH does not do a perfect job of estimating and forecasting volatility. In fact, it might not even be superior, from a strategist's viewpoint, to using the simple minimum/maximum techniques outlined in the previous section. It is really best geared to predicting short-term volatility and is favored most heavily by dealers in currency options who must adjust their markets constantly. For longer-term volatility projections, which is what a position trader of volatility is interested in, GARCH may not be all that useful. However, it is considered state-of-the-art as far as volatility pre­ dicting goes, so it has a following among theoretically oriented traders and analysts. MOVING AVERAGES Some traders try to use moving averages of daily composite implied volatility read­ ings, or use a smoothing of recent past historical volatility readings to make volatility estimates. As mentioned in the chapter on mathematical applications, once the com­ posite daily implied volatility has been computed, it was recommended that a smoothing effect be obtained by taking a moving average of the 20 or 30 days' implied volatilities. In fact, an exponential moving average was recommended, because it does not require one to keep accessing the last 20 or 30 days' worth of data in order to compute the moving average. Rather, the most recent exponential mov­ ing average is all that's needed in order to compute the next one. IMPLIED VOLATILITY Implied volatility has been mentioned many times already, but we want to expand on its concept before getting deeper into its measure and uses later in this section. Implied volatility pertains only to options, although one can aggregate the implied volatilities of the various options trading on a particular underlying instrument to produce a single number, which is often referred to as the implied volatility of the underlying. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:785 SCORE: 60.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 733 At any one point in time, a trader knows for certain the following items that affect an option's price: stock price, strike price, time to expiration, interest rate, and dividends. The only remaining factor is volatility - in fact, implied volatility. It is the big "fudge factor" in option trading. If implied volatility is too high, options will be overpriced. That is, they will be relatively expensive. On the other hand, if implied volatility is too low, options will be cheap or underpriced. The terms "overpriced" and "underpriced" are not really used by theoretical option traders much anymore, because their usage implies that one knows what the option should be worth. In the modem vernacular, one would say that the options are trading with a "high implied volatility" or a "low implied volatility," meaning that one has some sense of where implied volatility has been in the past, and the current measure is thus high or low in comparison. Essentially, implied volatility is the option market's guess at the forthcoming sta­ tistical volatility of the underlying over the life of the option in question. If traders believe that the underlying will be volatile over the life of the option, then they will bid up the option, making it more highly priced. Conversely, if traders envision a non­ volatile period for the stock, they will not pay up for the option, preferring to bid lower; hence the option will be relatively low-priced. The important thing to note is that traders normally do not know the future. They have no way of knowing, for sure, how volatile the underlying is going to be during the life of the option. Having said that, it would be unrealistic to assume that inside information does not leak into the marketplace. That is, if certain people possess nonpublic knowledge about a company's earnings, new product announcement, takeover bid, and so on, they will aggressively buy or bid for the options and that will increase implied volatil­ ity. So, in certain cases, when one sees that implied volatility has shot up quickly, it is perhaps a signal that some traders do indeed know the future - at least with respect to a specific corporate announcement that is about to be made. However, most of the time there is not anyone trading with inside information. Yet, every option trader - market-maker and public alike - is forced to make a "guess" about volatility when he buys or sells an option. That is true because the price he pays is heavily influenced by his volatility estimate ( whether or not he realizes that he is, in fact, making such a volatility estimate). As you might imagine, most traders have no idea what volatility is going to be during the life of the option. They just pay prices that seem to make sense, perhaps based on historic volatility. Consequently, today's implied volatility may bear no resemblance to the actual statistical volatility that later unfolds during the life of the option. For those who desire a more mathematical definition of implied volatility, con­ sider this. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:786 SCORE: 66.00 ================================================================================ 734 Part VI: Measuring and Trading Volatillty Opt price = f(Stock price, Strike price, Time, Risk-free rate, Volatility, Dividends) Furthermore, suppose that one knows the following information: XYZ price: 52 April 50 call price: 6 Time remaining to April expiration: 36 days Dividends: $0.00 Risk-free interest rate: 5% This information, which is available for every option at any time, simply from an option quote, gives us everything except the implied volatility. So what volatility would one have to plug in the Black-Scholes model ( or whatever model one is using) to make the model give the answer 6 (the current price of the option)? That is, what volatility is necessary to solve the equation? 6 = f(52, 50, 36 days, 5%, Volatility, $0.00) Whatever volatility is necessary to make the model yield the current market price (6) as its value, is the implied volatility for the XYZ April 50 call. In this case, if you're interested, the implied volatility is 75.4%. The actual process of determining implied volatility is an iterative one. There is no formula, per se. Rather, one keeps trying var­ ious volatility estimates in the model until the answer is close enough to the market value. THE VOLATILITY OF VOLATILITY In order to discuss the implied volatility of a particular entity - stock, index, or futures contract one generally refers to the implied volatility of individual options or perhaps the composite implied volatility of the entire option series. This is gener­ ally good enough for strategic comparisons. However, it turns out that there might be other ways to consider looking at implied volatility. In paiticular, one might want to consider how wide the range of implied volatility is - that is, how volatile the indi­ vidual implied volatility numbers are. It is often conventional to talk about the percentile of implied volatility. That is a way to rank the current implied volatility reading with past readings for the same underlying instrument. However, a fairly important ingredient is missing when percentiles are involved. One can't really tell if "cheap" options are cheap as a practical matter. That's because one doesn't know how tightly packed together the past implied volatility readings are. For example, if one were to discover that the entire past range of implied volatility for XYZ stretched only from 39% to 45%, then a current reading of 40%, while low, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:787 SCORE: 71.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 135 might not seem all that attractive. That is, if the first percentile of XYZ options were at an implied volatility reading of 39% and the 100th percentile were at 45%, then a reading of 40% is really quite mundane. There just wouldn't be much room for implied volatility to increase on an absolute basis. Even if it rose to the 100th per­ centile, an individual XYZ option wouldn't gain much value, because its implied volatility would only be increasing from about 40% to 45%. However, if the distribution of past implied volatility is wide, then one can truly say the options are cheap if they are currently in a low percentile. Suppose, rather than the tight range described above, that the range of past implied volatilities for XYZ instead stretched from 35% to 90% - that the first percentile for XYZ implied volatility was at 35% and the 100th percentile was at 90%. Now, if the current read­ ing is 40%, there is a large range above the current reading into which the options could trade, thereby potentially increasing the value of the options if implied volatil­ ity moved up to the higher percentiles. What this means, as a practical matter, is that one not only needs to know the current percentile of implied volatility, but he also needs to know the range of num­ bers over which that percentile was derived. If the range is wide, then an extreme percentile truly represents a cheap or expensive option. But if the range is tight, then one should probably not be overly concerned with the current percentile of implied volatility. Another facet of implied volatility that is often overlooked is how it ranges with respect to the time left in the option. This is particularly important for traders of LEAPS (long-term) options, for the range of implied volatility of a LEAPS option will not be as great as that of a short-term option. In order to demonstrate this, the implied volatilities of $OEX options, both regular and LEAPS, were charted over several years. The resulting scatter diagram is shown in Figure 36-3. Two curved lines are drawn on Figure 36-3. They contain most of the data points. One can see from these lines that the range of implied volatility for near-term options is greater than it is for longer-term options. For example, the implied volatil­ ity readings on the far left of the scatter diagram range from about 14% to nearly 40% (ignore the one outlying point). However, for longer-term options of 24 months or more, the range is about 17% to 32%. While $0EX options have their own idiosyn­ cracies, this scatter diagram is fairly typical of what we would see for any stock or index option. One conclusion that we can draw from this is that LEAPS option implied volatilities just don't change nearly as much as those of short-term options. That can be an important piece of information for a LEAPS option trader especially if he is comparing the LEAPS implied volatility with a composite implied volatility or with the historical volatility of the underlying. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:788 SCORE: 40.00 ================================================================================ 736 Part VI: Measuring and Trading Volatility Once again, consider Figure 36-3. While it is difficult to discern from the graph alone, the 10th percentile of $OEX composite implied volatility, using all of the data points given, is 17%. The line that marks this level (the tenth percentile) is noted on the right side of the scatter diagram. It is quite easy to see that the LEAPS options rarely trade at that low volatility level. In Figure 36-3, the distance between the curved lines is much greater on the left side (i.e., for shorter-term options) than it is on the right side (for longer-term options). Thus, it's difficult for the longer-term options to register either an extreme­ ly high or extremely low implied volatility reading, when all of the options are con­ sidered. Consequently, LEAPS options will rarely appear "cheap" when one looks at their percentile of implied volatility, including all the short-term options, too: One might say that, if he were going to buy long-term options, he should look only at the size of the volatility range on the right side of the scatter diagram. Then, he could make his decision about whether the options are cheap or not by only com­ paring the current reading to past readings of long-term options. This line of think­ ing, though, is somewhat fallacious reasoning, for a couple of reasons: First, if one holds the option for any long period of time, the volatility range will widen out and there is a chance that implied volatility could drop substantially. Second, the long­ term volatility range might be so small that, even though the options are initially cheap, quick increase in implied volatility over several deciles might not translate into much of a gain in price in the short term. FIGURE 36-3. Implied volatilities of $OEX options over several years. 50 45 40 ~ 35 ~ 30 g 25 "O .91 20 C. E 15 -0th 10 5 0 0 10 20 30 40 Time to Expiration (months) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:789 SCORE: 52.00 ================================================================================ Chapter 36: The Basics ol Volatility Trading 737 It's important for anyone using implied volatility in his trading decisions to understand that the range of past implied volatilities is important, and to realize that the volatility range expands as time shrinks. IS IMPLIED VOLATILITY A GOOD PREDICTOR OF ACTUAL VOLATILITY? The fact that one can calculate implied volatility does not mean that the calculation is a good estimate of forthcoming volatility. As stated above, the marketplace does not really know how volatile an instrument is going to be, any more than it knows the forthcoming price of the stock. There are clues, of course, and some general ways of estimating forthcoming volatility, but the fact remains that sometimes options trade with an implied volatility that is quite a bit out of line with past levels. Therefore, implied volatility may be considered to be an inaccurate estimate of what is really going to happen to the stock during the life of the option. Just remember that implied volatility is a forward-looking estimate, and since it is based on traders' suppositions, it can be wrong - just as any estimate of future events can be in error. The question posed above is one that should probably be asked more often than it is: "Is implied volatility a good predictor of actual volatility?" Somehow, it seems logical to assume that implied and historical (actual) volatility will converge. That's not really true, at least not in the short term. Moreover, even if they do converge, which one was right to begin with - implied or historical? That is, did implied volatil­ ity move to get more in line with actual movements of the underlying, or did the stock's movement speed up or slow down to get in line with implied volatility? To illustrate this concept, a few charts will be used that show the comparison between implied and historical volatility. Figure 36-4 shows information for the $0EX Index. In general, $0EX options are overpriced. See the discussion in Chapter 29. That is, implied volatility of $0EX options is almost always higher than what actual volatility turns out to be. Consider Figure 36-4. There are three lines in the figure: (a) implied volatility, (b) actual volatility, and (c) the difference between the two. There is an important distinction here, though, as to what comprises these curves: (a) The implied volatility curve depicts the 20-day moving average of daily compos­ ite implied volatility readings for $0EX. That is, each day one number is com­ puted as a composite implied volatility for $0EX for that day. These implied volatility figures are computed using the averaging formula shown in the chapter on mathematical applications, whereby each option's implied volatility is weight­ ed by trading volume and by distance in- or out-of-the-money, to arrive at a sin­ gle composite implied volatility reading for the trading day. To smooth out those daily readings, a 20-day simple moving average is used. This daily implied volatil- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:790 SCORE: 37.00 ================================================================================ 738 Part VI: Measuring and Trading Volatility FIGURE 36-4. $OEX implied versus historical volatility. 10 Implied minus Actual 1999 Date ity of $OEX options encompasses all the $OEX options, so it is different from the Volatility Index ($VIX), which uses only the options closest to the money. By using all of the options, a slightly different volatility figure is arrived at, as com­ pared to $VIX, but a chart of the two would show similar patterns. That is, peaks in implied volatility computed using all of the $OEX options occur at the same points in time as peaks in $VIX. (b) The actual volatility on the graph is a little different from what one normally thinks of as historical volatility. It is the 20-day historical volatility, computed 20 days later than the date of the implied volatility calculation. Hence, points on the implied volatility curve are matched with a 20-day historical volatility calculation that was made 20 days later. Thus, the two curves more or less show the predic­ tion of volatility and what actually happened over the 20-day period. These actu­ al volatility readings are smoothed as well, with a 20-day moving average. (c) The difference between the two is quite simple, and is shown as the bottom curve on the graph. A "zero" line is drawn through the difference. When this "difference line" passes through the zero line, the projection of volatility and what actually occurred 20 days later were equal. If the difference line is above the zero line, then implied volatility was too high; the options were over­ priced. Conversely, if the difference line is below the zero line, then actual volatility turned out to be greater than implied volatility had anticipated. The options were underpriced in that case. Those latter areas are shaded in Figure 36-4. Simplistically, you would want to own options during the shaded periods on the chart, and would want to be a seller of options during the non-shaded areas. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:791 SCORE: 40.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 739 Note that Figure 36-4 indeed confirms the fact that $OEX options are consis­ tently overpriced. Very few charts are as one-dimensional as the $OEX chart, where the options were so consistently overpriced. Most stocks find the difference line oscillating back and forth about the zero mark. Consider Figures 36-5 and 36-6. Figure 36-5 shows a chart similar to Figure 36-4, comparing actual and implied volatility, and their difference, for a particular stock. Figure 36-6 shows the price graph of that same stock, overlaid on implied volatility, during the period up to and including the heavy shading. The volatility comparison chart (Figure 36-5) shows several shaded areas, dur­ ing which the stock was more volatile than the options had predicted. Owners of options profited during these times, provided they had a more or less neutral outlook on the stock. Figure 36-6 shows the stock's performance up to and including the March-April 1999 period - the largest shaded area on the chart. Note that implied volatility was quite low before the stock made the strong move from 10 to 30 in little more than a month. These graphs are taken from actual data and demonstrate just how badly out of line implied volatility can be. In February and early March 1999, implied volatility was at or near the lowest levels on these charts. Yet, by the end of March, a major price explosion had begun in the stock, one that tripled its value in just over a month. Clearly, implied volatility was a poor predictor of forthcoming actual volatility in this case. What about later in the year? In Figure 36-5, one can observe that implied and actual volatility oscillated back and forth quite a few times during the rest of 1999. It might appear that these oscillations are small and that implied volatility was actually doing a pretty good job of predicting actual volatility, at least until the final spike in December 1999. However, looking at the scale on the left-hand side of Figure 36-5, one can see that implied volatility was trying to remain in the 50% to 60% range, but actual volatility kept bolting higher rather frequently. One more example will be presented. Figures 36-7 and 36-8 depict another stock and its volatilities. On the left half of each graph, implied volatility was quite high. It was higher than actual volatility turned out to be, so the difference line in Figure 36-7 remains above the zero line for several months. Then, for some reason, the option market decided to make an adjustment, and implied volatility began to drop. Its lowest daily point is marked with a circle in Figure 36-8, and the same point in time is marked with a similar circle in Figure 36-7. At that time, options traders were "saying" that they expected the stock to be very tame over the ensuing weeks. Instead, the stock made two quick moves, one from 15 down to 11, and then anoth­ er back up to 17. That movement jerked actual volatility higher, but implied volatili­ ty remained rather low. After a period of trading between 13 and 15, during which time implied volatility remained low, the stock finally exploded to the upside, as evi­ denced by the spikes on the right-hand side of both Figures 36-7 and 36-8. Thus, ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:794 SCORE: 30.00 ================================================================================ 742 Part VI: Measuring and Trading Volatility implied volatility was a poor predictor of actual volatility for most of the time on these graphs. Moreover, implied volatility remained low at the right-hand side of the charts (January 2000) even though the stock doubled in the course of a month. The important thing to note from these figures is that they clearly show that implied volatility is really not a very good predictor of the actual volatility that is to follow. If it were, the difference line would hover near zero most of the time. Instead, it swings back and forth wildly, with implied volatility over- or underestimating actu­ al volatility by quite wide levels. Thus, the current estimates of volatility by traders (i.e., implied volatility) can actually be quite wrong. Conversely, one could also say that historical volatility is not a great predictor of volatility that is to follow, either, especially in the short term. No one really makes any claims that it is a good predictor, for historical volatility is merely a reflection of what has happened in the past. All we can say for sure is that implied and historical volatil­ ity tend to trade within a range. One thing that does stand out on these charts is that implied volatility seems to fluctuate less than actual volatility. That seems to be a natural function of the volatil­ ity predictive process. For example, when the market collapses, implied volatilities of options rise only modestly. This can be observed by again referring to Figure 36-4, the $0EX option example. The only shaded area on the graph occurred when the market had a rather sharp sell-off during October 1999. In previous years, when there had been even more severe market declines (October 1997 or August-October 1998) $0EX actual volatility had briefly moved above implied volatility (this data for 1997 and 1998 is shown in Figure 36-9). In other words, option traders and market­ makers are predicting volatility when they price options, and one tends to make a FIGURE 36-9. $OEX implied versus historical volatility, 1997-1998. Actual 40 30 10 0 D J F M A -20 1997 1998 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:795 SCORE: 46.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 743 prediction that is somewhat "middle of the road," since an extreme prediction is more likely to be wrong. Of course, it turns out to be wrong anyway, since actual volatility jumps around quite rapidly. The few charts that have been presented here don't constitute a rigorous study upon which to draw the conclusion that implied volatility is a poor predictor of actu­ al volatility, but it is this author's firm opinion that that statement is true. A graduate student looking for a master's thesis topic could take it from here. VOLATILITY TRADING As a result of the fact that implied volatility can sometimes be at irrational extremes, options may sometimes trade with implied volatilities that are significantly out of line with what one would normally expect. For example, suppose a stock is in a relatively nonvolatile period, like the price of the stock in Figure 36-2, just before point A on the graph. During that time, option sellers would probably become more aggressive while option buyers, who probably have been seeing their previous purchases decay­ ing with time, become more timid. As a result, option prices drop. Alternatively stat­ ed, implied volatility drops. When implied volatilities are decreasing, option sellers are generally happy (and may often become more aggressive), while option buyers are losing money (and may often tend to become more timid). This is just a function of looking at the profit and loss statements in one's option account. But anyone who took a longer backward look at the volatility of the stock in Figure 36-2 would see that it had been much more volatile in the past. Consequently, he might decide that the implied volatility of the options had gotten too low and he would be a buyer of options. It is the volatility trader's objective to spot situations when implied volatility is possibly or probably erroneous and to take a position that would profit when the error is brought to light. Thus, the volatility trader's main objective is spotting situa­ tions when implied volatility is overvalued or undervalued, irrespective of his outlook for the underlying stock itself. In some ways, this is not so different from the funda­ mental stock analyst who is attempting to spot overvalued or undervalued stocks, based on earnings and other fundamentals. From another viewpoint, volatility trading is also a contrarian theory of invest­ ing. That is, when everyone else thinks the underlying is going to be nonvolatile, the volatility trader buys volatility. When everyone else is selling options and option buy­ ers are hard to find, the volatility trader steps up to buy options. Of course, some rig­ orous analysis must be done before the volatility trader can establish new positions, but when those situations come to light, it is most likely that he is taking positions opposite to what "the masses" are doing. He will be buying volatility when the major- ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:796 SCORE: 40.00 ================================================================================ 744 Part VI: Measuring and Trading Volatility ity has been selling it (or at least, when the majority is refusing to buy it), and he will be selling volatility when everyone else is panicking to buy options, making them quite expensive. WHY DOES VOLATILITY REACH EXTREMES? One can't just buy every option that he considers to be cheap. There must be some consideration given to what the probabilities of stock movement are. Even more important, one can't just sell every option that he values as expensive. There may be valid reasons why options become expensive, not the least of which is that someone may have inside information about some forthcoming corporate news (a takeover or an earnings surprise, for example). Since options off er a good deal of leverage, they are an attractive vehicle to any­ one who wants to make a quick trade, especially if that person believes he knows something that the general public doesn't know. Thus, if there is a leak of a takeover rumor - whether it be from corporate officers, investment bankers, printers, or accountants - whoever possesses that information may quite likely buy options aggressively, or at least bid for them. Whenever demand for an option outstrips sup­ ply - in this case, the major supplier is probably the market-maker - the options quickly get more expensive. That is, implied volatility increases. In fact, there are financial analysts and reporters who look for large increases in trading volume as a clue to which stocks might be ready to make a big move. Invariably, if the trading volume has increased and if implied volatility has increased as well, it is a good warning sign that someone with inside information is buying the options. In such a case, it might not be a good idea to sell volatility, even though the options are mathematically expensive. Sometimes, even more minor news items are known in advance by a small seg­ ment of the investing community. If those items will be enough to move the stock even a couple of points, those who possess the information may try to buy options in advance of the news. Such minor news items might include the resignation or firing of a high-ranking corporate officer, or perhaps some strategic alliance with another company, or even a new product announcement. The seller of volatility can watch for two things as warning signs that perhaps the options are "predicting" a corporate event (and hence should be avoided as a "volatility sale"). Those two things are a dramatic increase in option volume or a sud­ den jump in implied volatility of the options. One or both can be caused by traders with inside information trying to obtain a leveraged instrument in advance of the actual corporate news item being made public. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:797 SCORE: 52.00 ================================================================================ Chapter 36: The Basics of Volatility Trading 745 A SUDDEN INCREASE IN OPTION VOLUME OR IMPLIED VOLATILITY The symptoms of insider trading, as evidenced by a large increase in option trading activity, can be recognized. Typically, the majority of the increased volume occurs in the near-term option series, particularly the at-the-money strike and perhaps the next strike out-of-the-money. The activity doesn't cease there, however. It propagates out to other option series as market-makers (who by the nature of their job function are short the near-term options that those with insider knowledge are buying) snap up everything on the books that they can find. In addition, the market-makers may try to entice others, perhaps institutions, to sell some expensive calls against a portion of their institutional stock holdings. Activity of this sort should be a warning sign to the volatility seller to stand aside in this situation. Of course, on any given day there are many stocks whose options are extraordi­ narily active, but the increase in activity doesn't have anything to do with insider trad­ ing. This might include a large covered call write or maybe a large put purchase established by an institution as a hedge against an existing stock position, or a rela­ tively large conversion or reversal arbitrage established by an arbitrageur, or even a large spread transaction initiated by a hedge fund. In any of these cases, option vol­ ume would jump dramatically, but it wouldn't mean that anyone had inside knowl­ edge about a forthcoming corporate event. Rather, the increases in option trading volume as described in this paragraph are merely functions of the normal workings of the marketplace. What distinguishes these arbitrage and hedging activities from the machina­ tions of insider trading is: (1) There is little propagation of option volume into other series in the "benign" case, and (2) the stock price itself may languish. However, when true insider activity is present, the market-makers react to the aggressive nature of the call buying. These market-makers know they need to hedge themselves, because they do not want to be short naked call options in case a takeover bid or some other news spurs the stock dramatically higher. As mentioned earlier, they try to buy up any other options offered in "the book," but there may not be many of those. So, as a last result, the way they reduce their negative position delta is to buy stock. Thus, if the options are active and expensive, and if the stock is rising too, you probably have a reasonably good indication that "someone knows something." However, if the options are expensive but none of the other factors are present, espe­ cially if the stock is declining in price - then one might feel more comfortable with a strategy of selling volatility in this case. However, there is a case in which options might be the object of pursuit by someone with insider knowledge, yet not be accompanied by heavy trading volume. This situation could occur with illiquid options. In this case, a floor broker holding ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:798 SCORE: 32.00 ================================================================================ 746 Part VI: Measuring and Trading Volatility the order of those with insider information might come into the pit to buy options, but the market-makers may not sell them many, preferring to raise their offering price rather than sell a large quantity. If this happens a few times in a row, the options will have gotten very expensive as the floor broker raises his bid price repeatedly, but only buys a few contracts each time. Meanwhile, the market-maker keeps raising his offering price. Eventually, the floor broker concludes that the options are too expensive to bother with and walks away. Perhaps his client then buys stock. In any case, what has happened is that the options have gotten very expensive as the bids and offers were repeatedly raised, but not much option volume was actually traded because of the illiquidity of the contracts. Hence the normal warning light associated with a sudden increase in option volume would not be present. In this case, though, a volatility sell­ er should still be careful, because he does not want to step in to sell calls right before some major corporate news item is released. The clue here is that implied volatility literally exploded in a short period of time (one day, or actually less time), and that alone should be enough warning to a volatility seller. The point that should be taken here is that when options suddenly become very expensive, especially if accompanied by strong stock price movement and strong stock volume, there may very well be a good reason why that is happening. That rea­ son will probably become public knowledge shortly in the form of a news event. In fact, a major market-maker once said he believed that rrwst increases in implied volatility were eventually justified - that is, some corporate news item was released that made the stock jump. Hence, a volatility seller should avoid situations such as these. Any sudden increase in implied volatility should probably be viewed as a potential news story in the making. These situations are not what a neutral volatility seller wants to get into. On the other hand, if options have become expensive as a result of corporate news, then the volatility seller can feel more comfortable making a trade. Perhaps the company has announced poor earnings and the stock has taken a beating while implied volatility rose. In this situation, one can assess the information and analyze it clearly; he is not dealing with some hidden facts known to only a few insider traders. With clear analysis, one might be able to develop a volatility selling strategy that is prudent and potentially profitable. Another situation in which options become expensive in the wake of market action is during a bear market in the underlying. This can be true for indices, stocks, and futures contracts. The Crash of '87 is an extreme example, but implied volatility shot through the roof during the crash. Other similar sharp market collapses - such as October 1989, October 1997, and August-September 1998 - caused implied volatility to jump dramatically. In these situations, the volatility seller knows why ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:799 SCORE: 30.00 ================================================================================ Chapter 31,: 1be Basics of Volatility Trading 747 implied volatility is high. Given that fact, he can then construct positions around a neutral strategy or around his view of the future. The time when the volatility seller must be careful is when the options are expensive and no one seems to know why. That's when insider trading may be present, and that's when the volatility seller should defer from selling options. CHEAP OPTIONS When options are cheap, there are usually far less discernible reasons why they have become cheap. An obvious one may be that the corporate structure of the company has changed; perhaps it is being taken over, or perhaps the company· has acquired another company nearly its size. In either case, it is possible that the combined enti­ ty's stock will be less volatile than the original company's stock was. As the takeover is in the process of being consummated, the implied volatility of the company's options will drop, giving the false impression that they are cheap. In a similar vein, a company may mature, perhaps issuing more shares of stock, or perhaps building such a.., good earnings stream that the stock is considered less volatile than it formerly was. Some of the Internet companies will be classic cases: In the beginning they were high-flying stocks with plenty of price movement, so the options traded with a relatively high degree of implied volatility. However, as the com­ pany matures, it buys other Internet companies and then perhaps even merges with a large, established company (America Online and Time-Warner Communications, for example). In these cases, actual (statistical) volatility will diminish as the company matures, and implied volatility will do the same. On the surface, a buyer of volatility may see the reduced volatility as an attractive buying situation, but upon further inspection he may find that it is justified. If the decrease in implied volatility seems justified, a buyer of volatility should ignore it and look for other opportunities. All volatility traders should be suspicious when volatility seems to be extreme - either too expensive or too cheap. The trader should investigate the possibilities as to why volatility is trading at such extreme levels. In some cases, the supply and demand of the public just pushes the options to extreme levels; there is nothing more involved than that. Those are the best volatility trading situations. However, if there is a hint that the volatility has gotten to an extreme reading because of some logical (but per­ haps nonpublic) reason, then the volatility trader should be suspicious and should probably avoid the trade. Typically this happens with expensive options. Buyers of volatility really have little to fear if they miscalculate and thus buy an option that appears inexpensive but turns out not to be, in reality. The volatility buyer might lose money if he does this, and overpaying for options constantly will lead to ruin, but an occasional mistake will probably not be fatal. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:800 SCORE: 15.00 ================================================================================ 748 Part VI: Measuring and Trading Volatility Sellers of volatility, however, have to be a lot more careful. One mistake could be the last one. Selling naked calls that seem terrifically expensive by historic stan­ dards could be ruinous if a takeover bid subsequently emerges at a large premium to the stock's current price. Even put sellers must be careful, although a lot of traders think that selling naked puts is safe because it's the same as buying stock. But who ever said buying stock wasn't risky? If the stock literally collapses - falling from 80, say, to 15 or 20, as Oxford Health did, or from 30 to 2 as Sunrise Technology did - then a put seller will be buried. Since the risk of loss from naked option selling is large, one could be wiped out by a huge gap opening. That's why it's imperative to study why the options are expensive before one sells them. If it's known, for exam­ ple, that a small biotech company is awaiting FDA trial results in two weeks,~and all the options suddenly become expensive, the volatility seller should not attempt to be a hero. It's obvious that at least some traders believe that there is a chance for the stock to gap in price dramatically. It would be better to find some other situation in which to sell options. The seller of futures options or index options should be cautious too, although there can't be takeovers in those markets, nor can there be a huge earnings surprise or other corporate event that causes a big gap. The futures markets, though do have things like crop reports and government economic data to deal with, and those can create volatile situations, too. The bottom line is that volatility selling - even hedged volatility selling - can be taxing and aggravating if one has sold volatility in front of what turns out to be a news item that justifies the expensive volatility. SUMMARY Volatility trading is a predictable way to approach the market, because volatility almost invariably trades in a range and therefore its value can be estimated with a great deal more precision than can the actual prices of the underlyings. Even so, one must be careful in his approach to volatility trading, because diligent research is needed to determine if, in fact, volatility is "cheap" or "expensive." As with any sys­ tematic approach to the market, if one is sloppy about his research, he cannot expect to achieve superior results. In the next few chapters, a good deal of time will be spent to give the reader a good understanding of how volatility affects positions and how it can be used to construct trades with positive expected rates of return. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:801 SCORE: 39.00 ================================================================================ · GHAR:f ER :8'7 . . - How Volatility Affects Popular Strategies The previous chapter addressed the calculation or interpretation of implied volatili­ ty, and how to relate it to historic volatility. Another, related topic that is important is how implied volatility affects a specific option strategy. Simplistically, one might think that the effect of a change in implied volatility on an option position would be a sim­ ple matter to discern; but in reality, most traders don't have a complete grasp of the ways that volatility affects option positions. In some cases, especially option spreads or more complex positions, one may not have an intuitive "picture" of how his posi­ tion is going to be affected by a change in implied volatility. In this chapter, we'll attempt a relatively thorough review of how implied volatility changes affect most of the popular option strategies. There are ways to use computer analysis to "draw" a picture of this volatiiity effect, of course, and that will be discussed momentarily. But an option strategist should have some idea of the general changes that a position will undergo if implied volatility changes. Before getting into the individual strategies, it is important that one understands some of the basics of the effect of volatility on an option's price. VEGA Technically speaking, the term that one uses to quantify the impact of volatility changes on the price of an option is called the vega of the option. In this chapter, the references will be to vega, but the emphasis here is on practicality, so the descriptions 749 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:802 SCORE: 74.00 ================================================================================ 750 Part VI: Measuring and Trading Volatility of how volatility affects option positions will be in plain English as well as in the more mathematical realm of vega. Having said that, let's define vega so that it is understood for later use in the chapter. Simply stated, vega is the amount by which an option's price changes when volatility changes by one percentage point. Example: XYZ is selling at 50, and the July 50 call is trading at 7.25. Assume that there is no dividend, that short-term interest rates are 5%, and that July expiration is exactly three months away. With this information, one can determine that the implied volatility of the July 50 call is 70%. That's a fairly high number, so one can surmise that XYZ is a volatile stock. What would the option price be if implied volatility were rise to 71 %? Using a model, one can determine that the July 50 call would theoreti­ cally be worth 7.35 if that happened. Hence, the vega of this option is 0.10 (to two decimal places). That is, the option price increased by 10 cents, from 7.25 to 7.35, when volatility rose by one percentage point. (Note that "percentage point" here means a full point increase in volatility, from 70% to 71 %.) What if implied volatility had decreased instead? Once again, one can use the model to determine the change in the option price. In this case, using an implied volatility of 69% and keeping everything else the same, the option would then theo­ retically be worth 7.15- again, a 0.10 change in price (this time, a decrease in price). This example points out an interesting and important aspect of how volatility affects a call option: If implied volatility increases, the price of the option will increase, and if implied volatility decreases, the price of the option will decrease. Thus, there is a direct relationship between an option's price and its implied volatili- ty. Mathematically speaking, vega is the partial derivative of the Black-Scholes model (or whatever model you're using to price options) with respect to volatility. In the above example, the vega of the July 50 call, with XYZ at 50, can be computed to be 0.098 - very near the value of 0.10 that one arrived at by inspection. Vega also has a direct relationship with the price of a put. That is, as implied volatility rises, the price of a put will rise as well. Example: Using the same criteria as in the last example, suppose that XYZ is trading at 50, that July is three months away, that short-term interest rates are 5%, and that there is no dividend. In that case, the following theoretical put and call prices would apply at the stated implied volatilities: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:803 SCORE: 49.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies 751 Stock Price July 50 call July 50 put Implied Volatility Put's Vega 50 7.15 6.54 69% 0.10 7.25 6.64 70% 0.10 7.35 6.74 71% 0.10 Thus, the put's vega is 0.10, too - the same as the call's vega was. In fact, it can be stated that a call and a put with the same terms have the same vega. To prove this, one need only refer to the arbitrage equation for a conversion. If the call increases in price and everything else remains equal - interest rates, stock price, and striking price - then the put price must increase by the same amount. A change in implied volatility will cause such a change in the call price, and a similar change in the put price. Hence, the vega of the put and the call must be the same. It is also important to know how the vega changes as other factors change, par­ ticularly as the stock price changes, or as time changes. The following examples con­ tain several tables that illustrate the behavior of vega in a typically fluctuating envi­ ronment. Example: In this case, let the stock price fluctuate while holding interest rate (5% ), implied volatility (70%), time (3 months), dividends (0), and the strike price (50) con­ stant. See Table 37-1. In these cases, vega drops when the stock price does, too, but it remains fairly constant if the stock rises. It is interesting to note, though, that in the real world, when the underlying drops in price especially if it does so quickly, in a panic mode - implied volatility can increase dramatically. Such an increase may be of great ben­ efit to a call holder, serving to mitigate his losses, perhaps. This concept will be dis­ cussed further later in this chapter. TABLE 37-1 Implied Volatility Theoretical Stock Price July 50 Call Price Coll Price Vega 30 70% 0.47 0.028 40 2.62 0.073 50 7.25 0.098 60 14.07 0.092 70 22.35 0.091 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:804 SCORE: 67.00 ================================================================================ 752 Part VI: Measuring and Trading Volatility The above example assumed that the stock was making instantaneous changes in price. In reality, of course, time would be passing as well, and that affects the vega too. Table 37-2 shows how the vega changes when time changes, all other factors being equal. Example: In this example, the following items are held fixed: stock price (50), strike price (50), implied volatility (70%), risk-free interest rate (5%), and dividend\(0). But now, we let time fluctuate. Table 37-2 clearly shows that the passage of time results not only in a decreas­ ing call price, but in a decreasing vega as well. This makes sense, of course, since one cannot expect an increase in implied volatility to have much of an effect on a very short-term option - certainly not to the extent that it would affect a LEAPS option. Some readers might be wondering how changes in implied volatility itself would affect the vega. This might be called the "vega of the vega," although I've never actu­ ally heard it referred to in that manner. The next table explores that concept. Example: Again, some factors will be kept constant - the stock price (50), the time to July expiration (3 months), the risk-free interest rate (5%), and the dividend (0). Table 37-3 allows implied volatility to fluctuate and shows what the theoretical price of a July 50 call would be, as well as its vega, at those volatilities. Thus, Table 37-3 shows that vega is surprisingly constant over a wide range of implied volatilities. That's the real reason why no one bothers with "vega of the vega." Vega begins to decline only if implied volatility gets exceedingly high, and implied volatilities of that magnitude are relatively rare. One can also compute the distance a stock would need to rise in order to over­ come a decrease in volatility. Consider Figure 37-1, which shows the theoretical price TABLE 37-2 Implied Time Theoretical Stock Price Volatility Remaining Call Price Vega 50 70% One year 14.60 0.182 Six months 10.32 0.135 Three months 7.25 0.098 Two months 5.87 0.080 One month 4.16 0.058 Two weeks 2.87 0.039 One week 1.96 0.028 One day 0.73 0.010 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:805 SCORE: 65.00 ================================================================================ Chapter 37: How Volatility Affeds Popular Strategies TABLE 37-3 Implied Stock Price Volatility 50 10% 30% 50% 70% 100% 150% 200% Theoretical Coll Price 1.34 3.31 5.28 7.25 10.16 14.90 19.41 753 Vega 0.097 0.099 0.099 0.098 0.096 0.093 0.088 of a 6-month call option with differing implied volatilities. Suppose one buys an option that currently has implied volatility of 170% (the top curve on the graph). Later, investor perceptions of volatility diminish, and the option is trading with an implied volatility of 140%. That means that the option is now "residing" on the sec­ ond curve from the top of the list. Judging from the general distance between those two curves, the option has probably lost between 5 and 8 points of value due to the drop in implied volatility. Here's another way to think about it. Again, suppose one buys an at-the-money option (stock price = 100) when its implied volatility is 170%. That option value is marked as point A on the graph in Figure 37-1. Later, the option's implied volatility drops to 140%. How much does the stock have to rise in order to overcome the loss of implied volatility? The horizontal line from point A to point B shows that the option value is the same on each line. Then, dropping a vertical line from B down to point C, we see that point C is at a stock price of about 109. Thus, the stock would have to rise 9 points just to keep the option value constant, if implied volatility drops from 170% to 140%. IMPLIED VOLATILITY AND DELTA Figure 37-1 shows another rather unusual effect: When implied volatility gets very high, the delta of the option doesn't change much. Simplistically, the delta of an option measures how much the option changes in price when the stock moves one point. Mathematically, the delta is the first partial derivative of the option model with respect to stock price. Geometrically, that means that the delta of an option is the slope of a line drawn tangent to the curve in the preceding chart. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:806 SCORE: 63.00 ================================================================================ 754 Part VI: Measuring and Trading Volatility FIGURE 37-1. Theoretical option prices at differing implied volatilities (6-month calls). 80 70 Q) 60 (.) ·;::: Cl.. 50 C: 0 ·a 40 0 30 20 10 Stock Price 60 80 100 C 120 140 _JY.._ 170% 140% 110% 80% 50% 20% The bottom line in Figure 37-1 (where implied volatility= 20%) has a distinct curvature to it when the stock price is between about 80 and 120. Thus the delta ranges from a fairly low number (when the stock is near 80) to a rather high number (when the stock is near 120). Now look at the top line on the chart, where implied volatility= 170%. It's almost a straight line from the lower left to the upper right! The slope of a straight line is constant. This tells us that the delta (which is the slope) barely changes for such an expensive option - whether the stock is trading at 60 or it's trading at 150! That fact alone is usually surprising to many. In addition, the value of this delta can be measured: It's 0. 70 or higher from a stock price of 80 all the way up to 150. Among other things, this means that an out~ of-the-money option that has extremely high implied volatility has a fairly high delta - and can be expected to mirror stock price movements more closely than one might think, were he not privy to the delta. Figure 37-2 follows through on this concept, showing how the delta of an option varies with implied volatility. From this chart, it is clear how much the delta of an option varies when the implied volatility is 20%, as compared to how little it varies when implied volatility is extremely high. That data is interesting enough by itself, but it becomes even more thought-pro­ voking when one considers that a change in the implied volatility of his option (vega) also can mean a significant change in the delta of the option. In one sense, it explains why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option holder made nothing, because implied volatility declined from 170% to 140%. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:807 SCORE: 45.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies EFFECTS ON NEUTRALITY 755 A popular concept that uses delta is the "delta-neutral" spread a spread whose prof­ itability is supposedly ambivalent to market movement, at least for short time frames and limited stock price changes. Anything that significantly affects the delta of an option can affect this neutrality, thus causing a delta-neutral position to become unbalanced ( or, more likely, causing one's intuition to be wrong regarding what con­ stitutes a delta-neutral spread in the first place). Let's use a familiar strategy, the straddle purchase, as an example. Simplistically, when one buys a straddle, he merely buys a put and a call with the same terms and doesn't get any fancier than that. However, it may be the case that, due to the deltas of the options involved, that approach is biased to the upside, and a neutral straddle position should be established instead. Example: Suppose that XYZ is trading at 100, that the options have an implied volatility of 40%, and that one is considering buying a six-month straddle with a strik­ ing price of 100. The following data summarize the situation, including the option prices and the deltas: XYZ Common: l 00; Implied Volatility: 40% Option XYZ October l 00 call XYZ October l 00 put FIGURE 37-2. Price 12.00 10.00 Delta 0.60 -0.40 Value of delta of a 6-month option at differing implied volatilities. 90 80 70 .!!l ai 60 Cl C: 50 ,g 8° 40 30 20 10 60 80 100 Stock Price 120 140 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:808 SCORE: 79.00 ================================================================================ 756 Part VI: Measuring and Trading Volatility Notice that the stock price is equal to the strike price (100). However, the deltas are not at all equal. In fact, the delta of the call is 1.5 times that of the put (in absolute value). One must buy three puts and two calls in order to have a delta-neutral posi­ tion. Most experienced option traders know that the delta of an at-the-money call is somewhat higher than that of an at-the-money put. Consequently, they often esti­ mate, without checking, that buying three puts and two calls produces a delta-neu­ tral "straddle buy." However, consider a similar situation, but with a much higher implied volatility- 110%, say. AAA Common: 100; Implied Volatility: 110% Option AAA October 100 call AAA October 1 00 put Price 31.00 28.00 Delta 0.67 -0.33 The delta-neutral ratio here is two-to-one (67 divided by 33), not three-to-two as in the earlier case - even though both stock prices are 100 and both sets of options have six months remaining. This is a big difference in the delta-neutral ratio, espe­ cially if one is trading a large quantity of options. This shows how different levels of implied volatility can alter one's perception of what is a neutral position. It also points out that one can't necessarily rely on his intuition; it is always best to check with a model. Carrying this thought a step further, one must be mindful of a change in implied volatility if he wants to keep his position delta-neutral. If the implied volatility of AAA options should drop significantly, the 2-to-l ratio will no longer be neutral, even if the stock is still trading at 100. Hence, a trader wishing to remain delta-neutral must monitor not only changes in stock price, but changes in implied volatility as well. For­ more complex strategies, one will also find the delta-neutral ratio changing due to a change in implied volatility. The preceding examples summarize the major variables that might affect the vega and also show how vega affects things other than itself, such as delta and, there­ fore, delta neutrality. By the way, the vega of the underlying is zero; an increase in implied volatility does not affect the price of the underlying instrument at all, in the­ ory. In reality, if options get very expensive (i.e., implied volatility spikes up), that usually brings traders into a stock and so the stock price will change. But that's not a mathematical relationship, just a market cause-and-effect relationship. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:809 SCORE: 90.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies POSITION VEGA 757 As can be done with delta or with any other of the partial derivatives of the model, one can compute a position vega - the vega of an entire position. The position vega is determined by multiplying the individual option vegas by the quantity of options bought or sold. The "position vega" is merely the quantity of options held, times the vega, times the shares per options ( which is normally 100). Example: Using a simple call spread as an example, assume the following prices exist: Security Position Vega Position Vego XYZ Stock No position XYZ July 50 call Long 3 calls 0.098 +0.294 XYZ July 70 call Short 5 calls 0.076 -0.380 Net Position Vega: -0.086 This concept is very important to a volatility trader, for it tells him if he has con­ structed a position that is going to behave in the manner he expects. For example, suppose that one identifies expensive options, and he figures that implied volatility will decrease, eventually becoming more in line with its historical norms. Then he would want to construct a position with a negative position vega. A negative position vega indicates that the position will profit if implied volatility decreases. Conversely, a buyer of volatility - one who identifies some underpriced situation - would want to construct a position with a positive position vega, for such a position will profit if implied volatility rises. In either case, other factors such as delta, time to expiration, and so forth will have an effect on the position's actual dollar profit, but the concept of position vega is still important to a volatility trader. It does no good to identify cheap options, for example, and then establish some strange spread with a negative position vega. Such a construct would be at odds with one's intended purpose - in this case, buying cheap options. OUTRIGHT OPTION PURCHASES AND SALES Let us now begin to investigate the affects of implied volatility on various strategies, beginning with the simplest strategy of all - the outright option purchase. It was already shown that implied volatility affects the price of an individual call or put in a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:810 SCORE: 66.00 ================================================================================ 758 Part VI: Measuring and Trading Volatility direct manner. That is, an increase in implied volatility will cause the option price to rise, while a decrease in volatility will cause a decline in the option price. That piece of information is the most important one of all, for it imparts what an option trader needs to know: An explosion in implied volatility is a boon to an option owner, but can be a devastating detriment to an option seller, especially a naked option seller. A couple of examples might demonstrate more clearly just how powerful the effect of implied volatility is, even when there isn't much time remaining in the life of an option. One should understand the notion that an increase in implied volatility can overcome days, even weeks, of time decay. This first example attempts to quan­ tify that statement somewhat. Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3- month call with striking price of 100. Furthermore, suppose that implied volatility is currently at 20%. Given these assumptions, the Black-Scholes model tells us that the call would be trading at a price of 4.64. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 3 months 20% 4.64 Now, suppose that a month passes. If implied volatility remained the same (20% ), the call would lose nearly a point of value due to time decay. However, how much would implied volatility have had to increase to completely counteract the effect of that time decay? That is, after a month has passed, what implied volatility will yield a call price of 4.64? lt turns out to be just under 26%. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 2 months 25.9% 4.64 What would happen after another month passes? There is, of course, some implied volatility at which the call would still be worth 4.64, but is it so high as to be unreasonable? Actually, it turns out that if implied volatility increases to about 38%, the call will still be worth 4.64, even with only one month of life remaining: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:811 SCORE: 51.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 1 month 38.1% 4.64 759 So, if implied volatility increases from 20% to 26% over the first month, then this call option would still be trading at the same price - 4.64. That's not an unusual increase in implied volatility; increases of that magnitude, 20% to 26%, happen all the time. For it to then increase from 26% to 38% over the next month is probably less likely, but it is certainly not out of the question. There have been many times in the past when just such an increase has been possible - during any of the August, September, or October bear markets or mini-crashes, for example. Also, such an increase in implied volatility might occur if there were takeover rumors in this stock, or if the entire market became more volatile, as was the case in the latter half of the 1990s. Perhaps this example was distorted by the fact that an implied volatility of 20% is a fairly low number to begin with. What would a similar example look like if one started out with a much higher implied volatility - say, 80%? Example: Making the same assumptions as in the previous example, but now setting the implied volatility to a much higher level of 80%, the Black-Scholes model now says that the call would be worth a price of 16.45: Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 3 months 80% 16.45 Again, one must ask the question: "If a month passes, what implied volatility would be necessary for the Black-Scholes model to yield a price of 16.45?" In this case, it turns out to be an implied volatility of just over 99%. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 2 months 99.4% 16.45 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:812 SCORE: 66.00 ================================================================================ 758 Part VI: Measuring and Trading Volatility direct manner. That is, an increase in implied volatility will cause the option price to rise, while a decrease in volatility will cause a decline in the option price. That piece of information is the most important one of all, for it imparts what an option trader needs to know: An explosion in implied volatility is a boon to an option owner, but can be a devastating detriment to an option seller, especially a naked option seller. A couple of examples might demonstrate more clearly just how powerful the effect of implied volatility is, even when there isn't much time remaining in the life of an option. One should understand the notion that an increase in implied volatility can overcome days, even weeks, of time decay. This first example attempts to quan­ tify that statement somewhat. Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3- month call with striking price of 100. Furthermore, suppose that implied volatility is currently at 20%. Given these assumptions, the Black-Scholes model tells us that the call would be trading at a price of 4.64. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 3 months 20% 4.64 Now, suppose that a month passes. If implied volatility remained the same (20% ), the call would lose nearly a point of value due to time decay. However, how much would implied volatility have had to increase to completely counteract the effect of that time decay? That is, after a month has passed, what implied volatility will yield a call price of 4.64? It turns out to be just under 26%. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 2 months 25.9% 4.64 What would happen after another month passes? There is, of course, some implied volatility at which the call would still be worth 4.64, but is it so high as to be unreasonable? Actually, it turns out that if implied volatility increases to about 38%, the call will still be worth 4.64, even with only one month of life remaining: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:813 SCORE: 51.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 1 month 38.1% 4.64 759 So, if implied volatility increases from 20% to 26% over the first month, then this call option would still be trading at the same price 4.64. That's not an unusual increase in implied volatility; increases of that magnitude, 20% to 26%, happen all the time. For it to then increase from 26% to 38% over the next month is probably less likely, but it is certainly not out of the question. There have been many times in the past when just such an increase has been possible - during any of the August, September, or October bear markets or mini-crashes, for example. Also, such an increase in implied volatility might occur if there were takeover rumors in this stock, or if the entire market became more volatile, as was the case in the latter half of the 1990s. Perhaps this example was distorted by the fact that an implied volatility of 20% is a fairly low number to begin with. What would a similar example look like if one started out with a much higher implied volatility say, 80%? Example: Making the same assumptions as in the previous example, but now setting the implied volatility to a much higher level of 80%, the Black-Scholes model now says that the call would be worth a price of 16.45: Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 3 months 80% 16.45 Again, one must ask the question: "If a month passes, what implied volatility would be necessary for the Black-Scholes model to yield a price of 16.45?" In this case, it turns out to be an implied volatility of just over 99%. Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 2 months 99.4% 16.45 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:814 SCORE: 36.00 ================================================================================ 760 Part VI: Measuring and Trading Volatility Finally, to be able to completely compare this example with the previous one, it is necessary to see what implied volatility would have to rise to in order to offset the effect of yet another month's time decay. It turns out to be over 140%: Stock Price: Strike Price: Time Remaining: Implied Volatility: Theoretical Call Value: 100 100 1 month 140.9% 16.45 Table 37-4 summarizes the results of these examples, showing the levels to which implied volatility would have to rise to maintain the call's value as time passes. Are the volatility increases in the latter example less likely to occur than the ones in the former example? Probably yes - certainly the last one, in which implied volatility would have to increase from 80% to nearly 141 % in order to maintain the call's value. However, in another sense, it may seem more reasonable: Note that the increase in volatility from 20% to 26% is a 30% increase. That is, 20% times 1.30 equals 26%. That's what's required to maintain the call's value for the lower volatility over the first month - an increase in the magnitude of implied volatility of 30%. At the higher volatility, though, an increase in magnitude of only about 25% is required (from 80% to 99%). Thus, in those terms, the two appear on more equal footing. What makes the top line of Table 37-4 appear more likely than the bottom line is merely the fact that an experienced option trader knows that many stocks have implied volatilities that can fluctuate in the 20% to 40% range quite easily. However, there are far fewer stocks that have implied volatilities in the higher range. In fact, until the Internet stocks got hot in the latter portion of the 1990s, the only ones with volatilities like those were very low-priced, extremely volatile stocks. Hence one's experience factor is lower with such high implied volatility stocks, but it doesn't mean that the volatility fluctuations appearing in Table 37-4 are impossible. If the reader has access to a software program containing the Black-Scholes model, he can experiment with other situations to see how powerful the effect of implied volatility is. For example, without going into as much detail, if one takes the case of a 12-month option whose initial implied volatility is 20%, all it takes to main- TABLE 37-4 Initial Implied Volatility 20% 80% Volatility Leveled Required to Maintain Call Value ... ... After One Month ... After Two Months 26% 99% 38% 141% ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:815 SCORE: 47.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies 761 tain the call's value over a 6-month time period is an increase in implied volatility to 27%. Taken from the viewpoint of the option seller, this is perhaps most enlighten­ ing: If you sell a one-year (LEAPS) option and six months pass, during which time implied volatility increases from 20% to 27% - certainly quite possible -you will have made nothing! The call will still be selling for the same price, assuming the stock is still selling for the same price. Finally, it was mentioned earlier that implied volatility often explodes during a market crash. In fact, one could determine just how much of an increase in implied volatility would be necessary in a market crash in order to maintain the call's value. This is similar to the first example in this section, but now the stock price will be allowed to decrease as well. Table 37-5, then, shows what implied volatility would be required to maintain the call's initial value (a price of 4.64), when the stock price falls. The other factors remain the same: time remaining (3 months), striking price (100), and interest rate (5% ). Again, this table shows instantaneous price changes. In real life, a slightly higher implied volatility would be necessary, because each market crash could take a day or two. Thus, from Table 37-5, one could say that even if the underlying stock dropped 20 points (which is 20% in this case) in one day, yet implied volatility exploded from 20% to 67% at the same time, the call's value would be unchanged! Could such an outrageous thing happen? It has: In the Crash of '87, the market plummeted 22% in one day, while the Volatility Index ($VIX) theoretically rose from 36% to 150% in one day. In fact, call buyers of some $OEX options actually broke even or made a little money due to the explosion in implied volatility, despite the fact that the worst mar­ ket crash in history had occurred. If nothing else, these examples should impart to the reader how important it is to be aware of implied volatility at the time an option position is established. If you are buying options, and you buy them when implied volatility is "low," you stand to TABLE 37-5 Stock Price 100 95 90 85 80 75 70 Implied Volatility Necessary for Call to Maintain Value 20% (the initial parameters) 33% 44% 55% 67% 78% 89% ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:816 SCORE: 97.00 ================================================================================ 762 Part VI: Measuring and Trading Volatility benefit if implied volatility merely returns to "normal" levels while you hold the posi­ tion. Of course, having the underlying increase in price is also important. Conversely, an option seller should be keenly aware of implied volatility when the option is initially sold - perhaps even more so than the buyer of an option. This pertains equally well to naked option writers and to covered option writers. If implied volatility is "too low" when the option writing position is established, then an increase (or worse, an explosion) in implied volatility will be very detrimental to the position, completely overcoming the effects of time decay. Hence, an option writer should not just sell options because he thinks he is collecting time decay each day that passes. That may be true, but an increase in implied volatility can completely domin.ate what little time decay might exist, especially for a longer-term option. In a similar manner, a decrease in implied volatility can be just as important. Thus, if the call buyer purchases options that are "too costly," ones in which implied volatility is "too high," then he could lose money even if the underlying makes a mod­ est move in his favor. In the next chapters, the topic of just how an option buyer or seller should measure implied volatility to determine what is "too low" or "too high" will be dis­ cussed. For now, suffice it to grasp the general concept that a change in implied volatility can have substantial effects on an option's price far greater effects than the passage of time can have. In fact, all of this calls into question just exactly what time value premium is. That part of an option's value that is not intrinsic value is really affected much more by volatility than it is by time decay, yet it carries the term "time value premium." TIME VALUE PREMIUM IS A MISNOMER Many (perhaps novice) option traders seem to think of time as the main antagonist to an option buyer. However, when one really thinks about it, he should realize that the portion of an option that is not intrinsic value is really much more related to stock price movement and/or volatility than anything else, at least in the short term. For this reason, it might be beneficial to more closely analyze just what the "excess value" portion of an option represents and why a buyer should not primarily think of it as time value premium. An option's price is composed of two parts: (1) intrinsic value, which is the "real" part of the option's value - the distance by which the option is in-the-money, and (2) "excess value" - often called time value premium. There are actually five factors that affect the "excess value" portion of an option. Eventually, time will dominate them ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:817 SCORE: 64.00 ================================================================================ Chapter 37: How Volah'lity Affects Popular Strategies 763 all, but the longer the life of the option, the more the other factors influence the "excess value." The five factors influencing excess value are: 1. stock price movements, 2. changes in implied volatility, 3. the passage of time, 4. changes in the dividend (if any exist), and 5. changes in interest rates. Each is stated in terms of a movement or change; that is, these are not static things. In fact, to measure them one uses the "greeks": delta, vega, theta, (there is no "greek" for dividend change), and rho. Typically, the effect of a change in dividend or a change in interest rate is small (although a large dividend change or an interest rate change on a very long-term option can produce visible changes in the prices of options). If everything remains static, then time decay will eventually wipe out all of the excess value of an option. That's why it's called time value premium. But things don't ever remain static, and on a daily basis, time decay is small, so it is the remaining two factors that are most important. Example: XYZ is trading at 82 in late November. The January 80 call is trading at 8. Thus, the intrinsic value is 2 (82 minus 80) and the excess value is 6 (8 minus 2). If the stock is still at 82 at January expiration, the option will of course only be worth 2, and one will say that the 6 points of excess value that was lost was due to time decay. But on that day in late November, the other factors are much more dominant. On this particular day, the implied volatility of this option is just over 50%. One can determine that the call's greeks are: Delta: 0.60 Vega: 0.13 Theta: -0.06 This means, for example, that time decay is only 6 cents per day. It would increase as time went by, but even with a day or so to go, theta would not increase above about 20 cents unless volatility increased or the stock moved closer to the strike price. From the above figures, one can see - and this should be intuitively appealing that the biggest factor influencing the price of the option is stock price movement (delta). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:818 SCORE: 78.00 ================================================================================ 764 Part VI: Measuring and Trading VolatiRty It's a little unfair to say that, because it's conceivable (although unlikely) that volatil­ ity could jump by a large enough margin to become a greater factor than delta for one day's move in the option. Furthermore, since this option is composed mostly of excess value, these more dominant forces influence the excess value more than time decay does. There is a direct relationship between vega and excess value. That is, if implied volatility increases, the excess value portion of the option will increase and, if implied volatility decreases, so will excess value. The relationship between delta and excess value is not so straightforward. The farther the stock moves away from the strike, the more this will have the effect of shrinking the excess value. If the call is in-the-money (as in the above example), then an increase in stock price will result in a decrease of excess value. That is, a deeply in­ the-money option is composed primarily of intrinsic value, while excess value is quite small. However, when the call is out-of-the-money, the effect is just the opposite: Then, an increase in call price will result in an increase in excess value, because the stock price increase is bringing the stock closer to the option's striking price. For some readers, the following may help to conceptualize this concept. The part of the delta that addresses excess value is this: Out-of-the-money call: 100% of the delta affects the excess value. In-the-money call: "1.00 minus delta" affects the excess value. (So, if a call is very deeply in-the-money and has a delta of 0.95, then the delta only has 1.00 - 0.95, or 0.05, room to increase. Hence it has little effect on what small amount of excess value remains in this deeply in-the-money call.) These relationships are not static, of course. Suppose, for example, that in the same situation of the stock trading at 82 and the January 80 call trading at 8, there is only week remaining until expiration! Then the implied volatility would be 155% (high, but not unheard of in volatile times). The greeks would bear a significantly dif­ ferent relationship to each other in this case, though: Delta: 0.59 Vega: 0.044 Theta: -0 .5 1 This very short-term option has about the same delta as its counterpart in the previ­ ous example (the delta of an at-the-money option is generally slightly above 0.50). Meanwhile, vega has shrunk. The effect of a change in volatility on such a short-term option is actually about a third of what it was in the previous example. However, time decay in this example is huge, amounting to half a point per day in this option. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:819 SCORE: 68.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies 765 So now one has the idea of how the excess value is affected by the "big three" of stock price movement, change in implied volatility, and passage of time. How can one use this to his advantage? First of all, one can see that an option's excess value may be due much more to the potential volatility of the underlying stock, and there­ fore to the option's implied volatility, than to time. As a result of the above information regarding excess value, one shouldn't think that he can easily go around selling what appear to be options with a lot of excess value and then expect time to bring in the profits for him. In fact, there may be a lot of volatility both actual and implied - keeping that excess value nearly intact for a fairly long period of time. In fact, in the coming chapters on volatility estimation, it will be shown that option buyers have a much better chance of success than conven­ tional wisdom has maintained. VOLATILITY AND THE PUT OPTION While it is obvious that an increase in implied volatility ½ill increase the price of a put option, much as was shown for a call option in. the preceding discussion, there are certain differences between a put and a call, so a little review of the put option itself may be useful. A put option tends to lose its premium fairly quickly as it becomes an in-the-money option. This is due to the realities of conversion arbitrage. In a con­ version arbitrage, an arbitrageur or market-maker buys stock and buys the put, while selling the call. If he carries the position to expiration, he will have to pay carrying costs on the debit incurred to establish the position. Furthermore, he would earn any dividends that might be paid while he holds the position. This information was pre­ sented in a slightly different form in the chapter on arbitrage, but it is recounted here: In a perfect world, all option prices would be so accurate that there would be no profit available from a conversion. That is, the following equation (1) would apply: (1) Call price+ Strike price - Stock price - Put price+ Dividend- Carrying cost= 0 where carrying cost = strike price/ (1 + r)t t = time to expiration r = interest rate Now, it is also known that the time value premium of a put is the amount by which its value exceeds intrinsic value. The intrinsic value of an in-the-money put option is merely the difference between the strike price and the stock price. Hence, one can write the following equation (2) for the time value premium (TVP) of an in-the­ money put option: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:820 SCORE: 119.00 ================================================================================ 766 Part VI: Measuring and Trading Volatility (2) Put TVP = Put price - Strike price + Stock price The arbitrage equation, (1), can be rewritten as: (3) Put price - Strike price+ Stock price= Call price+ Dividends - Carrying cost and substituting equation (2) for the terms in equation (3), one arrives at: ( 4) Put TVP = Call price + Dividends - Carrying cost In other words, the time value premium of an in-the-money put is the same as the (out-of-the-money) call price, plus any dividends to be ea med until expiration, less any carrying costs over that same time period. Assuming that the dividend is small or zero (as it is for most stocks), one can see that an in-the-money put would lose its time value premium whenever carrying costs exceed the value of the out-of-the-money call. Since these carrying costs can be rel­ atively large ( the carrying cost is the interest being paid on the entire debit of the position - and that debit is approximately equal to the strike price), they can quickly dominate the price of an out-of-the-money call. Hence, the time value premium of an in-the-money put disappears rather quickly. This is important information for put option buyers, because they must under­ stand that a put won't appreciate in value as much as one might expect, even when the stock drops, since the put loses its time value premium quickly. It's even more important information for put sellers: A short put is at risk of assignment as soon as there is no time value premium left in the put. Thus, a put can be assigned well in advance of expiration even a LEAPS put! Now, returning to the main topic of how implied volatility affects a position, one can ask himself how an increase or decrease in implied volatility would affect equa­ tion ( 4) above. If implied volatility increases, the call price would increase, and if the increase were great enough, might impart some time value premium to the put. Hence, an increase in implied volatility also may increase the price of a put, but if the put is too far in-the-nwney, a modest increase in implied volatility still won't budge the put. That is, an increase in implied volatility would increase the value of the call, but until it increases enough to be greater than the carrying costs, an in-the-money put will remain at parity, and thus a short put would still remain at risk of assignment. STRADDLE OR STRANGLE BUYING AND SELLING Since owning a straddle involves owning both a put and a call with the same terms, it is fairly evident that an increase in implied volatility will be very beneficial for a straddle buyer. A sort of double benefit occurs if implied volatility rises, for it will ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:821 SCORE: 81.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies 767 positively affect both the put and the call in a long straddle. Thus, if a straddle buyer is careful to buy straddles in situations in which implied volatility is "low," he can make money in one of two ways. Either (1) the underlying price makes a move great enough in magnitude to exceed the initial cost of the straddle, or (2) implied volatil­ ity increases quickly enough to overcome the deleterious effects of time decay. Conversely, a straddle seller risks just the opposite - potentially devastating loss­ es if implied volatility should increase dramatically. However, the straddle seller can register gains faster than just the rate of time decay would indicate if implied volatil­ ity decreases. Thus, it is very important when selling options - and this applies to cov­ ered options as well as to naked ones - to sell only when implied volatility is "high." A strangle is the same as a straddle, except that the call and put have different striking prices. Typically, the call strike price is higher than the put strike price. Naked option sellers often prefer selling strangles in which the options are well out­ of-the-money, so that there is less chance of them having any intrinsic value when they expire. Strangles behave much like straddles do with respect to changes in implied volatility. The concepts of straddle ownership will be discussed in much more detail in the following chapters. Moreover, the general concept of option buying versus option selling will receive a great deal of attention. CALL BULL SPREADS In this section, the bull spread strategy will be examined to see how it is affected by changes in implied volatility. Let's look at a call bull spread and see how implied volatility changes might affect the price of the spread if all else remains equal. Make the following assumptions: Assumption Set 1 : Stock Price: 1 00 Time to Expiration: 4 months Position: long Call Struck at 90 Short Call Struck at 110 Ask yourself this simple question: If the stock remains unchanged at 100, and implied volatility increases dramatically, will the price of the 90-110 call bull spread grow or shrink? Answer before reading on. The truth is that, if implied volatility increases, the price of the spread will shrink. I would suspect that this comes as something of a surprise to a good number of readers. Table 37-6 contains some examples, generated from a Black-Scholes ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:822 SCORE: 52.00 ================================================================================ 768 TABLE 37-6 Implied Volatility 20% 30% 40% 50% 60% 70% 80% Stock Price = I 00 Part VI: Measuring and Trading VolatHity 90-110 Call Bull Spread (Theoretical Value) 10.54 9.97 9.54 9.18 8.87 8.58 8.30 model, using the assumptions stated above, the most important of which is that the stock is at 100 in all cases in this table. One should be aware that it would probably be difficult to actually trade the spread at the theoretical value, due to the bid-asked spread in the options. Nevertheless, the impact of implied volatility is clear. One can quantify the amount by which an option position will change for each percentage point of increase in implied volatility. Recall that this measure is called the vega of the option or option position. In a call bull spread, one would subtract the vega of the call that is sold from that of the call that is bought in order to arrive at the position vega of the call bull spread. Table 37-7 is a reprint of Table 37-6, but now including the vega. Since these vegas are all negative, they indicate that the spread will shrink in value if implied volatility rises and that the spread will expand in value if implied TABLE 37-7 90-110 Call Implied Bull Spread Position Volatility (Theoretical Value) Vega 20% 10.54 -0.67 30% 9.97 -0.48 40% 9.54 -0.38 50% 9.18 -0.33 60% 8.87 -0.30 70% 8.58 -0.28 80% 8.30 -0.26 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:823 SCORE: 34.50 ================================================================================ Chapter 37: How VolatHity Afleds Popular Strategies 769 volatility decreases. Again, these statements may seem contrary to what one would expect from a bullish call position. Of course, it's highly unlikely that implied volatility would change much in the course of just one day while the stock price remained unchanged. So, to get a bet­ ter handle on what to expect, one really to needs to look at what might happen at some future time (say a couple of weeks hence) at various stock prices. The graph in Figure 37-3 begins the investigation of these more complex scenarios. The profit curve shown in Figure 37-3 makes certain assumptions: (1) The bull spread assumes the details in Assumption Set 1, above; (2) the spread was bought with an implied volatility of 20% and remained at that level when the profit picture above was drawn; and (3) 30 days have passed since the spread was bought. Under these assumptions, the profit graph shows that the bull spread conforms quite well to what one would expect; that is, the shape of this curve is pretty much like that of a bull spread at expiration, although if you look closely you'll see that it doesn't widen out to nearly its maximum gain or loss potential until the stock is well above llO or below 90 the strike prices used in the spread. Now observe what happens if one keeps all the other assumptions the same, except one. In this case, assume implied volatility was 80% at purchase and remains at 80% one month later. The comparison is shown in Figure 37-4. The 80% curve is overlaid on top of the 20% curve shown earlier. The contrast is quite startling. Instead of looking like a bull spread, the profit curve that uses 80% implied volatili- FIGURE 37-3. Bull spread profit picture in 30 days, at 20% IV. 1000 500 -500 130 140 iv= 20% -1000 Stock ty is a rather flat thing, sloping only slightly upward - and exhibiting far less risk and reward potential than its lower implied volatility counterpart. This points out anoth­ er important fact: For volatile stocks, one cannot expect a 4-rrwnth bull spread to expand or contract much during the first rrwnth of life, even if the stock makes a sub­ stantial rrwve. Longer-term spreads have even less movement. As a corollary, note that if implied volatility shrinks while the stock rises, the profit outlook will improve. Graphically, using Figure 37-4, if one's profit picture moves from the 80% curve to the 20% curve on the right-hand side of the chart, that is a positive development. Of course, if the stock drops and the implied volatility drops too, then one's losses would be worse - witness the left-hand side of the graph in Figure 37-4. A graph could be drawn that would incorporate other implied volatilities, but that would be overkill. The profit graphs of the other spreads from Tables 37-6 or 37-7 would lie between the two curves shown in Figure 37-4. If this discussion had looked at bull spreads as put credit spreads instead of call debit spreads, perhaps these conclusions would not have seemed so unusual. Experienced option traders already understand much of what has been shown here, but less experienced traders may find this information to be different from what they expected. Some general facts can be drawn about the bull spread strategy. Perhaps the most important one is that, if used on a volatile stock, you won't get much expansion in the spread even if the stock makes a nice move upward in your favor. In fact, for ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:825 SCORE: 53.50 ================================================================================ Cbapter 37: How Volatility Affects Popular Strategies 771 high implied volatility situations, the bull spread won't expand out to its maximum price until expiration draws nigh. That can be frustrating and disappointing. Often, the bull spread is established because the option trader feels the options are "too expensive" and thus the spread strategy is a way to cut down on the total debit invested. However, the ultimate penalty paid is great. Consider the fact that, if the stock rose from 100 to 130 in 30 days, any reasonable four-month call pur­ chase (i.e., with a strike initially near the current stock price) would make a nice profit, while the bull spread barely ekes out a 5-point gain. To wit, the graph in Figure 37-5 compares the purchase of the at-the-money call with a striking price of 100 and the 90-110 call bull spread, both having implied volatility of 80%. Quite clearly, the call purchase dominates to a great extent on an upward move. Of course, the call purchase does worse on the downside, but since these are bullish strategies, one would have to assume that the trader had a positive outlook for the stock when the position was established. Hence, what happens on the downside is not primary in his thinking. The bull spread and the call purchase have opposite position vegas, too. That is, a rise in implied volatility will help the call purchase but will harm the bull spread ( and vice versa). Thus, the call purchase and the bull spread are not very similar posi­ tions at all. If one wants to use the bull spread to effectively reduce the cost of buying an expensive at-the-money option, then at least make sure the striking prices are quite FIGURE 37-5. Call buy versus bull spread in 30 days; IV = 80%. Cl) ~ 2500 2000 1500 1000 e 500 Cl. -500 -1000 Outright Call Buy Bull Spread --- 140 Stock ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:826 SCORE: 49.00 ================================================================================ 772 Part VI: Measuring and Trading Volatility wide apart. That will allow for a reasonable amount of price appreciation in the bull spread if the underlying rises in price. Also, one might want to consider establishing the bull spread with striking prices that are both out-of-the-money. Then, if the stock rallies strongly, a greater percentage gain can be had by the spreader. Still, though, the facts described above cannot be overcome; they can only possibly be mitigated by such actions. A FAMILIAR SCENARIO? Often, one may be deluded into thinking that the two positions are more similar than they are. For example, one does some sort of analysis - it does not matter if it's fun­ damental or technical - and comes to a conclusion that the stock ( or futures contract or index) is ready for a bullish move. Furthermore, he wants to use options to imple­ ment his strategy. But, upon inspecting the actual market prices, he finds that the options seem rather expensive. So, he thinks, "Why not use a bull spread instead? It costs less and it's bullish, too." Fairly quickly, the underlying moves higher - a good prediction by the trader, and a timely one as well. If the move is a violent one, especially in the futures mar­ ket, implied volatility might increase as well. If you had bought calls, you'd be a happy camper. But if you bought the bull spread, you are not only highly disappointed, but you are now facing the prospect of having to hold the spread for several more weeks (perhaps months) before your spread widens out to anything even approaching the maximum profit potential. Sound familiar? Every option trader has probably done himself in with this line of thinking at one time or another. At least, now you know the reason why: High or increasing implied volatility is not a friend of the bull spread, while it is a friendly ally of the outright call purchase. Somewhat surprisingly, many option traders don't real­ ize the difference between these two strategies, which they probably consider to be somewhat similar in nature. So, be careful when using bull spreads. If you really think a call option is too expensive and want to reduce its cost, ti:y this strategy: Buy the call and simultane­ ously sell a credit put spread (bull spread) using slightly out-of-the-money puts. This strategy reduces the call's net cost and maintains upside potential (although it increases downside risk, but at least it is still a fixed risk). Example: With XYZ at 100, a trader is bullish and wants to buy the July 100 calls, which expire in two months. However, upon inspection, he finds that they are trad­ ing at 10 - an implied volatility of 59%. He knows that, historically, the implied volatility of this stock's options range from approximately 40% to 60%, so these are ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:827 SCORE: 28.00 ================================================================================ Chapter 37: How Volatility Affects Popular Strategies 773 very expensive options. If he buys them now and implied volatility returns to its median range near 50%, he will suffer from the decrease in implied volatility. As a possible remedy, he considers selling an out-of-the-money put credit spread at the same time that he buys the calls. The credit from this spread will act as a means of reducing the net cost of the calls. If he's right and the stock goes up, all will be well. However, the introduction of the put spread into the mix has introduced some additional downside risk. Suppose the following prices exist: XYZ: 100 July 100 call: 10 (as stated above) July 90 put: 5 July 80 put: 2 The entire bullish position would now consist of the following: Buy 1 July 100 call at 1 0 Buy 1 July 80 put at 2 Sell 1 July 90 put at 5 Net expenditure: 7 point debit (plus commission) Figure 37-6 shows the profitability, at expiration, of both the outright call pur­ chase and the bullish position constructed above. FIGURE 37-6. Profitability at expiration. 2000 Bullish Spread // / 1000 "' "' 0 ...J 87 :!:: Outright Call Purchase e 0 C. 70 80 90 40 Part VI: Measuring and Trading Volatility 45 55 60 At Expiration Stock Price Thus, a delta neutral straddle position would consist of buying 8 J anua:ry 50 calls and buying 11 Februa:ry 50 puts. The straddle has no market exposure, at least over the short term. Note that the delta neutral straddle has a significantly different prof­ it picture from the delta neutral ratio spread, but they are both neutral and are both based on the fact that the Janua:ry 50 call is cheap. The straddle makes money if the stock moves a lot, while the other makes money if the stock moves only a little. (See Figure 40-9.) Can these two vastly different profit pictures be depicting strategies in which the same thing is to be accomplished ( that is, to capture the underpriced nature of the XYZ Janua:ry 50 call)? Yes, but in order to decide which strategy is "best," the strategist would have to take other factors into consideration: the historical volatility of the underlying security, for example, or how much actual time remains until Janua:ry expiration, as well as his own psychological attitude toward selling uncovered calls. A more precise definition of the other risks of these two positions can be obtained by looking at their position gammas. Delta Neutral Is Not Entirely Neutral. In fact, delta neutral means that one is neutral only with respect to small price changes in the underlying securi­ ty. A delta neutral position may have seriously unneutral characteristics when ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:933 SCORE: 44.00 ================================================================================ Chapter 40: Advanced Concepts FIGURE 40-9. XYZ straddle buy. Cl) 8000 7000 6000 5000 4000 ~ 3000 ~ 2000 ! 1000 01------------------------ -1000 -2000 -3000 At January Expiration Stock Price 871 some of the other risk measurements are considered. Consequently, one cannot blithely go around establishing delta neutral positions and ignoring them, for they may have significant market risk as certain factors change. For example, it is obvious to the naked eye that the two positions described in the previous section - the ratio spread and the long straddle - are not alike at all, but both are delta neutral. If one incorporates the usage of some of the other risk measurements into his position, he will be able to quantify the differences between "neutral" strategies. The sale of a straddle will be used to examine how these vari­ ous factors work. Positions with naked options in them have negative position gamma. This means that as the underlying security moves, the position will acquire traits opposite to that movement: If the security rises, the position becomes short; if it falls, the posi­ tion becomes long. This description generally fits any position with naked options, such as a ratio spread, a naked straddle, or a ratio write. Example: XYZ is at 88. There are three months remaining until July expiration, and the volatility of XYZ is 30%. Suppose 100 July 90 straddles are sold for 10 points - the put and the call each selling for 5. Initially, this position is nearly delta neutral, as ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:934 SCORE: 66.00 ================================================================================ 872 Part VI: Measuring and Trading Volatility shown in Table 40-9. However, since both options are sold, each sale places negative gamma in the position. The usefulness of calculating gamma is shown by this example. The initial posi­ tion is NET short only 100 shares of XYZ, a very small delta. In fact, a person who is a trader of small amounts of stock might actually be induced into believing that he could sell these 100 straddles, because that is equivalent to being short merely 100 shares of the stock. TABLE 40-9. Position delta and gamma of straddle sale. XYZ = 88. Option Position Option Position Position Delto Delta Gamma Gamma Sell l 00 July 90 calls 0.505 -5,050 0.03 -300 Sell 1 00 July 90 puts 0.495 +4,950 0.03 -300 Total shares - 100 -600 Calculating the gamma quickly dispels those notions. The gamma is large: 600 shares of negative gamma. Hence, if the stock moves only 2 points lower, this trad­ er's straddle position can be expected to behave as if it were now long 1,100 shares (the original 100 shares short plus 1,200 that the gamma tells us we can expect to get long)! The position might look like this after the stock drops 2 points: XYZ: 86 Position Sold 1 00 July 90 calls Sold 100 July 90 puts Option Delta 0.44 0.55 Position Delta -4,400 +5,500 + 1 , 100 shares Hence, a 2-point drop in the stock means that the position is already acquiring a "long" look. Further drops will cause the position to become even "longer." This is certainly not a position - being short 100 straddles - for a small trader to be in, even though it might have erroneously appeared that way when one observed only the delta of the position. Paying attention to gamma more fully discloses the real risks. In a similar manner, if the stock had risen 2 points to 90, the position would quickly have become delta short. In fact, one could expect it to be short 1,300 shares in that case: the original short 100 shares plus the 1,200 indicated by the negative gamma. A rise to 90, then, would make the position look like this: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:935 SCORE: 62.00 ================================================================================ Chapter 40: Advanced Concepts XYZ:90 Position Sold 100 July 90 calls Sold 1 00 July 90 puts Option Delto 0.56 0.43 Position Delta -5,600 +4,300 873 1,300 shares These examples demonstrate how quickly a large position, such as being short 100 straddles, can acquire a large delta as the stock moves even a small distance. Extrapolating the moves is not completely correct, because the gamma changes as the stock price changes, but it can give the trader some feel for how much his delta will change. It is often useful to calculate this information in advance, to some point in the near future. Figure 40-10 depicts what the delta of this large short straddle position will be, two weeks after it was first sold. The points on the horizontal axis are stock prices. The quickness with which the neutrality of the position disappears is alarm­ ing. A small move up to 93 - only one standard deviation - in two weeks makes the overall position short the equivalent of about 3,300 shares of XYZ. Figure 40-10 real­ ly shows nothing more than the effect that gamma is having on the position, but it is presented in a form that may be preferable for some traders. What this means is that the position is "fighting" the market: As the market goes up, this position becomes shorter and shorter. That can be an unpleasant situation, both from the point of view of creating unrealized losses as well as from a psycho­ logical viewpoint. The position delta and gamma can be used to estimate the amount of unrealized loss that will occur: Just how much can this position be expected to lose if there is a quick move in the underlying stock? The answer is quickly obtained from the delta and gamma: With the first point that XYZ moves, from 88 to 89, the posi­ tion acts as if it is short 100 shares (the position delta), so it would lose $100. With the next point that XYZ rises, from 89 to 90, the position will act as if it is short the original 100 shares (the position delta), plus another 600 shares (the position gamma). Hence, during that second point of movement by XYZ, the entire position will act as if it is short 700 shares, and therefore lose another $700. Therefore, an immediate 2-point jump in XYZ will cause an unrealized loss of $800 in the position. Summarizing: Loss, first point of stock movement = position delta Loss, second point of stock movement = position delta + gamma Total loss for 2 points of stock movement = 2 x position delta + position gamma ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:936 SCORE: 34.00 ================================================================================ 874 Part VI: Measuring and Trading Volatility FIGURE 40· 1 O. Proiected delta, in 14 days. 6000 4500 3000 Cl) 1500 ~ ro .c (/) 0 'E (1) 80 85 ~ ·5 -1500 95 XYZ Stock Price C" UJ -3000 -4500 Using the example data: Loss, XYZ moves from 88 to 89: -$100 (the position delta) Loss, XYZ moves from 89 to 90: -$100 (delta) - $600 (gamma) : -$700 Total loss, XYZ moves from 88 to 90: -$100 x 2 - $600 = -$800 This can be verified by looking at the prices of the call and put after XYZ has jumped from 88 to 90. One could use a model to calculate expected prices if that happened. However, there is another way. Consider the following statements: If the stock goes up by 1 point, the call will then have a price of: p 1 = Po + delta 5.505 = 5.00 + 0.505 (if XYZ goes to 89 in the example) If the stock goes up 2 points, the call will have an increase of the above amount plus a similar increase for the next point of stock movement. The delta for that sec­ ond point of stock movement is the original delta plus the gamma, since gamma tells one how much his delta is going to change. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:937 SCORE: 72.00 ================================================================================ Chapter 40: Advanced Concepts p2 = p 1 +delta+ gamma, or substituting from above p2 = (p0 + delta) + delta + gamma = Po + 2 x delta + gamma 6.04 = 5.00 + 2 x 0.505 + 0.03 (in the example if XYZ = 90) 875 By the same calculation, the put in the example will be priced at 4.04 if XYZ imme­ diately jumps to 90: 4.04 = 5.00 - 2 X 0.495 + 0.03 So, overall, the call will have increased by 1.04, but the put will only have decreased by 0.96. The unrealized loss would then be computed as -$10,400 for the 100 calls, offset by a gain of $9,600 on the sale of 100 puts, for a net unrealized loss of $800. This verifies the result obtained above using position delta and position gamma. Again, this confirms the logical fact that a quick stock movement will cause unrealized losses in a short straddle position. Continuing on, let us look at some of the other factors affecting the sale of this straddle. The straddle seller has time working in his favor. After the position is estab­ lished, there will not be as much decay in the first two-week period as there will be when expiration draws near. The exact amount of time decay to expect can be calcu­ lated from the theta of the position: XYZ: 88 Position Sold l 00 July 90 calls Sold l 00 July 90 puts Option Theta -0.03 -0.03 Position Theta +$300 +$300 +$600 This is how the position looked with respect to time decay when it was first established (XYZ at 88 and three months remaining until expiration). The theta of the put and the call are essentially the same, and indicate that each option is losing about 3 cents of value each day. Note that the theta is expressed as a negative number, and since these options are sold, the position theta is a positive number. A positive posi­ tion theta means time decay is working in your favor. One could expect to make $300 per day from the sale of the 100 calls. He could expect to make another $300 per day from the sale of the 100 puts. Thus, his overall position is generating a theoretical profit from time decay of $600 per day. The fact that the sale of a straddle generates profits from time decay is not earth-shattering. That is a well-known fact. However, the amount of that time decay ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:938 SCORE: 66.00 ================================================================================ 876 Part VI: Measuring and Trading Volatility is quantified by using theta. Furthermore, it serves to show that this position, which is delta neutral, is not neutral with respect to the passage of time. Finally, let us examine the position with respect to changes in volatility. This is done by calculating the position vega. XYZ:88 Position Sold 1 00 July 90 calls Sold 100 July 90 puts Option Vega 0.18 0.18 Position Vega -$1,800 -$1,800 -$3,600 Again, this information is displayed at the time the position was established, three months to expiration, and with a volatility of 30% for XYZ. The vega is quite large. The fact that the call's vega is 0.18 means that the call price is expected to increase by 18 cents if the implied volatility of the option increases by one percent­ age point, from 30% to 31 %. Since the position is short 100 calls, an increase of 18 cents in the price of the call would translate into a loss of $1,800. The put has a sim­ ilar vega, so the overall position would lose $3,600 if the options trade with an increase in volatility of just one percentage point. Of course, the position would make $3,600 if the volatility decreased by one percentage point, to 29%. This volatility risk, then, is the greatest risk in this short straddle position. As before, it is obvious that an increase in volatility is not good for a position with naked options in it. The use of vega quantifies this risk and shows how important it is to attempt to sell overpriced options when establishing such positions. One should not adhere to any one strategy all the time. For example, one should not always be sell­ ing naked puts. If the implied volatilities of these puts are below historical norms, such a strategy is much more likely to encounter the risk represented by the posi­ tion vega. There have been several times in the recent past - mostly during market crashes - when the implied volatilities of both index and equity options have leaped tremendously. Those times were not kind to sellers of options. However, in almost every case, the implied volatility of index options was quite low before the crash occurred. Thus, any trader who was examining his vega risk would not have been inclined to sell naked options when they were historically "cheap." In summary then, this "neutral" position is, in reality, much more complex when one considers all the other factors. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:939 SCORE: 56.00 ================================================================================ Chapter 40: Advanced Concepts Position summary Risk Factor Position delta = l 00 Position gamma = -600 Position theta = +$600 Position vega = -$3,600 877 Comment Neutral; no immediate exposure to small market movements; lose $100 for 1 point move in underlying. Fairly negative; position will react inversely to market movements, causing losses of $700 for second point of movement by underlying. Favorable; the passage of time works in the position's favor. Very negative; position is extremely subject to changes in implied volatility. This straddle sale has only one thing guaranteed to work for it initially: time decay. (The risk factors will change as price, time, and volatility change.) Stock price movements will not be helpful, and there will always be stock price movements, so one can expect to feel the negative effect of those price changes. Volatility is the big unknown. If it decreases, the straddle seller will profit handsomely. Realistically, however, it can only decrease by a limited amount. If it increases, very bad things will happen to the profitability of the position. Even worse, if the implied volatility is increasing, there is a fairly likely chance that the underlying stock will be jumping around quite a bit as well. That isn't good either. Thus, it is imperative that the strad­ dle seller engage in the strategy only when there is a reasonable expectation that volatilities are high and can be expected to decrease. If there is significant danger of the opposite occurring, the strategy should be avoided. If volatility remains relatively stable, one can anticipate what effects the passage of time will have on the position. The delta will not change much, since the options are nearly at-the-money. However, the gamma will increase, indicating that nearer to expiration, short-term price movements will have more exaggerated effects on the unrealized profits of the position. The theta will grow even more, indicating that time will be an even better friend for the straddle writer. Shorter-term options tend to decay at a faster rate than do longer-term ones. Finally, the vega will decrease some as well, so that the effect of an increase in implied volatility alone will not be as dam­ aging to the position when there is significantly less time remaining. So, the passage ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:940 SCORE: 79.00 ================================================================================ 878 Part VI: Measuring and Trading Volatility of time generally will improve most aspects of this naked straddle sale. However, that does not mitigate the current situation, nor does it imply that there will be no risk if a little time passes. The type of analysis shown in the preceding examples gives a much more in­ depth look than merely envisioning the straddle sale as being delta short 100 shares or looking at how the position will do at expiration. In the previous example, it is known that the straddle writer will profit if XYZ is between 80 and 100 in three months, at expiration. However, what might happen in the interim is another matter entirely. The delta, gamma, theta, and vega are useful for the purpose of defining how the position will behave or misbehave at the current point in time. Refer back to the table of strategies at the beginning of this section. Notice that ratio writing or straddle selling ( they are equivalent strategies) have the characteris­ tics that have been described in detail: Delta is 0, and several other factors are neg­ ative. It has been shown how those negative factors translate into potential profits or losses. Observing other lines in the same table, note that covered writing and naked put selling ( they are also equivalent, don't forget) have a description very similar to straddle selling: Delta is positive, and the other factors are negative. This is a worse situation than selling naked straddles, for it entails all the same risks, but in addition will suffer losses on immediate downward moves by the underlying stock. The point to be made here is that if one felt that straddle selling is not a particularly attractive strategy after he had observed these examples, he then should feel even less inclined to do covered writing, for it has all the same risk factors and isn't even delta neutral. An example that was given in the chapter on futures options trading will be e,,'Panded as promised at this time. To review, one may often find volatility skewing in futures options, but it was noted that one should not normally buy an at-the-money call (the cheapest one) and sell a large quantity of out-of-the-money calls just because that looks like the biggest theoretical advantage. The following example was given. It will now be expanded to include the concept of gamma. Example: Heavy volatility skewing exists in the prices of January soybean options: The out-of-the-money calls are much more expensive than the at-the-money calls. The following data is known: January soybeans: 583 Option Price Implied Volatility Delta Gamma 575 call 19.50 15% 0.55 .0100 675 call 2.25 23% 0.09 .0026 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:941 SCORE: 36.00 ================================================================================ Chapter 40: Advanced Concepts Using deltas, the following spread appears to be neutral: Buy l January bean 57 5 call at 19 .50 Sell 6 January bean 675 calls at 2.25 Net position: 19.50 DB 13.50 CR 6 Debit 879 At the time the original example was presented, it was demonstrated through the use of the profit picture that the ratio was too steep and problems could result in a large rally. Now that one has the concept of gamma at his disposal, he can quantify what those problems are. The position gamma of this spread is quite negative: Position gamma = .01 - 6 x .0026 = -0.0056 That is, for every 10 points that January soybeans rally, the position will become short about 1/2 of one futures contract. The maximum profit point, 675, is 92 points above the current price of 583. While beans would not normally rally 92 points in only a few days, it does demonstrate that this position could become very short if beans quickly rallied to the point of maximum profit potential. Rest assured there would be no profit if that happened. Even a small rally of 20 cents (points) in soybeans - less than the daily limit - would begin to make this tiny spread noticeably short. If one had established the spread in some quantity, say buying 100 and selling 600, he could become seriously short very fast. A neutral spreader would not use such a large ratio in this spread. Rather, he would neutralize the gamma and then attempt to deal with the resulting delta. The next section deals with ways to accomplish that. CREATING MULTIFACETED NEUTRALITY So what is the strategist to do? He can attempt to construct positions that are neutral with respect to the other factors if he perceives them as a risk. There is no reason why a position cannot be constructed as veg a neutral rather than delta neutral, if he wants to eliminate the risk of volatility increases or decreases. Or, maybe he wants to elim­ inate the risk of stock price movements, in which case he would attempt to be gamma neutral as well as delta neutral. This seems like a simple concept until one first attempts to establish a position that is neutral with respect to more than one risk variable. For example, if one is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:942 SCORE: 88.00 ================================================================================ 880 Part VI: Measuring and Trading VolatiRty attempting to create a spread that is neutral with respect to both gamma and delta, he could attempt it in the following way: Example: XYZ is 60. A spreader wants to establish a spread that is neutral with respect to both gamma and delta, using the following prices: Option October 60 call October 70 call Delta 0.60 0.25 Gamma 0.050 0.025 The secret to determining a spread that is neutral with respect to both risk meas­ ures is to neutralize gamma first, for delta can always be neutralized by taking an off­ setting position in the underlying security, whether it be stock or futures. First, deter­ mine a gamma neutral spread by dividing the two gammas: Gamma neutral ratio= 0.050/0.025 = 2-to-l So, buying one October 60 and selling two October 70 calls would be a gamma neutral spread. Now, the position delta of that spread is computed: Position Long 1 October 60 call Short 2 October 70 calls Net position delta: Delta 0.60 0.25 Position Delta +60 shares -50 shares + 10 shares Hence, this gamma neutral ratio is making the position delta long by 10 shares of stock for each l-by-2 spread that is established. For example, if one bought 100 October 60 calls and sold 200 October 70 calls, his position delta would be long 1,000 shares. This position delta is easily neutralized by selling short 1,000 shares of the stock. The resulting position is both gamma neutral and delta neutral: Option Position Option Position Position Delta Delta Gamma Gamma Short 1,000 XYZ 1.00 -1,000 0 0 Long 1 00 October 60 calls 0.60 +6,000 0.050 + 500 Short 200 October 70 calls 0.25 -5,000 0.025 - 500 Net Position: 0 0 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:943 SCORE: 78.00 ================================================================================ Chapter 40: Advanced Concepts 881 Hence, it is always a simple matter to create a position that is both gamma and delta neutral. In fact, it is just as simple to create a position that is neutral with respect to delta and any other risk measure, because all that is necessary is to create a neutral ratio of the other risk measure (gamma, vega, theta, etc.) and then eliminate the resulting position delta by using the underlying. In theory, one could construct a position that was neutral with respect to all five risk measures (or six, if you really want to go overboard and include "gamma of the gamma" as well). Of course, there wouldn't be much profit potential in such a posi­ tion, either. But such constructions are actually employed, or at least attempted, by traders such as market-makers who try to make their profits from the difference between the bid and off er of an option quote, and not from assuming market risk Still, the concept of being neutral with respect to more than one risk factor is a valid one. In fact, if a strategist can determine what he is really attempting to accom­ plish, he can often negate other factors and construct a position designed to accom­ plish exactly what he wants. Suppose that one thought the implied volatility of a cer­ tain set of options was too high. He could just sell straddles and attempt to capture that volatility. However, he is then exposed to movements by the underlying stock He would be better served to construct a position with negative vega to reflect his expec­ tation on volatility, but then also have the position be delta neutral and gamma neutral, so that there would be little risk to the position from market movements. This can normally be done quite easily. An example will demonstrate how. Example: XYZ is 48. There are three months to expiration, and the volatility of XYZ and its options is 35%. The following information is also known: XYZ:48 Option Price Delta Gamma Vega April 50 call 2.50 0.47 0.045 0.08 April 60 call l.00 0.17 0.026 0.06 For whatever reasons - perhaps the historical volatility is much lower - the strategist decides that he wants to sell volatility. That is, he wants to have a negative position vega so that when the volatility decreases, he will make money. This can probably be accomplished by buying some April 50 calls and selling more April 60 calls. However, he does not want any risk of price movement, so some analysis must be done. First, he should determine a gamma neutral spread. This is done in much the same manner as determining a delta neutral spread, except that gamma is used. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:944 SCORE: 68.00 ================================================================================ 882 Part VI: Measuring and Trading Volatmty Merely divide the two gammas to determine the neutral ratio to be used. In this case, assume that the April 50 call and the April 60 call are to be used: Gamma neutral ratio: 0.045/0.026 = 1.73-to-l Thus, a gamma neutral position would be created by buying 100 April 50's and sell­ ing 173 April 60's. Alternatively, buying 10 and selling 17 would be close to gamma neutral as well. The larger position will be used for the remainder of this example. Now that this ratio has been chosen, what is the effect on delta and vega? Option Position Option Position Option Position Position Delta Delta Gamma Gamma Vega Vega Long 1 00 April 50 0.47 +4,700 0.045 +450 0.08 + $800 Short 173 April 60 0.17 -2,941 0.026 -450 0.06 -1,038 Total: + 1,759 0 - $238 The position delta is long 1,759 shares of XYZ. This can easily be "cured" by shorting 1,700 or 1,800 shares ofXYZ to neutralize the delta. Consequently, the com­ plete position, including the short 1,700 shares, would be neutral with respect to both delta and gamma, and would have the desired negative vega. The actual profit picture at expiration is shown in Figure 40-11. Bear in mind, however, that the strategist would normally not intend to hold a position like this until expiration. He would close it out if his expectations on volatility decline were fulfilled ( or proved false). FIGURE 40-11. Spread with negative vega; gamma and delta neutral. 40000...., .... 10000 50 55 60 XVZ :Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:945 SCORE: 68.00 ================================================================================ Chapter 40: Advanced Concepts 883 One other point should be made: The fact that gamma and delta are neutral to begin with does not mean that they will remain neutral indefinitely as the stock moves (or even as volatility changes). However, there will be little or no effect of stock price movements on the position in the short run. In summary, then, one can always create a position that is neutral with respect to both gamma and delta by first choosing a ratio that makes the gamma zero, and then using a position in the underlying security to neutralize the delta that is created by the chosen ratio. This type of position would always involve two options and some stock. The resulting position will not necessarily be neutral with respect to the other risk factors. THE MATHEMATICAL APPROACH The strategist should be aware that the process of determining neutrality in several of the risk variables can be handled quite easily by a computer. All that is required is to solve a series of simultaneous equations. In the preceding example, the resulting vega was negative: -$238. For each decline of 1 percentage point in volatility from .the current level of 35%, one could expect to make $238. This result could have been reached by another method, as long as one were willing to spell out in advance the amount of vega risk he wants to accept. Then, he can also assume the gamma is zero and solve for the quantity of options to trade in the spread. The delta would be neutralized, as above, by using the common stock. Example: Prices are the same as in the preceding example. XYZ is 48. There are three months to expiration, and the volatility of XYZ and its options is 35%. The fol­ lowing information is also the same: Option April 50 call April 60 call Price 2.50 1.01 Delta 0.47 0.17 Gamma 0.045 0.026 Vega 0.08 0.06 A spreader expects volatility to decline and is willing to set up a position where­ by he will profit by $250 for each one percentage decrease in volatility. Moreover, he wants to be gamma and delta neutral. He knows that he can eventually neutralize any delta by using XYZ common stock, as in the previous example. How many options should be spread to achieve the desired result? ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:946 SCORE: 29.00 ================================================================================ 884 Part VI: Measuring and Trading VolatiHty To answer the question, one must create two equations in two unknowns, x and y. The unknowns represent the quantities of options to be bought and sold, respec­ tively. The constants in the equations are taken from the table above. The first equation represents gamma neutral: 0.045 X + 0.026 y = 0, where xis the number of April 50's in the spread and y is the number of April 60's. Note that the constants in the equation are the gammas of the two calls involved. The second equation represents the desired vega risk of making 2.5 points, or $250, if the volatility decreases: 0.08 X + 0.06 y = - 2.5, where x and y are the same quantities as in the first equation, and the constants in this equa­ tion are the gammas of the options. Furthermore, note that the vega risk is negative, since the spreader wants to profit if volatility decreases. Solving the two equations in two unknowns by algebraic methods yields the fol­ lowing results: Equations: 0.045 X + 0.026 y = 0 0.08 X + 0.06 Y = - 2.5 Solutions: X = 104.80 y = -181.45 This means that one would buy 105 April 50 calls, since x being positive means that the options would be bought. He would also sell 181 April 60 calls (y is negative, which implies that the calls would be sold). This is nearly the same ratio determined in the previous example. The quantities are slightly higher, since the vega here is -$250 instead of the -$238 achieved in the previous example. Finally, one would again determine the amount of stock to buy or sell to neu­ tralize the delta by computing the position delta: Position delta = 105 x 0.47 - 181 x 0.17 = 18.58 Thus 1,858 shares of XYZ would be shorted to neutralize the position. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:947 SCORE: 34.00 ================================================================================ Chapter 40: Advanced Concepts 885 Note: All the equations cannot be set equal to zero, or the solution will be all zeros. This is easily handled by setting at least one equation equal to a small, nonzero quantity, such as 0.1. As long as at least one of the risk factors is nonzero, one can determine the neutral ratio for all other factors merely by solving these simultaneous equations. There are plenty of low-cost computer programs that can solve simultane­ ous equations such as these. This concept can be carried to greater lengths in order to determine the best spread to create in order to achieve the desired results. One might even try to use three different options, using the third option to neutralize delta, so that he wouldn't have to neutralize with stock. The third equation would use deltas as constants and would be set to equal zero, representing delta neutral. Solving this would require solving three equations in three unknowns, a simple matter for a computer. As long as at least one of the risk factors is nonzero, one can determine the neu­ tral ratio for all other factors merely by solving these simultaneous equations. Even more importantly, the computer can scan many combinations of options that produce a position that is both gamma and delta neutral and has a specific position vega (-$238, for example). One would then choose the "best" spread of the available pos­ sibilities by logical methods including, if possible, choosing one with positive theta, so time is working in his favor. To summarize, one can neutralize all variables, or he can specify the risk that he wants to accept in any of them. Merely write the equations and solve them. It is best to use a computer to do this, but the fact that it can be done adds an entirely new, broad dimension to option spreading and risk-reducing strategies. EVALUATING A POSITION USING THE RISK MEASURES The previous sections have dealt with establishing a new position and determining its neutrality or lack thereof. However, the most important use of these risk measures is to predict how a position will perform into the future. At a minimum, a serious strate­ gist should use a computer to print out a projection of the profits and losses and posi­ tion risk at future expected prices. Moreover, this type of analysis should be done for several future times in order to give the strategist an idea of how the passage of time and the resultant larger movements by the underlying security would affect the posi­ tion. First, one would choose an appropriate time period - say, 7 days hence - for the first analysis. Then he should use the statistical projection of stock prices (see Chapter 28 on mathematical applications) to determine probable prices for the underlying security at that time. Obviously, this stock price projection needs to use volatility, and ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:948 SCORE: 20.00 ================================================================================ 886 Part VI: Measuring and Trading Volatility that is somewhat variable. But, for the purposes of such a projection, it is acceptable to use the current volatility. The results of as many as 9 stock prices might be dis­ played: every one-half standard deviation from -2 through + 2 (-2.0, -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0). Example: XYZ is at 60 and has a volatility of 35%. A distribution of stock prices 7 days into the future would be determined using the equation: Future Price = Current Price x eav-ft where a corresponds to the constants in the following table: (-2.0 ... 2.0): # Standard Deviations -2.0 - 1.5 - 1.0 -0.5 0 0.5 1.0 1.5 2.0 Projected Stack Price 54.46 55.79 57.16 58.56 60.00 61.47 62.98 64.52 66.11 Again, refer to Chapter 28 on mathematical applications for a more in-depth discussion of this price determination equation. Note that the formula used to project prices has time as one of its components. This means that as we look further out in time, the range of possible stock prices will expand - a necessary and logical component of this analysis. For example, if the prices were being determined 14 days into the future, the range of prices would be from 52.31 to 68.82. That is, XYZ has the same probability of being at 54.46 in 7 days that it has of being at 52.31 in 14 days. At expiration, some 90 days hence, the range would be quite a bit wider still. Do not make the mistake of trying to evaluate the position at the same prices for each time period (7 days, 14 days, 1 rnonth, expiration, etc.). Such an analysis would be wrong. Once the appropriate stock prices have been determined, the following quanti­ ties would be calculated for each stock price: profit or loss, position delta, position gamma, position theta, and position vega. (Position rho is generally a less important risk measure for stock and futures short-term options.) Armed with this information, the strategist can be prepared to face the future. An important item to note: A model ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:949 SCORE: 79.00 ================================================================================ Chapter 40: Advanced Concepts 887 will necessarily be used to make these projections. As was shown earlier, if there is a distortion in the current implied volatilities of the options involved in the position, the strategist should use the current implieds as input to the model for future option price projections. If he does not, the position may look overly attractive if expensive options are being sold or cheap ones are being bought. A truer profit picture is obtained by propagating the current implied volatility structure into the near future. Using an example similar to the previous one a ratio spread using short stock to make it delta neutral - the concepts will be described. Initial Position. XYZ is at 60. The January 70 calls, which have three months until expiration, are expensive with respect to the January 60 calls. A strategist expects this discrepancy to disappear when the implied volatility of XYZ options decreases. He therefore established the following position, which is both gamma and delta neutral. Position Delta Gamma Long 100 January 60 calls 0.57 0.0723 Short 240 January 70 calls 0.20 0.0298 Short 800 XYZ The risk measures for the entire position are: Position delta: -38 shares (virtually delta neutral) Position gamma: + 7 shares (gamma neutral) Position theta: + $263 Position vega: -$827 Theta Vega -0.020 0.109 -0.019 0.080 Thus, the position is both gamma and delta neutral. Moreover, it has the attrac­ tive feature of making $263 per day because of the positive theta. Finally, as was the intention of the spreader, it will make money if the volatility of XYZ declines: $827 for each percentage point decrease in implied volatility. Two equations in two unknowns (gamma and vega) were solved to obtain the quantities to buy and sell. The resulting position delta was neutralized by selling 800 XYZ. The following analyses will assume that the relative expensiveness of the April 70 calls persists. These are the calls that were sold in the position. If that overpricing should disappear, the spread would look more favorable, but there is no guarantee that they will cheapen - especially over a short time period such as one or two weeks. How would the position look in 7 days at the stock prices determined above? ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:950 SCORE: 31.00 ================================================================================ 888 Part VI: Measuring and Trading Vo/atillty Stock Price P&L Delta Gamma Theta Vega 54.46 1905 - 7.40 1.62 0.94 - 1.57 55.79 1077 - 4.90 2.07 1.18 - 1.96 57.16 606 1.97 2.13 1.53 - 2.90 58.56 528 0.74 1.65 2.00 -4.62 60.00 771 2.38 0.56 2.63 -7.22 61.47 1127 2.07 - 1.01 3.38 -10.63 62.98 1252 - 0.87 - 2.85 4.22 -14.56 64.52 702 - 6.73 - 4.67 5.07 -18.61 66.11 - 1019 -15.42 - 6.21 5.85 -22.31 In a similar manner, the position would have the following characteristics after 14 days had passed: Stock Price P&L Delto Gamma Theta Vega 52.31 4221 - 9.10 0.69 0.55 - 0.98 54.14 2731 - 6.93 1.69 0.75 - 0.89 56.02 1782 - 2.87 2.51 1.06 - 1.21 57.98 1717 2.17 2.44 1.61 - 2.69 60.00 2577 5.85 1.00 2.51 -6.00 62.09 3839 5.29 - 1.63 3.73 -11.05 64.26 4361 - 1.55 - 4.61 5.09 -16.90 66.50 2631 -14.80 - 7.02 6.31 -22.17 68.82 - 2799 -32.83 - 8.32 7.18 -25.72 The same information will be presented graphically in Figure 40-13 so that those who prefer pictures instead of columns of numbers can follow the discussions easily. First, the profitability of the spread can be examined. This profit picture assumes that the volatility of XYZ remains unchanged. Note that in 7 days, there is a small profit if the stock remains unchanged. This is to be expected, since theta was positive, and therefore time is working in favor of this spread. Likewise, in 14 days, there is an even bigger profit if XYZ remains relatively unchanged - again due to the positive theta. Overall, there is an expected profit of $800 in 7 days, or $2,600 in 14 days, from this position. This indicates that it is an attractive situation statistically, but, of course, it does not mean that one cannot lose money. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:951 SCORE: 45.00 ================================================================================ Chapter 40: Advanced Concepts 889 Continuing to look at the profit picture, the downside is favorable to the spread since the short stock in the position would contribute to ever larger profits in the case that XYZ tumbles dramatically (see Figure 40-12). The upside is where problems could develop. In 7 days, the position breaks even at about 65 on the upside; in 14 days, it breaks even at about 67.50. The reader may be asking, "Why is there such a dramatic risk to the upside? I thought the position was delta neutral and gamma neutral." True, the position was originally neutral with respect to both those variables. That neutrality explains the flatness of the profit curves about the current stock price of 60. However, once the stock has moved 1.50 standard deviations to the upside, the neutrality begins to dis­ appear. To see this, let us look at Figures 40-13 and 40-14 that show both the posi­ tion delta and position gamma 7 days and 14 days after the spread was established. Again, these are the same numbers listed in the previous tables. First, look at the position delta in 7 days (Figure 40-13). Note that the position remains relatively delta neutral with XYZ between 57 and 63. This is because the gamma was initially neutral. However, the position begins to get quite delta short if XYZ rises above 63 or falls below 57 in 7 days. What is happening to gamma while this is going on? Since we just observed that the delta eventually changes, that has to mean that the position is acquiring some gamma. FIGURE 40-12. XYZ ratio spread, gamma and delta neutral. 4300 3400 2500 1600 ~ 700 a.. 0 -200 53 55 57 59 61 63 .-1100 -2000 Stock Price ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:953 SCORE: 59.00 ================================================================================ Chapter 40: Advanced Concepts 891 Figure 40-14 depicts the fact that gamma is not very stable, considering that it started at nearly zero. If XYZ falls, gamma increases a little, reflecting the fact that the position will get somewhat shorter as XYZ falls. But since there are only calls cou­ pled with short stock in this position, there is no risk to the downside. Positive gamma, even a small positive gamma like this one, is beneficial to stock movement. The upside is another matter entirely. The gamma begins to become seriously negative above a stock price of 63 in 7 days. Recall that negative gamma means that one's position is about to react poorly to price changes in the market - the position will soon be "fighting the market." As the stock goes even higher, the gamma becomes even more negative. These observations apply to stock price movements in either 7 days or 14 days; in fact, the effect on gamma does not seem to be particu­ larly dependent on time in this example, since the two lines on Figure 40-15 are very close to each other. The above information depicts in detailed form the fact that this position will not behave well if the stock rises too far in too short a time. However, stable stock prices will produce profits, as will falling prices. These are not earth-shattering con­ clusions since, by simple observation, one can see that there are extra short calls plus some short stock in the position. However, the point of calculating this information in advance is to be able to anticipate where to make adjustments and how much to adjust. Follow-Up Action. How should the strategist use this information? A sim­ plistic approach is to adjust the delta as it becomes non-neutral. This won't do anything for gamma, however, and may therefore not necessarily be the best approach. If one were to adjust only the delta, he would do it in the following manner: The chart of delta (Figure 40-13) shows that the position will be approximately delta short 800 shares if XYZ rises to 64.50 in a week. One sim­ ple plan would be to cover the 800 shares of XYZ that are short if the stock rises to 64.50. Covering the 800 shares would return the position to delta neutral at that time. Note that if the stock rises at a slower pace, the point at which the strategist would cover the 800 shares moves higher. For example, the delta in 14 days (again in Figure 40-13) shows that XYZ would have to be at about 65.50 for the position to be delta short 800 shares. Hence, if it took two weeks for XYZ to begin rising, one could wait until 65.50 before covering the 800 shares and returning the position to delta neutral. In either case, the purchase of the 800 shares does not take care of the negative gamma that is creeping into the position as the stock rises. The only way to counter negative gamma is to buy options, not stock. To return a position to neutrality with ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:954 SCORE: 69.00 ================================================================================ 892 Part VI: Measuring and Trading Volatility respect to more than one risk variable requires one to approach the problem as he did when the position was established: Neutralize the gamma first, and then use stock to adjust the delta. Note the difference between this approach and the one described in the previous paragraph. Here, we are trying to adjust gamma first, and will get to delta later. In order to add some positive gamma, one might want to buy back (cover) some of the January 70 calls that are currently short. Suppose that the decision is made to cover when XYZ reaches 65.50 in 14 days. From the graph above, one can see that the position would be approximately gamma short 700 shares at the time. Suppose that the gamma of the January 70 calls is 0.07. Then, one would have to cover 100 January 70 calls to add 700 shares of positive gamma to the position, returning it to gamma neutral. This purchase would, of course, make the position delta long, so some stock would have to be sold short as well in order to make the position delta neutral once again. Thus, the procedure for follow-up action is somewhat similar to that for estab­ lishing the position: First, neutralize the gamma and then eliminate the resulting delta by using the common stock. The resulting profit graph will not be shown for this follow-up adjustment, since the process could go on and on. However, a few observations are pertinent. First, the purchase of calls to reduce the negative gamma hurts the original thesis of the position - to have negative vega and positive theta, if possible. Buying calls will add vega to and subtract theta from the position, which is not desirable. However, it is more desirable than letting losses build up in the posi­ tion as the stock continues to run to the upside. Second, one might choose to rerrwve the position if it is profitable. This might happen if the volatility did decrease as expected. Then, when the stock rallies, producing negative gamma, one might actu­ ally have a profit, because his assumption concerning volatility had been right. If he does not see much further potential gains from decreasing volatility, he might use the point at which negative gamma starts to build up as the exit point from his position. Third, one might choose to accept the acquired gamma risk. Rather than jeopardize his initial thesis, one may just want to adjust the delta and let the gamma build up. This is no longer a neutral strategy, but one may have reasons for approaching the position this way. At least he has calculated the risk and is aware of it. If he chooses to accept it rather than eliminate it, that is his decision. Finally, it is obvious that the process is dynamic. As factors change (stock price, volatility, time), the position itself changes and the strategist is presented with new choices. There is no absolutely correct adjustment. The process is more of an art than a science at times. Moreover, the strategist should continue to recalculate these prof­ it pictures and risk measures as the stock moves and time passes, or if there is a ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:955 SCORE: 88.00 ================================================================================ Chapter 40: Advanced Concepts 893 change in the securities involved in the position. There is one absolute truism and that is that the serious strategist should be aware of the risk his position has with respect to at least the four basic measures of delta, gamma, theta, and vega. To be ignorant of the risk is to be delinquent in the management of the position. TRADING GAMMA FROM THE LONG SIDE The strategist who is selling overpriced options and hedging that purchase with other options or stock will often have a position similar to the one described earlier. Large stock movements - at least in one direction will typically be a problem for such positions. The opposite of this strategy would be to have a position that is long gamma. That is, the position does better if the stock moves quickly in one direction. While this seems pleasing to the psyche, these types of positions have their own brand of risk. The simplest position with long gamma is a long straddle, or a backspread (reverse ratio spread). Another way to construct a position with long gamma is to invert a calendar spread - to buy the near-term option and to sell a longer-term one. Since a near-term option has a higher gamma than a longer-term one with the same strike, such a position has long gamma. In fact, traders who expect violent action in a stock often construct such a position for the very reason that the public will come in behind them, bid up the short-term calls (increasing their implied volatility), and make the spread more profitable for the trader. Unfortunately, all of these positions often involve being long just about every­ thing else, including theta and vega as well. This means that time is working against the position, and that swings in implied volatility can be helpful or harmful as well. Can one construct a position that is long gamma, but is not so subject to the other variables? Of course he can, but what would it look like? The answer, as one might suspect, is not an ironclad one. For the following examples, assume these prices exist: XYZ: 60 Option March 60 call June 60 call Price 3.25 5.50 Delta 0.54 0.57 Gamma 0.0510 0.0306 Theta 0.033 0.021 Vega 0.089 0.147 Example: Suppose that a strategist wants to create a position that is gamma long, but is neutral with respect to both delta and vega. He thinks the stock will move, but is not sure of the price direction, and does not want to have any risk with respect to ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:956 SCORE: 69.00 ================================================================================ 894 Part VI: Measuring and Trading Volatility quick changes in volatility. In order to quantify the statement that he "wants to be gamma long," let us assume that he wants to be gamma long 1,000 shares or 10 con­ tracts. It is known that delta can always be neutralized last, so let us concentrate on the other two variables first. The two equations below are used to determine the quanti­ ties to buy in order to make gamma long and vega neutral: 0.0510x + 0.0306y = 10 (gamma, expressed in# of contracts) 0.089x + 0.147y = 0 (vega) The solution to these equations is: X = 308, y = -186 Thus, one would buy 308 March 60 calls and would sell 186 June 60 calls. This is the reverse calendar spread that was discussed: Near-term calls are bought and longer­ term calls are sold. Finally, the delta must be neutralized. To do this, calculate the position delta using the quantities just determined: Position delta= 0.54 x 308 - 0.57 x 186 = 60.30 So, the position is long 60 contracts, or 6,000 shares. It can be made delta neutral by selling short 6,000 shares of XYZ. The overall position would look like this: Position Short 6,000 XYZ Long 308 March 60 calls Short 186 June 60 calls Its risk measurements are: Delta 1.00 0.54 0.57 Position delta: long 30 shares (neutral) Position vega: $7 (neutral) Position gamma: long 1,001 shares Gamma 0 0.0510 0.0306 Vega 0 0.089 0.147 This position then satisfies the initial objectives of wanting to be gamma long 1,000 shares, but delta and vega neutral. Finally, note that theta = -$625. The position will lose $625 per day from time decay. The strategist must go further than this analysis, especially if one is dealing with positions that are not simple constructions. He should calculate a profit picture as ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:957 SCORE: 47.00 ================================================================================ Chapter 40: Advanced Concepts 895 well as look at how the risk measures behave as time passes and the stock price changes. Figure 40-15 (see Tables 40-10, 40-11, and 40-12) shows the profit potential in 7 days, in 14 days, and at March expiration. Figure 40-16 shows the position vega at the 7- and 14-day time intervals. Before discussing these items, the data will be pre­ sented in tabular form at three different times: in 7 days, in 14 days, and at March expiration. The data in Table 40-10 depict the position in 7 days. Table 40-11 represents the results in 14 days. Finally, the position as it looks at March expiration should be known as well (see Table 40-12). In each case, note that the stock prices are calculated in accordance with the statistical formula shown in the last section. The more time that passes, the further it is possible for the stock to roam from the current price. The profit picture (Figure 40-15) shows that this position looks much like a long straddle would: It makes large, symmetric profits if the stock goes either way up or way down. Moreover, the losses if the stock remains relatively unchanged can be large. These losses tend to mount right away, becoming significant even in 14 days. Hence, if one enters this type of position, he had better get the desired stock move­ ment quickly, or be prepared to cut his losses and exit the position. The most startling thing to note about the entire position is the devastating effect of time on the position. The profit picture shows that large losses will result if the stock movement that is expected does not materialize. These losses are completely due to time decay. Theta is negative in the initial position ($625 of losses per day), and remains negative and surprisingly constant - until March expiration ( when the long calls expire). Time also affects vega. Notice how the vega begins to get negative right away and keeps getting much more negative as time passes. Simply, it can be seen that as time passes, the position becomes vulnerable to increases in implied volatility. This relationship between time and volatility might not be readily apparent to the strategist unless he takes the time to calculate these sorts of tables or figures. In fact, one may be somewhat confounded by this observation. What is happening is that as time passes, the options that are owned are less explosive if volatility increas­ es, but the options that were sold have a lot of time remaining, and are therefore apt to increase violently if volatility spurts upward. Figures 40-17 and 40-18 provide less enlightening information about delta and gamma. Since gamma was positive to start with, the delta increases dramatically as the stock rises, and decreases just as fast if the stock falls (Figure 40-18). This is stan­ dard behavior for positions with long gamma; a long straddle would look very similar. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:958 SCORE: 25.00 ================================================================================ 896 FIGURE 40-15. Trading long gamma, profit picture. 80,000 60,000 40,000 20,000 -20,000 -40,000 -60,000 TABLE 40-1 O. Stock Price Part VI: Measuring and Trading Volatility Risk measures of long gamma position in 7 days. Stock Price P&L Delta Gamma Theta Vega 54.46 12259 - 58.72 8.28 4.15 - 5.74 55.79 5202 - 46.60 9.78 5.20 - 4.18 57.16 - 224 - 32.45 10.80 6.09 - 2.85 58.56 - 3670 - 16.91 11.25 6.73 - 1.94 60.00 - 4975 - 0.80 11.08 7.04 - l .63 61.47 - 3901 15.01 10.32 6.98 - 1.96 62.98 - 507 29.69 9.09 6.57 - 2.89 64.52 5105 42.56 7.54 5.87 -4.29 66. l l 12717 53. l 7 5.86 4.97 - 5.96 Notice that gamma remains positive throughout (Figure 40-17), although it falls to smaller levels if the stock moves toward the end of the pricing ranges used in the analyses. Again, this is standard action for a long straddle. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:959 SCORE: 25.00 ================================================================================ Chapter 40: Advanced Concepts FIGURE 40-16. Trading long gamma, position vega. 55 60 0 -2 -4 al 0) ~ -6 -8 -10 Stock Price TABLE 40-11. 65 Risk measures of long gamma position in 14 days. Stock Price P&L Delta Gamma 52.31 24945 - 79.34 4.75 54.14 11445 - 67.68 8.00 56.02 277 -49.79 10.79 57.98 - 7263 -26.87 12.42 60.00 - 10141 - 1.44 12.47 62.09 - 7784 23.32 10.99 64.26 347 44.47 8.45 66.50 11491 60.12 5.55 68.82 26672 69.81 2.92 891 Theta Vega 2.10 - 9.91 3.91 - 7.87 5.76 - 5.56 7.21 - 3.73 7.88 - 3.04 7.60 - 3.78 6.47 - 5.71 4.82 - 8.20 3.09 -10.48 So, is this a good position? That is a difficult question to answer unless one knows what is going to happen to the underlying stock. Statistically, this type of posi­ tion has a negative expected return and would generally produce losses over the long run. However, in situations in which the near-term options are destined to get over­ heated - perhaps because of a takeover rumor or just a leak of material information ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:960 SCORE: 23.00 ================================================================================ 898 Part VI: Measuring and Trading Volatility TABLE 40-12. Risk measures of long gamma position at March expiration. Stock Price P&L Delta 46.19 81327 - 75.69 49.31 55628 - 89.84 52.64 22378 -110.50 56.20 - 21523 -136.65 60.00 78907 144.68 64.06 - 25946 117.44 68.39 19787 95.03 73.01 59732 79.05 77.95 96062 69.19 FIGURE 40-17. Trading long gamma, position gamma. (J) (I) 1200 1000 800 ~ 600 .c (/) 400 200 55 60 Stock Price Gamma Theta Vega - 3.65 -1.32 - 6.88 - 5.39 -2.25 -11.43 - 6.89 -3.33 -16.50 - 7.62 -4.28 -20.67 - 7.29 -4.79 -22.49 - 6.03 -4.70 -21.26 - 4.31 -4.10 -17.44 - 2.67 -3.24 -12.43 - 1.43 -2.41 - 7.69 65 about a company - many sophisticated traders establish this type of position to take advantage of the expected explosion in stock price. Other Variations. Without going into as much detail, it is possible to com­ pare the above position with similar ones. The purpose in doing so is to illustrate how a change in the strategist's initial requirements would alter the established ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:961 SCORE: 39.00 ================================================================================ Chapter 40: Advanced Concepts FIGURE 40-1 8. Trading long gamma, position delta. 6000 4000 2000 "' ~ 01---------,-----~rr------,,----- .s::. (J) -2000 -4000 -8000 -8000 55 65 Stock Price 899 position. In the preceding position, the strategist wanted to be gamma long, but neutral with respect to delta and volatility. Suppose he not only expects price movement (meaning he wants positive gamma), but also expects an increase in volatility. If that were the case, he would want positive vega as well. Suppose he quantifies that desire by deciding that he wants to make $1,000 for every one percentage increase in volatility. The simultaneous equations would then be: 0.050lx + 0.0306y = 10 (gamma) 0.089x + 0.147y = 10 (vega) The solution to these equations is: X = 243, y = -80 Furthermore, 8,500 shares would have to be sold short in order to make the position delta neutral. The resulting position would then be: Short 8,500 XYZ Long 243 March 60 calls Short 80 June 60 calls Delta: neutral Gamma: long 1,000 shares Vega: long $1,000 Theta: long $630 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:962 SCORE: 53.00 ================================================================================ 900 Part VI: Measuring and Trading VolatiHty Recall that the position discussed in the last section was vega neutral and was: Short 6,000 XYZ Long 308 March 60 calls Short 186 June 60 calls Delta: neutral Gamma: long 1,000 shares Vega: neutral Theta: long $625 Notice that in the new position, there are over three times as many long March 60 calls as there are short June 60 calls. This is a much larger ratio than in the vega neutral position, in which about 1.6 calls were bought for each one sold. This even greater preponderance of near-term calls that are purchased means the newer posi­ tion has an even larger exposure to time decay than did the previous one. That is, in order to acquire the positive vega, one is forced to take on even more risk with respect to time decay. For that reason, this is a less desirable position than the first one; it seems overly risky to want to be both long gamma and long volatility. This does not necessarily mean that one would never want to be long volatility. In fact, if one expected volatility to increase, he might want to establish a position that was delta neutral and gamma neutral, but had positive vega. Again, using the same prices as in the previous examples, the following position would satisfy these criteria: Short 2,600 XYZ Short 64 March 60 calls Long 106 June 60 calls Delta: neutral Gamma: neutral Vega: long $1,000 Theta: long $11 This position has a more conventional form. It is a calendar spread, except that more long calls are purchased. Moreover, the theta of this position is only $11- it will only lose $11 per day to time decay. At first glance it might seem like the best of the three choices. Unfortunately, when one draws the profit graph (Figure 40-19), he finds that this position has significant downside risk: The short stock cannot com­ pensate for the large quantity of June 60 calls. Still, the position does make money on the upside, and will also make money if volatility increases. If the near-term March calls were overpriced with respect to the June calls at the time the position was estab­ lished, it would make it even more desirable. To summarize, defining the risks one wants to take or avoid specifies the con­ struction of the eventual position. The strategist should examine the potential risks and rewards, especially the profit picture. If the potential risks are not desirable, the strategist should rethink his requirements and try again. Thus, in the example pre­ sented, the strategist felt that he initially wanted to be long gamma, but it involved too ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:963 SCORE: 20.00 ================================================================================ Chapter 40: Advanced Concepts FIGURE 40-19. Trading long gamma, 11 conventional" calendar. 7500 5000 2500 fJ) fJ) .3 :;:, 0 '§ 45 50 Q. -2500 -5000 At March Expiration -7500 Stock Price 901 75 much risk of time decay. A second attempt was made, introducing positive volatility into the situation, but that didn't seem to help much. Finally, a third analysis was gen­ erated involving only long volatility and not long gamma. The resulting position has lit­ tle time risk, but has risk if the stock drops in price. It is probably the best of the three. The strategist arrives at this conclusion through a logical process of analysis. ADVANCED MATHEMATICAL CONCEPTS The remainder of this chapter is a short adjunct to Chapter 28 on mathematical applications. It is quite technical. Those who desire to understand the basic concepts behind the risk measures and perhaps to utilize them in more advanced ways will be interested in what follows. CALCULATING THE "'GREEKS" It is known that the equation for delta is a direct byproduct of the Black-Scholes model calculation: ~ = N(dl) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:964 SCORE: 82.00 ================================================================================ 902 Part VI: Measuring and Trading Volatility Each of the risk measures can be derived mathematically by taking the partial derivative of the model. However, there is a shortcut approximation that works just as well. For example, the formula for gamma is as follows: x=ln[ P ]/v-ft+v-ft s X (1 + r)t 2 r - e(-x212) - pv ✓ 27tt There is a simpler, yet correct, way to arrive at the gamma. The delta is the par­ tial derivative of the Black-Scholes model with respect to stock price - that is, it is the amount by which the option's price changes for a change in stock price. The gamma is the change in delta for the same change in stock price. Thus, one can approximate the gamma by the following steps: 1. Calculate the delta with p = Current stock price. 2. Set p = p + 1 and recalculate the delta. 3. Gamma = delta from step 1 - delta from step 2. The same procedure can be used for the other "greeks": Vega: 1. Calculate the option price with a particular volatility. 2. 3. Theta: 1. 2. 3. Rho: 1. 2. 3. Calculate another option price with volatility increased by 1 %. Vega = difference of the prices in steps 1 and 2. Calculate the option price with the current time to expiration. Calculate the option price with 1 day less time remaining to expiration. Theta = difference of the prices in steps 1 and 2. Calculate the option price with the current risk-free interest rate. Calculate the option price with the rate increased by 1 % . Rho = difference of the prices in steps 1 and 2. THE GAMMA OF THE GAMMA The discussion of this concept was deferred from earlier sections because it is some­ what difficult to grasp. It is included now for those who may wish to use it at some time. Those readers who are not interested in such matters may skip to the next sec­ tion. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:965 SCORE: 106.00 ================================================================================ Chapter 40: Advanced Concepts 903 Recall that this is the sixth risk measurement of an option position. The gamma of the gamma is the anwunt by which the gamma will change when the stock price changes. Recall that in the earlier discussion of gamma, it was noted that gamma changes. This example is based on the same example used earlier. Example: With XYZ at 49, assume the January 50 call has a delta of 0.50 and a gamma of 0.05. If XYZ moves up 1 point to 50, the delta of the call will increase by the amount of the gamma: It will increase from 0.50 to 0.55. Simplistically, if XYZ moves up another point to 51, the delta will increase by another 0.05, to 0.60. Obviously, the delta cannot keep increasing by 0.05 each time XYZ gains anoth­ er point in price, for it will eventually exceed 1.00 by that calculation, and it is known that the delta has a maximum of 1.00. Thus, it is obvious that the gamma changes. In reality, the gamma decreases as the stock moves away from the strike. Thus, with XYZ at 51, the gamma might only be 0.04. Therefore, if XYZ moved up to 52, the call's delta would only increase by 0.04, to 0.64. Hence, the gamma of the gamma is -0.01, since the gamma decreased from .05 to .04 when the stock rose by one point. As XYZ moves higher and higher, the gamma will get smaller and smaller. Eventually, with XYZ in the low 60's, the delta will be nearly 1.00 and the gamma nearly 0.00. This change in the gamma as the stock moves is called the gamma of the gamma. It is probably referred to by other names, but since its use is limited to only the most sophisticated traders, there is no standard name. Generally, one would use this measure on his entire portfolio to gauge how quickly the portfolio would be responding to the position gamma. Example: With XYZ at 31. 75 as in some of the previous examples, the following risk measures exist: Option Option Option Position Position Delta Gamma Gamma/Gamma Gamma/Gamma Short 4,500 XYZ 1.00 0.00 0.0000 0 Short 100 XYZ April 25 calls 0.89 0.01 -0.0015 -15 Long 50 XYZ April 30 calls 0.76 0.03 -0.0006 - 3 Long 139 XYZ July 30 calls 0.74 0.02 -0.0003 - 4 Total Gamma of Gamma: -22 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:966 SCORE: 119.00 ================================================================================ 904 Part VI: Measuring and Trading Volatility Recall that, in the same example used to describe gamma, the position was delta long 686 shares and had a positive gamma of 328 shares. Furthermore, we now see that the gamma itself is going to decrease as the stock moves up ( it is negative) or will increase as the stock moves down. In fact, it is expected to increase or decrease by 22 shares for each point XYZ moves. So, if XYZ moves up by 1 point, the following should happen: a. Delta increases from 686 to 1,014, increasing by the amount of the gamma. b. Gamma decreases from 328 to 306, indicating that a further upward move by XYZ will result in a smaller increase in delta. One can build a general picture of how the gamma of the gamma changes over different situations - in- or out-of-the-money, or with more or less time remaining until expiration. The following table of two index calls, the January 350 with one month of life remaining and the December 350 with eleven months of life remain­ ing, shows the delta, gamma, and gamma of the gamma for various stock prices. Index January 350 call December 350 call Price Delta Gamma Gamma/Gamma Delta Gamma Gamma/Gamma 310 .0006 .0001 .0000 .3203 .0083 .0000 320 .0087 .0020 .0004 .3971 .0082 .0000 330 .0618 .0100 .0013 .4787 .0080 -.0000 340 .2333 .0744 .0013 .5626 .0078 -.0001 350 .5241 .0309 -.0003 .6360 .0073 -.0001 360 .7957 .0215 -.0014 .6984 .0067 -.0001 370 .9420 .0086 -.0010 .7653 .0060 -.0001 380 .9892 .0021 -.0003 .8213 .0052 -.0001 Several conclusions can be drawn, not all of which are obvious at first glance. First of all, the gamma of the gamma for long-term options is very small. This should be expected, since the delta of a long-term option changes very slowly. The next fact can best be observed while looking at the shorter-term January 350 table. The gamma of the gamma is near zero for deeply out-of-the-money options. But, as the option comes closer to being in-the-money, the gamma of the gamma becomes a pos­ itive number, reaching its maximum while the option is still out-of-the-money. By the time the option is at-the-money, the gamma of the gamma has turned negative. It then remains negative, reaching its most negative point when slightly in-the-money. From there on, as the option goes even deeper into-the-money, the gamma of the gamma remains negative but gets closer and closer to zero, eventually reaching (minus) zero when the option is very far in-the-money. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:967 SCORE: 114.00 ================================================================================ Chapter 40: Advanced Concepts 905 Can one possibly reason this risk measurement out without making severe mathematical calculations? Well, possibly. Note that the delta of an option starts as a small number when the option is out-of-the-money. It then increases, slowly at first, then more quickly, until it is just below 0.60 for an at-the-money option. From there on, it will continue to increase, but much more slowly as the option becomes in-the­ money. This movement of the delta can be observed by looking at gamma: It is the change in the delta, so it starts slowly, increases as the stock nears the strike, and then begins to decrease as the option is in-the-money, always remaining a positive num­ ber, since delta can only change in the positive direction as the stock rises. Finally, the gamma of the gamma is the change in the gamma, so it in tum starts as a positive number as gamma grows larger; but then when gamma starts tapering off, this is reflected as a negative gamma of the gamma. In general, the gamma of the gamma is used by sophisticated traders on large option positions where it is not obvious what is going to happen to the gamma as the stock changes in price. Traders often have some feel for their delta. They may even have some feel for how that delta is going to change as the stock moves (i.e., they have a feel for gamma). However, sophisticated traders know that even positions that start out with zero delta and zero gamma may eventually acquire some delta. The gamma of the gamma tells the trader how much and how soon that eventual delta will be acquired. MEASURING THE DIFFERENCE OF IMPLIED VOLATILITIES Recall that when the topic of implied volatility was discussed, it was shown that if one could identify situations in which the various options on the same underlying securi­ ty had substantially different implied volatilities, then there might be an attractive neutral spread available. The strategist might ask how he is to determine if the dis­ crepancies between the individual options are significantly large to warrant attention. Furthermore, is there a quick way (using a computer, of course) to determine this? A logical way to approach this is to look at each individual implied volatility and compute the standard deviation of these numbers. This standard deviation can be converted to a percentage by dividing it by the overall implied volatility of the stock. This percentage, if it is large enough, alerts the strategist that there may be opportu­ nities to spread the options of this underlying security against each other. An exam­ ple should clarify this procedure. Example: XYZ is trading at 50, and the following options exist with the indicated implied volatilities. We can calculate a standard deviation of these implieds, called implied deviation, via the formula: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:968 SCORE: 18.00 ================================================================================ 906 Part VI: Measuring and Trading Volatility Implied deviation = sqrt (sum of differences from mean) 2/(# options - 1) XYZ:50 Implied Option Volatility October 45 call 21% November 45 call 21% January 45 call 23% October 50 call 32% November 50 call 30% January 50 call 28% October 55 call 40% November 55 call 37% January 55 call 34% Average: 30.44% Sum of ( difference from avg)2 = 389.26 Implied deviation = sqrt (sum of diff)2/(# options - 1) = sqrt (389.26 I 8) = 6.98 Difference from Average -9.44 -9.44 -7.44 + 1.56 -0.44 -2.44 +9.56 +6.56 +3.56 This figure represents the raw standard deviation of the implied volatilities. To convert it into a useful number for comparisons, one must divide it by the average implied volatility. P d . . Implied deviation ercent eV1at10n = A . 1. d verage imp ie = 6.98/30.44 = 23% This "percent deviation" number is usually significant if it is larger than 15%. That is, if the various options have implied volatilities that are different enough from each other to produce a result of 15% or greater in the above calculation, then the strategist should take a look at establishing neutral spreads in that security or futures contract. The concept presented here can be refined further by using a weighted average of the implieds ( taking into consideration such factors as volume and distance from the striking price) rather than just using the raw average. That task is left to the reader. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:969 SCORE: 24.00 ================================================================================ Chapter 40: Advanced Concepts 907 Recall that a computer can perform a large number of Black-Scholes calcula­ tions in a short period of time. Thus, the computer can calculate each option's implied volatility and then perform the "percent deviation" calculation even faster. The strategist who is interested in establishing this type of neutral spread would only have to scan down the list of percent deviations to find candidates for spreading. On a given day, the list is usually quite short - perhaps 20 stocks and 10 futures contracts will qualify. SUMMARY In today's highly competitive and volatile option markets, neutral traders must be extremely aware of their risks. That risk is not just risk at expiration, but also the cur­ rent risk in the market. Furthermore, they should have an idea of how the risk will increase or decrease as the underlying stock or futures contract moves up and down in price. Moreover, the passage of time or the volatility that the options are being assigned in the marketplace - the implied volatility - are important considerations. Even changes in short-term interest rates can be of interest, especially iflonger-term options (LEAPS) are involved. Once the strategist understands these concepts, he can use them to select new positions, to adjust existing ones, and to formulate specific strategies to take advan­ tage of them. He can select a specific criteria that he wants to exploit - selling high volatility, for example and use the other measures to construct a position that has little risk with respect to any of the other variables. Furthermore, the market-maker or specialist, who does not want to acquire any market risk if he can help it, will use these techniques to attempt to neutralize all of the current risk, if possible. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:970 SCORE: 41.00 ================================================================================ Taxes In this chapter, the basic tax treatment of listed options will be outlined and sev­ eral tax strategies will be presented. The reader should be aware of the fact that tax laws change, and therefore should consult tax counsel before actually implementing any tax-oriented strategy. The interpretation of certain tax strategies by the Internal Revenue Service is subject to reclarification or change, as well. An option is a capital asset and any gains or losses are capital gains or losses. Differing tax consequences apply, depending on whether the option trade is a complete transaction by itself, or whether it becomes part of a stock transaction via exercise or assignment. Listed option transactions that are closed out in the options market or are allowed to expire worthless are capital transactions. The holding period for option transactions to qualify as long-term is always the same as for stocks ( cur­ rently, it's one year). Gains from option purchases could possibly be long-term gains if the holding period of the option exceeds the long-term capital gains holding period. Gains from the sale of options are short-term capital gains. In addition, the tax treatment of futures options and index options and other listed nonequity options may differ from that of equity options. We will review these points individually. HISTORY In the short life of listed option trading. there have been several major changes in the tax rules. When options were first listed in 1973, the tax laws treated the gains and losses from writing options as ordinary income. That is, the thinking was that only professionals or those people in the business actually wrote over-the-counter options, and thus their gains and losses represented their ordinary income, or means of mak­ ing a living. This rule presented some interesting strategies involving spreads, because the long side of the spread could be treated as long-term gain (if held for 908 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:971 SCORE: 50.00 ================================================================================ Chapter 41: Taxes 909 more than 6 months, which was the required holding period for a long-term gain at that time), and the short side of the spread could be ordinary loss. Of course, the stock would have had to move in the desired direction in order to obtain this result. In 1976, the tax laws changed. The major changes affecting option traders were that the long-term holding period was extended to one year and also that gains or losses from writing options were considered to be capital gains. The extension of the long-term period essentially removed all possibilities of listed option holders ever obtaining a long-term gain, because the listed option market's longest-term options had only 9 months of life. All through this period there were a wide array of tax strategies that were avail­ able, legally, to allow investors to defer capital gains from one year to the next, there­ by avoiding payment of taxes. Essentially, one would enter into a spread involving deep in-the-money options that would expire in the next calendar year. Perhaps the spread would be established during October, using January options. Then one would wait for the underlying stock to move. Once a move had taken place, the spread would have a profit on one side and a loss on the other. The loss would be realized by rolling the losing option into another deep in-the-money option. The realized loss could thus be claimed on that year's taxes. The remaining spread - now an unrealized profit - would be left in place until expiration, in the next calendar year. At that time, the spread would be removed and the gain would be realized. Thus, the gain was moved from one year to the next. Then, later in that year, the gain would again be rolled to the next calendar year, and so on. These practices were effectively stopped by the new tax ruling issued in 1984. Two sweeping changes were made. First, the new rules stated that, in any spread position involving offsetting options - as the two deep in-the-money options in the previous example - the losses can be taken only to the extent that they exceed the unrealized gain on the other side of the spread. (The tax literature insists on calling these positions "straddles" after the old commodity term, but for options purposes they are really spreads or covered writes.) As a by-product of this rule, the holding period of stock can be terminated or eliminated by writing options that are too deeply in-the-money. Second, the new rules required that all positions in nonequity options and all futures be marked to market at the end of the tax year, and that taxes be paid on realized and unrealized gains alike. The tax rate for nonequity options was low­ ered from that of equity options. Then, in 1986, the long-term and short-term capi­ tal gains rates were made equal to the lowest ordinary rate. All of these points will be covered in detail. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:972 SCORE: 42.00 ================================================================================ 910 Part VI: Measuring and Trading Volatility BASIC TAX TREATMENT Listed options that are exercised or assigned fall into a different category for tax pur­ poses. The original premium of the option transaction is combined into the stock transaction. There is no tax liability on this stock position until the stock position itself is closed out. There are four different combinations of exercising or assigning puts or calls. Table 41-1 summarizes the method of applying the option premium to the stock cost or sale price. Examples of how to treat these various transactions are given in the following sections. In addition to examples explaining the basic tax treatment, some supple­ mentary strategies are included as well. CALL BUYER If a call holder subsequently sells the call or allows it to expire worthless, he has a capital gain or loss. For equity options, the holding period of the option determines whether the gain or loss is long-term or short-term. As mentioned previously, a long­ term gain would be possible if held for more than one year. For tax purposes, an option that expires worthless is considered to have been sold at zero dollars on the expiration date. Example: An investor purchases an XYZ October 50 call for 5 points on July l. He sells the call for 9 points on September 1. That is, he realizes a capital gain via a clos­ ing transaction. His taxable gain would be computed as shown in Table 41-1, assum­ ing that a $25 commission was paid on both the purchase and the sale. TABLE 41-1. Applying the option premium to the stock cost or sale price. Action Call buyer exercises Put buyer exercises Call writer assigned Put writer assigned Net proceeds of sale ($900 - $25) Net cost ($500 + $25) Short-term gain: Tax Treatment Add call premium to stock cost Subtract put premium from stock sale price Add call premium to stock sale price Subtract put premium from stock cost $875 -525 $350 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:973 SCORE: 33.00 ================================================================================ Chapter 41: Taxes 911 Alternatively, if the stock had fallen in price by October expiration and the October 50 call had expired worthless, the call buyer would have lost $525 - his entire net cost. If he had held the call until it expired worthless, he would have a short-term capital loss of $525 to report among his taxable transactions. PUT BUYER The holder of a put has much the same tax consequences as the holder of a call, pro­ vided that he is not also long the underlying stock. This initial discussion of tax con­ sequences to the put holder will assume that he does not simultaneously own the underlying stock. If the put holder sells his put in the option market or allows it to expire worthless, the gain or loss is treated as capital gain, long-term for equity puts held more than one year. Historically, the purchase of a put was viewed as perhaps the only way an investor could attain a long-term gain in a declining market. Example: An investor buys an XYZ April 40 put for 2 points with the stock at 43. Later, the stock drops in price and the put is sold for 5 points. The commissions were $25 on each option trade, so the tax consequences would be: Net sale proceeds ($500 - $25) Net cost ($200 + $25) Short-term capital gain: $475 -225 $250 Alternatively, if he had sold the put at a loss, perhaps in a rising market, he would have a short-term capital loss. Furthermore, if he allowed the put to expire totally worthless, his short-term loss would be equal to the entire net cost of $225. CALL WRITER Written calls that are bought back in the listed option market or are allowed to expire worthless are short-term capital gains. A written call cannot produce a long-term gain, regardless of the holding period. This treatment of a written call holds true even if the investor simultaneously owned the underlying stock (that is, he had a covered write). As long as the call is bought back or allowed to expire worthless, the gain or loss on the call is treated separately from the underlying stock for tax purposes. Example: A trader sells naked an XYZ July 30 call for 3 points and buys it back three months later at a price of 1. The commissions were $25 for each trade, so the tax gain would be: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:974 SCORE: 19.00 ================================================================================ 912 Net sale proceeds ($300 - $25) Net cost ($100 + $25) Short-term gain: Part VI: Measuring and Trading Volatility $275 -125 $150 If the investor had not bought the call back, but had been fortunate enough to be able to allow it to expire worthless, his gain for tax purposes would have been the entire $275, representing his net sale proceeds. The purchase cost is considered to be zero for an option that expires worthless. PUT WRITER The tax treatment of written puts is quite similar to that of written calls. If the put is bought back in the open market or is allowed to expire worthless, the transaction is a short-term capital item. Example: An investor writes an XYZ July 40 put for 4 points, and later buys it back for 2 points after a rally by the underlying stock. The commissions were $25 on each option trade, so the tax situation would be: Net put sale price ($400 - $25) Net put cost ($100 + $25) Short-term gain: $375 -125 $250 If the put were allowed to expire worthless, the investor would have a net gain of $375, and this gain would be short-term. THE 60/40 RULE As mentioned earlier, nonequity option positions and future positions must be marked to market at the end of the tax year and taxes paid on both the unrealized and realized gains and losses. This same rule applies to futures positions. The tax rate on these gains and losses is lower than the equity options rate. Regardless of the actual holding period of the positions, one treats 60% of his tax liability as long-term and 40% as short-term. This ruling means that even gains made from extremely short­ term activity such as day-trading can qualify partially as long-term gains. Since 1986, long-term and short-term capital gains rates have been equal. If long-term rates should drop, then the rule would again be more meaningful. Example: A trader in nonequity options has made three trades during the tax year. It is now the end of the tax year and he must compute his taxes. First, he bought S&P ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:975 SCORE: 37.00 ================================================================================ Chapter 41: Taxes 913 500 calls for $1,500 and sold them 6 weeks later for $3,500. Second, he bought an OEX January 160 call for 3.25 seven months ago and still holds it. It currently is trad­ ing at 11.50. Finally, he sold 5 SPX February 250 puts for 1.50 three days ago. They are currently trading at 2. The net gain from these transactions should be computed without regard to holding period. Nonequity Original Current Gain/ Contract Price Price Cost Proceeds Loss S&P calls $1,500 $3,500 +$2,000 realized OEX January 160 3.25 11.50 $ 325 $1,150 + 825 unrealized SPX February 250 1.50 2.00 $1,000 $ 750 250 unrealized Total caeital gains +$2,575 The total taxable amount is $2,575, regardless of holding period and regardless of whether the item is realized or unrealized. Of this total taxable amount, 60% ($1,545) is subject to long-term treatment and 40% ($1,030) is subject to short-term treat­ ment. In practice, one computes these figures on a separate form (Section 1256) and merely enters the two final figures - $1,545 and $1,030- on the tax schedule for cap­ ital gains and losses. Note that if one loses money in nonequity options, he actually has a tax disadvantage in comparison to equity options, because he must take some of his loss as a long-term loss, while the equity option trader can take all of his loss as short-term. EXERCISE AND ASSIGNMENT Except for a specified situation that we will discuss later, exercise and assignment do not have any tax effect for nonequity options because everything is marked to mar­ ket at the end of the year. However, since equity options are subject to holding peri­ od considerations, the following discussion pertains to them. CALL EXERCISE An equity call holder who has an in-the-money call might decide to exercise the call rather than sell it in the options market. If he does this, there are no tax consequences on the option trade itself. Rather, the cost of the stock is increased by the net cost of the original call option. Moreover, the holding period begins on the day the stock is ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:976 SCORE: 39.00 ================================================================================ 914 Part VI: Measuring and Trading Volatility purchased (the day after the call was exercised). The option's holding period has no bearing on the stock position that resulted from the exercise. Example: An XYZ October 50 call was bought for 5 points on July 1. The stock had risen by October expiration, and the call holder decided to exercise the call on October 20th. The option commission was $25 and the stock commission was $85. The cost basis for the stock would be computed as follows: Buy 1 00 XYZ at 50 via exercise ($5,000 plus $85 commission) Original call cost ($500 plus $25) Total tax basis of stock Holding period of stock begins on October 21. $5,085 525 $5,610 When this stock is eventually sold, it will be a gain or a loss, depending on the stock's sale price as compared to the tax basis of $5,610 for the stock. Furthermore, it will be a short-term transaction unless the stock is held until October 21st of the follow­ ing year. CALL ASSIGNMENT If a written call is not closed out, but is instead assigned, the call's net sale proceeds are added to the sale proceeds of the underlying stock. The call's holding period is lost, and the stock position is considered to have been sold on the date of the assign­ ment. Example: A naked writer sells an XYZ July 30 call for 3 points, and is later assigned rather than buying back the option when it was in-the-money near expiration. The stock commission is $75. His net sale proceeds for the stock would be computed as follows: Net call sale proceeds ($300 - $25) Net stock proceeds from assignment of 100 shares at 30 ($3,000 - $75) Net stock sale proceeds $ 275 2,925 $3,200 In the case in which the investor writes a naked, or uncovered, call, he sells stock short upon assignment. He may, of course, cover the short sale by purchasing stock in the open market for delivery. Such a short sale of stock is governed by the ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:977 SCORE: 21.00 ================================================================================ Chapter 41: Taxes 915 applicable tax rules pertaining to short sales that any gains or losses from the short sale of stock are short-term gains or losses. Tax Treatment for the Covered Writer. If, on the other hand, the investor was assigned on a covered call - that is, he was operating the covered writing strategy and he elects to deliver the stock that he owns against the assignment notice, he has a complete stock transaction. The net cost of the stock was determined by its purchase price at an earlier date and the net sale proceeds are, of course, determined by the assignment in accordance with the preceding example. Determining the proceeds from the stock purchase and sale is easy, but deter­ mining the tax status of the transaction is not. In order to prevent stockholders from using deeply in-the-money calls to protect their stock while letting it become a long­ term item, some complicated tax rules have been passed. They can be summarized as follows: 1. If the equity option was out-of-the-money when first written, it has no effect on the holding period of the stock. 2. If the equity option was too deeply in-the-money when first written and the stock was not yet held long-term, then the holding period of the stock is eliminated. 3. If the equity option was in-the-money, but not too deeply, then the holding peri­ od of the stock is suspended while the call is in place. These rules are complicated and merit further explanation. The first rule mere­ ly says that one can write out-of-the-money calls without any problem. If the stock later rises and is called away, the sale proceeds for the stock include the option pre­ mium, and the transaction is long-term or short-term depending on the holding peri­ od of the stock. Example: Assume that on September 1st of a particular year, an investor buys 100 XYZ at 35. He holds the stock for a while, and then on July 15th of the following year - after the stock has risen to 43 - he sells an October 45 call for 3 points. Net call sale proceeds ($300 - $25) Net stock proceeds from assignment ($4,500 - $75) Net stock sale proceeds Net stock cost ($3,500 + $75) Net long-term gain $ 275 $4,425 $4,700 $4,700 $3,575 +$1, 125 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:978 SCORE: 25.00 ================================================================================ 916 Part VI: Measuring and Trading Volatllity Thus, this covered writer has a net gain of $1,125 and it is a long-term gain because the stock was held for more than one year (from September 1st of the year in which he bought it, to October expiration of the next year, when the stock was called away). Note that in a similar situation in which the stock had been held for less than one year before being called away, the gain would be short-term. Let us now look at the other two rules. They are related in that their differen­ tiation relies on the definition of "too deeply in-the-money." They come into play only if the stock was not already held long-term when the call was written. If the writ­ ten call is too deeply in-the-money, it can eliminate the holding period of short-term stock. Otherwise, it can suspend it. If the call is in-the-money, but not too deeply in­ the-money, it is referred to as a qualified covered call. There are several rules regard­ ing the determination of whether an in-the-money call is qualified or not. Before actually getting to that definition, which is complicated, let us look at two examples to show the effect of the call being qualified or not qualified. Example: Qualified Covered Write: On March 1st, an investor buys 100 XYZ at 35. He holds the stock for 3% months, and, on July 15th, the stock has risen to 43. This time he sells an in-the-money call, the October 40 call for 6. By October expiration, the stock has declined and the call expires worthless. He would now have the following situation: a $575 short-term gain from the sale of the call, plus he is long 100 XYZ with a holding period of only 3% months. Thus, the sale of the October call suspended his holding period, but did not elimi­ nate it. He could now hold the stock for another 8½ months and then sell it as a long­ term item. If the stock in this example had stayed above 40 and been called away, the net result would have been that the option proceeds would have been added to the stock sale price as in previous examples, and the entire net gain would have been short­ term due to the fact that the writing of the qualified covered call had suspended the holding period of the stock at 3½ months. That example was one of writing a call which was not too deeply in-the-money. If, however, one writes a call on stock that is not yet held long-term and the call is too deeply in-the-money, then the holding period of the stock is eliminated. That is, if the call is subsequently bought back or expires worthless, the stock must then be held for another year in order to qualify as a long-term investment. This rule can work to an investor's advantage. If one buys stock and it goes down and he is in jeopardy of hav­ ing a long-term loss, but he really does not want to sell the stock, he can sell a call ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:979 SCORE: 25.00 ================================================================================ Chapter 41: Taxes 917 that is too deeply in-the-money (if one exists), and eliminate the holding period on the stock Qualified Covered Call. The preceding examples and discussion summa­ rize the covered writing rules. Let us now look at what is a qualified covered call. The following rules are the literal interpretation. Most investors work from tables that are built from these rules. Such a table may be found in Appendix E. (Be aware that these rules may change, and consult a tax advisor for the latest figures.) A covered call is qualified if: 1. the option has more than 30 days of life remaining when it is written, and 2. the strike of the written call is not lower than the following benchmarks: a. First determine the applicable stock price (ASP). That is normally the closing price of the stock on the previous day. However, if the stock opens more than ll0% higher than its previous close, then the applicable stock price is that higher opening. b. If the ASP is less than $25, then the benchmark strike is 85% of ASP. So any call written with a strike lower than 85% of ASP would not be qualified. (For example, if the stock was at 12 and one wrote a call with a striking price of 10, it would not be qualified- it is too deeply in-the-money.) c. If the ASP is between 25.13 and 60, then the benchmark is the next lowest strike. Thus, if the stock were at 39 and one wrote a call with a strike of 35, it would be qualified. d. If the ASP is greater than 60 and not higher than 150, and the call has more than 90 days of life remaining, the benchmark is two strikes below the ASP. There is a further condition here that the benchmark cannot be more than 10 points lower than the ASP. Thus, if a stock is trading at 90, one could write a call with a strike of 80 as long as the call had more than 90 days remaining until expiration, and still be qualified. e. If the ASP is greater than 150 and the call has more than 90 days of life remain­ ing, the benchmark is two strikes below the ASP. Thus, if there are 10-point striking price intervals, then one could write a call that was 20 points in-the­ money and still be qualified. Of course, if there are 5-point intervals, then one could not write a call deeper than 10 points in-the-money and still be qualified. These rules are complicated. That is why they are summarized in Appendix E. In addition, they are always subject to change, so if an investor is considering writing an in-the-money covered call against stock that is still short-term in nature, he should check with his tax advisor and/or broker to determine whether the in-the-money call is qualified or not. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:980 SCORE: 30.00 ================================================================================ 918 Part VI: Measuring and Trading Volatility There is one further rule in connection with qualified calls. Recall that we stat­ ed that the above rules apply only if the stock is not yet held long-term when the call is written. If the stock is already long-term when the call is written, then it is consid­ ered long-term when called away, regardless of the position of the striking price when the call was written. However, if one sells an in-the-money call on stock already held long-term, and then subsequently buys that call back at a loss, the loss on the call must be taken as a long-term loss because the stock was long-term. Overall, a rising market is the best, taxwise, for the covered call writer. If he writes out-of-the-money calls and the stock rises, he could have a short-term loss on the calls plus a long-term gain on the stock. Example: On January 2nd of a particular year, an investor bought 100 shares of XYZ at 32, paying $75 in commissions, and simultaneously wrote a July 35 call for 2 points. The July 35 expired worthless, and the investor then wrote an October 35 call for 3 points. In October, with XYZ at 39, the investor bought back the October 35 call for 6 points (it was in-the-money) and sold a January 40 call for 4 points. In January, on the expiration day, the stock was called away at 40. The investor would have a long­ term capital gain on his stock, because he had held it for more than one year. He would also have two short-term capital transactions from the July 35 and October 35 calls. Tables 41-2 and 41-3 show his net tax treatment from operating this covered writing strategy. The option commission on each trade was $25. Things have indeed worked out quite well, both profit-wise and tax-wise, for this covered call writer. Not only has he made a net profit of $850 from his transactions on the stock and options over the period of one year, but he has received very favorable tax treatment. He can take a short-term loss of $175 from the combined July and October option transactions, and is able to take the $1,025 gain as a long-term gain. TABLE 41-2. Summary of trades. January 2 July October January Bought 100 XYZ at 32 Sold 1 July 35 call at 2 July call expired worthless (XYZ at 32) Sold 1 October 35 call at 3 Bought back October 35 call for 6 points (XYZ at 39) Sold 1 January 40 call for 4 points (of the following year) 1 00 XYZ called away at 40 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:981 SCORE: 34.00 ================================================================================ Chapter 41: Taxes TABLE 41-3. Tax treatment of trades. Short-term capital items: July 35 call: Net proceeds ($200 - $25) Net cost {expired worthless) Short-term capital gain October 35 call: Net proceeds ($300 - $25) Net cost ($600 + $25) Short-term capital loss 919 $175 0 $175 $275 - 625 ($350) Long-term capital item: 100 shares XYZ: Purchased January 2 of one year and sold at January expiration of the following year. Therefore, held for more than one year, qualifying for long-term treatment. Net sale proceeds of stock {assigned call): January 40 call sale proceeds ($400 - $25) Sold 1 00 XYZ at 40 strike {$4,000 $75) Net cost of stock (January 2 trade): Bought 100 at 32 {$3,200 + $75) Long-term capital gain $375 + 3,925 $4,300 - 3,275 $1,025 This example demonstrates an important tax consequence for the covered call writer: His optimum scenario tax-wise is a rising market, for he may be able to achieve a long-term gain on the underlying stock if he holds it for at least one year, while simultaneously subtracting short-term losses from written calls that were closed out at higher prices. Unfortunately, in a declining market, the opposite result could occur: short-term option gains coupled with the possibility of a long-term loss on the underlying stock. There are ways to avoid long-term stock losses, such as buy­ ing a put ( discussed later in the chapter) or going short against the box before the stock becomes long-term. However, these maneuvers would interrupt the covered writing strategy, which may not be a wise tactic. In summary, then, the covered call writer who finds himself with an in-the­ money call written and expiration date drawing near may have several alternatives open to him. If the stock is not yet held long-term, he might elect to buy back the written call and to write another call whose expiration date is beyond the date required for a long-term holding period on the stock. This is apparently what the hypothetical investor in the preceding example did with his October 35 call. Since ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:982 SCORE: 34.00 ================================================================================ 920 Part VI: Measuring and Trading VolatiRty that call was in-the-money, he could have elected to let the call be assigned and to take his profit on the position at that time. However, this would have produced a short-term gain, since the stock had not yet been held for one year, so he elected instead to terminate the October 35 call through a closing purchase transaction and to simultaneously write a call whose expiration date exceeded the one year period required to make the stock a long-term item. He thus wrote the January 40 call, expiring in the next year. Note that this investor not only decided to hold the stock for a long-term gain, but also decided to try for more potential profits: He rolled the call up to a higher striking price. This lets the holding period continue. An in-the­ money write would have suspended it. DELIVERING .,.,NEW" STOCK TO AVOID A LARGE LONG· TERM GAIN Some covered call writers may not want to deliver the stock that they are using to cover the written call, if that call is assigned. For example, if a covered writer were writing against stock that had an extremely low cost basis, he might not be willing to take the tax consequences of selling that particular stock holding. Thus, the writer of a call that is assigned may sometimes wish to buy stock in the open market to deliv­ er against his assignment, rather than deliver the stock he already owns. Recall that it is completely in accordance with the Options Clearing Corporation rules for a call writer to buy stock in the open market to deliver against an assignment. For tax pur­ poses, the confirmation that the investor receives from his broker for the sale of the stock via assignment should clearly specify which particular shares of stock are being sold. This is usually accomplished by having the confirmation read "Versus Purchase" and listing the purchase date of the stock being sold. This is done to clearly identify that the "new" stock, and not the older long-term stock, is being delivered against the assignment. The investor must give these instructions to his broker, so that the brokerage firm puts the proper notation on the confirmation itself. If the investor realizes that his stock might be in danger of being called away and he wants to avail himself of this procedure, he should discuss it with his broker beforehand, so that the proper procedures can be enacted when the stock is actually called away. Example: An investor owns 100 shares ofXYZ and his cost basis, after multiple stock splits and stock dividends over the years, is $2 per share. With XYZ at 50, this investor decides to sell an XYZ July 50 call for 5 points to bring in some income to his port­ folio. Subsequently, the call is assigned, but the investor does not want to deliver his XYZ, which he owns at a cost basis of $2 per share, because he would have to pay cap­ ital gains on a large profit. He may go into the open market and buy another 100 shares of XYZ at its current market price for delivery against the assignment notice. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:983 SCORE: 52.00 ================================================================================ Chapter 41: Taxes 921 Suppose he does this on July 20th, the day he receives the assignment notice on his XYZ July 50 call. The confirmation that he receives from his broker for the sale of 100 XYZ at 50 - that is, the confirmation for the call assignment - should be marked "Versus Purchase July 20th." The year of the sale date should be noted on the con­ firmation as well. This long-term holder of XYZ stock must, of course, pay for the additional XYZ bought in the open market for delivery against the assignment notice. Thus, it is imperative that such an investor have a reserve of funds that he can fall back on if he thinks that he must ever implement this sort of strategy to avoid the tax consequences of selling his low-cost-basis stock. PUT EXERCISE If the put holder does not choose to liquidate the option in the listed market, but instead exercises the put - thereby selling stock at the striking price - the net cost of the put is subtracted from the net sale proceeds of the underlying stock. Example: Assume an XYZ April 45 put was bought for 2 points. XYZ had declined in price below 45 by April expiration, and the put holder decides to exercise his in-the­ money put rather than sell it in the option market. The commission on the stock sale is $85, so the net sale proceeds for the underlying stock would be: Sale of 100 XYZ at 45 strike ($4,500 - $85) Net cost of put ($200 + 25) Net sale proceeds on stock for tax purposes: $4,415 - 225 $4,190 If the stock sale represents a new position - that is, the investor has shorted the underlying stock - it will eventually be a short-term gain or loss, according to pres­ ent tax rules governing short sales. If the put holder already owns the underlying stock and is using the put exercise as a means of selling that stock, his gain or loss on the stock transaction is computed, for tax purposes, by subtracting his original net stock cost from the sale proceeds as determined above. PUT ASSIGNMENT If a written put is assigned, stock is bought at the striking price. The net cost of this purchased stock is reduced by the amount of the original put premium received. Example: If one initially sold an XYZ July 40 put for 4 points, and it was assigned, the net cost of the stock would be determined as follows, assuming a $75 commission charge on the stock purchase: ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:984 SCORE: 34.00 ================================================================================ 922 Cost of 100 XYZ assigned at 40 ($4,000 + $75) Net proceeds of put sale ($400 - $25) Net cost basis of stock Part VI: Measuring and Trading Volatility $4,075 - 375 $3,700 The holding period for stock purchased via a put assignment begins on the day of the put assignment. The period during which the investor was short the put has no bear­ ing on the holding period of the stock. Obviously, the put transaction itself does not become a capital item; it becomes part of the stock transaction. SPECIAL TAX PROBLEMS THE WASH SALE RULE The call buyer should be aware of the wash sale rule. In general, the wash sale rule denies a tax deduction for a security sold at a loss if a substantially identical security, or an option to acquire that security, is purchased within 30 days before or 30 days after the original sale. This means that one cannot sell XYZ to take a tax loss and also purchase XYZ within the 61-day period that extends 30 days before and 30 days after the sale. Of course, an investor can legally make such a trade, he just cannot take the tax loss on the sale of the stock. A call option is certainly an option to acquire the security. It would thus invoke the wash sale rule for an investor to sell XYZ stock to take a loss and also purchase any XYZ call within 30 days before or after the stock sale. Various series of call options are not generally considered to be substantially identical securities, however. If one sells an XYZ January 50 call to take a loss, he may then buy any other XYZ call option without jeopardizing his tax loss from the sale of the January 50. It is not clear whether he could repurchase another January 50 call­ that is, an identical call - without jeopardizing the taxable loss on the original sale of the January 50. It would also be acceptable for an investor to sell a call to take a loss and then immediately buy the underlying security. This would not invoke the wash sale rule. Avoiding a Wash Sale. It is generally held that the sale of a put is not the acquisition of an option to buy stock, even though that is the effect of assign­ ment of the written put. This fact may be useful in certain cases. If an investor holds a stock at a loss, he may want to sell that stock in order to take the loss on his taxes for the current year. The wash sale rule prevents him from repurchas­ ing the same stock, or a call option on that stock, within 30 days after the sale. Thus, the investor will be "out of" the stock for a month; that is, he will not be ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:985 SCORE: 33.00 ================================================================================ Chapter 41: Taxes 923 able to participate in any rally in the stock in the next 30 days. If the underlying stock has listed put options, the investor may be able to partially offset this neg­ ative effect. By selling an in-the-money put at the same time that the stock is sold, the investor will be able to take his stock loss on the current year's taxes and also will be able to participate in price movements on the underlying stock. If the stock should rally, the put will decrease in price. However, if the stock ral­ lies above the striking price of the put, the investor will not make as much from the put sale as he would have from the ownership of the stock. Still, he does realize some profits if the stock rallies. Conversely, if the stock falls in price, the investor will lose on the put sale. This certainly represents a risk although no more of a risk than owning the stock did. An additional disadvantage is that the investor who has sold a put will not receive the div­ idends, if any are paid by the underlying stock. Once 30 days have passed, the investor can cover the put and repurchase the underlying stock. The investor who utilizes this tactic should be careful to select a put sale in which early assignment is minimal. Therefore, he should sell a long-term, in­ the-money put when utilizing this strategy. (He needs the in-the-money put in order to participate heavily in the stock's movements.) Note that if stock should be put to the investor before 30 days had passed, he would thus be forced to buy stock, and the wash sale rule would be invoked, preventing him from taking the tax loss on the stock at that time. He would have to postpone taking the loss until he makes a sale that does not invoke the wash sale rule. Finally, this strategy must be employed in a margin account, because the put sale will be uncovered. Obviously, the money from the sale of the stock itself can be used to collateralize the sale of the put. If the stock should drop in value, it is always possible that additional collateral will be required for the uncovered put. THE SHORT-SALE RULE - PUT HOLDER'S PROBLEM A put purchase made by an investor who also owns the underlying stock may have an effect on the holding period of the stock. If a stock holder buys a put, he would nor­ mally do so to eliminate some of the downside risk in case the stock falls in price. However, if a put option is purchased to protect stock that is not yet held long enough to qualify for long-term capital gains treatment, the entire holding period of the stock is wiped out. Furthermore, the holding period for the stock will not begin again until the put is disposed of. For example, if an investor has held XYZ for 11 months - not quite long enough to qualify as a long-term holding - and then buys a put on XYZ, he will wipe out the entire accrued holding period on the stock. Furthermore, when he finally disposes of the put, the holding period for the stock must begin all over ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:986 SCORE: 39.00 ================================================================================ 924 Part VI: Measuring and Trading VolatHity again. The previous 11-month holding period is lost, as is the holding period during which the stock and put were held together. This tax consequence of a put purchase is derived from the general rules governing short sales, which state that the acquisi­ tion of an option to sell property at a fixed price (that is, a put) is treated as a short sale. This ruling has serious tax consequences for an investor who has bought a put to protect stock that is still in a short-term tax status. ✓,,Married" Put and Stock. There are two cases in which the put purchase does not affect the holding period of the underlying stock. First, if the stock has already been held long enough to qualify for long-term capital treatment, the purchase of a put has no bearing on the holding period of the underlying stock. Second, if the put and the stock that it is intended to protect are bought at the same time, and the investor indicates that he intends to exercise that particular put to sell those particular shares of stock, the put and the stock are considered to be "married" and the normal tax rulings for a stock holding would apply. The investor must actually go through with the exercise of the put in order for the "married" status to remain valid. If he instead should allow the put to expire worthless, he could not take the tax loss on the put itself but would be forced to add the put' s cost to the net cost of the underlying stock. Finally, if the investor neither exercises the put nor allows it to expire worthless but sells both the put and the stock in their respective markets, it would appear that the short sale rules would come back into effect. This definition of "married" put and stock, with its resultant ramifications, is quite detailed. What exactly are the consequences? The "married" rule was original­ ly intended to allow an investor to buy stock, protect it, and still have a chance of real­ izing a long-term gain. This is possible with options with more than one year of life remaining. The reader must be aware of the fact that, if he initially "marries" stock and a listed 3-month put, for example, there is no way that he can replace that put at its expiration with another put and still retain the "married" status. Once the original "married" put is disposed of - through sale, exercise, or expiration - no other put may be considered to be "married" to the stock. Protecting a Long· Term Gain or Avoiding a Long-Term Loss. The investor may be able, at times, to use the short-sale aspect of put purchases to his advantage. The most obvious use is that he can protect a long-term gain with a put purchase. He might want to do this if he has decided to take the long-term gain, but would prefer to delay realizing it until the following tax year. A pur­ chase of a put with a maturity date in the following year would accomplish that purpose. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:987 SCORE: 48.00 ================================================================================ Chapter 41: Taxes 92S Another usage of the put purchase, for tax purposes, might be to avoid a long­ term loss on a stock position. If an investor owns a stock that has declined in price and also is about to become a long-term holding, he can buy a put on that stock to eliminate the holding period. This avoids having to take a long-term loss. Once the put is removed, either by its sale or by its expiring worthless, the stock holding peri­ od would begin all over again and it would be a short-term position. In addition, if the investor should decide to exercise the put that he purchased, the result would be a short-term loss. The sale basis of the stock upon exercise of the put would be equal to the striking price of the put less the amount of premium paid for the put, less all commission costs. Furthermore, note that this strategy does not lock in the loss on the underlying stock. If the stock rallies, the investor would be able to participate in that rally, although he would probably lose all of the premium that he paid for the put. Note that both of these long-term strategies can be accomplished via the sale of a deeply in-the-money call as well. SUMMARY This concludes the section of the tax chapter dealing with listed option trades and their direct consequences on option strategies. In addition to the basic tax treatment for option traders of liquidation, expiring worthless, or assignment or exercise, sev­ eral other useful tax situations have been described. The call buyer should be aware of the wash sale rule. The put buyer must be aware of the short sale rules involving both put and stock ownership. The call writer should realize the beneficial effects of selling an in-the-money call to protect the underlying stock, while waiting for a real­ ization of profit in the following tax year. The put writer may be able to avoid a wash sale by utilizing an in-the-money put write, while still retaining profit potential from a rally by the underlying stock. TAX PLANNING STRATEGIES FOR EQUITY OPTIONS DEFERRING A SHORT· TERM CALL GAIN The call holder may be interested in either deferring a gain until the following year or possibly converting a short-term gain on the call into a long-term gain on the stock. It is much easier to do the former than the latter. A holder of a profitable call that is due to expire in the following year can take any of three possible actions that might let him retain his profit while deferring the gain until the following tax year. One way in which to do this would be to buy a put option. Obviously, he would want to buy an ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:988 SCORE: 61.00 ================================================================================ 926 Part VI: Measuring and Trading Volatillty in-the-money put for this purpose. By so doing, he would be spending as little as pos­ sible in the way of time value premium for the put option and he would also be lock­ ing in his gain on the call. The gains and losses from the put and call combination would nearly equal each other from that time forward as the stock moves up or down, unless the stock rallies strongly, thereby exceeding the striking price of the put. This would be a happy event, however, since even larger gains would accrue. The combi­ nation could be liquidated in the following tax year, thus achieving a gain. Example: On September 1st, an investor bought an XYZ January 40 call for 3 points. The call is due to expire in the following year. XYZ has risen in price by December 1st, and the call is selling for 6 points. The call holder might want to take his 3-point gain on the call, but would also like to defer that gain until the following year. He might be able to do this by buying an XYZ January 50 put for 5 points, for example. He would then hold this combination until after the first of the new year. At that time, he could liquidate the entire combination for at least 10 points, since the strik­ ing price of the put is 10 points greater than that of the call. In fact, if the stock should have climbed to or above 50 by the first of the year, or should have fallen to or below 40 by the first of the year, he would be able to liquidate the combination for more than 10 points. The increase in time value premium at either strike would also be a benefit. In any case, he would have a gain - his original cost was 8 points (3 for the call and 5 for the put). Thus, he has effectively deferred taking the gain on the orig­ inal call holding until the next tax year. The risk that the call holder incurs in this type of transaction is the increased commission charges of buying and selling the put as well as the possible loss of any time value premium in the put itself. The investor must decide for himself whether these risks, although they may be relatively small, outweigh the potential benefit from deferring his tax gain into the next year. Another way in which the call holder might be able to defer his tax gain into the next year would be to sell another XYZ call against the one that he currently holds. That is, he would create a spread. To assure that he retains as much of his current gain as possible, he should sell an in-the-money call. In fact, he should sell an in-the­ money call with a lower striking price than the call held long, if possible, to ensure that his gain remains intact even if the underlying stock should collapse substantial­ ly. Once the spread has been established, it could be held until the following tax year before being liquidated. The obvious risk in this means of deferring gain is that one could receive an assignment notice on the short call. This is not a remote possibility, necessarily, since an in-the-money call should be used as protection for the current gain. Such an assignment would result in large commission costs on the resultant pur­ chase and sale of the underlying stock, and could substantially reduce one's gain. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:989 SCORE: 38.00 ================================================================================ Chapter 41: Taxes 927 Thus, the risk in this strategy is greater than that in the previous one (buying a put), but it may be the only alternative available if puts are not traded on the underlying stock in question. Example: An investor bought an XYZ February 50 call for 3 points in August. In December, the stock is at 65 and the call is at 15. The holder would like to "lock in" his 12-point call profit, but would prefer deferring the actual gain into the following tax year. He could sell an XYZ February 45 call for approximately 20 points to do this. If no assignment notice is received, he will be able to liquidate the spread at a cost of 5 points with the stock anywhere above 50 at February expiration. Thus, in the end he would still have a 12-point gain - having received 20 points for the sale of the February 45 and having paid out 3 points for the February 50 plus 5 points to liqui­ date the spread to take his gain. If the stock should fall below 50 before February expiration, his gain would be even larger, since he would not have to pay out the entire 5 points to liquidate the spread. The third way in which a call holder could lock in his gain and still defer the gain into the following tax year would be to sell the stock short while continuing to hold the call. This would obviously lock in the gain, since the short sale and the call pur­ chase will offset each other in profit potential as the underlying stock moves up or down. In fact, if the stock should plunge downward, large profits could accrue. However, there is risk in using this strategy as well. The commission costs of the short sale will reduce the call holder's profit. Furthermore, if the underlying stock should go ex-dividend during the time that the stock is held short, the strategist will be liable for the dividend as well. In addition, more margin will be required for the short stock. The three tactics discussed above showed how to defer a profitable call gain into the following tax year. The gain would still be short-term when realized. The only way in which a call holder could hope to convert his gain into a long-term gain would be to exercise the call and then hold the stock for more than one year. Recall that the holding period for stock acquired through exercise begins on the day of exercise - the option's holding period is lost. If the investor chooses this alternative, he of course is spending some of his gains for the commissions on the stock purchase as well as sub­ jecting himself to an entire year's worth of market risk. There are ways to protect a stock holding while letting the holding period accrue - for example, writing out-of­ the-money calls - but the investor who chooses this alternative should carefully weigh the risks involved against the possible benefits of eventually achieving a long­ term gain. The investor should also note that he will have to advance considerably more money to hold the stock. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:990 SCORE: 49.00 ================================================================================ 928 Part VI: Measuring and Trading Volatility DEFERRING A PUT HOLDER'S SHORT· TERM GAIN Without going into as much detail, there are similar ways in which a put holder who has a short-term gain on a put due to expire in the following tax year can attempt to defer the realization of that gain into the following tax year. One simple way in which he could protect his gain would be to buy a call option to protect his profitable put. He would want to buy an in-the-money call for this purpose. This resulting combina­ tion is similar in nature to the one described for the call buyer in the previous section. A second way that he could attempt to protect his gain and still defer its real­ ization into the following tax year would be to sell another XYZ put option against the one that he holds long. This would create a vertical spread. This put holder should attempt to sell an in-the-money put, if possible. Of course, he would not want to sell a put that was so deeply in-the-money that there is risk of early assignment. The results of such a spread are analogous to the call spread described in detail in the last section. Finally, the put holder could buy the underlying stock if he had enough avail­ able cash or collateral to finance the stock purchase. This would lock in the profit, as the stock and the put would offset each other in terms of gains or losses while the stock moved up or down. In fact, if the stock should experience a large rally, rising above the striking price of the put, even larger profits would become possible. In each of the tactics described, the position would be removed in the follow­ ing tax year, thereby realizing the gain that was deferred. DIFFICULTY OF DEFERRING GAINS FROM WRITING As a final point in this section on deferring gains from option transactions, it might be appropriate to describe the risks associated with the strategy of attempting to defer gains from uncovered option writing into the following tax year. Recall that in the previous sections, it was shown that a call or put holder who has an unrealized profit in an option that is due to expire in the following tax year could attempt to "lock in" the gain and defer it. The dollar risks to a holder attempting such a tax deferral were mainly commission costs and/or small amounts of time value premium paid for options. However, the option writer who has an unrealized profit may have a more difficult time finding a way to both "lock in" the gain and also defer its realization into the following tax year. It would seem, at first glance, that the call writer could mere­ ly take actions opposite to those that the call buyer takes: buying the underlying stock, buying another call option, or selling a put. Unfortunately, none of these actions "locks in" the call writer's profit. In fact, he could lose substantial investment dollars in his attempt to defer the gain into the following year. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:991 SCORE: 57.00 ================================================================================ Chapter 41: Taxes 929 Example: An investor has written an uncovered XYZ January 50 call for 5 points and the call has dropped in value to 1 point in early December. He might want to take the 4-point gain, but would prefer to defer realization of the gain until the following tax year. Since the call write is at a profit, the stock must have dropped and is prob­ ably selling around 45 in early December. Buying the underlying stock would not accomplish his purpose, because if the stock continued to decline through year-end, he could lose a substantial amount on the stock purchase and could make only 1 more point on the call write. Similarly, a call purchase would not work well. A call with a lower striking price - for example, the XYZ January 45 or the January 40- could lose substantial value if the underlying stock continued to drop in price. An out-of-the­ money call - the XYZ January 60 - is also unacceptable, because if the underlying stock rallied to the high 50's, the writer would lose money both on his January 50 call write and on his January 60 call purchase at expiration. Writing a put option would not "lock in" the profit either. If the underlying stock continued to decline, the loss­ es on the put write would certainly exceed the remaining profit potential of 1 point in the January 50 call. Alternatively, if the stock rose, the losses on the January 50 call could offset the limited profit potential provided by a put write. Thus, there is no rel­ atively safe way for an uncovered call writer to attempt to "lock in" an unrealized gain for the purpose of deferring it to the following tax year. The put writer seeking to defer his gains faces similar problems. UNEQUAL TAX TREATMENT ON SPREADS There are two types of spreads in which the long side may receive different tax treat­ ment than the short side. One is the normal equity option spread that is held for more than one year. The other is any spread between futures, futures options, or cash­ based options and equity options. With equity options, if one has a spread in place for more than one year and if the movement of the underlying stock is favorable, one could conceivably have a long-term gain on the long side and a short-term loss on the short side of the spread. Example: An investor establishes an XYZ bullish call spread in options that have 15 months of life remaining: In October of one year, he buys the January 70 LEAPS call expiring just over a year in the future. At the same time, he sells the January 80 LEAPS call, again expiring just over a year hence. Suppose he pays 13 for the January 70 call and receives 7 for the January 80 call. In December of the following year, he decides to remove the spread, after he has held it for more than one year - specifi­ cally, for 14 months in this case. XYZ has advanced by that time, and the spread is worth 9. With XYZ at 90, the January 70 call is trading at 20 and the January 80 call is trading at 11. The capital gain and loss results for tax purposes are summarized in the following table (commissions are omitted from this example): ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:992 SCORE: 38.00 ================================================================================ 930 Option XYZ January 70 LEAPS call XYZ January 80 LEAPS call Cost $1,300 $1,100 Part VI: Measuring and Trading Volatllity Proceeds $2,000 $ 700 Goin/Loss $700 long-term gain $400 short-term loss No taxes would be owed on this spread since one-half of the long-term gain is less than the short-term loss. The investor with this spread could be in a favorable position since, even though he actually made money in the spread - buying it at a 6- point debit and selling it at a 9-point credit - he can show a loss on his taxes due to the disparate treatment of the two sides of the spread. The above spread requires that the stock move in a favorable direction in order for the tax advantage to materialize. If the stock were to move in the opposite direc­ tion, then one should liquidate the spread before the long side of the spread had reached a holding period of one year. This would prevent taking a long-term loss. Another type of spread may be even more attractive in this respect. That is a spread in which nonequity options are spread against equity options. In this case, the trader would hope to make a profit on the nonequity or futures side, because part of that gain is automatically long-term gain. He would simultaneously want to take a loss on the equity option side, because that would be entirely short-term loss. There is no riskless way to do this, however. For example, one might buy a pack­ age of puts on stocks and hedge them by selling an index put on an index that per­ forms more or less in line with the chosen stocks. If the index rises in price, then one would have short-term losses on his stock options, and part of the gain on his index puts would be treated as long-term. However, if the index were to fall in price, the opposite would be true, and long-term losses would be generated - not something that is normally desirable. Moreover, the spread itself has risk, especially the tracking risk between the basket of stocks and the index itself. This brings out an important point: One should be cautious about establishing spreads merely for tax purposes. He might wind up losing money, not to mention that there could be unfavorable tax consequences. As always, a tax advisor should be con­ sulted before any tax-oriented strategy is attempted. SUMMARY Options can be used for many tax purposes. Short-term gains can be deferred into the next tax year, or can be partially protected with out-of-the-money options until they mature into long-term gains. Long-term losses can be avoided with the purchase of a put or sale of a deeply in-the-money call. Wash sales can be avoided without giv­ ing up the entire ownership potential of the stock. There are risks as well as rewards ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:993 SCORE: 14.00 ================================================================================ Chapter 41: Taxes 931 in any of the strategies. Commission costs and the dissipation of time value premium in purchased options will both work against the strategist. A tax advisor should be consulted before actually implementing any tax strate­ gy, whether that strategy employs options or not. Tax rules change from time to time. It is even possible that a certain strategy is not covered by a written rule, and only a tax advisor is qualified to give consultation on how such a strategy might be inter­ preted by the IRS. Finally, the options strategist should be careful not to confuse tax strategies with his profit-oriented strategies. It is generally a good idea to separate profit strategies from tax strategies. That is, if one finds himself in a position that conveniently lends itself to tax applications, fine. However, one should not attempt to stay in a position too long or to close it out at an illogical time just to take advantage of a tax break. The tax consequences of options should never be considered to be more important than sound strategy management. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:995 SCORE: 50.00 ================================================================================ Chapter 42: The Best Strategy? 933 is generally called volatility trading. If the net change in the market is small over a period of time, these strategies should perform well: ratio writing, ratio spreading (especially "delta neutral spreads"), straddle and strangle writing, neutral calendar spreading, and butterfly spreads. On the other hand, if options are cheap and the market is expected to be volatile, then these would be best: straddle and strangle buys, backspreads, and reverse hedges and spreads. Certain other strategies overlap into more than one of the three broad categories. For example, the bullish or bearish calendar spread is initially a neutral position. It only assumes a bullish or bearish bias after the near-term option expires. In fact, any of the diagonal or calendar strategies whose ultimate aim is to generate profits on the sale of shorter-term options are similar in nature. If these near-term profits are generated, they can offset, partially or completely, the cost oflong options. Thus, one might potentially own options at a reduced cost and could profit from a definitive move in his favor at the right time. It was shown in Chapters 14, 23, and 24 that diagonalizing a spread can often be very attractive. This brief grouping into three broad categories, does not cover all the strategies that have been discussed. For example, some strategies are generally to be avoided by most investors: high-risk naked option writing (selling options for fractional prices) and covered or ratio put writing. In essence, the investor will normally do best with a position that has limited risk and the potential of large profits. Even if the profit potential is a low-probability event, one or two successful cases may be able to over­ come a series of limited losses. Complex strategies that fit this description are the diagonal put and call combinations described in Chapters 23 and 24. The simplest strategy fitting this description is the T-bill/option purchase program described in Chapter 26. Finally, many strategies may be implemented in more than one way. The method of implementation may not alter the profit potential, but the percentage risk levels can be substantially different. Equivalent strategies fit into this category. Example: Buying stock and then protecting the stock purchase with a put purchase is an equivalent strategy in profit potential to buying a call. That is, both have limit­ ed dollar risk and large potential dollar profit if the stock rallies. However, they are substantially different in their structure. The purchase of stock and a put requires substantially more initial investment dollars than does the purchase of a call, but the limited dollar risk of the strategy would normally be a relatively small percentage of the initial investment. The call purchase, on the other hand, involves a much small­ er capital outlay; in addition, while it also has limited dollar risk, the l~ss may easily represent the entire initial investment. The stockholder will receive cash dividends while the call holder will not. Moreover, the stock will not expire as the call will. This ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:996 SCORE: 23.00 ================================================================================ 934 Part VI: Measuring and Trading Volatility provides the stock/put holder with an additional alternative of choosing to extend his position for a longer period of time by buying another put or possibly by just contin­ uing to hold the stock after the original put expires. Many equivalent positions have similar characteristics. The straddle purchase and the reverse hedge (short stock and buy calls) have similar profit and loss poten­ tial when measured in dollars. Their percentage risks are substantially different, how­ ever. In fact, as was shown in Chapter 20, another strategy is equivalent to both of these-buying stock and buying several puts. That is, buying a straddle is equivalent to buying 100 shares of stock and simultaneously buying two puts. The "buy stock and puts" strategy has a larger initial dollar investment, but the percentage risk is small­ er and the stockholder will receive any dividends paid by the common stock. In summary, the investor must know two things well: the strategy that he is con­ templating using, and his own attitude toward risk and reward. His own attitude represents suitability, a topic that is discussed more fully in the following section. Every strategy has risk. It would not be proper for an investor to pursue the best strategy in the universe (such a strategy does not exist, of course) if the risks of that strategy violated the investor's own level of financial objectives or accepted investment methodology. On the other hand, it is also not sufficient for the investor to merely feel that a strategy is suitable for his investment objectives. Suppose an investor felt that the T-bill/option strategy was suitable for him because of the profit and risk levels. Even if he understands the philosophies of option purchasing, it would not be proper for him to utilize the strategy unless he also understands the mechanics of buying Treasury bills and, more important, the concept of annualized risk. WHAT IS BEST FOR ME MIGHT NOT BE BEST FOR YOU It is impossible to classify any one strategy as the best one. The conservative investor would certainly not want to be an outright buyer of options. For him, covered call writing might be the best strategy. Not only would it accomplish his financial aims­ moderate profit potential with reduced risk-but it would be much more appealing to him psychologically. The conservative investor normally understands and accepts the risks of stock ownership. It is only a small step from that understanding to the covered call writing strategy. The aggressive investor would most likely not consider covered call writing to be the best strategy, because he would consider the profit potential too small. He is willing to take larger risks for the opportunity to make larg­ er profits. Outright option purchases might suit him best, and he would accept, by his aggressive stature, that he could lose nearly all his money in a relatively short time ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:997 SCORE: 28.00 ================================================================================ Chapter 42: The Best Strategy? 935 period. ( Of course, one would hope that he uses only 15 to 20% of his assets for spec­ ulative option buying.) Many investors fit somewhere in between the conservative description and the aggressive description. They might want to have the opportunity to make large prof­ its, but certainly are not willing to risk a large percentage of their available funds in a short period of time. Spreads might therefore appeal to this type of investor, espe­ cially the low-debit bullish or bearish calendar spreads. He might also consider occa­ sional ventures into other types of strategies-bullish or bearish spreads, straddle buys or writes, and so on-but would generally not be into a wide range of these types of positions. The T-bill/option strategy might work well for this investor also. The wealthy aggressive investor may be attracted by strategies that offer the opportunity to make money from credit positions, such as straddle or combination writing. Although ratio writing is not a credit strategy, it might also appeal to this type of investor because of the large amounts of time value premium that are gathered in. These are generally strategies for the wealthier investor because he needs the "stay­ ing power" to be able to ride out adverse cycles. If he can do this, he should be able to operate the strategy for a sufficient period of time in order to profit from the con­ stant selling of time value premiums. In essence, the answer to the question of "which strategy is best" again revolves around that familiar word, "suitability." The financial needs and investment objectives of the individual investor are more important than the merits of the strategy itself. It sounds nice to say that he would like to participate in strategies with limited risk and potentially large profits. Unfortunately, if the actual mechanics of the strategy involve risk that is not suitable for the investor, he should not use the strategy, no matter how attractive it sounds. Example: The T-bill/option strategy seems attractive: limited risk because only 10% of one's assets are subjected to risk annually; the remaining 90% of one's assets earn interest; and if the option profits materialize, they could be large. What if the worst scenario unfolds? Suppose that poor option selections are continuously made and there are three or four years of losses, coupled with a declining rate of interest earned from the Treasury bills (not to mention the commission charges for trading the secu­ rities). The portfolio might have lost 15 or 20% of its assets over those years. A good test of suitability is for the investor to ask himself, in advance: "How will I react if the worst case occurs?" If there will be sleepless nights, pointing of fingers, threats, and so forth, the strategy is unsuitable. If, on the other hand, the investor believes that he would be disappointed (because no one likes to lose money), but that he can with­ stand the risk, the strategy may indeed be suitable. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:998 SCORE: 41.00 ================================================================================ 936 Part VI: Measuring and Trading Volatility MATHEMATICAL RANKING The discussion above demonstrates that it is not possible to ultimately define the best strategy when one considers the background, both financial and psychological, of the individual investor. However, the reader may be interested in knowing which strate­ gies have the best mathematical chances of success, regardless of the investor's per­ sonal feelings. Not unexpectedly, strategies that take in large amounts of time value premium have high mathematical expectations. These include ratio writing, ratio spreading, straddle writing, and naked call writing (but only if the "rolling for cred­ its" follow-up strategy is adhered to). The ratio strategies would have to be operated according to a delta-neutral ratio in order to be mathematically optimum. Unfor­ tunately, these strategies are not for everyone. All involve naked options, and also require that the investor have a substantial amount of money ( or collateral) available to make the strategies work properly. Moreover, naked option writing in any form is not suitable for some investors, regardless of their protests to the contrary. Another group of strategies that rank high on an expected profit basis are those that have limited risk with the potential of occasionally attaining large profits. The T­ hill/option strategy is a prime example of this type of strategy. The strategies in which one attempts to reduce the cost of longer-term options through the sale of near-term options fit in this broad category also, although one should limit his dollar commit­ ment to 15 to 20% of his portfolio. Calendar spreads such as the combinations described in Chapter 23 (calendar combination, calendar straddle, and diagonal but­ terfly spread) or bullish call calendar spreads or bearish put calendar spreads are all examples of such strategies. These strategies may have a rather frequent probability of losing a small amount of money, coupled with a low probability of earning large profits. Still, a few large profits may be able to more than overcome the frequent, but small, losses. Ranking behind these strategies are the ones that offer limited profits with a reasonable probability of attaining that profit. Covered call writing, large debit bull or bear spreads (purchased option well in-the-money and possible written option as well), neutral calendar spreads, and butterfuly spreads fit into this category. Unfortunately, all these strategies involve relatively large commission costs. Even though these are not strategies that normally require a large investment, the investor who wants to reduce the percentage effect of commissions must take larger positions and will therefore be advancing a sizable amount of money. Speculative buying and spreading strategies rank the lowest on a mathematical basis. The T-bill/option strategy is not a speculative buying strategy. In-the-money purchases, including the in-the-money combination, generally outrank out-of-the­ money purchases. This is because one has the possibility of making a large percent­ age profit but has decreased the chance of losing all his investment, since he starts ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:999 SCORE: 8.00 ================================================================================ Chapter 42: The Best Strategy? 937 out in-the-money. In general, however, the constant purchase of time value premi­ ums, which must waste away by the time the options expire, will have a burdensome negative effect. The chances of large profits and large losses are relatively equal on a mathematical basis, and thus become subsidiary to the time premium effect in the long run. This mathematical outlook, of course, precludes those investors who are able to predict stock movements with an above-average degree of accuracy. Although the true mathematical approach holds that it is not possible to accurately predict the market, there are undoubtedly some who can and many who try. SUMMARY Mathematical expectations for a strategy do not make it suitable even if the expect­ ed returns are good, for the improbable may occur. Profit potentials also do not determine suitability; risk levels do. In the final analysis, one must determine the suitability of a strategy by determining if he will be able to withstand the inherent risks if the worst scenario should occur. For this reason, no one strategy can be des­ ignated as the best one, because there are numerous attitudes regarding the degree of risk that is acceptable. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1000 SCORE: 20.00 ================================================================================ Postscript Option strategies cannot be unilaterally classified as aggressive or conservative. There are certainly many aggressive applications, the simplest being the outright pur­ chase of calls or puts. However, options can also have conservative applications, most notably in reducing some of the risks of common stock ownership. In addition, there are less polarized applications, particularly spreading techniques, that allow the investor to take a middle-of-the-road approach. Consequently, the investor himself-not options--becomes the dominant force in determining whether an option strategy is too risky. It is imperative that the investor understand what he is trying to accomplish in his portfolio before actually implementing an option strategy. Not only should he be cognizant of the factors that go into determining the initial selection of the position, but he must also have in mind a plan of follow-up action. If he has thought out, in advance, what action he will take if the underlying entity rises or falls, he will be in a position to make a more rational decision when and if it does indeed make a move. The investor must also determine if the risk of the strategy is acceptable according to his financial means and objec­ tives. If the risk is too high, the strategy is not suitable. Every serious investor owes it to himself to acquire an understanding of listed option strategies. Since various options strategies are available for a multitude of pur­ poses, alrrwst every money manager or dedicated investor will be able to use options in his strategies at one time or another. For a stock-oriented investor to ignore the potential advantages of using options would be as serious a mistake as it would be for a large grain company to ignore the hedging properties available in the futures mar­ ket, or as it would be for an income-oriented investor to concentrate only in utilities and Treasury bills while ignoring less well known, but equally compatible, alterna­ tives such as GNMAs. 938 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1005 SCORE: 22.00 ================================================================================ Strategy Sullllllary Except for arbitrage strategies and tax strategies, the strategies we have described deal with risk of market movement. It is therefore often convenient to summarize option strategies by their risk and reward characteristics and by their market out­ look-bullish, bearish, or neutral. Table A-1 lists all the risk strategies that were dis­ cussed and gives a general classification of their risks and rewards. If a strategist has a definite attitude about the market's outlook or about his own willingness to accept risks, he can scan Table A-1 and select the strategies that most closely resemble his thinking. The number in parentheses after the strategy name indicates the chapter in which the strategy was discussed. Table A-1 gives a broad classification of the various risk and reward potentials of the strategies. For example, a bullish call calendar spread does not actually have unlimited profit potential unless its near-tenn call expires worthless. In fact, all cal­ endar spread or diagonal spread positions have limited profit potential at best until the near-term options expire. Also, the definition of limited risk can vary widely. Some strategies do have a risk that is truly limited to a relatively small percentage of the initial investment-the protected stock purchase, for example. In other cases, the risk is limited but is also equal to the entire initial investment. That is, one could lose 100% of his investment in a short time period. Option purchases and bull, bear, or calendar spreads are examples. Thus, although Table A-1 gives a broad perspective on the outlook for various strategies, one must be aware of the differences in reward, risk, and market outlook when actually implementing one of the strategies. 943 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1006 SCORE: 73.00 ================================================================================ 944 TABLE A-1. General strategy summary. Strategy (Chapter) Bullish strategies Call purchase (3) Synthetic long stock (short put/long call) (21) Bull spread-puts or calls (7 and 22) Protected stock purchase (long stock/long put) ( 17) Bullish call calendar spread (9) Covered call writing (2) Uncovered put write ( 19) Bearish Strategies Put purchase ( 16) Protected short sale (synthetic put) (4 and 16) Synthetic short sale (long put/short call) (21) Bear spread-put or call (and 22) Covered put write ( 19) Bearish put calendar spread (22) Naked call write (5) Neutral strategies Straddle purchase ( 1 8) Reverse hedge (simulated straddle buy) (4) Fixed income + option purchase (25) Diagonal spread (14, 23, and 24) Neutral calendar spread-puts or calls (9 and 22) Butterfly spread ( 10 and 23) Calendar straddle or combination (23) Reverse spread ( 13) Ratio write-put or call (6 and 19) Straddle or combination write (20) Ratio spread-put or call ( 11 and 24) Ratio calendar spread-put or call (12 and 24) Risk Limited Unlimited 0 Limited Limited Limited Unlimited 0 Unlimited 0 Limited Limited Unlimited Limited Unlimited Limited Unlimited Limited Limited Limited Limited Limited Limited Limited Limited Unlimited Unlimited Unlimited Unlimited Appendix A Reward Unlimited Unlimited Limited Unlimited Unlimited Limited Limited Unlimited 0 Unlimited 0 Unlimited 0 Limited Limited Unlimited 0 Limited Unlimited Unlimited Unlimited Unlimited Limited Limited Unlimited Unlimited Limited Limited Limited Unlimited 0 Wherever the risk or reword is limited only by the fact that o stock cannot foll below zero in price, the entry is marked. Obviously, although the potential may technically be limited, it could still be quite large if the underlying stock did foll a large distance. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1008 SCORE: 114.00 ================================================================================ 946 TABLE B-1. Equivalent strategies. This Strategy is equivalent to Call purchase Put purchase Long stock Short stock Naked call write Naked put write Bullish call spread (long call at lower strike/ short call at higher strike) Bearish call spread (long call at higher strike/ short call at lower strike) Ratio call write (long stock/short calls) ... and is also equivalent to ... Straddle buy (long call/long put) Appendix B This Strategy Long stock/long put Short stock/long call (synthetic put) Long call/ short put (synthetic stock) Long put/ short call (synthetic short sale) Short stock/short put Covered call write (long stock/ short call) Bullish put spread (long put at lower strike/ short put at higher strike) Bearish put spread (long put at higher strike/ short put at lower strike) Straddle write (short put/short call) Ratio put write (short stock/ short puts) Reverse hedge (short stock/long calls) or buy stock/buy puts Butterfly call spread Butterfly put spread (long 1 call at each outside strike/ (long one put at each outer strike/ short 2 calls at middle strike) short two calls at middle strike) All four of these "butterfly" strategies are equivalent Butterfly combination Protected straddle write (bullish call spread at two (short straddle at middle strike/ lower strikes/bearish put spread at two higher strikes) long call at highest strike/ long put at lowest strike ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1010 SCORE: 14.00 ================================================================================ 948 Annualized Risk (Ch. 26) Annualized risk = L INV 360 i 1 Hi where INVi = percent of total assets invested in options with holding periods, Hi length of holding period in days Bear Spread -Calls (Ch. 8) -Puts (Ch. 22) p = Cl - C2 R = s2 - s1 - P B = s1 + P R = P2 - Pl p = S2 - S1 - R B = s1 + P = s2 + Pl - P2 Black Model (Ch. 34): X s C p r Theoretical futures call price= e-rt x BSM[r = 0%] where BSM[r = O) is the Black-Scholes Model using r = 0% as the short-term interest rate Put price = Call price - e-rt x (f - s) where f = futures price current stock price striking price call price put price interest rate time (in years) B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential f futures price Appendix C Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1012 SCORE: 8.00 ================================================================================ 950 -if using call bull spread and put bear spread ( Ch. 23) R = P2 + c2 - PI c3 - s3 + s2 Then P = s3 - s2 - R or R = s3 - s2 - P D = s1 + R U = S3-R Combination Buy (Ch. 18) S1 < S2 Out-of-the-money: R = c2 + PI In-the-money: R = c1 + p2 - s2 + s1 D = s1 -P U = s2 + P Combination Sale (Ch. 20) X s C p r Out-of-the-money: P = c2 + PI In-the-money: P = c1 + p2 - s2 + s1 D = s1 -P current stock price striking price call price put price interest rate time (in years) B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential f futures price Appendix C Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a fonnula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1013 SCORE: 8.00 ================================================================================ 950 -if using call bull spread and put bear spread ( Ch. 23) R = p2 + c2 - Pl - c3 - s3 + s2 Then P = s3 - s2 - R or R = s3 - s2 - P D = s1 + R U = S3-R Combination Buy (Ch. 18) S1 < S2 Out-of-the-money: R = c2 + Pl In-the-money: R = c1 + p2 - s2 + s1 D = s1 -P U = s2 + P Combination Sale (Ch. 20) Out-of-the-money: P = c2 + PI In-the-money: P = c1 + p2 s2 + s1 D = s1 - P X s C p current stock price striking price call price put price r interest rate t ~ time (in years) f futures price U = s2 + P B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential Appendix C Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1014 SCORE: 8.00 ================================================================================ 950 -if using call bull spread and put bear spread ( Ch. 23) R = P2 + c2 - PI - c3 - s3 + s2 Then P = s3 - s2 - R or R = s3 - s2 - P D =SI+ R U = S3-R Combination Buy (Ch. 18) S1 < S2 Out-of-the-money: R = c2 + PI In-the-money: R = cI + p2 - s2 + sI D = SI -P U = s2 + P Combination Sale (Ch. 20) Out-of-the-money: P = c2 + PI In-the-money: P = cI + P2 - s2 + sI D = sI -P X s C p current stock price striking price call price put price r interest rate t = time ( in years) f futures price U = s2 + P B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential Appendix C Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1016 SCORE: 30.00 ================================================================================ 952 N t l t. Delta of long option eu ra ra 10 = -----=---=--­Delta of short option Equivalent Futures Position (Ch. 34) EFP = Delta x Number of options Equivalent Stock Position (Ch. 28) ESP = Unit of trading x Delta x number of options Appendix C where unit of trading is the number of shares of the underlying stock that can be bought or sold with the option (normally 100). Futures Contract Fair Value (Ch. 29) -Stock index futures Index value x (1 + rt) + Present worth (dividends) Also see Present worth. Future Stock Price (Ch. 28) where -lognormal distribution, assuming a movement of a fixed number of stan­ dard deviations q = future stock price Vt = volatility for the time period a = number of standard deviations of movement (normally-3.0::; a::; 3.0) Gamma (Ch. 40) X s C p r let z = In [ x ] /v --ft + v --ft S X (1 + r)t 2 Then (-x212) r- __ e-===-- - xv ✓ 2nt current stock price B striking price call price put price interest rate time (in years) u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1018 SCORE: 15.00 ================================================================================ 954 Appendix C Ratio Spread -Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher strike, s2 S1 < s2 n1 < n2 R = n1c1 - n2c2 P = (s2-s1)n1 -R p U=s2+ --­n2-n1 Break-even cost of long calls for follow-up action (Ch. 11) Break-even cost = n2(s2 - si) - R n2 n1 -Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower strike, s1 S1 < S2 n2 < n1 R = n2p2 - n1p1 P = n2(s2 - s1) - R p D =S1 ----n1 -n2 Reversal-See Conversion and Reversal Profit Reverse Hedge (Ch. 4)-simulated straddle purchase General case: short m round lots of stock and long n calls R = m(s -x) + nc U=s+-R-n-m R D=s--m X s C current stock price striking price call price p put price r interest rate t = time (in years) B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1020 SCORE: 15.00 ================================================================================ 954 Appendix C Ratio Spread -Calls (Ch. 11): buy n1 calls at lower strike, s1, and sell n2 calls at higher strike, s2 s1 < s2 n1 < n2 R = n1c1 - n2c2 P = (s2 - s1)n1 -R p U=s 2 +--­n2-n1 Break-even cost oflong calls for follow-up action (Ch. 11) Break-even cost = n2(s2 - si) - R n2-n1 -Puts (Ch. 24): buy n2 puts at higher strike, s2, and sell n1 puts at lower strike, s1 S1 < S2 n2 < n1 R = n2p2 - n1p1 P = n2(s2 - s1) - R p D =S1---- n1 -n2 Reversed-See Conversion and Reversal Profit Reverse Hedge (Ch. 4)-simulated straddle purchase General case: short m round lots of stock and long n calls R = m(s -x) + nc U=s+-R-n-m R D=s--m X s C current stock price striking price call price p put price r interest rate t = time (in years) B u D p R break-even point upside break-even point downside break-even point maximum profit potential maximum risk potential Subscripts indicate multiple items. For example s1, s2, s3 would designate three striking prices in a formula. The formulae are arranged alphabetically by title or by strategy. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1028 SCORE: 28.00 ================================================================================ TABLE E-1. ~ Qualified covered call options. ~ Call is not "deep-in-the-money" Call is not II deep-in-the-money" Applicable if Strike Price2 is at least: Applicable if Strike Price2 is at least: Stock More than Stock More than Price1 31-90-Day Call 90-Day Call Price1 31-90-Day Call 90-Day Call 5.13-5.88 5 5 75.13-80 75 70 6-10 None None 80.13-85 80 75 10.13-11.75 10 10 85.13-90 85 80 11.88-15 None None 90.13-95 90 85 15.13-17.63 15 15 95.13-100 95 90 17.75-20 None None 100.13-105 100 95 20.13-23.50 20 20 105.13-110 100 100 23.63-25 None None 110.13-120 110 110 25.13-30 25 25 120.13-130 120 120 30.13-35 30 30 130.13-140 130 130 35.13-40 35 35 140.13-150 140 140 40.13-45 40 40 150.13-160 150 140 45.13-50 45 45 160.13-170 160 150 50.13-55 50 50 170.13-180 170 160 55.13-60 55 55 180.13-190 180 170 60.13-65 60 55 190.13-200 190 180 65.13-70 65 60 200.13-210 200 190 70.13-75 70 65 210.13-220 210 200 1 Applicable stock price is either the closing price of the stock on the day preceding the date the option was granted, or the opening price on t the day the option is granted if such price is greater than 100% of the preceding day's closing price. 2Assumption is that strike prices are only at $5 intervals up to $ 100 and $10 intervals over $100. Note: If the stock splits, option strike prices 5:c· will have smaller intervals for a period of time. ""' ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1029 SCORE: 47.00 ================================================================================ Glossary American Exercise: a feature of an option that indicates it may be exercised at any time. Therefore, it is subject to early assignment. Arbitrage: the process in which professional traders simultaneously buy and sell the same or equivalent securities for a riskless profit. See also Risk Arbitrage. Assign: to designate an option writer for fulfillment of his obligation to sell stock (call option writer) or buy stock (put option writer). The writer receives an assignment notice from the Options Clearing Corporation. See also Early Exercise. Assignment Notice: see Assign. Automatic Exercise: a protection procedure whereby the Options Clearing Corporation attempts to protect the holder of an expiring in-the-money option by automatically exercising the option on behalf of the holder. Average Down: to buy more of a security at a lower price, thereby reducing the holder's average cost. (Average Up: to buy more at a higher price.) Backspread: see Reverse Strategy. Bear Spread: an option strategy that makes its maximum profit when the underly­ ing stock declines and has its maximum risk if the stock rises in price. The strate­ gy can be implemented with either puts or calls. In either case, an option with a higher striking price is purchased and one with a lower striking price is sold, both options generally having the same expiration date. See also Bull Spread. Bearish: an adjective describing an opinion or outlook that expects a decline in price, either by the general market or by an underlying stock, or both. See also Bullish. 963 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1030 SCORE: 73.00 ================================================================================ 964 Glossary Beta: a measure of how a stock's movement correlates to the movement of the entire stock market. The beta is not the same as volatility. See also Standard Deviation, Volatility. Black Model: a model used to predict futures option prices; it is a modified version of the Black-Scholes model. See Model. Board Broker: the exchange member in charge of keeping the book of public orders on exchanges utilizing the "market-maker" system, as opposed to the "spe­ cialist system," of executing orders. See also Market-Maker, Specialist. Box Spread: a type of option arbitrage in which both a bull spread and a bear spread are established for a riskless profit. One spread is established using put options and the other is established using calls. The spreads may both be debit spreads ( call bull spread vs. put bear spread), or both credit spreads (call bear spread vs. put bull spread). Break-Even Point: the stock price (or prices) at which a particular strategy neither makes nor loses money. It generally pertains to the result at the expiration date of the options involved in the strategy. A "dynamic" break-even point is one that changes as time passes. Broad-Based: generally referring to an index, it indicates that the index is composed of a sufficient number of stocks or of stocks in a variety of industry groups. Broad­ based indices are subject to more favorable treatment for naked option writers. See also Narrow- Based. Bull Spread: an option strategy that achieves its maximum potential if the underly­ ing security rises far enough, and has its maximum risk if the security falls far enough. An option with a lower striking price is bought and one with a higher strik­ ing price is sold, both generally having the same expiration date. Either puts or calls may be used for the strategy. See also Bear Spread. Bullish: describing an opinion or outlook in which one expects a rise in price, either by the general market or by an individual security. See also Bearish. Butterfly Spread: an option strategy that has both limited risk and limited profit potential, constructed by combining a bull spread and a bear spread. Three strik­ ing prices are involved, with the lower two being utilized in the bull spread and the higher two in the bear spread. The strategy can be established with either puts or calls; there are four different ways of combining options to construct the same basic position. Calendar Spread: an option strategy in which a short-term option is sold and a longer-term option is bought, both having the same striking price. Either puts or ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1031 SCORE: 65.00 ================================================================================ Glossary 965 calls may be used. A calendar combination is a strategy that consists of a call cal­ endar spread and a put calendar spread at the same time. The striking prices of the calls would be higher than the striking prices of the puts. A calendar straddle consists of selling a near-term straddle and buying a longer-term straddle, both with the same striking price. Calendar Straddle or Combination: see Calendar spread. Call: an option that gives the holder the right to buy the underlying security at a specified price for a certain, fixed period of time. See also Put. Call Price: the price at which a bond or preferred stock may be called in by the issu­ ing corporation; see Redemption Price. Capitalization-Weighted Index: a stock index that is computed by adding the cap­ italizations (float times price) of each individual stock in the index, and then divid­ ing by the divisor. The stocks with the largest market values have the heaviest weighting in the index. See also Divisor, Float, Price-Weighted Index. Carrying Cost: the interest expense on a debit balance created by establishing a position. Cash- Based: Referring to an option or future that is settled in cash when exercised or assigned. No physical entity, either stock or commodity, is received or delivered. CBOE: the Chicago Board Options Exchange; the first national exchange to trade listed stock options. Circuit Breaker: a limit applied to the trading of index futures contracts designed to keep the stock market from crashing. Class: a term used to refer to all put and call contracts on the same underlying secu­ rity. Closing Transaction: a trade that reduces an investor's position. Closing buy trans­ actions reduce short positions and closing sell transactions reduce long positions. See also Opening Transaction. Collateral: the loan value of marginable securities; generally used to finance the writing of uncovered options. Combination: (1) any position involving both put and call options that is not a strad­ dle. See also Straddle. (2) the name given to the trade at expiration whereby an arbitrageur rolls his options from one month to the next. For example, if he sells his synthetic long stock position in June and reestablishes it by buying a synthetic long stock position in September, the entire four-sided trade is called a combina­ tion by floor traders. See also Straddle, Strangle. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1032 SCORE: 52.00 ================================================================================ 966 Glossary Commodities: see Futures Contract. Contingent Order: an order whose execution or price is dependent on the align­ ment or price of the underlying security and/or its options. Most commonly it is an order to buy stock and sell a covered call option that is given as one order to the trading desk of a brokerage firm. Also called a "net order." This is a "not held" order. See also Market Not Held Order. Conversion Arbitrage: a riskless transaction in which the arbitrageur buys the underlying security, buys a put, and sells a call. The options have the same terms. See also Reversal Arbitrage. Conversion Ratio: see Convertible Security. Converted Put: see Synthetic Put. Convertible Security: a security that is convertible into another security. Generally, a convertible bond or convertible preferred stock is convertible into the underly­ ing stock of the same corporation. The rate at which the shares of the bond or pre­ ferred stock are convertible into the common is called the conversion ratio. Cover: to buy back as a closing transaction an option that was initially written, or stock that was initially sold short. Covered: a written option is considered to be covered if the writer also has an oppos­ ing market position on a share-for-share basis in the underlying security. That is, a short call is covered if the underlying stock is owned, and a short put is covered (for margin purposes) if the underlying stock is also short in the account. In addi­ tion, a short call is covered if the account is also long another call on the same secu­ rity, with a striking price equal to or less than the striking price of the short call. A short put is covered if there is also a long put in the account with a striking price equal to or greater than the striking price of the short put. Covered Call Write: a strategy in which one writes call options while simultane­ ously owning an equal number of shares of the underlying stock. Covered Put Write: a strategy in which one sells put options and simultaneously is short an equal number of shares of the underlying security. Covered Straddle Write: the term used to describe the strategy in which an investor owns the underlying security and also writes a straddle on that security. This is not really a covered position. Credit: money received in an account. A credit transaction is one in which the net sale proceeds are larger than the net buy proceeds ( cost), thereby bringing money into the account. See also Debit. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1033 SCORE: 97.00 ================================================================================ Glossary 967 Cycle: the expiration dates applicable to various classes of options. There are three cycles: January/April/July/October, February/May/ August/November, and March/J une/Septem ber/Decem ber. Debit: an expense, or money paid out from an account. A debit transaction is one in which the net cost is greater than the net sale proceeds. See also Credit. Deliver: to take securities from an individual or firm and transfer them to another individual or firm. A call writer who is assigned must deliver stock to the call hold­ er who exercised. A put holder who exercises must deliver stock to the put writer who is assigned. Delivery: the process of satisfying an equity call assignment or an equity put exer­ cise. In either case, stock is delivered. For futures, the process of transferring the physical commodity from the seller of the futures contract to the buyer. Equivalent delivery refers to a situation in which delivery may be made in any of various, similar entities that are equivalent to each other (for example, Treasury bonds with differing coupon rates). Delta: (1) the amount by which an option's price will change for a corresponding 1- point change in price by the underlying entity. Call options have positive deltas, while put options have negative deltas. Technically, the delta is an instantaneous measure of the option's price change, so that the delta will be altered for even frac­ tional changes by the underlying entity. Consequently, the terms "up delta" and "down delta" may be applicable. They describe the option's change after a full 1- point change in price by the underlying security, either up or down. The "up delta" may be larger than the "down delta" for a call option, while the reverse is true for put options. (2) the percent probability of a call being in-the-money at expiration. See also Hedge Ratio. Delta Neutral Spread: a ratio spread that is established as a neutral position by uti­ lizing the deltas of the options involved. The neutral ratio is determined by divid­ ing the delta of the purchased option by the delta of the written option. See also Delta, Ratio Spread. Depository Trust Corporation (OTC): a corporation that will hold securities for member institutions. Generally used by option writers, the DTC facilitates and guarantees delivery of underlying securities when assignment is made against securities held in DTC. Diagonal Spread: any spread in which the purchased options have a longer matu­ rity than do the written options, as well as having different striking prices. Typical ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1034 SCORE: 74.00 ================================================================================ 968 Glossary types of diagonal spreads are diagonal bull spreads, diagonal bear spreads, and diagonal butterfly spreads. Discount: an option is trading at a discount if it is trading for less than its intrinsic value. A future is trading at a discount if it is trading at a price less than the cash price of its underlying index or commodity. See also Intrinsic Value, Parity. Discount Arbitrage: a riskless arbitrage in which a discount option is purchased and an opposite position is taken in the underlying security. The arbitrageur may either buy a call at a discount and simultaneously sell the underlying security (basic call arbitrage), or buy a put at a discount and simultaneously buy the under­ lying security (basic put arbitrage). See also Discount. Discretion: see Limit Order, Market Not Held Order. Dividend Arbitrage: in the riskless sense, an arbitrage in which a put is purchased and so is the underlying stock. The put is purchased when it has time value pre­ mium less than the impending dividend payment by the underlying stock. The transaction is closed after the stock goes ex-dividend. Also used to denote a form of risk arbitrage in which a similar procedure is followed, except that the amount of the impending dividend is unknown and therefore risk is involved in the trans­ action. See also Ex-Dividend, Time Value Premium. Divisor: a mathematical quantity used to compute an index. It is initially an arbitrary number that reduces the index value to a small, workable number. Thereafter the divisor is adjusted for stock splits (price-weighted index) or additional issues of stock (capitalization-weighted index). Downside Protection: generally used in connection with covered call writing, this is the cushion against loss, in case of a price decline by the underlying security, that is afforded by the written call option. Alternatively, it may be expressed in terms of the distance the stock could fall before the total position becomes a loss (an amount equal to the option premium), or it can be expressed as percentage of the current stock price. See also Covered Call Write. Dynamic: for option strategies, describing analyses made during the course of changing security prices and during the passage of time. This is as opposed to an analysis made at expiration of the options used in the strategy. A dynamic break­ even point is one that changes as time passes. A dynamic follow-up action is one that will change as either the security price changes or the option price changes or time passes. See also Break-Even Point, Follow-Up Action. Early Exercise (assignment): the exercise or assignment of an option contract before its expiration date. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1037 SCORE: 72.00 ================================================================================ Glossary 969 Equity Option: an option that has common stock as its underlying security. See also Non-Equity Option. Equity Requirement: a requirement that a minimum amount of equity must be present in a margin account. Normally, this requirement is $2,000, but some bro­ kerage firms may impose higher equity requirements for uncovered option writing. Equivalent Positions: positiohs that have similar profit potential, when measured in dollars, but are constructed with differing securities. Equivalent positions have the same profit graph. A covered call write is equivalent to an uncovered put write, for example. See also Profit Graph. Escrow Receipt: a receipt issued by a bank in order to verify that a customer ( who has written a call) in fact owns the stock and therefore the call is considered covered. European Exercise: a feature of an option that stipulates that the option may be exercised only at its expiration. Therefore, there can be no early assignment with this type of option. Exchange-Traded Fund (ETF): an index fund that is listed on a stock exchange. Options are listed on some ETFs. See also Index Fund. Ex-Dividend: the process whereby a stock's price is reduced when a dividend is paid. The ex-dividend date (ex-date) is the date on which the price reduction takes place. Investors who own stock on the ex-date will receive the dividend, and those who are short stock must pay out the dividend. Exercise: to invoke the right granted under the terms of a listed options contract. The holder is the one who exercises. Call holders exercise to buy the underlying security, while put holders exercise to sell the underlying security. Exercise Limit: the limit on the number of contracts a holder can exercise in a fixed period of time. Set by the appropriate option exchange, it is designed to prevent an investor or group of investors from "cornering" the market in a stock. Exercise Price: the price at which the option holder may buy or sell the underlying security, as defined in the terms of his option contract. It is the price at which the call holder may exercise to buy the underlying security or the put holder may exer­ cise to sell the underlying security. For listed options, the exercise price is the same as the striking price. See also Exercise. Expected Return: a rather complex mathematical analysis involving statistical dis­ tribution of stock prices, it is the return an investor might expect to make on an investment if he were to make exactly the same investment many times through­ out history. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1038 SCORE: 69.00 ================================================================================ 970 Glossary Expiration Date: the day on which an option contract becomes void. The expiration date for listed stock options is the Saturday after the third Friday of the expiration month. All holders of options must indicate their desire to exercise, if they wish to do so, by this date. See also Expiration Time. Expiration Time: the time of day by which all exercise notices must be received on the expiration date. Technically, the expiration time is currently 5:00 P.M. on the expiration date, but public holders of option contracts must indicate their desire to exercise no later than 5:30 P.M. on the business day preceding the expiration date. The times are Eastern Time. See also Expiration Date. Facilitation: the process of providing a market for a security. Normally, this refers to bids and offers made for large blocks of securities, such as those traded by insti­ tutions. Listed options may be used to offset part of the risk assumed by the trad­ er who is facilitating the large block order. See also Hedge Ratio. Fair Value: normally, a term used to describe the worth of an option or futures con­ tract as determined by a mathematical model. Also sometimes used to indicate intrinsic value. See also Intrinsic Value, Model. First Notice Day: the first day upon which the buyer of a futures contract can be called upon to take delivery. See also Notice Period. Float: the number of shares outstanding of a particular common stock. Floor Broker: a trader on the exchange floor who executes the orders of public cus­ tomers or other investors who do not have physical access to the trading area. Follow-Up Action: any trading in an option position after the position is established. Generally, to limit losses or to take profits. Fundamental Analysis: a method of analyzing the prospects of a security by observ­ ing accepted accounting measures such as earnings, sales, assets, and so on. See also Technical Analysis. Futures Contract: a standardized contract calling for the delivery of a specified quantity of a commodity at a specified date in the future. Gamma: a measure of risk of an option that measures the amount by which the delta changes for a I-point change in the stock price; alternatively, when referring to an entire option position, the amount of change of the delta of the entire position when the stock changes in price by one point. Gamma of the Gamma: a mathematical measure of risk that measures by how much the gamma will change for a I-point move in the stock price. See Gamma. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1039 SCORE: 51.00 ================================================================================ Glossary 971 Good Until Canceled (GTC): a designation applied to some types of orders, mean­ ing that the order remains in effect until it is either filled or canceled. See also Limit, Stop-Limit Order, Stop Order. Hedge Ratio: the mathematical quantity that is equal to the delta of an option. It is useful in facilitation in that a theoretically riskless hedge can be established by tak­ ing offsetting positions in the underlying stock and its call options. See also Delta, Facilitation. Historic Volatility: See Volatility. Holder: the owner of a security. Horizontal Spread: an option strategy in which the options have the same striking price, but different expiration dates. Implied Volatility: a prediction of the volatility of the underlying stock, it is deter­ mined by using prices currently existing in the option market at the time, rather than using historical data on the price changes of the underlying stock See also Volatility. Incremental Return Concept: a strategy of covered call writing in which the investor is striving to earn an additional return from option writing against a stock position that he is targeted to sell, possibly at substantially higher prices. Index: a compilation of the prices of several common entities into a single number. See also Capitalization-Weighted Index, Price-Weighted Index. Index Arbitrage: a form of arbitraging index futures against stock If futures are trading at prices significantly higher than fair value, the arbitrager sells futures and buys the exact stocks that make up the index being arbitraged; if futures are at a discount to fair value, the arbitrage entails buying futures and selling stocks. Index Fund: a mutual fund whose components exactly match the stocks that make up a widely disseminated index, such as the S&P 500, Dow-Jones, Russell 2000, or NASDAQ-100. See also Exchange-Traded Fund. Index Option: an option whose underlying entity is an index. Most index options are cash-based. Institution: an organization, probably very large, engaged in investing in securities. Normally a bank, insurance company, or mutual fund. Intermarket Spread: a futures spread in which futures contracts in one market are spread against futures contracts trading in another market. Examples: Currency spreads (yen vs. deutsche mark) or TED spread (T-Bills vs. Eurodollars). ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1040 SCORE: 43.00 ================================================================================ 972 Glossary In-the-Money: a term describing any option that has intrinsic value. A call option is in-the-money if the underlying security is higher than the striking price of the call. A put option is in-the-money if the security is below the striking price. See also Intrinsic Value, Out-of-the-Money. Intramarket Spread: a futures spread in which futures contracts are spread against other futures contracts in the same market; example, buy May soybeans, sell March soybeans. Intrinsic Value: the value of an option if it were to expire immediately with the underlying stock at its current price; the amount by which an option is in-the­ money. For call options, this is the difference between the stock price and the striking price, if that difference is a positive number, or zero otherwise. For put options it is the difference between the striking price and the stock price, if that difference is positive, and zero otherwise. See also In-the-Money, Parity, Time Value Premium. Last Trading Day: the third Friday of the expiration month. Options cease trading at 3:00 P.M. Eastern Time on the last trading day. LEAPS: Long-term Equity Anticipation Securities. These are long-term listed options, currently having maturities as long as two and one-half years. Leg: a risk-oriented method of establishing a two-sided position. Rather than enter­ ing into a simultaneous transaction to establish the position (a spread, for exam­ ple), the trader first executes one side of the position, hoping to execute the other side at a later time and a better price. The risk materializes from the fact that a better price may never be available, and a worse price must eventually be accept­ ed. Letter of Guarantee: a letter from a bank to a brokerage firm stating that a cus­ tomer (who has written a call option) does indeed own the underlying stock and the bank will guarantee delivery if the call is assigned. Thus, the call can be con­ sidered covered. Not all brokerage firms accept letters of guarantee. Leverage: in investments, the attainment of greater percentage profit and risk potential. A call holder has leverage with respect to a stockholder-the former will have greater percentage profits and losses than the latter, for the same movement in the underlying stock. Limit: see Trading Limit. Limit Order: an order to buy or sell securities at a specified price (the limit). A limit order may also be placed "with discretion" -a fixed; usually small, amount such as 1/s or ¼ of a point. In this case, the floor broker executing the order may use his ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1041 SCORE: 22.00 ================================================================================ Glossary 973 discretion to buy or sell at 1/s or ¼ of a point beyond the limit if he feels it is nec­ essary to fill the order. Listed Option: a put or call option that is traded on a national option exchange. Listed options have fixed striking prices and expiration dates. See also Over-the­ Counter Option. Local: a trader on a futures exchange who buys and sells for his own account and may fill public orders. Lognormal Distribution: a statistical distribution that is often applied to the move­ ment of the stock prices. It is a convenient and logical distribution because it implies that stock prices can theoretically rise forever but cannot fall below zero-­ a fact which is, of course, true. Margin: to buy a security by borrowing funds from a brokerage house. The margin requirement-the maximum percentage of the investment that can be loaned by the broker firm-is set by the Federal Reserve Board. Market Basket: a portfolio of common stocks whose performance is intended to simulate the performance of a specific index. See Index. Market-Maker: an exchange member whose function is to aid in the making of a market, by making bids and offers for his account in the absence of public buy or sell orders. Several market-makers are normally assigned to a particular security. The market-maker system encompasses the market-makers and the board bro­ kers. See also Board Broker, Specialist. Market Not Held Order: also a market order, but the investor is allowing the floor broker who is executing the order to use his own discretion as to the exact timing of the execution. If the floor broker expects a decline in price and he is holding a "market not held" buy order, he may wait to buy, figuring that a better price will soon be available. There is no guarantee that a "market not held" order will be filled. Market Order: an order to buy or sell securities at the current market. The order will be filled as long as there is a market for the security. Married Put and Stock: a put and stock are considered to be married if they are bought on the same day, and the position is designated at that time as a hedge. Model: a mathematical formula designed to price an option as a function of certain variables-generally stock price, striking price, volatility, time to expiration, divi­ dends to be paid, and the current risk-free interest rate. The Black­ Scholes model is one of the more widely used models. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1042 SCORE: 44.00 ================================================================================ 974 Glossary Monte Carlo Simulation: a model designed to simulate a real-world event that can­ not be approximated merely with a mathematical formula. The Monte Carlo sim­ ulation approximates such an event (the movement of the stock market, for exam­ ple) and then it is simulated a great number of times. The net result of all the sim­ ulations is then interpreted as the result, generally expressed as a probability of occurrence. For example, a Monte Carlo simulation can be used to determine how stocks might behave under certain stock price distributions that are different from the lognormal distribution. Naked Option: see Uncovered Option. Narrow-Based: Generally referring to an index, it indicates that the index is com­ posed of only a few stocks, generally in a specific industry group. Narrow-based indices are not subject to favorable treatment for naked option writers. See also Broad-Based. "Net" Order: see Contingent Order. Neutral: describing an opinion that is neither bearish or bullish. Neutral option strategies are generally designed to perform best if there is little nor no net change in the price of the underlying stock. See also Bearish, Bullish. Non-Equity Option: an option whose underlying entity is not common stock; typi­ cally refers to options on physical commodities, but may also be extended to include index options. "Not Held": see Market Not Held Order. Notice Period: the time during which the buyer of a futures contract can be called upon to accept delivery. Typically, the 3 to 6 weeks preceding the expiration of the contract. Open Interest: the net total of outstanding open contracts in a particular option series. An opening transaction increases the open interest, while any closing trans­ action reduces the open interest. Opening Transaction: a trade that adds to the net position of an investor. An open­ ing buy transaction adds more long securities to the account. An opening sell transaction adds more short securities. See also Closing Transaction. Option Pricing Curve: a graphical representation of the projected price of an option at a fixed point in time. It reflects the amount of time value premium in the option for various stock prices, as well. The curve is generated by using a mathe­ matical model. The delta ( or hedge ratio) is the slope of a tangent line to the curve at a fixed stock price. See also Delta, Hedge Ratio, Model. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1043 SCORE: 59.00 ================================================================================ Glossary 975 Options Clearing Corporation (OCC): the issuer of all listed option contracts that are trading on the national option exchanges. Original Issue Discount (O1D): the initial price of a zero-coupon bond. The owner owes taxes on the theoretical interest, or phantom income, generated by the annu­ al appreciation of the bond toward maturity. In reality, no interest is paid by the zero-coupon bond, but the government is taxing the appreciation of the bond as if it were interest. Out-of-the-Money: describing an option that has no intrinsic value. A call option is out-of-the-money if the stock is below the striking price of the call, while a put option is out-of-the-money if the stock is higher than the striking price of the put. See also In-the-Money, Intrinsic Value. Over-the-Counter Option (OTC): an option traded over-the-counter, as opposed to a listed stock option. The OTC option has a direct link between buyer and sell­ er, has no secondary market, and has no standardization of striking prices and expi­ ration dates. See a'lso Listed Option, Secondary Market. Overvalued: describing a security trading at a higher price than it logically should. Normally associated with the results of option price predictions by mathematical models. If an option is trading in the market for a higher price than the model indi­ cates, the option is said to be overvalued. See a'/so Fair Value, Undervalued. Pairs Trading: a hedging technique in which one buys a particular stock and sells short another stock. The two stocks are theoretically linked in their price history, and the hedge is established when the historical relationship is out of line, in hopes that it will return to its former correlation. Parity: describing an in-the-money option trading for its intrinsic value: that is, an option trading at parity with the underlying stock. Also used as a point of refer­ ence-an option is sometimes said to be trading at a half-point over parity or at a quarter-point under parity, for example. An option trading under parity is a dis­ count option. See a'/so Discount, Intrinsic Value. PERCS: Preferred Equity Redemption Cumulative Stock. Issued by a corporation, this preferred stock pays a higher dividend than the common and has a price at which it can be called in for redemption by the issuing corporation. As such, it is really a covered call write, with the call premium being given to the holder in the form of increased dividends. See Call Price, Covered Call Write, Redemption Price. Physical Option: an option whose underlying security is a physical commodity that is not stock or futures. The physical commodity itself, typically a currency or ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1044 SCORE: 32.00 ================================================================================ 976 Glossary Treasury debt issue, underlies that option contract. See also Equity Option, Index Option. Portfolio Insurance: a method of selling index futures or buying index put options to protect a portfolio of stocks. Position: as a noun, specific securities in an account or strategy. A covered call writ­ ing position might be long 1,000 XYZ and short 10 XYZ January 30 calls. As a verb, to facilitate; to buy or sell-generally a block of securities-thereby establishing a position. See also Facilitation, Strategy. Position Limit: the maximum number of put or call contracts on the same side of the market that can be held in any one account or group of related accounts. Short puts and long calls are on the same side of the market. Short calls and long puts are on the same side of the market. Premium: for options, the total price of an option contract. The sum of the intrinsic value and the time value premium. For futures, the difference between the futures price and the cash price of the underlying index or commodity. Present Worth: a mathematical computation that determines how much money would have to be invested today, at a specified rate, in order to produce a desig­ nated amount at some time in the future. For example, at 10% for one year, the present worth of $ll0 is $100. Price-Weighted Index: a stock index that is computed by adding the prices of each stock in the index, and then dividing by the divisor. See also Capitalization­ Weighted Index, Divisor. Profit Graph: a graphical representation of the potential outcomes of a strategy. Dollars of profit or loss are graphed on the vertical axis, and various stock prices are graphed on the horizontal axis. Results may be depicted at any point in time, although the graph usually depicts the results at expiration of the options involved in the strategy. Profit Range: the range within which a particular position makes a profit. Generally used in reference to strategies that have two break-even points-an upside break­ even and a downside break-even. The price range between the two break-even points would be the profit range. See also Break-Even Point. Profit Table: a table of results of a particular strategy at some point in time. This is usually a tabular compilation of the data drawn on a profit graph. See also Profit Graph. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1045 SCORE: 50.00 ================================================================================ Glossary 917 Program Trading: the act of buying or selling a particular portfolio of stocks and hedging with an offsetting position in index futures. The portfolio of stocks may be small or large, but it is not the makeup of any stock index. See also Index Arbitrage. Protected Strategy: a position that has limited risk. A protected short sale (short stock, long call) has limited risk, as does a protected straddle write ( short straddle, long out-of-the-money combination). See also Combination, Straddle. Public Book (of orders): the orders to buy or sell, entered by the public, that are away from the current market. The board broker or specialist keeps the public book. Market-makers on the CBOE can see the highest bid and lowest offer at any time. The specialist's book is closed ( only he knows at what price and in what quan­ tity the nearest public orders are). See also Board Broker, Market-Maker, Specialist. Put: an option granting the holder the right to sell the underlying security at a cer­ tain price for a specified period of time. See also Call. Put-Call Ratio: the ratio of put trading volume divided by call trading volume; sometime~ calculated with open interest or total dollars instead of trading volume. Can be calculated daily, weekly, monthly, etc. Moving averages are often used to smooth out short-term, daily figures. Ratio Calendar Combination: a strategy consisting of a simultaneous position of a ratio calendar spread using calls and a similar position using puts, where the strik­ ing price of the calls is greater than the striking price of the puts. Ratio Calendar Spread: selling more near-term options than longer-term ones purchased, all with the same strike, either puts or calls. Ratio Spread: constructed with either puts or calls, the strategy consists of buying a certain amount of options and then selling a larger quantity of out-of-the-money options. Ratio Strategy: a strategy in which one has an unequal number of long securities and short securities. Normally, it implies a preponderance of short options over either long options or long stock. Ratio Write: buying stock and selling a preponderance of calls against the stock that is owned. ( Occasionally constructed as shorting stock and selling puts.) Redemption Price: the price at which a structured product may be redeemed for cash. This is distinctly different from a "call price," which is the price at which an issue may be called away by the issuer. See also Call Price, PERCS, Structured Product. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1046 SCORE: 51.00 ================================================================================ 978 Glossary Resistance: a term in technical analysis indicating a price area higher than the cur­ rent stock price where an abundance of supply exists for the stock, and therefore the stock may have trouble rising through the price. See also Support. Return (on investment): the percentage profit that one makes, or might make, on his investment. Return if Exercised: the return that a covered call writer would make if the under­ lying stock were called away. Return if Unchanged: the return that an investor would make on a particular posi­ tion if the underlying stock were unchanged in price at the expiration of the options in the position. Reversal Arbitrage: a riskless arbitrage that involves selling the stock short, writing a put, and buying a call. The options have the same terms. See also Conversion Arbitrage. Reverse Hedge: a strategy in which one sells the underlying stock short and buys calls on more shares than he has sold short. This is also called a synthetic straddle and is an outmoded strategy for stocks that have listed puts trading. See also Ratio Write, Straddle. Reverse Strategy: a general name that is given to strategies that are the opposite of better-known strategies. For example, a ratio spread consists of buying calls at a lower strike and selling more calls at a higher strike. A reverse ratio spread, also known as a backspread, consists of selling the calls at the lower strike and buying more calls at the higher strike. The results are obviously directly opposite to each other. See also Reverse Hedge Ratio Write, Reverse Hedge. Rho: the measure of how much an option changes in price for an incremental mov<' (generally l % ) in short-term interest rates; more significant for longer-term or i11- the-money options. Risk Arbitrage: a form of arbitrage that has some risk associated with it. Commonly refers to potential takeover situations in which the arbitrageur buys the stock of the company about to be taken over and sells the stock of the company that is effecting the takeover. See also Dividend Arbitrage. Roll: a follow-up action in which the strategist closes options currently in the posi­ tion and opens other options with different terms, on the same underlying stock. See also Roll Down, Roll Forward, and Roll Up. Roll Down: close out options at one strike and simultaneously open other options al a lower strike. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1047 SCORE: 71.00 ================================================================================ Glossary 979 Roll Forward: close out options at a near-term expiration date and open options at a longer-term expiration date. Roll Up: close out options at a lower strike and open options at a higher strike. Rotation: a trading procedure on the open exchanges whereby bids and offers, but not necessarily trades, are made sequentially for each series of options on an underlying stock or index. Secondary M~ket: any market in which securities can be readily bought and sold after their initial issuance. The national listed option exchanges provided, for the first time, a secondary market in stock options. Serial Option: a futures option for which there is no corresponding futures contract expiring in the same month. The underlying futures contract is the next futures contract out in time. Example: There is no March gold futures contract, but there is an April gold futures contract, so March gold options, which are serial options, are options on April gold futures. Series: all op,tion contracts on the same underlying stock having the same striking price, expiration date, and unit of trading. Skew: See Volatility Skew. Specialist: an exchange member whose function it is both to make markets-buy and sell for his own account in the absence of public orders-and to keep the book of public orders. Most stock exchanges and some option exchanges utilize the spe­ cialist system of trading Spread Order: an order to simultaneously transact two or more option trades. Typically, one option would be bought while another would simultaneously be sold. Spread orders may be limit orders, not held orders, or orders with discretion. They cannot be stop orders, however. The spread order may be either a debit or a credit. Spread Strategy: any option position having both long options and short options of the same type on the same underlying security. Standard Deviation: a measure of the volatility of a stock. It is a statistical quanti­ ty measuring the magnitude of the daily price changes of that stock. See also, Volatility. Stop Order: an order, placed away from the current market, that becomes a market order if the security trades at the price specified on the stop order. Buy stop orders are placed above the market, while sell stop orders are placed below. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1048 SCORE: 30.00 ================================================================================ 980 Glossary Stop-Limit Order: similar to a stop order, the stop-limit order becomes a limit order, rather than a market order, when the security trades at the price specified on the stop. See also Stop Order. Straddle: the purchase or sale of an equal number of puts and calls having the same terms. Strangle: a combination involving a put and a call at different strikes with the same expiration date. Strategy: with respect to option investments, a preconceived, logical plan of position selection and follow-up action. Striking Price: see Exercise Price. Striking Price Interval: the distance between striking prices on a particular under­ lying security. For stocks, the interval is normally 2.5 points for lower-priced stocks and 5 points for higher-priced stocks. For indices, the interval is either 5 or 10 points. For futures, the interval is often as low as one or two points. Structured Product: a combination of securities and possibly options into a single security that behaves like stock and trades on a listed stock exchange. Structured products are created by many of the largest financial institutions (banks and bro­ kerage firms). Many of the more popular ones are known by their acronyms, cre­ ated by the institutions that issued them: MITTS, TARGETS, BRIDGES, LINKS, DINKS, ELKS, and PERCS. See also PERCS. Subindex: see Narrow-Based. Suitable: describing a strategy or trading philosophy in which the investor is operat­ ing in accordance with his financial means and investment objectives. Support: a term in technical analysis indicating a price area lower than the current price of the stock, where demand is thought to exist. Thus, a stock would stop declining when it reached a support area. See also Resistance. Synthetic Put: a strategy constructed by shorting the underlying instrument and buying a call. The resulting position has the same profit and loss characteristics as a long put option. Synthetic Stock: an option strategy that is equivalent to the underlying stock. A long call and a short put is synthetic long stock. A long put and a short call is synthetic short stock. Technical Analysis: the method of predicting future stock price movements based on observation of historical stock price movements. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1049 SCORE: 56.00 ================================================================================ Glossary 981 Terms: the collective name denoting the expiration date, striking price, and under­ lying stock of an option contract. Theoretical Value: the price of an option, or a spread, as computed by a mathe­ matical model. Theta: the measure of how much an option's price decays for each day of time that passes. Time Spread: see Calendar Spread. Time Value Premium: the amount by which an option's total premium exceeds its intrinsic value. Total Return Concept: a covered call writing strategy in which one views the potential profit of the strategy as the sum of capital gains, dividends, and option premium.income, rather than viewing each one of the three separately. Tracking Error: the amount of difference between the performance of a specific portfolio of stocks and a broad-based index with which they are being compared. See Market Basket. Trader: a speculative investor or professional who makes frequent purchases and sales. Trading Limit: the exchange-imposed maximum daily price change that a futures contract or futures option contract can undergo. Treasury BilVOption Strategy: a method of investment in which one places approximately 90% of his funds in risk-free, interest-bearing assets such as Treasury bills, and buys options with the remainder of his assets. Type: the designation to distinguish between a put or call option. Uncovered Option: a written option is considered to be uncovered if the investor does not have a corresponding position in the underlying security. See also Covered. Underlying Security: the security that one has the right to buy or sell via the terms of a listed option contract. Undervalued: describing a security that is trading at a lower price than it logically should. Usually determined by the use of a mathematical model. See also Fair Value, Overvalued. Variable Ratio Write: an option strategy in which the investor owns 100 shares of the underlying security and writes two call options against it, each option having a different striking price. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1050 SCORE: 37.00 ================================================================================ 982 Glossary Vega: the measure of how much an option's price changes for an incremental change-usually one percentage point-in volatility. Vertical Spread: any option spread strategy in which the options have different striking prices but the same expiration dates. Volatility: a measure of the amount by which an underlying security is expected to fluctuate in a given period of time. Generally measured by the annual standard deviation of the daily price changes in the security, volatility is not equal to the beta of the stock. Also called historical volatility, statistical volatility, or actual volatility. See also Implied Volatility. Volatility Skew: the term used to describe a phenomenon in which individual options on a single underlying instrument have different implied volatilities. I 11 general, not only are the individual options' implied volatilities different, but they form a pattern. If the lower striking prices have the lowest implied volatilities, and then implied volatility progresses higher as one moves up through the striking prices, that is called a forward or positive skew. A reverse or negative skew works in the opposite way: The higher strikes have the lowest implied volatilities. Warrant: a long-term, nonstandardized security that is much like an option. Warrants on stocks allow one to buy (usually one share of) the common at a ("(•r­ tain price until a certain date. Index warrants are generally warrants on the pri<·<· of foreign indices. Warrants have also been listed on other things such as cross-('m rency spreads and the future price of a barrel of oil. Write: to sell an option. The investor who sells is called the writer. ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1051 SCORE: 64.00 ================================================================================ Index Adjusted volatility, 539 Advanced concepts, 846-907 "greeks," 848-866, 902-905 delta, 848-853, 866 gamma, 853-859, 867, 882 gamma of the gamma, 865-866, 902-905 rho, 864-865 "six measures of risk," 865 strategy considerations using, 866-901 (see also Advanced concepts, strategy considerations, using greeks) summary, 866 theta, 862-864, 866 vega/tau, 859-862, 866 mathematical concepts, advanced, 901-907 difference of implied volatilities, measuring, 905-907 gamma of the gamma, 902-905 "greeks," calculating, 901-902 neutrality, 846-847 strategy considerations, using "greeks," 866-901 delta neutral, 868-879 evaluating position using risk measures, 885-892 mathematical approach, 883-885 multifaceted neutrality, creating, 879-883 risk exposure, general, of common, 866-868 trading gamma from long side, 893-901 summary, 907 tau, 859-862 American exercise, 501-504 American Stock Exchange, 22 Index,497,500 structured products listed, 618 Arbitrage, 251-252, 253-255, 422-455, 641-644 block positioning, 455 boxspreads,439-443,643-644 risks, 443 call arbitrage, 444 carrying costs, 430-431 conversions and reversals, 428-430, 431-438, 642-643 borrowing stock to sell short, 432-433 risksin,fou½433-437 summary, 437-438 "using box stock," 432 discounting, 423-425, 641-642 dividend, 425-428 effects, 444-445 equivalence, variations on, 443-444 facilitation (block positioning), 455 "interest play" strategy, 438-439 pairs trading, 454-455 as hedged strategy, 454 put arbitrage, 445 put and call, basic (discounting), 423-425 risk arbitrage, 21, 426-427 definition, 445 risk arbitrage using options, 445-454 "hooks," 449-450 limits on merger, 448-450 mergers, 445-448 profitability, 454 short tendering, 453 tender offers, 451-454 (see also Tender offers) synthetic put, 439-440 Arbitrageurs, 19-21 (see also Arbitrage) definition, 422 role of in butterfly spread, 338 box spread, 338 983 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1052 SCORE: 91.00 ================================================================================ 984 Assignment of options, 7, 16-22 anticipating, 18-22 automatic, 18-19 call options, 7 of cash-based options, 501 commissions, 17-18 margin requirements, 16-17 put options, 7 Backspreads, 232-235 (see also Reverse spreads) diagonal, 240-241 effect on of implied volatility changes, 781-782 and LEAPS, 407-408 Bear spreads using call options, 186-190 call bear spread, 186-188 as credit spread, 186 follow-up action, 190 assignment of short call, impending, 190 selecting, 189-190 an aggressive position usually, 189 summary, 190 Bear spread, put, 329-332 (see also Put spreads, basic) Beta, 533-539 Black, Fisher, 459 Black-Scholes model, 456-466, 538, 610, 611, 635, 640, 644-645,646,647-648,651,677,678, 731,734, 758, 767-768, 798,902 (see also Mathematical applications) Black model, 647-648, 651, 677 characteristics, 459-461 dividends paid by common stock not included, 459 formula, 456-457 hedge ratio, 457 historical volatility, lognormal, computing, 461-466 lognormal distribution of stock prices, 460 vega, 750 volatility, computation of, 460-466 weighting factor, 459-460, 463-465 Block positioning, 455, 482-485 (see also Mathematical applications) Board broker system, 22 Box spread, 338, 439-44,3, 643-644 risks, 443 "Box" stock, 432 Broad-based indices, 500 Brownian motion, 806 Bull spread, structured product as, 608-612 valuing, 610-612 Bull spreads, 110-111, 113-116, 117, 172-185 aggressiveness, degrees of, 175-176 call bull spread, 172-173 effect on of implied volatility changes, 767-775 follow-up action, 178-180 credit spread, 179 "legging" out of spread, 180 and outright purchase, comparison of, 179 and LEAPS, 403-404 ranking, 176-178 diagonal bull spread, 177 summary, 185 uses, other, 180-184 Index break-even price on common stock, lowering, 182, 183 simple form of spreading, 180, 185 as "substitute" for covered writing, 182-184 vertical, 172 when options are expensive, 177 Bull spread, put, 332-333 (see also Put spreads, basic) Bullish calendar spread, 196-198 (see also Calendar spread) Butterfly spread, 200-209, 336-338 (see also Put spreads, basic) combination of bull and bear spreads, 200, 209 commissions costly, 200, 203 example, 201 follow-up action, 206-209 assignment, 206 "legging out," 207 neutral position, 200 results of at expiration, 201-203 selecting, 203-206 striking prices, three, 200-203 summary, 209 Calendar combination of calls and puts, 345-348 Calendar spread, 116-117, 191-199 as antivolatility strategy, 194 bullish, 196-198, 199 follow-up action, 197-198 definition, 191 expiration series, using all three, 198-199 horizontal spread, 191 in volatility trading, 825-826 and LEAPS, 408-409 mathematical calculations of volatility, applying lo. 478-480 neutral, 192-194, 199 follow-up action, 194-196 volatility, effect of, 194 summary, 199 time spread another name, 191 volatility changes, effect of on, 778-780 with futures options, 704-709 (see also Futtm's options and strategies) ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1053 SCORE: 100.00 ================================================================================ Index Calendar spread, put, 333-335 (see also Put spreads, basic) 333-335 Calendar and ratio spreads, combining, 222-229 choosing spread, 225-226 pricing model, using, 225 delta-neutral calendar spreads, 227-228 in-the-money, 228 follow-up action, 226-227, 229 probabilities, good, 226-227 out-of-the-money call spread, 222-225 (see also Calendar and ratio spreads, combining, ratio calendar spread) ratio calendar spread, 222-225 collateral requirements possibly large, 223-224 profitability of, 227 Calendar straddle, 348-350 (see also Spreads combining calls and puts) Call arbitrage, 444 (see also Arbitrage) Call bull spread, effect on of implied volatility changes, 767-775 Call buying, 95-117 advanced selection criteria, 103-107 overpriced/underpriced calls, 106-107 time value premium and volatility trading, 106-107 volatilities of underlying stock, 103-106 follow-up actions, 107-117 bull spread, 110-111, 113-116, 117 calendar spread, creating, 116-117 commissions, 108 defensive action, two strategies for, 112-117 locking in profits, four strategies for, 108-111 "mental" stop to cut losses, 107 rolling down strategy, 112-116 rolling up, 109-110 frustrations, 107 mathematical calculations of volatility, applying, 47 4 option to buy, selecting, 101-103 day trading, 101-102 intermediate-term trading, 102-103 long-term trading, 103 short-term trading, 102 time horizon as criterion, 101 risk and reward, 97-101 delta, 99-101 hedge ratio, 99-101 intermediate-term call most attractive, 98 option pricing curve, 99 timing, certainty of, 98-99 simplest form of option investment, 95 strategies, other, 118-131 (see also Call buying strategies) why buy, 95-96 and LEAPS, 95 985 Call buying strategies, 118-131 altering ratio oflong calls to short stock, 128-131 protected short sale, 118-122 at-the-money or out-of-the-money as protection, 120 follow-up action, 122 margin requirements, 121 reverse hedge, 123-128, 130, 131 follow-up action, 126-128 limited loss potential and unlimited profit poten­ tial, 123, 128 trading against the straddle, 126-127 volatile stock preferred, 126 simulated straddle, 123-128 (see also Call buying strategies, reverse hedge) summary, 131 "synthetic" strategies, 118 put, 118-121 (see also Call buying strategies, pro­ tected short sale) Call option price curve, 10-13 Call option strategies, 37-241 (see also under particular heading) bear spreads using call options, 186-190 bull spreads, 172-185 butterfly spreads, 200-209 calendar spreads, 191-199 calendar and ratio spreads, combining, 222-229 call buying, 95-117 call buying strategies, 118-131 covered call writing, 39-94 diagonalizing spread, 236-241 naked call writing, 132-145 ratio call spreads, 210-221 ratio call writing, 146-171 reverse spreads, 230-235 summary, 241 Call options: assignment of, 7 Call writing, applying mathematical calculations of volatility to, 4 72-4 7 4 Capitalization-weighted indices, 494-497 divisor, 494-496 float, 494-495 largest market value stocks have most weight, 496 most prevalent, 497 Cash-based futures, 653 Cash-based options, 500-506 (see also Index option products) European versus American exercise, 501-504 Cash-based put writing, 294-295 Cash dividend role of underlying stock as factor in option price, 14-15 Cash settlement futures, 653 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1054 SCORE: 54.00 ================================================================================ 986 Chicago Board Options Exchange (CBOE), 22 structured products listed, 618 Chicago Mercantile Exchange, 507, 509, 510, 672 option quotes, 515-516 trading limits on futures options, 680 Chicago Board of Trade: trading limits on futures contracts, 658 trading limits on futures options, 680 Classes of options, 5-6 Closing transactions, 6 Collar, 275, 840 no-cost, 278-280 Commissions, 17-18 Concepts, advanced, 846-907 (see also Advanced concepts) Conservative covered write, 46 Contango, 697 Conversion, 253-255, 428-430, 431-438 (see also Put options basics and Arbitrage) reversal, 254, 428-430, 431-438 risks in, four, 433-43 7 summary, 437-438 Convertible security, covered writing against, 88-90, 94 Covered call writing, 39-94 definition, 39 diversifying return and protection, 66-70 "combined" write, 67-69 techniques, fundamental, 66-69 techniques, other, 69-70 execution of order, 56-58 contingent order, 57 net position, establishing, 57-58 follow-up action, 70-87, 94 aggressive action if stock rises, 71, 79-81 assignment, action to avoid if time premium disappears, 71, 86-87 expiration, at or near, 83-85 getting out, 82-83 locked-in loss, 73 protective action if stock drops, 71-79 rolling action, 71-80 (see also Rolling action) rolling forward/down, 83-85 spread, 76 uncovered position, avoiding, 86 when to let stock be called away, 86-87 importance, 39-42 for downside protection, 39 increase in stock price, benefits of, 40-41 profit graph, 41-42 quantification, 41-42 and naked put writing, differences between, 294-295 objective, 42 Index PERCS (Preferred Equity Redemption Cumulative Stock), 91 philosophy, 42-45 annual returns, 47 as conservative strategy, 46-4 7 Depository Trust Corp (DTC), role of, 43 in-the-money covered writes, 43-45, 93 letter of guarantee, 43 out-of-the-money covered writes, 43-45, 93 physical location of stock, 43 total return concept, 45-47, 60-61, 93 return on investment, computing, 47-56 compound interest, 53-54 downside break-even point, 48, 49-50 in margin accounts, 50-53 price,changesin,55-56 return if exercised, 47-48 return if unchanged, 48, 49 size of position, 54-55 static return, 49 selecting position, 58-62 downside protection, 59-60 returns, projected, 59 strategy, importance of, 60-62 total return concept, 60-61 special writing situations, 87-93 against convertible security, 88-90, 94 against LEAPS, 91, 94 against warrants, 90-91 incremental return concept, 87-88, 91-93 and stock ownership, 42 summary, 93-94 and uncovered put writing strategy, similarity of, 293-294 writing against stock already owned, 62-66 caution, 65-66 Covered pit sale, 300 Covered straddle write, 302-305 Crack spread, 702-704 Credit spread, 170, 179 Cross-currency spreads, 701 Cumulative density function (CDF), 806 Customer margin method, 5 Customer margin option requirements, 667 Day trading, call buying and, 101-102 Debit spread, 170 Definitions, 3-35 (see also under particular definition or under Options) Delta, 848-853, 866 calculation of by Black-Scholes model, 457 excess value, 764 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1055 SCORE: 111.00 ================================================================================ Index Delta (continued) and implied volatility, 753-754, 755-756 of LEAPS, 387-390 put delta, 389-390 option delta, 849 position delta, 849-853 spread, 484 Delta-neutral spreads: calendar spreads, 227-228 (see also Calendar and ratio spreads) effects on of implied volatility changes, 755-756 Delta-neutral trading, 167-168, 868-879 Delta of option, 99-101 of futures aption, 676-677 "Delta spread," 213, 216-217 (see also Ratio call spread) for ratio put spread, 361 Depository Trust Corp. (DTC), 43 Diagonal butterfly spread, 350-353 (see also Spreads combining calls and puts) Diagonal spread, 169, 236-241 (see also Spread, diagonalizing) backspreads, 240-241 bear spread, 239-240 bull spread, 177, 236-239 and LEAPS, 405-407 backspread,407-408 Dividend arbitrage, 425-428 Dividends: influence of on option price, 14-15 and LEAPS, effect on, 371-374 put option premiums, effect of on, 248-250 from structured products, 594 Divisor, 494-496, 497-500, 568 "Dogs of the Dow" Index, 594 Dow Jones Industrial Average, 494, 499, 793 30 Industrials ($DIX), 501, 502, 582 Top 10 Yield index ($XMT), 594 Down delta concept, 100-101 Elliott Wave theory, 796 Equity-linked notes, 618 Equivalent futures position (EFP), 676-677, 853 Equivalent stock position (ESP), 162-163, 167, 853 in ratio call spreads, 220-221 of straddle, 312-313 Equivalent strategies, 943-944 "European" exercise, 501-504, 647 options, 7 Even money spread, 240 "Ever" probability calculator, 805-806 Excess value of option price, effect on of implied volatility changes, 762-765 "greeks" to measure, 763-764 Exchange-Traded Funds (ETFs), 637-639 987 Holding Company Depository Receipts (HOLD RS), 639 iShares, 638 options on, 637 sector, 638 Standard & Poor's Depository Receipt (SPDR), 637- 638 Creation Units, 638 Exercise of cash-based options, 501-504 Exercise price, definition, 3-4 Exercising option, 6-7, 15-16 after, 17 commissions, 17-18 early, due to discount, 19-20 early, due to dividends on underlying stock, 20-22 Exotic options, 590 Expiration date, 4 standardization, 5 Exxon (XON), 567 Facilitation, 455, 482-485 (see also Mathematical applications) Fat tails, 790- 792, 810, 828 Financial engineers, role of in structured products, 590 Foreign currency options, 671-673 Formulae, 947-956 "Fudge factor," 731, 733 Futures, 506-512 (see also Index option products) calculating fair value of, 533-534 factors, four, 533 T-bill rate, use of, 534 contracts, 653-660 (see also Futures and futures options) on physicals, 653 (see also Futures and future options) Futures and futures options, 652-695 futures contracts, 653-660 "cash," 653-654 cash-based/cash settlement futures, 653 delivery, 658-659 expiration dates, 656-657 first notice day, 659 futures on physicals, 653 hedging, 653-655 limits, 657-658 month symbols, 665 notice period, 659 and options, differences between, 653 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1056 SCORE: 76.00 ================================================================================ 988 Futures and futures options (continued) position limits, 657 pricing, 659-660 speculating, 655-656 spot and spot price, 658 as stock with expiration date, 653 tenns, 656-657 trading hours, 657 trading limits, 657-658 units of trading, 657 futures options trading strategies, 67 4-683 delta, 676-677 equivalent futures position (EFP), 676-677 follow-up actions, 692-694 limit bid, 679 limit offered, 680 mathematical considerations, 677-679 mispricing strategies, common, 683-694 (see also Futures and futures option, mispricing strate­ gies) price relationships, 67 4-676 summary, 694 and trading limits, 679-683 mispricing strategies, common, for futures options, 683-694 backspreading puts, 686-688 follow-up action, 692-694 implied volatility, 685 points, 687-688 ratio spreading calls, 688-689 strategies for profiting, two, 685-689 summary, 694 volatility skewing, 683, 685, 693-694 which strategy to use, 690-692 options on futures, 660-673 assignment, 673 automatic exercise, 662-663 bid-offer spread, 665 cash settlement future, 661 commissions, 665 customer margin system, 667, 671 definition, 660 description, 660-662 exercise, 673 foreign currency options, 671-673 margins, 666-671 mathematical considerations, 677-679 month symbols, 665 notice day, 661-662 Philadelphia Stock Exchange (PHUC), 671, 673, 678-679 physical currency options, 671-673 on physical futures, 661, 678-679 position limits, 666 quote symbols, 664 "round-tum" commission, 665-666 serial options, 663-666 Index SPAN margin (Standard Portfolio Analysis of Risk), 667-671 (see also SPAN) striking price intervals, 662 standardization less than for equity or index options, 652 summary, 695 Futures Magazine, 661 Futures option strategies for futures spreads, 696-721 futures options, using in futures spreads, 704-720 calendar spread, 704-709 follow-up considerations, 714-719 intramarket spread strategy, 719 long combinations, 709-714 spreading futures against stock sector indices, 719-720 futures spreads, 696-704 contango, 697 crack spread, 702-704 cross-currency spreads, 701 intermarket, 700-704 intramarket, 697-700 pricing differentials, 696-697 reverse carrying charge market, 697 TED spread, 701-702, 712-714 summary, 720-721 Futures spread, futures option strategies for, 696-721 (see also Futures option strategies) Gamma, 853-859, 867, 882 neutral spread, 882 Gamma of the gamma, 865-866, 902-905 GARCH (Generalizes Autoregressive Conditional Heteroskedasticity), 731-732, 814, 819 General Electric (GE), 567 General Motors (GM), 567 Gold and Silver Index (XAU), 588, 719 Good-until-canceled order, 34 Government National Mortgage Association certificates, 420 Graphs, 957-960 "Greeks," 848-866 (see also Advanced concepts) calculating, 901-902 to measure excess value, 763-764 Hedge ratio, 99-101, 457 advantages of, 482-485 delta spread, 484 neutral spread, 483-485 Hedge wrapper, 275 Hedging, futures contracts and, 653-655 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1057 SCORE: 76.00 ================================================================================ Index Historical volatility, 461, 728-731 lognormal, computation of, 461-466 Holder, 6 HOLDRS, 639 "Hooks," 449-450 Horizontal spread, 169 IBM (International Business Machines), 567 Implied volatility, 132, 248, 685, 727, 734-743 (see also Volatility trading) difference of, measuring, 905-907 effect of on specific option strategies, 7 49-782 (see also Volatility, effects of) and delta, 753-754 in trading techniques, 812-845 (see also Volatility trading) In-the-money: calendar spread, 228 covered writes, 43-45, 93 definition, 7, 8 for put options, 246-247 Incremental return concept of covered writing, 91-93 (see also Covered call writing) rolling for credit, 92 Index arbitrage, 547-556 (see also Stock index hedging strategies) Index calls, hedging with, 545-547 Index option products and futures, introduction to, 493-530 cash-based options, 500-506 assignment, 501 commissions, 503 European versus American exercise, 501-504 exercise, 501-504 indices underlying, 500-501 naked margin, 504-505 definition, 493 and equity options, difference between, 493 futures, 506-512 cash-based only, 506 "circuit breakers," 511 commodities contract, definition, 506 contract, terms of, 507-508 hedgers, 506-507 limits, 511 "locals," 509 maintenance margin, 509 margin, limits, and quotes, 509-510 "open outcry" method, 508-509 quotes, 511-512 speculators, 506-507 S&P 500 Index, 507-509 S&P and NYSE expiration, 510-511 989 and stock trading, differences between, 508, 512 traders, types of, 506-507 LEAPS (Long-term Equity AnticiPation Securities) index options, 367-410, 505-506 options on index futures, 512-516 caution,516 customer margin method, 515 expiration dates, 513 option margin, 514-515 premiums, 514 quotes, 515-516 SPAN (Standard Portfolio Analysis of Risk), 514-515 terms, other, 515 put-call ratio, 520-530 figures, 524-530 interpreting, 522-523 standard options strategies using index options, 516-520 conclusion, 519-520 early assignment of cash-based options, handling, 518-519 option buying, 516-517 selling index options, 517-518 volatility skewing, 517 stock indices, 493-500 broad-based, 500, 504-505 capitalization-weighted indices, 494-497 (see also Capitalization-weighted indices) narrow-based, 500, 505 price-weighted indices, 500 (see also Price­ weighted indices) sector, 500 summary, 523 Index options and futures, 138, 491-721 (see also under particular heading) futures and futures options, 652-695 futures option strategies for futures spreads, 696-721 hedging portfolios with, 541-543 index spreading, 579-588 introduction, 493-530 mathematical considerations for index products, 641-651 products and futures, introduction to, 493-530 stock index hedging strategies, 531-578 structured products, 589-640 Index puts, hedging with, 543-545 Index spreading, 579-588 approaches,two,580-581 characteristics, 682-583 inter-index spreading, 579-587 philosophy, 579 S&P 100,583 S&P 500, 583, 584 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1058 SCORE: 46.00 ================================================================================ 990 Index spreading (continued) spreads using options, 583-584 options, using in index spreads, 584-587 striking price differential, 587 volatility differential, 587 summary, 588 Value Line Index, 579, 582 Inflection points, 792-793 Insider trading, 7 45-7 46 Institutional block positioning, 482-485 (see also Mathematical applications) Institutional use of market basket strategies, 556 Inter-index spreading, 579-587 (see also Index spreading) "Interest play" strategy, 438-439 Interest rates, effects of on LEAPS, 371-37 4 Intermarket futures spreads, 700-704 Intermediate-term trading, call buying and, 102-103 Intramarket futures spreads, 697-700 iShares, 638 Japanese Nikkei 225 Index, 532, 601 Kicker, 136, 169 LEAPS (Long-term Equity AnticiPation Securities), 5, 367-410 basics, 368-369 expiration date, 368 standardization less, 368 striking price, 369 type,368 underlying stock and quote symbol, 368 and call buying, 95 definition, 367 dividends, effects of, 371-37 4 to establish collar, 279 history, 367 and implied volatility, 735, 736 index options, 505-506 interest rates, effects of, 371-372 and long-term trading, 103 options, 616-617 popularity, 367 pricing, 369-37 4 rho, 864-865 selling, 390-403 assignment, early, 401-402 covered writing, 390-396 incremental return, 391 rolling down, 394 Index short LEAPS instead of short stock, 400-402 straddle selling, 402-403 uncovered call selling, 399-400 uncovered LEAPS, 396-399 whipsaw, 403 short-term options, three sets of comparison with, 374-375 and speculative option buying, 382-390 buying "cheap," advantages of, 385-386 delta, 387-390 less risk of time decay, 383-385 spreads using, 403-409 backspreads,407-408 bull spread using calls, 403-404 calendar spreads, 408-409 diagonal, 405-407 strategies, 375-382 buying LEAPS as initial purchase instead of buy- ing common stock, 378-381 LEAPS instead of short stock, 382 margin, using, 380-381 protecting existing stock holdings with LEAPS puts, 381-382 as stock substitute, 375-378 summary, 409-410 symbols, 26-27 writing against, 91, 94 "Leg" into spread, 171 out of spread, 180, 207 out of put calendar spread, 335 Letter of guarantee, 43 Limit bid, 679 Limit offered, 680 Limit order, 28, 33 "Locals," 509 Locked-in loss, 73-76 Locking in profits, four strategies for, 108-1 11 Lognormal distribution of stock prices, 783-81 I (See also Stock prices, distribution oO Long-term Equity AnticiPation Securities (LEAl'Si See also LEAPS Long-term trading, call buying and, 103 Maintenance margin, 509 Major Market Index (XMI), 499 Market basket of stocks, 531-537 (see also Stock ind,·\ hedging strategies) Market dynamics, nonquantifiable, as influt·11t·,· 011 market price, 15 Market-makers, 22 Market order, 32 Market not held order, 33 "Married" put and stock for tax purposC's, !J:l I ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1059 SCORE: 69.00 ================================================================================ Index Martingale strategy, 140, 145 Mathematical applications, 456-489 Black-Scholes model, 456-466 (see also Black-Scholes model) expected return, 466-472 calculation of, 467, 4 71 definition,466 expected profit, computation of, 468 lognormal distribution, typical, 469 Simpson's Rule, 471 Trapezoidal Rule, 471 facilitation (institutional block positioning), 482-485 delta spread, 484 follow-up action, computer as aid in, 485-488 implementation, 488-489 neutral spread, 483-485 hedge ratio, 482-485 (see also Mathematical applica­ tions, facilitation [institutional block position­ ing]) strategy decisions, applying calculations to, 4 72-482 calendar spreads, 479-480 call buying, 474 call writing, 472-474 profitability, 474-475 put buying, 478-479 put option, pricing, 477-478 ratio strategies, 480-482 risk, 4 75-4 77 theoretical value of spread, using, 480 summary, 489 Mathematical applications for index options, 644-651 Black model, 647-648, 651 Black-Scholes model, 644-645, 646, 651 cash-based, 644-646 deltas, 648 European exercise, 647 follow-up action, 648-651 for inter-index spreads, 648-649 "sliding scale," 649-650 futures, 644 options, 647-648 implied dividend, 646 Mathematical concepts, advanced, 901-907 Mathematical considerations for index products, 641-651 Mathematical models: for index products, 641-651 arbitrage, 641-644 (see also Arbitrage) graph, three-dimensional, 651 mathematical applications, 644-651 (see also Mathematical applications) summary, 651 for pricing options, 14 Mayhew, Dr. Stewart, 806 Mergers, risk arbitrage and, 445-450 Monte Carlo analysis, 806 simulation, 807-809, 828 991 Morgan Stanley High-Tech index ($MSH), 639, 788 Naked call writing, 132-145 high risk strategy, 135-136 "kicker," 136 marked to market daily, 136 implied volatility, 132 investment required, 134-137 margin requirements, 134-137 not same as short sale of underlying stock, 133-134 risk and reward, 138-145 Martingale strategy, 140, 145 rolling for credits, 140-144 time value as misnomer, 144 selling naked options, philosophy of, 137-138 index options, 138 summary, 144-145 uncovered (naked) call option, 133-134 Naked put write, evaluating, 296-298 Narrow-based indices, 500 NASDAQ: Index ($NDX), 501 -100 (NDX), 588 tracking stock (QQQ), 638,639 Neutral calendar spread, 192-194 Neutrality: effects of implied volatility changes on, 755-756 in options positions, 846-84 7 New York Stock Exchange: "circuit breaker," 562 expiration, 510-511 Index,497,500,532 limits on index futures traded, 511 POT system, 555-556 Nikkei 225 Index, 532, 601 No-cost collars, 278-280 Notice period, 659, 661-662 OEX, 497, 500-501 Oil and Gas Index (XOI), 588, 719 Open interest, 6 "Open outcry" method of trading futures, 508-509 Opening transactions, 6 Option markets, 22 board broker system, 22 Chicago Board Options Exchange (CBOE), 22 Web site, 23 market-makers, 22 Option Price Reporting Authority (OPRA), 368 Option pricing curve, 99 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1060 SCORE: 80.00 ================================================================================ 992 Option purchase and spread, combining, 339-341 (see also Spreads combining calls and puts) Options: arbitrageurs, role of, 19-21 risk arbitrage, 21 assignment, 7, 16-17 anticipating, 18-22 (see also Assignment) margin requirements, 15-17 classes and series, 5-6 closing transaction, 6 commissions, 17-18 definition, 3-4 as derivative security, 4 "European" exercise options, 7 exercising, 6-7, 15-16 after, 17 early, due to discount, 19-20 early, due to dividends on underlying stock, 20-22 premature, 19-22 holder, 6 in-the-money, 7, 8 LEAPS, 5 symbols, 26-27 markets, 22 (see also Option markets) open interest, 6 opening transaction, 6 option price and stock price, relationship of, 7-9 order entry, 32-34 good-until-canceled order, 34 information, 32 limit order, 33 market order, 32 market not held order, 33 stop-limit order, 33-34 stop order, 33 out-of-the-money, 7 parity, 8-9 premature exercise, 19-22 (see also Options, exercis­ ing) premium, 7-8 price, factors influencing, 9-15 (see also Price of option) profits and profit graphs, 34-35 specifications, four, 4 standardization, 4-5 expiration dates, 5 striking price, 5 symbology, 23-27 CBOE's Web site, 23 expiration month code, 23 LEAPS, 26-27 option base symbol, 23 stock splits, 27 striking price code, 24-25 summary, 27 wraps, 25-26 time value premium, 7-8, 11 trading details, 27-32 limit order, 28 one-day settlement cycle, 28 position limit and exercise limit, 31-32 rotation, 28 value, 4 as "wasting" asset, 4 writer, 6 Index Options to buy, selecting, 101-103 (see also Call buying) Options Clearing Corp. (OCC), 6, 15-16, 673 Options on futures, 660-673 (see also Futures and futures options) Options and Treasury bills, buying, 413-421 advantages, 413, 421 annualized risk, 416-418 excessive risk, avoiding, 420-421 how strategy works, 413-421 risk adjustment, 418-420 risk level, keeping even, 415-416 summary, 421 synthetic convertible bond, 414 Order entry for options, 32-34 (see also Options) Original Issue Discount (OID), 592-593 Out-of-the-money: call spread, 222-225 covered writes, 43-45, 93 definition, 7 for put options, 246-247 Outright option purchases and sales, effect of, on implied volatility changes on, 757-762 Pairs trading, 454-455 Parity, 8-9 Percentile of implied volatility approach, 814-818 composite implied volatility reading, 815 historical and implied volatility, comparing, 817-818 PERCS (Preferred Equity Redemption Cumulative Stock), 91, 619-637 call feature, 620-622 redemption price, 622 sliding scale, 620-621 covered call write, equivalent to, 622-623 definition, 619 life span, 619 owning as equivalent to sale of naked put, 626 price behavior, 623-625 strategies, 625-636 delta of imbedded call, using, 630-631 hedging PERCS with common stock, 631-6:32 issue price, determining, 633-634 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1061 SCORE: 86.00 ================================================================================ Index PERCS (Preferred Equity Redemption Cumulative ' Stock) (continued) pricing, 634-636 protecting PERCS with listed options, 625-626 redemption feature, removing, 626-627 redemption price, changing, 627-629 rolling down/up, 628-629 selling call against long PERCS as ratio write, 629-631 selling short, 632-633 summary, 636-637 Phantom interest, 592 Philadelphia Stock Exchange (PHLX), 671, 673, 678-679 Portfolio hedge, 539-541 Portfolio insurance, 563-564 Position delta, 162-163, 167 Position limit rule, 253 Position vega, 757 POT system of NYSE, 555-556 Premium, 7-8 time value, 7-8 Price of option, factors influencing, 9-15 cash dividend rate of underlying stock, 14-15 dividends and lower call option price, 14-15 call option price curve, 10-13 market dynamics, nonquantitative, 15 risk-free interest rate, 14 striking price of option, 9-10 time remaining until expiration, 11-13 time value premium decay, 13-14 underlying stock, price of, 9-10 volatility of underlying stock, 13-14 Price-weighted indices, 497-500 computing, 497-498 divisor, 497-500 Dow Jones indices, 499 each stock with equal number of shares, 497, 499 Major Market Index (XMI), 499 Probability calculator, 798-799, 824, 827-829 Probability of stock price movement, 798-809 (see also Stock prices) Profits, locking in, four strategies for, 108-111 Program trading, 537-547 (see also Stock index hedging) Protected short sale, 118-121, 270 (see also Call buying strategies) Protective collar, 275 no-cost, 278-280 and splitting strikes, 328 Put, sale of, 291-301 buying stock below its market price, 299-300 caution, 299-300 covered put, 300 follow-up action, 295-296 naked put write, evaluating, 296-298 ratio put writing, 300-301 uncovered, 292-295 cash-based put writing, 294-295 993 covered call writing, similarity to, 293-294 naked put writing, differences between, 294-295 Put arbitrage, 445 (see also Arbitrage) Put bear spreads, effects on of implied volatility changes, 777-778 Put buying: in conjunction with call purchases, 281-291 mathematical calculations of volatility, applying to, 478-479 straddle buying, 282-288 equivalences, 283-284 follow-up action, 285-288 reverse hedge, equivalent to, 283 reverse hedge with puts, 284 selecting, 285 strangle, buying, 288-291 trading against straddle, 287 Put buying in conjunction with common stock owner­ ship, 271-280 as protection for covered call writer, 275-278 bull spread as equivalent, 278 long-term effects, 277-278 protective collar, 275, 278-280 rolling down, 276 no-cost collars, 278-280 lower strikes as partial covered write, 279-280 synthetic long call, 271 tax considerations, 275 which put to buy, 273-274 equivalent strategies, 27 4 slightly out-of-the-money put preferable, 27 4 Put option: effects on of implied volatility changes, 765-766 pricing, applying mathematical calculations of volatility to, 4 77-4 78 Put option basics, 245-255 assignment, 250-253 anticipating, 251-252 and dividend payment dates, 252 position limits, 253 conversion, 253-255 no risk, 254 reversal. 254 dividends, effect of on premiums, 248-250 exercise, 250-253 in-the-money, 246-247 out-of-the-money, 246-247 pricing, 247-248, 249 implied volatility, 248 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1062 SCORE: 116.00 ================================================================================ 994 Put option basics (continued) strategies, 245-247 time value premium, 246-247 Put option buying, 256-270 as alternative to short sale of stock, 256-258 purpose, 256 equivalent positions, 270 protected short sale, 270 follow-up action, 262-266 call option, 264 listed call, buying, 263 profits, five tactics for locking in, 262-266 loss-limiting actions, 267-270 calendar spread strategy, 269-270 "rolling-up" strategy, 267-269 margin account required, 269 ranking prospective purchases, 261-262 selection of which put to buy, 258-261 delta, 260-261 in-the-money puts, concentrating on, 259 Put option strategies, 243-410 (see also under particular heading) basics, 245-255 buying, 256-270 call and put strategies, similarities between, 244 LEAPS, 367-410 listed put options newer than listed call options, 244 put, sale of, 292-301 put buying in conjunction with call purchases, 281-291 put buying in conjunction with common stock own- ership, 271-280 put spreads, basic, 329-335 ratio spreads using puts, 358-366 spreads combining calls and puts, 336-357 straddle, sale of, 302-320 summary, 366 synthetic stock positions created by puts and calls, 321-328 Put options, assignment of, 7 Put spreads, basic, 329-335 bear spread, 329-332 advantage over call bear spread, 330-332 as debit spread, 329 bull spread, 332-333 as credit spread, 332 formulae, 333 risk limited, 333 calendar spread, 333-335 bearish, 334-335 neutral, 334 option spreads, three simplest forms of, 329 Index Qualified covered calls, 961-962 Ratio calendar combination, 364-366 (see also Ratio spreads using puts) Ratio calendar spread, 222-225 (see also Calendar and ratio spreads) Ratio call spreads, 210-221 and calendar spreads, combining, 222-229 (see also Calendar and ratio spreads) combination of bull spread and naked call write, 212 definition, 210 follow-up action, 217-221 delta, adjusting with, 219-221 equivalent stock position (ESP), using, 220-221 profits, taking, 221 ratio, reducing, 218-218 philosophies, three differing, 213-217 altering ratio, 215-216 as ratio write, 213-214 "delta spread," 213, 216-217 for credits, 213, 214-215 preferred over ratio writes, 211-212 ratio write, similarity to, 210 dissimilarity, 210-211 summary, 221 Ratio call write equivalent to naked straddle write, 306 Ratio call writing, 146-171 call spread strategies, introduction to, 168-171 credit/debit spread, 170 diagonal spread, 169 horizontal spread, 169 kicker, 169 "leg" into spread, 171 long/short side, 170 splitting quote, 171 spread, definition, 168 spread order, 169-171 vertical spread, 169 combination of covered call writing and naked call writing, 146, 150 definition, 146 delta-neutral trading, 167-168 follow-up action, 158-168 altering ration of covered write, 160 closing out write, 166-167 delta, adjusting with, 160-163 equivalent stock position (ESP), 162-163, 167 position delta, 162-163, 167 rolling up/down as defensive action, 160 stop orders, using as defensive strategy, 163-166 "telescoping" action points, 166-167 investment required, 150-151 and ratio call spreads, similarity to, 210 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1063 SCORE: 74.00 ================================================================================ Index Ratio call writing (continued) dissimilarity, 210-211 ratio write, 146-149 objections, two, 148-149 probability curve for stock movement, 149 profit range, 14 7 ratio spread as, 213-214 (see also Ratio call spreads) and reverse hedge (simulated straddle), similarity of, 154 risk, two-sided, 146 selection criteria, 151-155 break-even points of position, 151-152 neutral ratio, 152-154 volatile stocks preferred, 152 summary, 168 not suitable for all investors, 168 variable, 155-157 trapezoidal hedge, 155, 156, 157 Ratio put spread, 358-361 (see also Ratio spreads) calendar spread, 361-364 Ratio put writing, 300-301 Ratio spreads, effects on of implied volatility changes, 780-781 Ratio spreads using puts, 358-366 ratio calendar combination, 364-366 ratio put spread, 358-361 deltas, 361 follow-up action, 360-361 limited upside risk, large downside risk, 358, 359 ratio put calendar spread, 361-364 and naked options, 362-363 Ratio strategies, applying mathematical calculations of volatility to, 480-482 Regression analysis, 566 Reversals, 254-255, 428-430, 431-438 (see also Arbitrage) risks in, four, 433-437 Reverse calendar spread, 230-232 (see also Reverse spreads) selling, 833-834 Reverse carrying charge market, 697 Reverse conversion, 428-430, 431-438 risks in, four, 433-437 Reverse hedge 123-128, 130, 131 (see also Call buying strategies) ratio writing, similarity to, 154-155 straddle buying, equivalent to, 283 Reverse ratio spread (backspread), 232-235 (see also Reverse spreads) Reverse spreads, 230-235 backspread, 232-235 (see also Reverse spreads, reverse ratio spread) reverse calendar spread, 230-232 margin requirements onerous, 230, 231-232 used infrequently, 230 reverse ratio spread (backspread), 232-235 and delta-neutral spread, 234-235 early exercise, possibility of, 235 established for credits, 233 investment small, 233-234 limited risk, 233 volatile stocks preferable, 235 Rho, 864-865 for LEAPS or warrants, 873 Risk arbitrage, 21, 426-427, 445-454 (see also Arbitrage) "hooks," 449-450 limits on merger, 448-450 mergers, 445-448 tender offers, 451-454 Risk-free interest rate, 14 Rolling action, 71-80, 94, 158-160 alternative, 76-77 debit incurred in roll-up, 80-81 different expiration series, using, 78-79 partial, 77 Rolling for credits, 140-144 Martingale strategy, 140, 145 Rolling down strategy, 112-116, 628-629 LEAPS, 394 and protective put, 276 Rolling forward/down, 83-85 Rolling up, 109-110, 267-269, 628-629 "Round-tum" commission, 665-666 Rubenstein, Professor Mark, 797 Russell 2000 Growth Fund, 638, 788 Russell 2000 Value Fund, 638, 788 S&P: see also Standard & Poor Scientific American, 796 Sector, 500 Semiconductor Index ($SOX), 588, 6,39 HOLDRS, 639 Serial options, 663-666 Series of options, ,5-6 Short-sale rule, 923-924 Short tendering, 453 Short-term trading, call buying and, 102 Sigma, 783-786 Simpson's Rule, 471 Simulated straddle, 123-128 (see also Call buying strategies) ratio writing, similarity to, 154-155 SIS (Stock Index return Security), 596-601 cash value formula, 596-597 imbedded call, 597-598 issued in 1993 and matured in 2000, 596 995 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1064 SCORE: 66.00 ================================================================================ 996 SIS (Stock Index return Security) (continued) track record, 598, 599 trading at discount to cash value, 598-600 trading at discount to guarantee price, 600-601 60/40 rule, 919-920 SPAN (Standard Portfolio Analysis of Risk), 514-515, 667-671 advantages,667 example, 668, 669, 670 how it works, 667-671 maintenance margin, 667 purpose, 667 risk array, 667, 668, 669 Speculating in futures contracts, 655-656 Splitting quote, 171 Splitting strikes, 325-328 (see also Synthetic stock positions) Spot/spot price for futures contracts, 658 Spread, diagonalizing, 236-241 advantage,236,241 backspreads,240-241 even-money spread, 240 bear spread, 239-240 bull spread, 236-239 often improvement over normal bull spread, 239 definition, 236 for any type of spread, 241 Spreads, 76, 168-171 (see also under particular head) backspread,232-235 diagonal, 240-241 bear, using call options, 186-190 bull, 110-111, 113-116, 117, 172-185 butterfly, 200-209 calendar, 116-117, 191-199 categories, three, 169 definition, 168 diagonal, 169, 236-241 (see also Spreads, diagonalizing) even money, 240 horizontal, 169 using LEAPS, 403-409 (see also LEAPS) "leg" into, 171 out of, 180, 207 out-of-the-money call spread, 222-225 ratio call, 210-221 reverse, 230-235 reverse calendar, 230-232 reverse ratio, 232-235 unequal tax treatment on, 929-930 vertical, 169 Spread order, 169-171 Spreads combining calls and puts, 336-357 butterfly spread, 336-338 arbitrageur, role of, 338 box spread, 338 commissions high, 338 Index equivalent of completely protected straddle write, 338 establishing, four ways for, 336-338 striking prices, three, 336 calendar combination, 345-348, 353-354, 356-357 superior to calendar straddle, 349-350 calendar straddle, 348-350, 354, 356-357 as neutral strategy, 349 criteria for, three, 354 inferior to calendar combination, 349-350 diagonal butterfly spread, 350-353, 354-355, 356-357 criteria, four, 355 legging out, 351-352 follow-up action for bull or bear spreads, 341-344 option purchase and spread, combining, 339-341 bearish scenario, 341, 342 bullish scenario, 339-340, 342 selecting, 353-356 criteria, five, 353-354 summary, 356-357 Standard Portfolio Analysis of Risk (SPAN), 514-515 Standard & Poor (S&P): Depository Receipt (SPDR), 637-638 expiration, 510-511 100 Index (OEX), 497, 500-501, 582-583 400 Index, 497 500 Futures, 532 500 Index (SPX), 497, 502, 507, 583, 584 Standard & Poor's Stock/Bond Guide, 88 Stock: buying below its market price, 299-300 underlying, price of as related to option price, 9-10 Stock index hedging strategies, 531-578 follow-up strategies, 557-559 rolling to another month, 557-559 impact on stock market, 561-565 "circuit breaker" of NYSE, 562 at expiration, 564-565 before expiration, 561-563 portfolio insurance, 563-564 regulatory bodies, concern of, 562 trading ban, 562 index, simulating, 566-574 hedge, monitoring, 572-573 high-capitalization stocks, using, 566-571 largest-capitalization stocks, four, 567 options instead of futures, using, 573-57 4 regression analysis, 566 tracking error risk, 571-572 index arbitrage, 547-556 commissions, 552-554 computerized method of order entry, 555-556 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1065 SCORE: 52.00 ================================================================================ Index Stock index hedging strategies (continued) hedging price-weighted index, 547,548 how many shares to buy, 547-552 institutional strategies, 556 POT system of NYSE, 555-556 profitability, 552-554 trade execution, 554-556 market baskets, 531-537 dividends, inverse correlation of to premium value, 534-537 execution risk, 560 futures fair value, 533-534 risk, 560-561 tracking error, 538,561, 571-572 "mini-index," creating, 566-574 (see also Stock index hedging strategies, index, simulating) program trading, 537-547 adjusted volatility, 539 arbitrage approach, 537 hedging with index calls, 545-547 hedging with index puts, 543-545 hedging portfolios with index options, 541-543 market risk, removing, 538 portfolio hedge, 539-541 tracking error, 538, 561, 571-572 volatility versus Beta, 538-539 summary, 577-578 tracking error, trading, 57 4-577 collateral requirements, 577 Stock indices, 493-500 Stock options: basic properties of, 1-35 definitions, 3-35 definition, 3-35 Stock price and option price, relationship between, 7-9 Stock prices, distribution of, 783-811 distribution, 789-795 "big" picture, 790 fat tails, 790-792, 810 inflection points, 792-793 normal, 780-795 risk of too conservative estimate of stock price movement, 796 summary, 796-797 Elliott Wave theory, 796 expected return, 809-810 lognormal distribution, 783-789 options, pricing of, 798 probability of stock price movement, 798-809 Brownian motion, 806 calculation mechanisms, 803-805 cumulative density function (CDF), 806 delta, 805 "ever" probability calculator, 805-806 Monte Carlo analysis, 806, 807-809 probability calculator, 798-799 summary, 810-811 volatility, prediction of, 799-803 sigma, 783-784 volatility buyer's rule, 787-789 volatility, misconceptions about, 783-787 standard deviations, 783-786 what this means for option traders, 795-796 Stock splits, symbols for, 27 997 Stock trading and futures trading, difference between, 508,512 Stop order, 33 Stop-limit order, 33-34 Straddle: buying, 282-288 (see also Put buying) equivalent stock position follow-up, 312-313 follow-up action, 308-312 "legging out," 310 risk large, 308, 314 rolling up/down, 310 in volatility trading, 824, 825, 829 sale of, 302-320 covered, 302-305 uncovered, 305-307 selecting write, 307-308 selling, LEAPS and, 402-403 starting out with protection in place, 313-314 strangle (combination) writing, 315-320 credits, using, 320 definition, 315 deltas, 318-319 excess trading, avoiding, 319-320 margin requirements, 317-318 Straddle calendar spread, 348-350 (see also Spreads combining calls and puts) Straddle/strangle buying and selling, effects on of implied volatility changes, 766-767 Strangle, 281 buying, 288-291 definition, 315 in volatility trading, 824, 825, 828-829 strangle (combination) writing, 315-320 (see also Straddle) Strategy, best, 932-937 investor as dominant force in determining strategy, 938 market attitude and equivalent positions, 932-934 mathematical ranking, 936-937 strategies to be avoided, 933 summary, 937 volatility trading, 932-933 Strategy summary, 943-944 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1066 SCORE: 59.00 ================================================================================ 998 Striking price: as factor influencing price, 9-10 code, 24-25 definition, 3, 4 fractional, 29 standardization, 5 Structured products, 589-640 adjustment factor, 602-604 cost, measuring, 605-607, 608 break-even final index value, 604-605 exotic options, 590 imbedded call, computing value of when underlying is trading at discount, 602 income, products designed to provide, 618-639 covered write of call option, resembling, 619 Creation Units, 638 Diamonds, 638 Exchange-Traded Funds (ETFs), 637-639 (see also Exchange-Traded Funds) HOLDRS, 639 iShares, 638 NASDAQ-100 tracking stock (QQQ), 638, 639 options on ETFs, 639 PERCS (Preferred Equity Redemption Cumulative Stock (PERCS), 619-637 (see also PERCS) Russell 2000 Value Fund and 2000 Growth Fund, 638 more appeal for investors than for traders, 589 "riskless" ownership of stock or index, 590-618 annual adjustment factor, 594 bull spread, 608-612 cash value, 593-594 constructs, other, 607-613 dividends, 594 equity-linked notes, 618 financial engineers, role of in structured products, 590,607 imbedded call option, cost of, 594-595 income tax consequences, 592-593 LEAPS options, 616-617 list, 618 multiple expiration dates, 613 multiplier, 614 option strategies involving structured products, 613-618 Original Issue Discount (OID), 592-593 phantom interest, 592 price behavior p1ior to maturity, 595-596 SIS (Stock Index return Security), 596-601 (see also SIS) strike price, 592, 615-618 structure, 590-593 when underlying index drops, 617 Index summary, 640 Suitability of strategy for individual investor, 3 Swiss franc contract for foreign currency options, 672 Symbology, options, 23-27 (see also Options) Synthetic convertible bond, 441 (see also Options and Treasury bills) Synthetic long call, 271 Synthetic long stock, 321-323 Synthetic stock positions created by puts and calls, 321- 328 splitting strikes, 325-328 bearishly oriented, 327-328 bullishly oriented, 325-327 protective collar, 328 summary, 328 synthetic long stock, 321-323 synthetic short sale, 323-325 leverage, 324 "Synthetic" strategies, 118 put, 118-121 Tau, 859-862 Tax considerations, put purchase, 275 Taxes, 908-931 assignment, 914-920 applicable stock price (ASP), 917 qualified covered call, 917-920, 961-962 "too-deeply-in-the-money" definition, 916 equity options, strategies for, 925-930 deferring put holder's short-term gain, 928 deferring short-term call gain, three tactics for, 928 difficulty of deferring gains from writing, 928-929 spreads, unequal tax treatment on, 929-930 exercise, 913-914 history, 908-909 "married" put and stock, 924 "new" stock, delivering to avoid large long-term gain, 920-921 "versus purchase" notation 921 option as capital asset, 908 problems, special, 922-925 (see also under particular problem heading) profit strategies and tax strategies, separating, 931 protecting long-term gain/avoiding long-term loss, 924-925 put assignment, 921-922 put exercise, 921 short sale rule, 923-925 summary, 925, 930-931 tax treatment, basic, 910-913 call buyer, 910-911 call writer, 910, 911-912 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1067 SCORE: 128.00 ================================================================================ Index Taxes (continued) put buyer, 910 put writer, 910, 912 60/40 rule, 912-913 wash sale rule, 922-923 TED spread, 701-702, 712-714 carrying cost, 702 Tender offers, risk arbitrage and, 451-454 partial, 454 short tendering, 453 two-tier offers, 454 Theta, 862-864, 866 position theta, 877 Time spread, 191-199 (see also Calendar spread) . Time value premium, 7-8, 11, 762-765 and volatility trading, 106-107 decay, 13-14 for put options, 246-247 "greeks" to measure, 763 Total return concept of covered writing, 45-47, 60-61, 93 Tracking error: risk, index hedging and, 538,561, 571-572 trading, 574-577 Trading against the straddle strategy, 126-127, 287 Trading options, details of, 27-32 (see also Options) Trapezoidal hedge, 155, 156, 157 Trapezoidal Rule, 471 Treasury bills, 413-421 (see also Options and Treasury bills) Uncovered call writing, 132-145 (see also Naked call writing) call option, 133-134 Uncovered straddle write equivalent to ratio call write, 306 Underlying security, definition, 3 Underlying stock, price of as factor influencing option price, 9-10 Up delta concept, 100-101 "Using box stock," 432 Value Line Index, 532, 579, 582 Vega of option, 749-753, 860-862 (see also Volatility, effects of) and excess value, 764 option or position vega, 757,862 Vertical put spreads, effect on of implied volatility, 775-777 Vertical spread, 169, 186 Volatility, effect of on popular strategies, 7 49-782 backspreads, 781-782 calendar spreads, 778-780 call bull spreads, 767-775 vega of option, 768 implied volatility, effect of, 749-782 and delta, 753-754 neutrality, effects on, 755-756 outright option purchases and sales, 757-762 position vega, 757 put bear spreads, 777-778 put option, 765-766 ratio spreads, 780-781 straddle/strangle buying and selling'. 766-767 summary, 782 999 time value premium, 762-765 delta, 764 factors, five, 762-763 "greeks" to measure, 763-764 vega, 7 49-753 and excess value, 764 definition, 7 49-750 vertical put spreads, 775-777 Volatility, measuring and trading, 723-931 (see also under particular heading) advanced concepts, 846-907 basics of volatility trading, 727-7 48 definition, 859-860 most important concept in option trading, 724 stock prices, distribution of, 783-811 taxes, 908-931 volatility, effect of on popular strategies, 7 49-782 volatility trading techniques, 812-845 why trade "the market," 724-726 Volatility, misconceptions about, 783-787 buyer's rule, 787-789 Volatility, prediction of, 799-803 Volatility backspread, 827, 834-836, 841 margin, 836 not for LEAPS options, 835 Volatility in Black-Scholes model, 460 historical, 461-466 (see also Historical volatility) Volatility Index ($VIX), 738, 761, 785-786 Volatility of stocks, 538-539 adjusted, 539 of underlying stock: as factor in option price, 13-14 call option rankings and, 103-106 Volatility skew, 517, 683, 685, 693-694, 813 trading, 837-844 (see also Volatility trading) Volatility trading, basics of, 727-7 48 definitions, 728-731 historical volatility, 728-731 implied volatility, 727, 732-743 GARCH (Generalized Autoregressive Conditional Heteroskedasticity), 731-732 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1068 SCORE: 36.00 ================================================================================ 1000 Volatility trading, basics of (continued) "fudge factor," 731, 733 implied volatility, 727, 732-743 as predictor of actual volatility, 737-7 43 LEAPS, 735, 736 percentile, 734-735 range, 735-737 time left in option, 736-737 Volatility Index ($VIX), 738 moving averages, 732 summary, 748 trading, 7 43-7 44 why volatility reaches extremes, 7 44-7 48 bear market in underlying stock, 746-747 cheap options, 747-748 illiquid options, 745-746 insider trading, 7 45 sellers of volatility, danger for, 7 48 supply and demand of public, 747 Volatility trading techniques, 812-845 as art and science, 812 summary, 844-845 trading volatility prediction, 814-837 backspreads, 827, 834-836 (see also Volatility trading techniques, volatility backspread) calendar spread, selling, 833 composite implied volatility reading, 815 histogram, construction of, 831-832 historical volatility, comparing current and past, 821-824 implied and historical volatility, comparing, 817- 818 percentile of implied volatility approach, 814-817 probability calculator, 824, 827-829 reverse calendar spread, 833-834 selecting strategy to use, 824-826 selling volatility, 826-827, 833-836 stock price history, using, 829-832 summary, 836-837 volatility chart, reading, 818-821 when volatility is out of line, determining, 814 volatility backspread, 827, 834-836, 841 margin, 836 not for LEAPS options, 835 volatility skew, trading, 837-844 collar, 840 Index differing implied volatilities on same underlying security, 837-838 forward/positive volatility skew, 843 reverse/negative volatility skew, 839-840 summary, 844 wrong predictions, two ways for, 813 volatility skew, 813 Warrants: covered writing against, 90-91 rho, 872-873 Wash sale rule, 922-923 Whipsaw, 403 Wrap symbols, 25-26 Writer, definition, 6 XMI (Major Market Index), 499 ================================================================================ SOURCE: eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf#page:1069 SCORE: 19.00 ================================================================================ Index 1001 SPECIAL OFFER Trial subscriptions to the advisory services published by McMillan Analysis Corp. are available to owners of this book. All of these services make specific recommendations in the stock, index, and futures option markets, including detailed follow-up action - with recommendations regarding broad market movements, implemented with index options. • The Option Strategist Published twice per month by email, US Mail, or fax (additional charge for fax) Contains educational and topical articles Covers a wide variety of option strategies FREE telephone or web site HOTLINE updated weekly • The Daily Strategist Published once or twice per day by email or fax Follows many of the same strategies as The Option Strategist above Covers put-call ratios, market commentary, momentum trading, and volatility trading • Daily Volume Alerts Published once per day, before the trading day begins, via email or fax Analysis of stocks with unusually heavy option activity Looking for takeovers, earnings surprises, and momentum plays Track records and further descriptions off all these services are available on our web site at www.optionstrategist.com. YES! Sign me up for the following trial subscriptions: 0 3 months of The Option Strategist ( 6 issues) 0 1 month of Daily Volume Alerts for $75 (regularly $95) 0 1 month of The Daily Strategist for $250 (regularly $350) Name __________________________ _ Address ---------------------------City __________ State/Province __ Zip/Postal _____ _ Charge to my: 0 VISA O Mastercard O American Express 0 Discover Card Number Expiration Date ____ _ Call 800-724-1817 or 908-850-7113 or shop at http://www.optionstrategist.com Or copy this form and mail to: McMillan Analysis Corp., P. 0. Box 1323, Morristown, NJ 07962-1323 ================================================================================ SOURCE: eBooks\Options Trading Crash Course_\Options Trading Crash Course_ The #1 Beginner_s Guide to Make Money with Trading Options in 7 Days or Less!.epub#section:text00000.html SCORE: 1053.00 ================================================================================ Options Trading Crash Course • The #1 Beginner’s Guide to Make Money With Trading Options in 7 Days or Less! • By Frank Richmond Copyright © 2020 . All rights reserved. No part of this book may be reproduced or transmitted in any form or any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the written permission of the author. Disclaimer Please note that the information contained within this document is for educational purposes only. Every attempt has been made to provide accurate, up to date, and reliably complete information. No warranties of any kind are expressed or implied. Readers acknowledge that the author is not engaging in the rendering of legal, financial, medical, or professional advice. The content of this book has been derived from various sources. Please consult a licensed professional before attempting any techniques outlined in this book. By reading this document, the reader agrees that under no circumstances is the author responsible for any losses, direct or indirect, which are incurred as a result of the use of information contained within this document including but not limited to errors, omissions, or inaccuracies. Table of Contents Taking the Risk What is an Option? Why Options Rather than Stocks? Why is Options trading Worth the Risk? How to Get Started in Options trading Learning the Lingo The Role of the Underlying Stock Understanding the Strike Price Basic Trading: Selling Covered Calls Strategy for Selling Covered Calls Outcomes of a Covered Sell Stepping Up a Tier: Buying Calls Strategies for Buying Calls Understanding Time Value Understanding Volatility Keeping an Eye on Your Calls Exercising Your Right to Buy the Stock How to Buy and Sell Puts Strategies for New Options Traders In Conclusion Special Thanks Before we begin, I would like to give you something back in return – exclusive ONLY to my readers - an IMPERATIVE bonus chapter of my options trading book. FOR FREE . This offer is extremely time limited, so go get it now while it’s still available: CLICK HERE! Taking the Risk For the novice, options trading is a daunting concept. Packed with jargon and seeming to need a degree in math to figure it all out, the very idea of learning the basics has put off countless curious traders. I’ve written this book to bridge the gap, taking you from thoroughly confused to fully aware of what options trading entails. It’s aimed either at complete beginners who have no idea where to get started or at readers who have dipped their toes in the waters and found themselves floundering. The book is also aimed at readers who think that options trading is far more risky than its siblings—stocks, bonds, and mutual funds. If you think those are the safer way to go and you’ve avoided options trading until now, I’m here to show you that options are just as fruitful a direction, if not more. Much as with any other skill in life, options trading gets easier over time. Once you’ve mastered the basics and are fluent in the language, you’ll find that it becomes less and less difficult to decipher the possibilities in front of you and pick the best one. In fact, eventually it becomes like learning to use a tool or ride a bike—you know it so well that you barely need to think about what you’re doing. So, put your feet up, grab a coffee, and prepare to start the process of understanding. Trust me when I tell you that it’s not nearly so daunting as you might have thought. What is an Option? Let’s start out with a basic overview of what options are. An option is a contract that confers upon you the right to buy or sell an underlying stock at what’s known as a “specified strike price.” It comes with a deadline—a date by which you must buy or sell in order to attain that price. You are not obligated to buy or sell by that date— hence, it is called an “option” rather than a “demand.” However, the cost of purchasing that possibility is set at a premium. There are two contract types on offer: one allows you to buy a stock at a specified price, which is known as a “call,” and the other allows you to sell a stock at a specified price, which is called a “put.” In order to start options trading, you first need to select a broker and open a “margin account.” Those accounts usually have a minimum starting amount attached to them that is often set at around $5,000. Those are the basics of options trading, but what does it actually mean and why would you want to do it? That is where the risk comes in because options trading is all about predicting what a certain stock is going to do in the near future. To illustrate, let’s use an example that’s easily familiar from everyday life such as buying a car. You’ve been saving up for a few months, but you’re not quite ready to head to the dealership—except, one day, you drive past a local salesroom and spot the hatchback of your dreams. Because you want to buy that car, you decide to speak with the dealer and negotiate. You work out a deal that will allow you to buy the vehicle from him in two months for the price of $10,000. Because the dealer is agreeing to keep the car for you and fix the price, you will also be paying $300 to secure that option for yourself. The two months start to pass and one of two things might happen: The dealer opens the hood of the vehicle and discovers it has an engine system that’s completely one of a kind and was a test by the manufacturer. That makes the car ultra valuable as a collector’s item. Under normal circumstances, the dealer would instantly double its asking price—but, because he made an agreement with you, he can’t. He is obligated to sell that car to you as long as you buy it before the two months are up. Obviously, you’re keen to exercise that right, so, you purchase the car for $10,000 and decide to sell it for $20,000—doubling your money in the process. The dealer opens the trunk of the vehicle and discovers that it contains a dead body. It’s removed and the car is cleaned but the police investigation causes quite a bit of damage. The value of the vehicle halves and, under normal circumstances, the dealer would slash the asking price to $5,000. However, because you entered into the agreement, the dealer must still sell you that car at the agreed price of $10,000. On the other hand, because you as the buyer are not obligated to make the purchase, you can always decide to walk away and see what the Toyota dealer has in stock instead. You won’t have lost because of the $5,000 value, but the dealer will get to keep the $300 you paid to create the opportunity for yourself in the first place. That, in a nutshell, is how options trading works. As the buyer of an option, you are in exactly the same position as you would be if you had gone out to buy that car. You cannot know what the future will bring—and it does have a habit of throwing out the unexpected—but you can make a decent prediction. Now, let’s zoom in a little bit closer. Though options trading really is as simple as the example we just looked at, there are a few more things you need to know in more detail before we move on. First, as mentioned above, there are two types of options: Calls: They give the right to BUY an asset at a specified price before the time limit expires. You’d do this, for example, if you felt confident that a certain stock was going to continue rising in price for a period of time. The call allows you to purchase that stock at a lower price at a time when it has risen to a much greater value. Puts: They give the right to SELL an asset at a specified price before the time limit expires. You’d do this, for example, if you felt confident that a certain stock was going to continue dropping in price for a period of time. That would allow you to sell that stock at a higher price at a time when it is worth a whole lot less. Let’s translate what we know into a trading example so that you can see how options trading works in the real world. This time, we’ll look at a put because, as you are now aware, the example of purchasing a vehicle was an illustration of a call—you obtained the right to BUY before the deadline. This time, we’ll look at what might happen if you purchased a put option which would give you the right but not the obligation to SELL before a deadline. We’ll assume you’re looking at a particular stock in your portfolio that is currently trading at $1. Knowing the market, you have predicted that it is going to drop to $0.50 within the next three months. You purchase an option with a trader that will allow you to sell the stock in three months at $0.75. If, during the interim, it turns out you are correct and the stock drops to $0.50 you have made a profit of $0.25 on the sale. If, on the other hand, you were wrong in your prediction and the stock climbs to $1.20 you have no obligation to sell it and lose that $0.20 profit. To understand this example fully, it’s important to know the difference between a buyer and a seller as it’s likely that you’ll end up filling both roles over the course of your options trading experience. A buyer is NOT OBLIGATED to actually buy or sell the stock when the deadline arrives. What he or she has bought is the right to make that purchase or sale but it is not an obligation. A seller is OBLIGATED to buy or sell the stock when the deadline arrives. As the seller, you made a promise when the contract was agreed to and you must fulfill it when the time comes no matter what the consequences might be. If follows, therefore, that you could find yourself in four very different situations during an options trading event. Let’s outline them for your reference as that is often where it can start to seem confusing. Call buyer —you have the choice to buy a stock at the deadline but you are not obligated to do so. Put buyer —you have the choice to sell a stock at the deadline but you are not obligated to do so. Call seller —you are obligated to sell a stock at the deadline and you will keep the premium that was included to secure the deal. Put seller —you are obligated to buy a stock at the deadline and you will keep the premium that was included to secure the deal. There are more intricacies to options trading but we’ll cover those in more detail later. First, make sure you have a full understanding of the basics—they are the essence of options trading and the heart of your experience as a trader. Why Options Rather than Stocks? One very good question that newcomers often ask is why a trader would want to trade in options rather than stocks. What’s the difference? Is one better than the other? It’s true that the stock market is less complicated to work with. All you really need to worry about in the case of the stock market is the direction things are heading. Down is bad for your shares but could be good for buying. Up is good for your shares and could be good for selling. With stock trading, you are also seldom going to lose 100 percent of your investment if things go sideways. If you pick a stock thinking it will climb but instead it plummets, you can sell quickly and lose only the difference between your initial investment and the price of that stock as you sell. Not so with options trading, where you will lose the lot if you make a bad judgment call. Stock trading can be a great introduction to the market but it is not as flexible and it is less likely to win big compared to an options trade. When you enter the options trading market, you quickly find out that you actually have three things to worry about—and what those things are doing is not so simple as “down is bad, up is good.” You are interested in the direction stocks are heading but you can make big money on a downward direction as easily as upward if you make the right call. Meanwhile, you are also concerned about your timing and the magnitude of the trade. In a nutshell, the biggest reason to choose options over stocks is that it provides you with flexibility within your own portfolio and allows you to play the market at its own game whether you are a bull or a bear. So let’s take a closer look at options trading and its benefits, shall we? Why is Options trading Worth the Risk? So, what’s the point of all this horse trading? If, while reading the previous chapters, it seemed that options trading involves a lot of risk and an uncertain gain, you might be interested to know that that’s not necessarily the case. It all depends how you go about trading your options. While, yes, you can place your focus on a whole slew of risky ventures and you would stand to either lose a fortune or gain even more, that’s not the only way to trade options. Let’s take a look at the advantages of options trading. When you trade in options, the uncertainty lessens. You create an option that tells you exactly how much you will either lose or gain once the deadline arrives—unlike trading in stocks, you are not at the mercy of the markets. You have confirmation from the outset as to what you will either receive or spend on a particular date. Options are more versatile than stocks and that means you can make money no matter what the state of the market is. It doesn’t matter if stocks are dropping as it would if you were simply trading in stocks. With an option strategy, you can take advantage of what’s happening in the markets in either direction. You can also use options trading as a form of security to protect your investments. That might sound strange, but it’s actually a very common strategy known as “hedging.” If, for instance, you are concerned that a stock you own a large amount of is set to drop, but you’re not completely sure, you can use an options trade to protect yourself against that possibility. You would simply buy a put that would allow you to sell that stock at a greatly reduced loss at the deadline—you wouldn’t be obligated to make that sale if you turned out to be wrong but you can do so if your fears prove to be well founded. You can also “hedge” to protect yourself against risk altogether. If it seems that the market as a whole is set to drop over the coming months, you can hedge your entire portfolio by buying exchange-traded funds. Those will actually gain value as the market drops in value—it’s a very common strategy among the experts. The opposite of “hedge” is to “speculate” and it’s one of the most profitable ways to invest if it’s done properly. Beware, however, that it is also the strategy that carries the most risk. By speculating, you can leverage the investments you have made and you have the chance to make a lot of money in the process—all for a relatively small cost. Finally, arguably the most important advantage of options trading is that you don’t need to know the complicated and advanced strategies in order to prevail. Actually, it’s the simple strategies that are very often the best. That means you can dive into options trading with the confidence that you can learn as you go without sacrificing your potential for profit. How to Get Started in Options trading Walking you through the learning curve of options trading will always start with the most basic move you’ll need to make—setting yourself up in a position to actually be able to trade. To trade in options, you’re going to need an options account. Don’t worry, we’re going to talk a whole lot more in the coming chapters about what to do with your account once you have it. For now, it’s important that you know your starting point and just how easy it is to reach it. One thing to know before you pick your firm is that times have changed considerably over the last couple of decades when it comes to options trading. Back before the internet became such a constant part of our lives, your brokerage firm—or, at least, your personal representative at the firm—would make your options trades on your behalf and you paid a hefty price for their services. Nowadays, however, you’ll be doing most of your trades yourself. Commissions for your representative is, thus, a whole lot lower than it used to be which means it won’t cost you an arm and both legs to rely on your rep in the early days of your experience with options. While you are learning, feel free to make use of your firm’s services to place and confirm your trades if it helps you to feel more comfortable getting to know the process. With that in mind, there are going to be certain things to look for when you select your firm. Compare commission prices to make sure you’re getting a great deal. Make sure the firm has up-to-date software and is capable of setting up trades quickly and reliably to make sure you get the trades you want at the best prices. Check out the hours of service to ensure the firm is compatible with your needs. In these days of online firms, you could be dealing with a firm that’s across the ocean from the markets you have an interest in. Or you might find that a firm only makes its reps available for the length of the working day and that might not suit your own timing. Speak personally with the reps at the firm because these are the people who are going to help you during the process of setting up your strategy. You want someone who is personable and knowledgeable—and, most importantly, who speaks in terms that you personally find easy to comprehend. Take a look at the additional services the firm supplies. Many will offer learning materials, guides, and even classes or webinars to help you hone your strategies. Even if you feel that you already know what you need to know, there’s no harm in a refresher course or a little nugget of inspiration every once in awhile. Once you select a firm, you’ll then need to consider signing a “margin agreement” with that firm. That agreement allows you to borrow money from the firm in order to purchase your stocks, which is known as “buying on margin.” Understandably, your brokerage firm is not going to allow you to buy on margin if you don’t have the financial status to pay them back. They will, therefore, run a credit check on you and ask you for information about your resources and your knowledge. A margin account is not a necessity for options trading—you don’t actually use margin to purchase an option because it must be paid for in full. However, a margin account can be useful as you graduate to more advanced strategies and, in some cases, it will be obligatory. If you opt to sign a margin agreement, talk it through thoroughly with the firm as there are certain restrictions on the type of money you can use that may apply to you. Next, you’ll need to sign an “options agreement.” This time, it’s an obligatory step. That agreement is designed to figure out how much you know about options and how much experience you have with trading them. It also aims to ensure that you are absolutely aware of the risks you take by trading options and it is to make sure that you are financially able to handle those risks. By ascertaining those things, your firm can determine what level of options trading you should be aiming for. It will, therefore, approve your “trading level” and there are five levels. Level 1: You may sell covered calls. Level 2: You may buy calls and puts and also buy strangles, straddles, and collars. You may also sell puts that are covered by cash and by options on exchange-traded funds and indexes. Level 3: You may utilize credit and debit spreads. Level 4: You may sell “naked puts,” straddles, and strangles. Level 5: You may sell “naked indexes” and “index spreads.” Don’t worry if you’re not sure yet what each of those things means. You will understand them by the time you finish reading this book. For now, all you need to be aware of is that your firm will determine what level is appropriate for you. As a beginner, don’t be surprised if you only reach the first two levels. Once you’ve signed the option agreement, you’ll be handed a booklet that contains a mine of information about the risks and rewards within options trading. Right now, if you were to read that booklet, it would seem to be in a foreign language. By the time you finish this crash course, it will be a lot more understandable—and it’s very important for your success that you do read it. Finally, your firm will present you with a “standardized option contract.” It’s the same for every trader, which means you stand the same chance of success as every other person out there in the options market. By trading an option, you are entering into a legal agreement that is insured by the Options Clearing Corporation, which guarantees the contract will be honored in full. Make sure you read that contract to be aware of not only the rights you have as a trader, but also the obligations you must follow in the same role. Congratulations, you now have an options account. That is the conduit through which you will create and implement your strategies and begin your adventure in options trading. Learning the Lingo Options traders speak their own language. It’s not meant to confuse you, it’s just the natural process of creating a shorthand by which one trader can converse with another more easily and thoroughly. Of course, it does make it difficult to plunge into the waters of options trading if you can’t speak the language. It is a lot like trying to decipher road signs in a foreign country. It makes it hard to know the right direction—or even where you’re standing right now. We’re going to take a look at the common terms you’ll be dealing with as you enter the world of options trading before we begin taking a deeper look at your strategies. Don’t worry about trying to learn the terms by rote. They will all become clear as you forge onward. This glossary will always be available to you so that you can check on a meaning if you need to. Strike Price: A price per share agreed upon before an option is traded. At that price, stock may be bought or sold under the terms of your option contract. This price is also known as the “exercise price.” Bid/Ask: The latest price that a market maker has offered for an option is its “ask” price. In other words, it’s what the seller is willing to accept for the trade. The latest amount that a buyer has offered for an option is the “bid” price. Premium: The premium is a per-share amount paid to the seller in order to procure an option. The seller will keep that premium whether or not the buyer exercises their right to buy or sell the stock at the deadline. In-the-Money: Often shortened to ITM, that means that the stock price is above the strike price for a call or below the strike price for a put. In other words, it is now at the right price to be traded. Out-of-the-Money: Often shortened to OTM, that means the current price is below the strike price for a call or above it for a put. Such an option is priced according to “time value.” At-the-Money: The strike price is equal to the current stock price. Long: In this context, “long” is used to imply ownership. Once you purchase a stock or option, you are “long” that item in your account. Short: If you sell an option or stock that you do not actually own, you are “short” that security in your account. Exercise: The owner of the option takes advantage of the right to buy or sell what they purchased with the option by “exercising” it. Assigned: When an owner of an option exercises it, the seller is “assigned” and must make good on the trade. In other words, the seller must fulfill their obligation to buy or sell. Intrinsic Value/Time Value: The intrinsic value of an option refers to how much it is ITM. Most options also include time value and that refers to how long is left until the option expires. That time has value because during that time the stock can still change in price. An OTM option has no intrinsic value because it’s a loss but it does have time value because that loss might change. Time Decay: Linked to time value, that term refers to the fact that, as time ticks on, the amount of time value slowly decreases. At the expiration date of an option contract, the contract has NO time value and is worth only its intrinsic value. Index Options/Equity Options: Index options are settled by cash whereas equity options involve trading stock. The main difference between those two types of options is that an index option usually cannot be exercised before the expiration date while an equity option usually can. Stop-Loss Order: That is an order to sell either an option or a stock when it reaches a particular price. Its purpose is to set a point at which you, as the trader, would like to get out of your position. At that price, your stop order is activated as a market order. In other words, a market order looks for the best available price at that moment in order to close out your position. Those are the most common terms you will hear used as you venture into the world of options trading. It’s worth mentioning that, as you extend your understanding, you’ll encounter more terms. However, the above terms are enough in order to help you understand your first trades. The Role of the Underlying Stock It’s vital to understand that stocks do play a fundamental role in options trading—even though they may not be what you are buying and selling. Bear in mind that an option is only a piece of paper that gives you the right to buy or sell a stock. Without the stock, you would have nothing to buy or sell. You might say that the stock is Oz behind the curtain, changing and moving while your attention is fixed elsewhere. Letting Oz get up to his tricks without you is a bad idea. You need to be keeping an eye on your stocks just as much as you follow the options themselves. Not every stock is allowed to have its options traded on an options exchange. In total, you’ll find somewhere in the region of 3,600 stocks spread across twelve different exchanges, although that number changes all the time. What does that mean? Well, the exchanges have in place some very solid rules that dictate which stocks may and may not participate in options trading. You’ll find some of the biggest business names on the planet have options, and you’ll also find what are known as “penny stocks” which buy and sell for less than $3. In general, penny stocks won’t do you much good for options trading. There simply isn’t enough liquidity in such a small price for you to bother with the effort required to trade them. Instead, I would recommend sticking with the big names—the recognizable companies such as Microsoft, Apple, Google, and McDonalds. Another point to bear in mind is that there is a fixed relationship between options trading and the underlying stock. One option contract will always be equal to 100 stock shares. In other words, a single contract will give you the right to buy or sell 100 shares of a stock. Multiply the number of contracts involved in a trade by 100 and you’ll know how many shares are involved. A third factor of that relationship between an option and its underlying stock is that whenever the stock goes up or down, in most cases so, too, will the option contract. Because a stock and its options are so inextricably linked, you will need to study the stock market in detail to be a whiz at options trading. You will need to be able to predict which stocks are going to head in which direction and when—only if you get that right will your trading be truly successful. For that reason, a lot of options traders started with the stock market, itself, and gave themselves the experience of the market’s whims before taking a step up to the next level. If you haven’t done that, it will be worth spending a month or more trading on the stock market. Even a theoretical portfolio that you manage and never pay a penny to invest in is a helpful step. Doing that will allow you to get a sense of how the market functions overall and it will familiarize you with some of the stocks you might be interested in for trading with options. The best options traders have almost a sixth sense of how an underlying stock is going to perform. The only way to develop that uncanny ability is through exposure, research, and experience. Understanding the Strike Price We previously touched on the idea of the strike price, but it’s such a fundamental aspect of options trading that it bears looking at in greater detail. To review, the strike price is the fixed price at which the underlying stock can either be bought or sold. When you purchase a call option, what you are purchasing is the right to buy a stock at a certain price. Selling a call option means that you are selling your buyer the right to purchase a stock at a certain price. The strike price is an aspect of every options trade and you will want to hone in on that every time. It’s that important. Never forget that, if the underlying stock never reaches the strike price, the trade is worthless because the option will simply expire on the expiration date. The difference between the current market price of the stock and the strike price of the option also represents the profit-per-share you can expect to make if you are successful. Let’s say, for example, that you find two trades for a stock that is currently worth $150. One has a strike price of $125 and the other has a strike price of $100. In the first trade, the stock price will need to drop to $125 before you have the right to buy it or sell it (depending on whether the option is a call or a buy). In the second, it will need to drop to $100 before you have that right. The value of the option is simple to calculate. It’s the difference between the strike price and the current price of the stock. In the first of these examples, the trade has a potential worth of $25; in the second, the potential worth is $50. At first glance, that would seem to mean that the second option is the one to go for because its value is so much higher. However, you also need to bear in mind that you cannot dictate what the market does. That is where risk comes in. How confident are you, in this example, that the stock will plummet $50 before the expiration date of the option? If you’re as certain as it’s possible to be, it’s a great investment. If you’re not, you stand to lose the premium you paid for the option because it will never reach the price at which you have the right to realize the trade. The trade that has a strike price of $125 is, therefore, a surer bet because it’s always going to be more likely that a stock will rise or fall by the smaller amount than the larger one. The trade-off, as you can see, is that you won’t make nearly the profit you would on the riskier option, so, you have to ask yourself whether the premium you’d be paying is worthwhile. Basic Trading: Selling Covered Calls As beginners, most people choose to dip their toes in the complicated waters of options trading by selling covered calls. It’s arguably the most basic level of options trading and, while also not the most adrenaline-inducing, it is a great way to find your feet before moving on to more complicated strategies. Selling covered calls is also likely to be an aspect of your options portfolio in the long-term. Many traders use it as a steady way of generating income and it is a conservative baseline for their account. A third benefit to starting with covered calls is that it includes the majority of the knowledge and strategies that you will use as an options trader, so, it’s a perfect training ground. Using that strategy, you are going to be selling the right to buy underlying stocks that you own. A “covered” call is when you own the shares and, therefore, you have the sale covered. Before you can begin, therefore, you will need to own at least 100 shares of a stock. By writing an option on those shares, you are offering buyers the right to buy them by the expiration date if the share price hits your strike price. When a buyer takes advantage of your offer, you will receive a premium. That’s yours to take home. You will never have to give it back whether the strike price is met or not and the buyer exercises their right or not. That, right there, is your reason for selling covered calls—the steady influx of cash from the premiums. Covered calls are also a good way to sell your stock. A clever trader will use that strategy to clear their portfolio of shares they no longer want to own. There is an advantage to owning a stock in the interim, too, because you may receive a dividend. You’ll receive capital gains (the difference between the price now and the increased price at time of sale) if the stock meets your strike price when the expiration date arrives. One final advantage of covered calls is that the strategy can be used in a tax-deferred account or an IRA. You won’t be taxed on the revenue from your trade until you take out money at the time of your retirement. There are caveats to that rule, of course, so you may want to book an appointment with your accountant to make sure it works for you. The downside? There is always the danger that your shares skyrocket before the deadline is up and you are forced to sell them to your buyer anyway, which means you’re losing out on a potential big win. That’s the gamble and the truth is that even that risk will even out in the end because you’ll be making money on the premiums for those trades that didn’t turn out to be a bad idea. When the expiration date arrives, you will EITHER have the premium in your pocket and no shares or you will have both the premium and the shares because the buyer didn’t choose to purchase them after all. Either way, you’re always walking away with something. So, let’s work through selling a covered call, step by step, and take a look at every aspect of the process. First, choose a stock that’s already in your portfolio and has been performing well recently. It also needs to be one that you are willing to no longer own if the buyer exercises their right to buy it. In your account’s online space, you will first bring up the underlying stock by entering its symbol. That will allow you to see its option chain—in other words, all the bids and calls currently on the table for those particular shares. Obviously, we’re interested right now in the calls. You’re going to be picking one of these offers to sell your shares. First, take a look at the premiums on those calls. Take a look at the “bid price” column. These are displayed per share, so it’s the amount you will receive for every share that you trade on. You’ll probably find that there is a huge range of premiums for the same stock—that’s a function of the market. To be clear on your potential profits—for every option (100 shares of one stock), you will receive the premium for every share. If, for example, the premium is listed as $2.50, you’ll make that amount for every share of the stock. If it’s a single stock, that’s $2.50 multiplied by 100 or $250. You want to focus on pulling up options a few months from now, so pick a date range about two or three months down the line. That is because the premium will increase the later the expiration date. You want to be reasonable in your expectations, however, because there are downsides to going too far out, so, a few months is usually a golden spot. Take a look at the other columns. Compare the “bid price” and “ask price” columns on that list of options. The bid price is the amount that a trader out there somewhere is prepared to pay to own the call option. The ask price is the amount that a trader somewhere has said they are prepared to sell that call option for. You can accept that bid price and you’ll sell your covered call instantly for that amount. Alternatively, you can instruct your broker to sell your option at a certain ask price or better. That won’t be fulfilled immediately, but it will mean a better return for you in the long-term if there’s a buyer out there who is willing to accept your price. Take a look at the list for options that are currently “in the money.” Most lists will have a mark of some kind to denote the ones that are. If an option is in the money, it means that exercising it instantly will yield a profit—although it does not factor in the cost of buying that option in the first place, i.e., the premium. As an example to illustrate this, imagine that there is a contract with a strike price of $50 and the stock is priced at $52 right now. If the buyer of the option immediately exercises their right to buy that stock, they’d make a profit of $2 per share. However, if the premium per share for the option was also $2, the buyer wouldn’t actually gain any net profit. What you should be looking for is a covered call contract with a strike price that’s slightly “out of the money.” You want to unload your shares at a slightly higher price than they are currently worth to make it a good purchase for your buyer and because you will make a profit on the actual sale as well as on the premium. If the shares never reach that price, you won’t have to sell them, of course. If that happens, you can simply pocket the premium and list the shares again. You can also consider a contract slightly “in the money” if the premium is high enough to offset the loss you would make on the sale. You should be calculating overall profits rather than relying on just the sale price or the premium alone. The bottom line is that you will need to calculate a strike price you’re happy to sell a stock at, whether it’s a loss or a gain, with a premium that makes the sale worthwhile. Once you’ve chosen the contract that best suits your needs, you can simply enter into it and wait for the expiration date. At that time, though sometimes before, your broker will let you know whether the buyer exercised their right or that you still own the stock. Keep in mind that, if your buyer does NOT exercise their right, you have generated a certain amount of money because of the premium. When you repeat the exercise, you can factor that overall profit into your thinking to help guide you toward the next contract. To sell a call option on your stock, select the “Action” that says “Sell to Open” because that is the one that applies for selling a covered call. Now, enter the number of contracts you want to sell—and remember that one contract equals 100 shares. Now, you must choose between a market order or a limit order. A market order allows the market makers to figure out the price to fill your order while a limit order allows you to choose your own price. The latter is usually the better option. Once you’ve selected it, you can decide on your price. The risk is that you might not sell for the price you pick. Now, enter the information for how long you want the option to appear in the marketplace. I would recommend selecting “day” rather than “until cancelled” because you want to be able to relist with new information if it isn’t purchased. Next, set your bid price, which will likely appear under the heading “Limit Price.” Ignore the information about last sale when you are doing this as there is no way to tell when that last sale actually happened, so, it may not reflect the current bid and ask prices you should be using as a guide. That’s it. Hit the order button. Your first covered sell is now in the marketplace and awaiting a buyer. Strategy for Selling Covered Calls We’ve covered the process but what about the strategy behind covered calls? In the last chapter, we looked at the absolute basics of that strategy but an experienced trader knows there’s always going to be more to an option than meets the eye. There’s a whole list of considerations that you will eventually want to bear in mind as you expand your knowledge and develop your own personal strategy. Every trader has a different attitude toward what works and what doesn’t. There are plenty of ways to make selling a covered call work but you’ll probably find yourself preferring one or two strategies. We’ll take a look now at those considerations in more detail in order to guide you as you delve into covered calls more deeply: The Market Environment: You are no doubt aware that traders of stocks are happy in a bull market and disgruntled in a bear market. You may also know that such traders hate a flat market most of all because very little is happening and there aren’t many big profits to be made. For you, as a seller of covered calls, the opposite is true. I highly recommend waiting for the market to temporarily flatten before embarking on a spate of covered call sales. That is because you’re only really interested in small changes to your share prices. If they are skyrocketing, you’re losing money on your contract. There also isn’t as much danger of the bottom falling out of the market with your stock prices plummeting at the same time which would be problematic. Your Underlying Stock: There is nothing more important to your success than choosing the right stocks to invest in. I cannot stress strongly enough that your success will be heightened if you pick stocks that move up very slowly. You don’t want stocks that rise and fall very quickly, especially as a beginner, because they have a habit of making surprising moves that ruin your strategy. If they drop too far, you stand to lose a lot of money if you sell. If they rise too high, you lose the money you could have made if you’d sold them at the higher price. Traders who deal in risk often enjoy those stocks because they have higher premiums and a chance for huge profits but that goes against the idea of selling covered calls. You’re looking for a steady income that will underpin your riskier strategies elsewhere. By all means, go for the riskier stock elsewhere in your strategy but avoid it like the plague for covered calls. The Premium: Always remember that the premium is your guaranteed profit. Whatever else happens, you’re going to walk away with that cash. When you factor in the cost to list the option and any commission you will lose to your broker, you’ll be able to calculate the actual profit you’ll make on a premium. Set yourself a minimum premium—a number that you consider to be enough to provide a profit you’ll be happy with on the assumption that it’s the only profit you make. When you move ahead on setting the strike price, you’ll likely adjust that base figure up or down based on what you think the underlying stock is going to do before the expiration date. Remember that the premium is only one component of the overall profit you will make. If you set a strike price that means you lose the same amount of cash on selling the shares as you made with the premium, the trade wasn’t worth doing in the first place. The Expiration Date: There’s a reason that the premiums on covered calls get higher when the expiration date is further out. It’s because, much like the weather forecasts we all deride on a daily basis, it gets harder and harder to predict what’s going to happen to a share price the further out you go. Also, bear in mind that your money is going to be tied up until the expiration date, so, the premium will increase as a nod to that sacrifice. Most investors believe that a time span of between a month and three months works best. The Strike Price: You might think that the strike price you set should be based on what you, as the seller, are comfortable with but actually it’s the opposite. You’re looking for a strike price that your buyer will feel comfortable with because otherwise they aren’t going to buy. That, in turn, is going to be dictated by the expiration date you set as well as the premium you’re asking for and how stable or volatile the underlying stock is. Your best bet is to put yourself in the shoes of your buyer. Would you purchase that contract? How much would you stand to gain? Set your strike price accordingly and then take a look at it from your own point of view. Would that be an acceptable profit for you? If so, you’ve hit the nail on the head. With all of those factors in mind, you are likely starting to see that there is no single “correct decision” when it comes to selling covered calls. It’s going to take practice and concentration to figure out which ones work best for you. It’s also important to note that your strategy is probably going to change as you gain experience. The more options you sell, the more you will see new and more advanced ways to take advantage of the market. For now, I urge you to be conservative in your approach and accept that selling covered options is not going to win you your fortune but it is going to help you increase the seed money you have available to do just that. * * * * * Before we continue, I have a small favor to ask: Could you please take a minute of your time to write an honest review of the book? Your reviews are what keeps me going. I read every single one of them, and would be extremely thankful if you choose to share your thoughts with me. Click Here to Leave Your Review * * * * * Outcomes of a Covered Sell As we’re using the idea of selling covered calls as a trade example to help you learn the basics of options trading overall, let’s now take a close look at what is going to happen to your option once you’ve listed it. The stock increases in value: If the stock moves up and hits your strike price, that means that your buyer can now exercise their right and buy the shares. The more the stock rises, the more likely it is that the buyer will do exactly that. When your goal is to sell shares, that is what you want to happen. You will pocket the premium as well as the difference between the shares as they were valued when you listed them and the value they are at on the expiration date. In other words, you will have capital gains in addition to the premium you received. The stock value doesn’t move: If the shares don’t change either up or down during the time the option is open, then they won’t hit the strike price and you won’t have to sell. You will pocket the premium and can factor that into your overall profits when you relist the stock. Many options traders actually count on that outcome. It’s the one they are hoping for because it means they make a profit AND keep the shares. Feel free to follow the same logic but make sure your entire plan doesn’t hinge on it. You don’t control the market, so, you could find yourself with a nasty surprise. The stock drops in value: If that happens, the outcome is very similar to the share price not moving at all. The difference is that you are losing money on the shares themselves all the time they are dropping. They might bounce back but, if they don’t, then the expiration date will arrive and you’ll be holding shares that are now worth a lot less than they used to be and that constitutes a loss in value. If, while monitoring your option contracts, you see that a stock is starting to drop, you need to prepare to take emergency action. Do that by calculating your “breakeven” price. Subtract the premium per share from the price of the share at the time you listed it. For example, if the share was worth $50 and the premium per share is $1.50, your breakeven price per share is $48.50. If it falls below that price, you can buy back your option. That is not something you should rely on or do often but it is good as an emergency action. To do that, go back to the order entry and select “Buy to Close.” Enter either the current ask price or something lower, depending how risky you want to be. Once the trade goes through, you are back in control of your shares and can either keep or sell them as you deem fit. As an aside, you should know that buying back your options is actually a deliberate strategy used by some people who trade in covered calls. Doing so allows you to manage your own risk and to end trades that are likely to be disadvantageous for you so that you can list those stocks again at a later date. For instance, let’s say that your underlying stock is rising fast and you think you’re going to lose out on a lot of potential profit as it continues to skyrocket. You could “roll up” your options by buying back your call at the current ask price or lower and then selling it again at a higher strike price. Simply setting your stock to sell is enough to garner you a regular income with your options trading but there are other ways you can make the most of the market. A typical strategy for a person who deals in selling covered calls is to purchase a stock and sell a covered call on that stock at the exact same time. It’s called a “Buy-Write Strategy.” Your brokerage firm will almost certainly allow you to do that and may even have it listed on their online order screen for you to select. So what would you be looking for if you did that? A stock that you would be happy to have in your share portfolio, assuming that the buyer never realized their right to purchase it. A stock that is showing a premium rate in the marketplace you would be happy to accept. A stock that is predictable in that it is rising or dipping in worth slowly over time. Keep your eyes firmly on the stock market over time and you will start to see those trends. You’ll also develop an eye for spotting good trades—the ones where you can make a quick profit by selling a few contracts at a good premium price. A second advanced strategy is to use options trading to get rid of stocks you don’t want to own any more. Maybe, for instance, they’ve been flat for a long time and you aren’t seeing enough movement to make them worthwhile. You can set up a sell that would return a good premium while allowing you to get rid of your stock at close to its current price. Instead of simply unloading them, you’d walk away with a premium and a potentially tidy profit. Third, you can choose to use the “half and half” strategy. Keep some of your shares in a particular company and sell the rest. That works well if you aren’t really sure whether you should sell them all but make sure you are keeping records of what you have done. Stepping Up a Tier: Buying Calls We’re ready to move on to the more sophisticated areas of options trading. You have tested the waters, made a little cash, and you feel comfortable with the mechanics of the market. Now, you can start actually buying calls and begin to hopefully make some real money. It’s actually simple to buy a call in terms of physically going ahead and doing it. However, it’s not quite so easy to make a profit. You’re going to need to start small and dedicate yourself to a learning curve—and you need to understand that there is a risk involved in buying calls, so, you don’t want to stake your life savings on your efforts. My advice is that you build up slowly over time rather than jumping straight in with several buys in a single day. Be circumspect about your actions. A small profit is better than no profit at all. Save your riskiest ideas for when you’ve set up a nest egg with your sells and you feel confident enough in your own judgment that you’re as sure as it’s possible to be that your risk will pay off. As a reminder, what you are actually doing when you buy a call is purchasing the right to buy the underlying stock if it reaches the strike price before the deadline. You aren’t obligated to buy it. If you choose not to, all you have lost is the premium you paid for that right. The best case scenario for you, as the buyer, is that the stock suddenly starts rising at a high speed before the expiration date arrives. You want it to go beyond the strike price so that, when it comes time to exercise your right, you are purchasing your stock at a lower price than it is now worth. Obviously, you then have the option to instantly list that stock as a covered sell, which would allow you to realize more profit in real money. That final piece of the puzzle is the important one. As an options trader, you are not in the business of building a stock portfolio. You don’t really want to actually own shares—you want to make a profit on them as they pass through your hands. You want to buy them for less than they are worth and then sell them for more than they are worth if you are lucky. It’s within those transactions that your money will be made. Buying calls has several advantages for you as an options trader. It doesn’t cost much to get involved in the movement of a particular stock. You only need fork out the amount for the premium. You can sit back and wait to see what the stock does before making your purchase decision based on actual information rather than on speculating what the market will do. It allows you to make use of the kinds of “tips” that market experts have a bad habit of swearing by. You read the news, you’re watching the markets, and you have information that makes you think a certain stock is about to rise fast and hard. You want to take advantage of that, obviously, and options trading allows you to do so in a safe way rather than simply buying the stock. If you’re wrong, you’ll only lose your premium and you may even make a small profit. If you purchased the stock and then it plummeted rather than rose, you stand to lose a whole lot more cash. Buying calls also allows you to consider shares that would ordinarily be out of your price range. You can play around with the big boys, like Walmart and Apple without putting a second mortgage on the house. Buying options on those stocks is a whole lot less expensive than buying the stocks themselves, so, if you see something on the horizon that makes you think the trade would be worthwhile—like a new product or service, for instance, or a change in leadership—you can use call buying to get in on the game. That is called “leverage” which is the ability to control thousands of dollars in stock for just hundreds of dollars in premiums. One thing to note before you start buying calls is that you’ll want to wait for the right time. You are no longer interested in a flat market. This time, you want a bull market where stock prices are rising. What you are looking for is an underlying stock you have faith in. You think it’s going to rise in value over the next few months. Let’s say you’ve found a stock that’s currently at $50 and you believe it will continue to rise steadily. Predicting the rate of its growth, you think it will be at $80 in two months’ time. What you would be looking for in that scenario is a call contract that would allow you to purchase shares for LESS than the $80 you think they will rise to in two months. You must also juggle the math to make sure that you will not be paying a premium that would wipe out the profit you would make. For example, you might find a contract option that will allow you to buy the stock at $80 per share on the expiration date with a premium of $1 per share. You think the stock is actually going to be worth $85 on that date, so, you would actually be making a profit of $4 per share. You would make no profit at all if the premium had been $5. Bear in mind, of course, that you won’t walk away from a call option with cash in hand. The profit we are talking about in this case is “intrinsic value.” You can now take that stock and write a covered call on it, hopefully selling it, and making a tangible profit in the process. That was what we were discussing in the previous chapter. As an options trader, you’re not looking to hold a stock portfolio. You’re purchasing stocks with call contracts in order to turn around and sell for a profit. Strategies for Buying Calls I have urged you several times throughout this book to start paying attention to the stock market and learn how to spot trends in the ups and downs of particular shares. As you become increasingly familiar with that part of your options trading experience, you can also make use of a column in the trading screen itself to guide you. That column is titled “Open Interest” and it represents the total amount of open contracts on a particular underlying stock that are still running at the time you are viewing the page. What you are looking at is the supply and demand on the stock. The more open interest there is on a particular contract, the more people believe it’s a sure bet. You can also watch for sudden changes. If a call contract has 500 in that column one day and 2000 the next, it means that a significant number of traders believe that stock is going to move in that price direction. Those people aren’t necessarily right, so, it’s up to you to use your judgment. Nevertheless, it can be a very helpful addition to your tool kit when it comes to predicting the movement of the stock market and making the right decisions in your own trading. At the same time, there are a number of factors that should be guiding you as you choose the right contract. The following factors can help you: In or Out of the Money: As a call seller, you were mostly interested in the premium. As a buyer, you want a bargain. You’ll find that the premium is cheaper the more out of the money a contract is. In other words, the further the stock needs to climb before you can call in your option, the cheaper the premium will be. That doesn’t mean it’s the best bet. If you don’t believe the stock will climb that high, it doesn’t matter how cheap the premium is as you’re not going to be able to purchase that stock. Calls that are slightly in the money are a good option for beginners and more likely to bring you a modest or sometimes larger profit. Stock Movement: There is absolutely no point buying a bargain call that has a strike price higher than you believe it will go. If it never reaches that price, you’ve lost the premium you paid. Sometimes it can be worth the risk if you are reasonably sure the stock has a chance of rising that high but that doesn’t happen very often. Time Value: If you’re purchasing a contract that would require the stock to rise above a price, it stands to reason that you need to give it enough time to do that. Premiums also are lower on short term contracts but that’s because there’s probably not enough time for the stock to reach its target. Be circumspect when looking for contracts with cheap premiums. The lowest price is often not the best one. It’s important to give your strategy breathing room, so, lean toward the calls with long enough expiration dates to allow the stock to do what you hope it will. Spread: This is the difference between the bid and ask price and it has a direct impact on the price you will pay. A fair price usually falls somewhere between the two. The higher you pay, the more you are taking from your profit. Bear in mind that you will usually begin at a loss in your trade. If you pay $1.50 when the bid price is $1, that’s a $0.50 loss on each share. Because the whole idea is that the stock will rise in value, that’s not necessarily a big issue although it can be. As a general rule, if there is a wide spread, you should aim for somewhere in the middle. If it’s narrow, you can probably pay the ask price without too much concern. To make a profit buying covered calls, you have to be right on all of these fronts. You need to choose the right time, the right direction, and the right contract price if you’re going to be successful. If you get one of those things wrong, you will likely lose that profit. Be aware that buying calls is where the risk comes in for options traders. That is why I highly recommend balancing your activity and relying on covered sells for your steady income while keeping your buying activity relatively modest. Understanding Time Value At this stage, let’s take a deeper look at one of the factors influencing the price of the options you are considering. Time value, as we’ve mentioned before, is what’s left after you take the intrinsic value away from the premium. In other words, if your option is priced at $2 and the intrinsic value is $1.50—the premium minus the stock price will give the time value of $0.50. The time value will slowly bleed away as you get closer to the expiration date. Time value is your friend as a buyer but, as a seller, it’s quite the opposite. You are on a timer from the moment you buy a call because, the closer you are to the expiration date, the less time there is left for the underlying stock to do what you want it to do and for your option to increase in its value. The closer you get to the deadline, the faster the time value will trickle away. Be very aware of the time value, because it’s far more important than a lot of beginners realize. That is why you will want to factor it in very carefully to any decision you make. Too far out and your contract could start moving in the opposite direction again and the premium will be dauntingly high. Too close and you simply won’t have enough time to watch your stocks head for the magic value you were hoping for, leaving you out of pocket on the premium. Aim for two to three months, plenty of time for your strategy to see fruition without risking it heading in the opposite direction or paying a fortune in premiums. Understanding Volatility There’s one final factor that affects the prices of contracts on a fundamental basis and it’s not really something we’ve touched on so far. The volatility of a contract is, however, an incredibly important concept to grasp for an options trader. Volatility refers to the movement of the underlying stock. Some stocks will slowly wend their way up and down in a predictable manner and those stocks are not very volatile. Others change up and down on a day-to-day basis. To sum up the effect of volatility in a single sentence—the more volatile the stock, the more that an options trader is willing to pay for it. A volatile stock has a better chance of reaching a strike price and perhaps shooting far beyond it before the expiration date. However, volatility is also the most dangerous of the factors that you need to bear in mind because it’s arguably the most likely one to force you into a bad decision. A volatile stock, for example, can lead to a much higher premium and, therefore, a higher contract price. Unless that stock shoots through the roof, you could actually end up losing money even when you should be making it. One way to estimate the volatility of a stock is to take a look at what it has done in the recent past. That tells you how much it has moved up and down already, which is what some use as an indicator of how much it will move up and down in the future. Unfortunately, it’s not always true that the past repeats itself and you can’t predict the future based on what’s already happened. Instead, options traders use “implied volatility” to make their guesses and that is the value that the market believes the option is worth. You can see that reflected in the activity on the options for that stock. Buyers will be keen to get their hands on options before a certain event takes place, such as the announcement of a new product or a release about the company’s earnings. Because of that, options increase in price because there is implied volatility. The market thinks the stock is going to shoot up. You’ll see lower demand on a stock that’s flat or moving gently because there is no implied volatility and, therefore, no hurry to get in on the action. You’ll also see correspondingly low prices for options on that stock. Volatility is obviously a good thing. As a buyer, you want the stock to be volatile because you need it to climb to the strike price and beyond. However, there is also such a thing as too much volatility. It’s at that point that contracts become popular, the prices rise, and you stand to pay more for a contract than you will ultimately profit from. Your broker will likely be able to provide you with a program that will help you determine implied volatility by asking you to enter certain factors and then calculating it for you. However, it’s only with experience that you’ll learn how to spot a stock that’s just volatile enough to justify its higher price. Again, practice is key. It’s also worth noting that a lot of the risk in options trading comes from volatility largely because it’s impossible to be accurate in your estimates. What happens if an earthquake destroys a company’s headquarters? That stock will plummet and you had absolutely no way to see it coming. That’s why options traders are forced to accept that their fancy formulas are not going to be perfect predictors. They will help but you should still be conservative in your trading and avoid the temptation to sink everything into a trade that you believe could make your fortune thanks to its volatility. Keeping an Eye on Your Calls Once you’ve purchased a call contract, your job is not over. In fact, it has only just begun. From now until the expiration date, you need to keep an eye on what your stock is doing to see whether it goes up, down, or nowhere at all. Down: If the stock unexpectedly begins to move down, it’s moving further and further away from the strike price. If that trend continues, it’s going to mean that you can’t exercise your right to buy at the expiration date and you’ve lost out. You could choose to try to sell your option to regain some of that potential loss if there’s still time value enough to justify someone taking it off your hands. If you choose to keep it, remember that you don’t actually have to buy the stock. You are only going to lose the premium on the expiration date. No Movement: The stock is hovering around the strike price and is losing time value as it does. Again, you may want to think about selling the call option to reap back some of the premium. However, if you think there’s a chance that things will change before the expiration date and the stock will start moving up, that’s not always a good idea. It’s a tough call to make because you could end up losing out on a tidy profit if you don’t give the stock breathing room to start moving. Again, remember you’ll only lose the premium if it doesn’t reach the strike price or you decide not to buy. Up: Here’s where options traders have a habit of getting antsy. You’re watching the stock rise and it’s gone far beyond the strike price. Naturally, you want to call in the contract right away and you hit the “sell to close” button so you can sell it and bank that profit. If the stock has indeed reached the top of its curve and is about to start dropping again, that can indeed be the right call. However, you also have the option to “roll up” your call by closing out your position and moving it to one with a higher strike price. You can also “roll over” to a strike price with a later expiration. There is a third option which is to actually exercise the right to buy that you purchased in the first place. Exercising Your Right to Buy the Stock Bearing in mind that an option is all about the right to buy or sell a stock, it might seem strange that most traders are not looking to do that. Instead, they are looking to immediately pass the stock on as a sell and make a profit by taking the premium along with the increased price of the stock from what they paid for it. That’s what you should be basing your strategy around—the idea of gaining stocks and instantly selling them back into the options market and making your profit in the process. In most cases, that’s what you will be aiming to do. It is also worth noting that some traders who buy call options never want to own the underlying stock. They are only interested in making money on the options which they can do by buying and selling options without ever owning the stock. Nevertheless, there are still going to be times when you want to exercise your right in order to purchase the underlying stock itself. Usually, that is when you genuinely want to add a particular stock to your portfolio. It’s up to you to decide when those times arrive. First things first. Be very aware that you will automatically exercise your right at the expiration date if the option is in the money unless you tell your broker not to take that action. That won’t happen if it’s out of the money but it’s still imperative that you keep a calendar of your trades so that you aren’t surprised by the sudden arrival of stocks in your portfolio that you’d completely forgotten about. If and when you decide to exercise your right, you should almost always do it at the expiration date and not before because you’ll lose the time value if you exercise early. When you alert your broker to that decision, it’s also important to know that you cannot then change your mind—the decision is permanent. How to Buy and Sell Puts Buying puts can be a winning strategy if done right. The stock market wouldn’t be the stock market if it only moved in one direction. By buying puts as well as calls, you’re making the most of the market by profiting no matter which direction it’s heading. Puts are your ally during a bear market. Buying a put means that you are going to make a profit with a stock declining in price. Just as you’re looking for a stock to skyrocket in a call, you’re looking for one that will plunge in a put. The strategy is, therefore, very similar and it’s just that you’re looking in the opposite direction. Most traders buy puts either because they’re speculating on a stock and think they can make a profit in the short term as that stock plummets, or because the puts can function as insurance for your overall portfolio. If you actually own a stock in question, you can buy puts on it if you believe it’s at risk of heading downward. For instance, let’s say you own stock in a company and you think the share price will drop because of the business environment. You aren’t sure, but you can make an educated guess. Simply leaving that stock sitting in your portfolio means potentially watching as its value bleeds away. On the other hand, you could buy a put and give yourself the option to offload that stock if it does drop to a certain value. As the buyer, you are not obligated to sell your stock when the deadline arrives. You’re just giving yourself the option to do so. Of course, as always, you’ll lose the premium. The biggest difference between buying calls and puts is that the stock market has a habit of falling much faster than it rises. A stock can drop through the floor in just a single day whereas it can take weeks or months to climb to magical figures. To buy puts for the sake of speculation, you’ll need to master the art of spotting weaker stocks—the ones that are likely to fall. That is easiest during a bear market and when the overall economic outlook is poor. Even the most successful companies have down times and, if you own a put contract when that happens, you stand to make money. When buying a put, you’ll need to think in reverse. The lower the strike price, the cheaper the option will be. In other words, it is the opposite of buying a call. You should also factor in the speed of the market when looking at expiration dates. If you think the stock is going to drop hard and fast, you probably want a shorter deadline. If you think it will take a while for the full effects of the drop to realize, then you will want a longer one. The most successful put strategies, at least at first, will probably be slightly in the money because you can profit from a smaller change in the underlying value. Conversely, you’ll make more money on a smaller premium with an out of the money put but you have less chance of actually making that money. Selling puts can be a gamble. The idea behind it is that, by selling your promise to buy stocks, you are earning a steady premium but you’re choosing contracts that you believe will never hit the strike price. That way, you walk away having been paid for the contract without having to actually own the underlying stock. It’s also a way to increase your stock portfolio and get paid for doing so. That can be useful if you think a stock’s dropping price is temporary and you want to snap up a few of them before they start to rise again and you can sell them. Be aware, of course, that when selling a put you are obligating yourself to buy that stock if it does reach the strike price, so, it’s a bad gamble if you lack the funds to do that when the expiration date arrives. Strategies for New Options Traders Now that you know the basics of options trading, you’re no doubt raring to get started with your first trades. All that remains is to introduce you to some of the strategies you now have open to you. First up is the Greeks. You’re going to see of those all over the place and they can really help you understand your chances with a particular trade, so, it’s important to understand what they are. Delta: That stands for the change in price of the option when compared to the change in price of the underlying stock. For call options, it will be between 0 and 1; for put options, it will be between 0 and -1. The closer to 1 or -1, the more likely that the price of that option will increase or decrease dollar for dollar as the stock price changes. If it’s at 0.5 or -0.5, it will increase or decrease by 50 cents for every dollar of change on the stock. The further in the money the option is, the higher its delta will be. The higher the delta, the more likely your option is going to finish in the money. Gamma: That stands for the change in the delta of an option relative to the change in the price of the underlying stock. It tells you, therefore, what the rate of increase of the delta is. As a buyer, a high gamma is good assuming that your assumptions about what the underlying stock is going to do are correct. If you’re wrong, it can be very bad indeed because your mistake is going to work against you more quickly. Theta: That stands for the change in the price of an option relative to how much time is left until it expires. It is directly related to the time value and will decrease as that value does. You want a low theta risk with options more than 90 days before expiration if you are long on your position because you don’t want the time value to drop. You want a high theta if you are short with options less than 30 days to deadline. Vega: That stands for the change in price relative to the option’s change in volatility. Premiums increase with volatility so vega will, too. Specifically, it will tell you how every 1 percent point change in the implied volatility affects the premium. If the volatility drops or disappears altogether, it’s possible that your option could lose value, so, vega is important to keep an eye on. Now, for some of those all-important strategies you’ve been waiting for. Straddling a Stock: If you are good at spotting market trends, this strategy is for you. Let’s say that you think a company is about to have a big event or release an announcement, but you don’t know exactly what that will do to its shares. You just think that it’s bound to affect them. You could use a straddle strategy to purchase both a put and a call option at the same strike price, setting the expiration shortly after the date of the event in question. Your breakeven point on that is going to need to factor in both trades. You need to be doubling your profit, in other words, to justify the spend on two contracts. Therefore, you’ll need to include that thought in your choice of strike price and you’ll need to watch out for volatility. You need higher implied volatility for that to work. You should also be aware that you won’t be the only one who sees the change coming, so, the contracts could be pricey. The Strangle: That can be a better way to tackle the situation we just looked at. It’s the same idea except that the call and the put are set to different prices with the put strike price usually lower. When you do that, you will break even if the stock rises above a certain price OR drops below a certain price, “strangling” the possibilities from both ends. Bull and Bear Spreads: That strategy again tackles the question of, “What is going to happen to this stock?” It gives you a sure-fire way to see some cash but with the possibility of trading away a serious profit. Again, it’s all about flexibility. In an example, for a stock that’s now trading at $50, you could buy a call with a strike price of $55 and sell a call with a strike price of $60. You’ll likely pay more to buy your call than you gain from selling the second call. Let’s say it was $0.25 for the $55 contract and $0.60 for the $60, leaving you paying $0.35 in total to set your position. For this to work best, you’re hoping that the stock will end up somewhere between $55 and $60 at the deadline because the second contract will not be exercised and you will make a profit. If it rises above the $60, you’ll still make a profit but it will be capped at that exact profit if your buyer exercises their right to purchase the stock. The downside is that your stock could skyrocket to $65 and you won’t see a profit above the $60 but that can be acceptable if you’re looking to cut down your costs and still make a profit. The example above is a bull spread. That can also work on a bear spread if you reverse the trades and sell your call lower than you buy your call. Cash Secured Puts: That can be used as a way of purchasing a particular stock at a discount. It only works if your account has enough money to actually buy the stock because you will be obliged to do so if the option is exercised. If it isn’t, you’ve made some money because it will expire without forcing you to buy but you’ll still bank the premium in the process. Either way, assuming you really do want that stock, you win. In thats strategy, you’ll set the strike price at the exact price you’re looking to obtain that stock for. The only downside is that it could drop a lot lower and at that point you really won’t feel like you got the best bargain. Out of the money puts have a better chance of expiring without being exercised. If you’re only looking to make profit on the premium or you’re not desperate to own the underlying stock, that can often be your best bet. If you do end up owning the stock, your usual hope is that it will change direction and you can trade it to make another profit. Married Puts: To do that, purchase stock and a put at the same time. That provides an insurance for you and a “floor” to protect you if that stock suddenly plunges. It will make sure you don’t lose the clothes on your back if the stock does plummet but it also has the chance to make a little money if your timing is good and the stock price rises. Rolling Your Positions: We covered that briefly but, just as a reminder, rolling your position can help you increase your profit over time. When you do that, you simply set up a new call as soon as the old one expires in the hope that the stock will continue to move in the same direction it has been doing until now. You will be looking to go up in strike price and out in time to an expiration date. It can be risky because there is no guarantee that the stock will continue to do what it has been doing, so, it’s only worth taking the risk if you think there is a reasonable chance the stock will continue to move in the same direction. If you roll a put, on the other hand, you’re going down in strike price and out in time to deadline because you want to avoid actually selling the stock. For both those alternatives, you’ll be entering a buy to close order and initiating a new contract. In Conclusion From novice to initiated, you’ve now gained the basics of the knowledge that will help you enter the exciting world of options trading. It certainly isn’t everything there is to know, but you now have enough of a grounding to get started. From here on out, it’s all about practice and being conservative as you improve your understanding and develop your own strategies. Only you will know what works best for you, how much risk you want to play with, and how your personal ability to predict and determine the stock market can be best put into practice. As you dip your feet into the water, you’ll start to see profits coming in and you’ll feel that buzz that all options traders enjoy. The more you trade, the more you’ll see all of the fundamental mechanics at play and the more you’ll start to connect the dots and figure out your own personality as a trader. You’re in for a treat. Options trading is rewarding and exciting when done right. Remember to keep that calendar updated and to stay conservative at least in the beginning and you’ll enjoy the learning curve every step of the way! Special Thanks I would like to give special thanks to all the readers from around the globe who chose to share their kind and encouraging words with me. Knowing even just one person found this book helpful means the world to me. If you've benefited from this book at all, I would be honored to have you share your thoughts on it, so that others would get something valuable out of this book too. Your reviews are the fuel for my writing soul, and I'd be forever grateful to see your review, too. Thank you all! Click Here to Leave Your Review Psst… don't forget to grab your FREE bonus chapter while it's still available: CLICK HERE! Table of Contents Taking the Risk What is an Option? Why Options Rather than Stocks? Why is Options trading Worth the Risk? How to Get Started in Options trading Learning the Lingo The Role of the Underlying Stock Understanding the Strike Price Basic Trading: Selling Covered Calls Strategy for Selling Covered Calls Outcomes of a Covered Sell Stepping Up a Tier: Buying Calls Strategies for Buying Calls Understanding Time Value Understanding Volatility Keeping an Eye on Your Calls Exercising Your Right to Buy the Stock How to Buy and Sell Puts Strategies for New Options Traders In Conclusion Special Thanks ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:f05.xhtml SCORE: 10.00 ================================================================================ Foreword I've come a long way from my knuckle‐dragging pit trading days of the 1980s and 1990s. I take the wrapper off hot dogs when I eat them now, and I have also learned a few things about investing after 20 years of meeting people all over the country and teaching them how to trade. One crazy takeaway: Unlucky investors usually make the best traders. Why? Because anyone can get lucky and profit from a random investment, but in the small world of successful traders, the common denominator is quantitative skill. Another crazy takeaway: Anyone can learn these skills with access to the right information. Way back when TD Ameritrade bought thinkorswim in 2009, I negotiated with every bit of leverage I had to personally keep the domain name, tastytrade.com . I had purchased the web address for $9.95 years earlier through GoDaddy, and I was convinced, just as I was with thinkorswim, that the name tastytrade would work. I have no idea why I loved tastytrade.com , but sometimes hunches just seem to work out. tastytrade's raison d'être was to fill the void in the financial media and offer up an untested, goodwill model built around raw, math‐based content. We've spent the last 10 years obsessively building client engagement by introducing complex financial strategies to retail investors. We still answer questions 24 hours a day and teach lessons from what we learned as market makers and software entrepreneurs: all for free. We truly are the guest who won't leave, but we believe that nonstop client engagement is core to motivating traders. I have so many special memories from the last two decades, but one of my favorites was a strange trading story from an early 2001 trip to the desert. It was the first time we did a live trading show in Las Vegas, and a big trader at the event asked me how long it would take to get a fill on a large order using our platform. When I asked for his order, the client told me he wanted 10,000 spreads. This was before electronic spread executions existed, and I figured he was bullshitting me. But, as a show of good faith (and because I didn't want to back down), I told him we'd fill the order within one second. The client was convinced it wasn't going to happen, so I was pretty pleased when I told him, hand signal and all, that his order was filled in less than a second and the price improved by a nickel. We made asses of ourselves, but this is how it all began. Over the years, we continued to form unbreakable relationships with hundreds of thousands of amazing friends, traders, and investors. We gambled together, ate dinner together, had drinks at the bar, laughed when we made money, and cried when we lost money. We told jokes, embarrassed ourselves, humbled each other, and tortured our friends. We focused on building those relationships not only because it was a blast but because we also really saw how it motivated people to learn how to trade and participate in the market. It was key to the success of thinkorswim, and it inspired the founding of tastytrade. When we started tastytrade, our proving ground was an old hip‐hop studio in downtown Chicago. It was a third‐floor walk‐up with a piano as the receptionist's desk and a drum set in the middle of the living room. Old album covers and broken musical instruments were everywhere, yet the energy was undeniable. Our research team consisted of a Guitar Hero champion in a hot dog suit, a few interns, and an ex‐market maker. Our mentor was a sports shock jock whose claim to fame was having sex on the 50‐yard line at Soldier Field, and to top it all off, we had hired a bunch of random comedians from Chicago's famed Second City. Thank God we knew how to trade because we had no clue how to do media. Even worse, I will never forget the day we decided to do HD quality video. I thought, “No way is that what I look like.” That's why tastytrade is so awesome because we figured out a totally new model of financial media when the odds were against us. Lucky investors never figure things out because they never have to: They simply follow the herd and hope for the best. We refused to follow traditional financial media down the path of self‐promotion and financial irrelevance. We found smart people, fed them cheap lunches, made them work crazy hours, gave them free snacks, and mostly let them do their own thing. The result? We changed the world of strategic investing. We knew early on that a book about options trading would add a new layer to our model of engagement and be a powerful tool for creating financial content. Eighteen years ago, I locked myself in our old conference room with one of our cofounders, and we tried to write a book. We hired a professional writer, cleared our schedules, and made the book a priority. Three days later and one and half pages in, we fired the writer and quit the book project to protect our friendship and the future of our firm. Fast forward to early 2021, and I was again bitten by the book bug, but this time, I knew I wasn't up to the task. I asked, as nicely as I am capable of, for two of our young, smart researchers to help. I said, “It's all yours.” Julia and Anton accepted the challenge, and they totally nailed it. I truly believe this is the most logical, informative, and comprehensive book on strategic options trading ever compiled. Unlucky investors can rejoice. No book will ever be a one‐size‐fits‐all holy grail for options trading, but The Unlucky Investor's Guide to Options Trading is the closest thing we have. Tom Sosnoff ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:f06.xhtml SCORE: 18.00 ================================================================================ Preface If the conditions are just right, extraordinary things happen when many individual pieces come together: Water molecules organize and form snowflakes; Cells arrange and create organs; Jet streams combine and cause tornadoes; Grains of sand rally and produce avalanches; Investors panic sell and induce financial crashes. Complex systems are composed of many interacting parts, and emergence occurs when these parts organize to create collective phenomena that no one part is capable of creating alone. Complex systems can be found in nearly every discipline, and the mathematics describing emergent properties is not only fascinating but indicates fundamental similarities between seemingly unrelated complex systems. The extinction of a species of fly due to an invasive species of frog has really nothing to do with financial markets, yet the dynamics of the fly population undergoing ecological collapse look nearly indistinguishable from that of a stock undergoing economic collapse. Many physicists gravitate toward finance because physical systems and financial systems can be analyzed with similar theoretical, statistical, and computational tools. It was my interest in those mathematical connections that drew me to finance initially. However, after placing my first trade at the start of the 2020 crash, I quickly learned the importance of financial intuition as well, particularly when trading options. A trader's intuition comes from experience, but a trader can more efficiently build that intuition by supplementing market engagement with some basic trading philosophies. Many of the papers, books, and blogs I read as a new options trader offered detailed coverage of options theory and its mathematics, but I never encountered a resource that explicitly laid out the most essential elements of practical strategy development. Without a system of core trading principles, applying financial theory, interpreting and analyzing data, and cultivating any sense of market intuition was challenging. However, once a foundation of options trading fundamentals was in place, overcoming the options learning curve became a considerably more manageable process. In my personal case, this foundation developed from conversations with my coworkers at tastytrade (most of which were debates with Anton Kulikov), watching options markets regularly, using options data and theory to build actionable strategies, and a lot of trial and error. My goal in writing this book is to help new traders build their own intuitions more effectively by breaking down the philosophies that formed the basis for my own, beginning with a bit of math and market theory and building from there. Nothing substitutes for experience, and investors' first options trade will likely teach them more than any book. However, it's my hope this framework that Anton and I organized will allow new traders to enter the options market with confidence and gain meaningful value from their first trading experiences, in both the monetary and educational senses. Julia Spina ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:f08.xhtml SCORE: 8.00 ================================================================================ About the Authors Julia Spina is member of the research team and podcast co‐host at tastytrade where she works as a financial educator and options strategist. Drawing from her background in physics and experience with signal processing and data analysis, Julia introduces viewers to topics in quantitative finance and their applications in options strategy development. Prior to transitioning into finance, Julia worked as a regenerative medicine research scientist before attending the University of Illinois at Urbana‐Champaign in 2015. At the University of Illinois, she earned bachelor's degrees in engineering physics (2017) and applied mathematics (2017) and a master's in physics (2018). Her research focus throughout her graduate and undergraduate studies was experimental quantum optics, and her primary projects included investigating the effects of measurement in optical quantum systems and using single‐photon sources to determine the lower limits of human vision and perception. Anton Kulikov is a member of the research team and podcast co‐host at tastytrade and a columnist for the financial lifestyle magazine, Luckbox . With a background in finance, data science, and education, he has spent the last four years developing innovative strategies for the retail options market and educating traders in fundamental economic theory on the show. Anton attended the University of Illinois at Urbana‐Champaign where he earned bachelor's degrees in finance (2018) and economics (2018) and worked at the Margolis Market Information Lab. During his time at the University of Illinois, Anton developed coursework on derivatives and capital markets, and taught classes and workshops on financial software at the Gies College of Business. Tom Sosnoff is an online brokerage innovator, financial educator, and the founder and co‐CEO of tastytrade. Tom is a serial entrepreneur who cofounded thinkorswim in 1999, tastytrade in 2011, tastyworks in 2017, helped to launch the award‐winning Luckbox magazine in 2019, and in 2020 created the first new futures exchange in 20 years, The Small Exchange. Leveraging more than 20 years of experience as a CBOE market maker, Tom is driven by the passion to educate self‐directed investors. After his years on the trading floor, he saw the need to build and design superior software platforms and brokerage firms that specialized in complex financial strategies. His efforts ultimately changed the way options and futures are traded and how digital financial media is produced and consumed. Currently, Tom hosts tastytrade LIVE and continues to drive innovation and know‐how for the do‐it‐yourself investor. Tom has been named to Techweek 's Tech 100 list, Crain's Chicago Business 's Tech 50, and has spoken at more than 500 events across the globe. Tom received the Ernst & Young Entrepreneur of the Year Award and has been featured by prominent publications such as the The Wall Street Journal, Investor's Business Daily, Chicago Tribune, Crain's Chicago Business, Traders Magazine , and Barron's . ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:f09.xhtml SCORE: 51.00 ================================================================================ Introduction: Why Trade Options? The house always wins . This cautionary quote is certainly true, but it does not tell the entire story. From table limits to payout odds, every game in a casino is designed to give the house a statistical edge. The casino may take large, infrequent losses at the slot machines or small, frequent losses at the blackjack table, but as long as patrons play long enough, the house will inevitably turn a profit. Casinos have long relied on this principle as the foundation of their business model: People can either bet against the house and hope that luck lands in their favor or be the house and have probability on their side. Unlike casinos, where the odds are fixed against the players, liquid financial markets offer a dynamic, level playing field with more room to strategize. However, similar to casinos, a successful trader does not rely on luck. Rather, traders' long‐term success depends on their ability to obtain a consistent, statistical edge from the tools, strategies, and information available to them. Today's markets are becoming increasingly accessible to the average person, as online and commission‐free trading have basically become industry standards. Investors have access to an almost unlimited selection of strategies, and options play an interesting role in this development. An option is a type of financial contract that gives the holder the right to buy or sell an asset on or before some future date, a concept that will be explained more in the following chapter. Options have tunable risk‐reward profiles, allowing traders to reliably select the probability of profit, max loss, and max profit of a position and potentially profit in any type of market (bullish, bearish, or neutral). These highly versatile instruments can be used to hedge risk and diversify a portfolio, or options can be structured to give more risk‐tolerant traders a probabilistic edge. In addition to being customizable according to specific risk‐reward preferences, options are also tradable with accounts of nearly any size because they are leveraged instruments. In the world of options, leverage refers to the ability to gain or lose more than the initial investment of a trade. An investor may pay $100 for an option and make $200 by the end of the trade, or an investor may make $100 by selling an option and lose $200 by the end of the trade. Leverage may seem unappealing because of its association with risk, but it is not inherently dangerous. When misused , leverage can easily wreak financial havoc. However, when used responsibly, the capital efficiency of leverage is a powerful tool that enables traders to achieve the same risk‐return exposure as a stock position with significantly less capital. There is no free lunch in the market. A leveraged instrument that has a 70% chance of profiting must come with some trade‐off of risk, risk which may even be undefined in some cases. This is why the core principle of sustainable options trading is risk management. Just as casinos control the size of jackpot payouts by limiting the maximum amount a player can bet, options traders must control their exposure to potential losses from leveraged positions by limiting position size. And just as casinos diversify risk across different games with different odds, strategy diversification is essential to the long‐term success of an options portfolio. Beyond the potential downside risk of options, other factors can make them unattractive to investors. Unlike equities, which are passive instruments, options require a more active trading approach due to their volatile nature and time sensitivity. Depending on the choice of strategies, options portfolios should be monitored anywhere from daily to once every two weeks. Options trading also has a fairly steep learning curve and requires a larger base of math knowledge compared to equities. Although the mathematics of options can easily become complicated and burdensome, for the type of options trading covered in this book, trading decisions can often be made with a selection of indicators and intuitive, back‐of‐the‐envelope calculations. The goal of this book is to educate traders to make personalized and informed decisions that best align with their unique profit goals and risk tolerances. Using statistics and historical backtests, this book contextualizes the downside risk of options, explores the strategic capacity of these contracts, and emphasizes the key risk management techniques in building a resilient options portfolio. To introduce these concepts in a straightforward way, this book begins with discussion of the math and finance basics of quantitative options trading ( Chapter 1 ), followed by an intuitive explanation of implied volatility ( Chapter 2 ) and trading short premium ( Chapter 3 ). With these foundational concepts covered, the book then moves onto trading in practice, beginning with buying power reduction and option leverage ( Chapter 4 ), followed by trade construction ( Chapter 5 ) and trade management ( Chapter 6 ). Chapter 7 covers essential topics in portfolio management, and Chapter 8 covers supplementary topics in advanced portfolio management. Chapter 9 provides a brief commentary on atypical trades (Binary Events). The book concludes with a final chapter of key takeaways ( Chapter 10 ) and an appendix of mathematical topics. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c01.xhtml SCORE: 815.00 ================================================================================ Chapter 1 Math and Finance Preliminaries The purpose of this book is to provide a qualitative framework for options investing based on a quantitative analysis of financial data and theory. Mathematics plays a crucial role when developing this framework, but it is predominantly a means to an end. This chapter therefore includes a brief overview of the prerequisite math and financial concepts required to understand this book. Because this isn't in‐depth coverage of the following topics, we encourage you to explore the supplemental texts listed in the references section for those mathematically inclined. Formulae and their descriptions are included in several sections for reference, but they are not necessary to follow the remainder of the book. Stocks, Exchange‐Traded Funds, and Options From swaptions to non‐fungible tokens (NFTs), new instruments and opportunities frequently emerge as markets evolve. By the time this book reaches the shelf, the financial landscape and the instruments occupying it may be very different from when it was written. Rather than focus on a wide range of instruments, this book discusses fundamental trading concepts using a small selection of asset classes (stocks, exchange‐traded funds, and options) to formulate examples. A share of stock is a security that represents a fraction of ownership of a corporation. Stock shares are normally issued by the corporation as a source of funding, and these instruments are usually publicly traded on stock exchanges, such as the New York Stock Exchange (NYSE) and the Nasdaq. Shareholders are entitled to a fraction of the company's assets and profits based on the proportion of shares they own relative to the number of outstanding shares. An exchange‐traded fund (ETF) is a basket of securities, such as stocks, bonds, or commodities. Like stocks, shares of ETFs are traded publicly on stock exchanges. Similar to mutual funds, these instruments represent a fraction of ownership of a diversified portfolio that is usually managed professionally. These assets track aspects of the market such as an index, sector, industry, or commodity. For example, SPDR S&P 500 (SPY) is a market index ETF tracking the S&P 500, Energy Select Sector SPDR Fund (XLE) is a sector ETF tracking the energy sector, and SPDR Gold Trust (GLD) is a commodity ETF tracking gold. ETFs are typically much cheaper to trade than the individual assets in an ETF portfolio and are inherently diversified. For instance, a share of stock for an energy company is subject to company‐specific risk factors, while a share of an energy ETF is diversified over several energy companies. When assessing the price dynamics of a stock or ETF and comparing the dynamics of different assets, it is common to convert price information into returns. The return of a stock is the amount the stock price increased or decreased as a proportion of its value rather than a dollar amount. Returns can be scaled over any time frame (daily, monthly, annual), with calculations typically calling for daily returns. The two most common types of returns are simple returns, represented as a percentage and calculated using Equation (1.1) , and log returns, calculated using Equation (1.2) . The logarithm's mathematical definition and properties are covered in the appendix for those interested, but that information is not necessary to know to follow the remainder of the book. (1.1) (1.2) where is the price of the asset on day and is the price of the asset the prior day. For example, an asset priced at $100 on day 1 and $101 on day 2 has a simple daily return of 0.01 (1%) and a log return of 0.00995. Simple and log returns have different mathematical characteristics (e.g., log returns are time‐additive), which impact more advanced quantitative analysis. However, these factors are not relevant for the purposes of this book because the difference between log returns and simple returns is fairly negligible when working on daily timescales. Simple daily returns are used for all returns calculations shown. An option is a type of financial derivative, meaning its price is based on the value of an underlying asset. Options contracts are either traded on public exchanges (exchange‐traded options) or traded privately with little regulatory oversight (over‐the‐counter [OTC] options). As OTC options are nonstandardized and usually inaccessible for retail investors, only exchange‐traded options will be discussed in this book. An option gives the holder the right (but not the obligation) to buy or sell some amount of an underlying asset, such as a stock or ETF, at a predetermined price on or before a future date. The two most common styles of options are American and European options. American options can be exercised at any point prior to expiration, and European options can only be exercised on the expiration date. 1 Because American options are generally more popular than European options and offer more flexibility, this book focuses on American options. The most basic types of options are calls and puts. American calls give the holder the right to buy the underlying asset at a certain price within a given time frame, and American puts give the holder the right to sell the underlying asset. The contract parameters must be specified prior to opening the trade and are listed below: The underlying asset trading at the spot price, or the current per share price . The number of underlying shares. One option usually covers 100 shares of the underlying, known as a one lot. The price at which the underlying shares can be bought or sold prior to expiration. This price is called the strike price . The expiration date, after which the contract is worthless. The time between the present day and the expiration date is the contract's duration or days to expiration (DTE). Note that the price of the option is commonly denoted as C for calls, P for puts, and V if the type of contract is not specified. Options traders may buy or sell these contracts, and the conditions for profitability differ depending on the choice of position. The purchaser of the contract pays the option premium (current market price of the option) to adopt the long side of the position. This is also known as a long premium trade. The seller of the contract receives the option premium to adopt the short side of the position, thus placing a short premium trade. The choice of strategy corresponds to the directional assumption of the trader. For calls and puts, the directional assumption is either bullish, assuming the underlying price will increase, or bearish, assuming the underlying price will decrease. The directional assumptions and scenarios for profitability for these contracts are summarized in the following table. Table 1.1 The definitions, conditions for profitability, and directional assumptions for long/short calls/puts. Call Put Long Purchase the right to buy an underlying asset at the strike price prior to the expiration date. Profits increase as the price of the underlying increases above the strike price . Directional assumption: Bullish Purchase the right to sell an underlying asset at the strike price prior to the expiration date. Profits increase as the price of the underlying decreases below the strike price . Directional assumption: Bearish Short Sell the right to buy an underlying asset at the strike price prior to the expiration date. Profits increase as the price of the underlying decreases below the strike price . Directional assumption: Bearish Sell the right to sell an underlying asset at the strike price prior to the expiration date. Profits increase as the price of the underlying increases above the strike price . Directional assumption: Bullish The relationship between the strike price and the current price of the underlying determines the moneyness of the position. This is equivalently the intrinsic value of a position, or the value of the contract if it were exercised immediately. Contracts can be described as one of the following, noting that options cannot have negative intrinsic value: In‐the‐money (ITM): The contract would be profitable if it was exercised immediately and thus has intrinsic value. Out‐of‐the‐money (OTM): The contract would result in a loss if it was exercised immediately and thus has no intrinsic value. At‐the‐money (ATM): The contract has a strike price equal to the price of the underlying and thus has no intrinsic value. The intrinsic value of a position is based entirely on the type of position and the choice of strike price relative to the price of the underlying: Call options Intrinsic Value = Either (stock price – strike price) or 0 ITM: OTM: ATM: Put options Intrinsic Value = Either or 0 ITM: OTM: ATM: For example, consider a 45 DTE put contract with a strike price of $100: Scenario 1 (ITM): The underlying price is $95. In this case, the intrinsic value of the put contract is $5 per share. Scenario 2 (OTM): The underlying price is $105. In this case, the put contract has no intrinsic value. Scenario 3 (ATM): The underlying price is $100. In this case, the put is also considered to have no intrinsic value. The value of an option also depends on speculative factors, driven by supply and demand. The extrinsic value of the option is the difference between the current market price for the option and the intrinsic value of the option. Again, consider a 45 DTE put contract with a strike price of $100 on an underlying with a current price per share of $105. Suppose that, due to a period of recent market turbulence, investors are fearful the underlying price will crash within the next 45 days and create a demand for these OTM put contracts. The surge in demand inflates the price of the put contract to $10 per share. Therefore, because the put contract has no intrinsic value but has a market price of $10, the extrinsic value of the contract is $10 per share. If, instead, the price of the underlying is $95 and the price of the ITM put is still $10 per share, then the contract will have $5 in intrinsic value and $5 in extrinsic value. The profitability of an option ultimately depends on both intrinsic and extrinsic factors, and it is calculated as the difference between the intrinsic value of an option and the cost of the contract. Mathematically, profit and loss (P/L) approximations for long calls and puts at exercise are given by the following equations: 2 (1.3) (1.4) where the max function simply outputs the larger of the two values. For instance, equals 1 while equals 0. The P/Ls for the corresponding short sides are merely Equations (1.3) and (1.4) multiplied by –1. Following is a sample trade that applies the long call profit formula. Example trade: A call with 45 DTE duration is traded on an underlying that is currently priced at $100 . The strike price is $105 and the long call is currently valued at $100 per one lot ($1 per share). Scenario 1: The underlying increases to $105 by the expiration date. Long call P/L: Short call P/L: +$100. Scenario 2: The underlying increases to $110 by the expiration date. Long call P/L: Short call P/L: –$400. Scenario 3: The underlying decreases to $95 by the expiration date. Long call P/L: Short call P/L: +$100. The trader adopting the long position pays the seller the option premium upfront and profits when the intrinsic value exceeds the price of the contract. The short trader profits when the intrinsic value remains below the price of the contract, especially when the position expires worthless (no intrinsic value). The extrinsic value of an option generally decreases over the duration of the contract, as uncertainty around the underlying price and uncertainty around the profit potential of the option decrease. As a position nears expiration, the price of an option converges toward its intrinsic value. Options pricing clearly plays a large role in options trading. To develop an intuitive understanding around how options are priced, understanding the mathematical assumptions around market efficiency and price dynamics is critical. The Efficient Market Hypothesis Traders must make a number of assumptions prior to placing a trade. Options traders must make directional assumptions about the price of the underlying over a given time frame: bearish (expecting price to decrease), bullish (expecting price to increase), or neutral (expecting price to remain relatively unchanged). Options traders also must make assumptions about the current value of an option. If options contracts are perceived as overvalued, long positions are less likely to profit. If options contracts are perceived as undervalued, short positions are less likely to profit. These assumptions about underlying and option price dynamics are a personal choice, but traders can formulate consistent assumptions by referring to the efficient market hypothesis (EMH). The EMH states that instruments are traded at a fair price, and the current price of an asset reflects some amount of available information. The hypothesis comes in three forms: Weak EMH: Current prices reflect all past price information. Semi‐strong EMH: Current prices reflect all publicly available information. Strong EMH: Current prices reflect all possible information. No variant of the EMH is universally accepted or rejected. The form that a trader assumes is subjective, and methods of market analysis available are limited depending on that choice. Proponents of the strong EMH posit that investors benefit from investing in low‐cost passive index funds because the market is unbeatable. Opponents believe the market is beatable by exploiting inefficiencies in the market. Traders who accept the weak EMH believe technical analysis (using past price trends to predict future price trends) is invalidated, but fundamental analysis (using related economic data to predict future price trends) is still viable. Traders who accept the semi‐strong EMH assume fundamental analysis would not yield systematic success but trading according to private information would. Traders who accept the strong EMH maintain that even insider trading will not result in consistent success and no exploitable market inefficiencies are available to anyone. This book focuses on highly liquid markets, and inefficiencies are assumed to be minimal. More specifically, this book assumes a semi‐strong form of the EMH. Rather than constructing portfolios according to forecasts of future price trends, the purpose of this text is to demonstrate how trading options according to current market conditions and directional volatility assumptions (rather than price assumptions) has allowed options sellers to consistently outperform the market. This “edge” is not the result of some inherent market inefficiency but rather a trade‐off of risk. Recall the example long call trade from the previous section. Notice that there are more scenarios in which the short trader profits compared to the long trader. Generally, short premium positions are more likely to yield a profit compared to long premium positions. This is because options are assumed to be priced efficiently and scaled according to the perceived risk in the market, meaning that long positions only profit when the underlying has large directional moves outside of expectations. As these types of events are uncommon, options contracts go unused the majority of the time and short premium positions profit more often than long positions. However, when those large, unexpected moves do occur, the short premium positions are subject to potentially massive losses. The risk profiles for options are complex, but they can be intuitively represented with probability distributions. Probability Distributions To better understand the risk profiles of short options, this book utilizes basic concepts from probability theory, specifically random variables and probability distributions. Random variables are formal stand‐ins for uncertain quantities. The probability distribution of a random variable describes possible values of that quantity and the likelihood of each value occurring. Generally, probability distributions are represented by the symbol , which can be read as “the probability that.” For example, . Random variables and probability distributions are tools for working with probabilistic systems (i.e., systems with many unpredictable outcomes), such as stock prices. Although future outcomes cannot be precisely predicted, understanding the distribution of a probabilistic system makes it possible to form expectations about the future, including the uncertainty associated with those expectations. Let's begin with an example of a simple probabilistic system: rolling a pair of fair, six‐sided dice. In this case, if represents the sum of the dice, then is a random variable with 11 possible values ranging from 2 to 12. Some of these outcomes are more likely than others. Since, for instance, there are more ways to roll a sum of 7 ([1,6], [2,5], [3,4], [4,3], [5,2], [6,1]) than a sum of 10 ([4,6], [5,5], [6,4]), there is a higher probability of rolling a 7 than a 10. Observing that there are 36 possible rolls ([1,1], [1,2], [2,1], etc.) and that each is equally likely, one can use symbols to be more precise about this: The distribution of can be represented elegantly using a histogram. These types of graphs display the frequency of different outcomes, grouped according to defined ranges. When working with measured data, histograms are used to estimate the true underlying probability distribution of a probabilistic system. For this fair dice example, there will be 11 bins, corresponding to the 11 possible outcomes. This histogram is shown below in Figure 1.1 , populated with data from 100,000 simulated dice rolls. Figure 1.1 A histogram for 100,000 simulated rolls for a pair of fair dice. This diagram shows the likelihood of each outcome occurring according to this simulation (e.g., the height of the bin ranging from 6.5 to 7.5 is near 17%, indicating that 7 occurred nearly 17% of the time in the 100,000 trials). Distributions like the ones shown here can be summarized using quantitative measures called moments . 3 The first two moments are mean and variance. Mean (first moment): Also known as the average and represented by the Greek letter (mu), this value describes the central tendency of a distribution. This is calculated by summing all the observed outcomes together and dividing by the number of observations : (1.5) For distributions based on statistical observations with a sufficiently large number of occurrences , the mean corresponds to the expected value of that distribution. The expected value of a random variable is the weighted average of outcomes and the anticipated average outcome over future trials. The expected value of a random variable , denoted , can be estimated using statistical data and Equation (1.5) , or if the unique outcomes ( ) and their respective probabilities are known, then the expected value can also be calculated using the following formula: (1.6) In the dice sum example, represented with random variable , the possible outcomes (2, 3, 4, …, 12) and the probability of each occurring (2.78%, 5.56%, 8.33%, …, 2.78%) are known, so the expected value can be determined as follows: The theoretical long‐term average sum is seven. Therefore, if this experiment is repeated many times, the mean of the observations calculated using Equation (1.5) should yield an output close to seven. Variance (second moment): This is the measure of the spread, or variation, of the data points from the mean of the distribution. Standard deviation, represented with by the Greek letter (sigma), is the square root of variance and is commonly used as a measure of uncertainty (equivalently, risk or volatility). Distributions with more variance are wider and have more uncertainty around future outcomes. Variance is calculated according to the following: 4 (1.7) When a large portion of data points are dispersed far from the mean, the variance of the entire set is large, and uncertainty on measurements from that system is significant. The variance of a random variable X , denoted ( X ), can also be calculated in terms of the expected value, [ X ]: (1.8) For the dice sum random variable, D , the possible outcomes (2, 3, 4, …, 12) and the probability of each occurring (2.78%, 5.56%, 8.33%, …, 2.78%) are known, so the variance of this experiment is as follows: This equation indicates that the spread of the distribution for this random variable is around 5.84 and the uncertainty (standard deviation) is approximately 2.4 (shown in Figure 1.2 ). One can compare these theoretical estimates for the mean and standard deviation of the dice sum experiment to the values measured from statistical data. The calculated first and second moments from the simulated dice roll experiment are plotted in Figure 1.2 for comparison. Obtaining a distribution average near 7.0 makes intuitive sense because 7 is the most likely sum to roll out of the possible outcomes. The standard deviation indicates that the uncertainty associated with that expected value is near 2.4. Inferring from the shape of the distribution, which has most of the probability mass concentrated near the center, one can conclude that on any given roll the outcome will most likely fall between five and nine. The distribution just shown is symmetric about the mean, but probability distributions are often asymmetric. To quantify the degree of asymmetry for a distribution, the third moment is used. Skew (third moment): This is a measure of the asymmetry of a distribution. A distribution's skew can be positive, negative, or zero and depends on whether the tail to the right of the mean is larger (positive skew), to the left is larger (negative skew), or equal on both sides (zero skew). Unlike mean and standard deviation, which have units defined by the random variable, skew is a pure number that quantifies the degree of asymmetry according to the following formula: (1.9) Figure 1.2 A histogram for 100,000 simulated dice rolls with fair dice. Included is the mean of the distribution (solid line) and the standard deviation of the distribution on either side of the mean (dotted line), both calculated using the observations from the simulated experiment. The average of this distribution was 7.0 and the standard deviation was 2.4, consistent with the theoretical estimates. The concept of skew and its applications can be best understood with a modification to the dice rolling example. Suppose that the dice are biased rather than fair. Let's consider two scenarios: a pair of unfair dice with a small number bias (two and three more likely) and a pair of unfair dice with a large number bias (four and five more likely). The probabilities of each number appearing on each die for the different cases are shown in Table 1.2 . Table 1.2 The probability of each number appearing on each die in the three different scenarios, one fair and two unfair. Probability of Number Appearing on Each Die Die Number Fair Unfair (Small Number Bias) Unfair (Large Number Bias) 1 16.67% 10% 10% 2 16.67% 30% 10% 3 16.67% 30% 10% 4 16.67% 10% 30% 5 16.67% 10% 30% 6 16.67% 10% 10% When rolling the fair pair and plotting the histogram of the possible sums, the distribution is symmetric about the mean and has a skew of zero. However, the distributions when rolling the unfair dice are skewed, as shown in Figures 1.3 (a) and (b). The skew of a distribution is classified according to where the majority of the distribution mass is concentrated. Remember that the positive side is to the right of the mean and the negative side is to the left. The histogram in Figure 1.3 (a) has a longer tail on the positive side and has the most mass concentrated on the negative side of the mean: This is an example of positive skew (skew = 0.45). The histogram in Figure 1.3 (b) has a longer tail on the negative side and has the majority of the mass concentrated on the positive side of the mean: This is an example of negative skew (skew = –0.45). When a distribution has skew, the interpretation of standard deviation changes. In the example with fair dice, the expected value of the experiment is 2.4, suggesting that any given trial will most likely have an outcome between five and nine. This is a valid interpretation because the distribution is symmetric about the mean and most of the distribution mass is concentrated around it. However, consider the distribution in the unfair example with the large number bias. This distribution has a mean of 7.8 and a standard deviation of 2.0, naively suggesting that the outcome will most likely be between six and nine with the outcomes on either side being equally probable. However, because the majority of the occurrences are concentrated on the positive side of the mean (roughly 60% of occurrences), the uncertainty is not symmetric. This concept will be discussed in more detail in a later chapter, as distributions of financial instruments are commonly skewed, and there is ambiguity in defining risk under those circumstances. Figure 1.3 (a) A histogram for 100,000 simulated dice rolls with unfair dice, biased such that smaller numbers (2 and 3) are more likely to appear on each die. (b) A histogram for 100,000 simulated dice rolls with unfair dice, biased such that larger numbers (4 and 5) are more likely to appear on each die. Mathematicians and scientists have encountered some probability distributions repeatedly in theory and applications. These distributions have, in turn, received a great deal of study. Assuming the underlying distribution of an experiment resembles a well known form can often greatly simplify statistical analysis. The normal distribution (also known as the Gaussian distribution or the bell curve) is arguably one of the most well‐known probability distributions and foundational in quantitative finance. It describes countless different real‐world systems because of a result known as the central limit theorem. This theorem says, roughly, that if a random variable is made by adding together many independently random pieces, then, regardless of what those pieces are, the result will be normally distributed. For example, the distribution in the two‐dice example is fairly non‐normal, being relatively triangular and lacking tails. If one considered the sum of more and more dice, each of which is an independent random variable, the distribution would gradually take on a bell shape. This is shown in Figure 1.4 . The normal distribution is a symmetric, bell‐shaped distribution, meaning that equidistant events on either side of the center are equally likely and the skew is zero. The distribution is centered around the mean, and outcomes further away from the mean are less likely. The normal distribution has the intriguing property that 68% of occurrences fall within of the mean, 95% of occurrences are within of the mean, and 99.7% of occurrences are within of the mean. Figure 1.5 plots a normal distribution. These probabilities can be used to roughly contextualize distributions with similar geometry. For example, in the fair dice pair model, the expected value of the fair dice experiment was 7.0, and the standard deviation was 2.4. With the assumption of normality, one would infer there is roughly a 68% chance that future outcomes will fall between five and nine. The true probability is 66.67% for this random variable, indicating that the normality assumption is not exactly correct but can be used for the purposes of approximation. As more dice are added to the example, this approximation becomes increasingly accurate. Figure 1.4 A histogram for 100,000 simulated rolls with a group of fair, six‐sided dice numbering (a) 2, (b) 4, or (c) 6. Understanding distribution statistics and the properties of the normal distribution is incredibly useful in quantitative finance. The expected return of a stock is usually estimated by the mean return, and the historic risk is estimated with the standard deviation of returns (historical volatility). Stock log returns are also widely assumed to be normally distributed. Although, this is only approximately true because the overwhelming majority of stocks and ETFs have skewed returns distributions. 5 Regardless, this normality estimation provides a quantitative framework for expectations around future price moments. This approximation also simplifies mathematical models of price dynamics and options pricing, the most notable of which is the Black‐Scholes model. Figure 1.5 A detailed plot of the normal distribution and the corresponding probabilities at each standard deviation mark. The Black‐Scholes Model The Black‐Scholes options pricing formalism revolutionized options markets when it was published in 1973. It provided the first popular quantitative framework for estimating the fair price of an option according to the contract parameters and the characteristics of the underlying. The Black‐Scholes equation models the price evolution of a European‐style option (an option that can only be exercised at expiration) within the context of the broader financial market. The corresponding Black‐Scholes formula uses this equation to estimate the theoretical price of that option according to its parameters. It's important to note that the purpose of this Black‐Scholes section is not to elucidate the underlying mathematics of the model, which can be quite complicated. The output of the model is merely a theoretical value for the fair price of an option. In practice, an option's price typically deviates from this value because of market speculation and supply and demand, which this model does not take into account. Rather, it is essential to have at least a superficial grasp of the Black‐Scholes model to understand (1) the foundational assumptions of financial markets and (2) where implied volatility (a gauge for the market's perception of risk) comes from. The Black‐Scholes model is based on a set of assumptions related to the dynamics of financial assets and the market as a whole. The assumptions are as follows: The market is frictionless (i.e., there are no transaction fees). Cash can be borrowed and lent in any amount, even fractional, at the risk‐free rate (the theoretical rate of return of an investment with no risk, a macroeconomic variable assumed to be constant). There is no arbitrage opportunity (i.e., profits in excess of the risk‐free rate cannot be made without risk). Stocks can be bought and sold in any amount, even fractional amounts. Stocks do not pay dividends. 6 Stock log returns follow Brownian motion with constant drift and volatility (the theoretical mean and standard deviation of annual log returns). A Brownian motion, or a Wiener process, is a type of stochastic process or a system that experiences random fluctuations as it evolves with time. Traditionally used to describe the positional fluctuations of a particle suspended in fluid at thermal equilibrium, 7 a standard Wiener process (denoted W ( t )) is mathematically defined by the conditions in the grey box. The mathematical definition can be overlooked if preferred, as the intuition behind the mathematics is more crucial for understanding the theoretical foundation of options pricing and follows after. (i.e., the process initially begins at location 0). is almost surely continuous. The increments of , defined as where , are normally distributed with mean 0 and variance (i.e., the steps of the Wiener process are normally distributed with constant mean of 0 and variance of ). Disjoint increments of are independent of one another (i.e., the current step of the process is not influenced by the previous steps, nor does it influence the subsequent steps). Simplified, a Wiener process is a process that follows a random path. Each step in this path is probabilistic and independent of one another. When disjoint steps of equal duration are plotted in a histogram, that distribution is normal with a constant mean and variance. Brownian motion dynamics are driven by this underlying process. These conditions can be best understood visually, which will also demonstrate why this assumption appears in the development of the Black‐Scholes model as an approximation for price dynamics. Figures 1.6 and 1.7 illustrate the characteristics of Brownian motion, and Figure 1.8 illustrates the dynamics of SPY from 2010–2015 8 for the purposes of comparison. The price trends of SPY in Figure 1.8 (b) appear fairly similar to the Brownian motion cumulative horizontal displacements shown in Figure 1.6 (c). The daily returns for SPY are more prone to outlier moves compared to the horizontal displacements of Brownian motion but share some characteristics. The symmetric geometry of the SPY returns histogram bears resemblance to the fairly normal distribution of horizontal displacements, with the tails of the distribution being more prominent as a result of the history of large price moves. Figure 1.6 (a) The 2D position of a particle in a fluid, moving with Brownian motion. The particle begins at a coordinate of and drifts to a new location over 1,000 steps. (b) The horizontal displacements 9 of the particle (i.e., the movements of the particle along the X‐axis over 1,000 steps). (c) The cumulative horizontal displacement of the particle over 1,000 steps. Similarities are clear between price dynamics and Brownian motion, but this remains a highly simplified model of price dynamics. In reality, stock log returns are not normal and are typically skewed to the upside or downside, depending on the specific underlying. Additionally, the drift and volatility of a stock are not directly observable, and it cannot be experimentally confirmed whether or not these variables are constant. Stock volatility approximated with historical return data is rarely constant with time (a phenomenon known as heteroscedasticity). Stock returns are also not typically independent of one another across time (a phenomenon known as autocorrelation), which is a requirement for this model. Figure 1.7 The distribution of the horizontal displacements of the particle over 1,000 steps. As characteristic of a Wiener process, the increments are normally distributed, have a mean of zero and variance (which equals 1 in this case). This figure indicates that horizontal step sizes between –1 and 1 are most common, and step sizes with a larger magnitude than 1 are less common. Figure 1.8 The (a) daily returns, (b) price, and (c) daily returns histogram for SPY from 2010–2015. Although the normality assumption is not entirely accurate, making this simplification allows the development of the rest of this theoretical framework shown in the gray box. The formalism in the gray box is supplemental material for the mathematically inclined. The interpretation of the math, which is more significant, follows after. It should be noted that the Black‐Scholes model technically assumes that stock prices follow geometric Brownian motion , which is more accurate because price movements cannot be negative. Geometric Brownian motion is a slight modification of Brownian motion and requires that the logarithm of the signal follow Brownian motion rather than the signal itself. As it relates to price dynamics, this suggests that the log returns are normally distributed with constant drift (return rate) and volatility. 10 For the price of a stock that follows a geometric Brownian motion, the dynamics of the asset price can be represented with the following stochastic differential equation: 11 (1.10) where is the price of the stock at time t , is the Wiener process at time , is a drift rate, and is the volatility of the stock. The drift rate and volatility of the stock are assumed to be constant, and it's important to reiterate that neither of these variables are directly observable. These constants can be approximated using the average return of a stock and the standard deviation of historical returns, but they can never be precisely known. The equation states that each stock price increment is driven by a predictable amount of drift (with expected return ) and some amount of random noise . In other words, this equation has two components: one that models deterministic price trends and one that models probabilistic price fluctuations . The important takeaway from this observation is that inherent uncertainty is in the price of stock, represented with the contributions from the Wiener process. Because the increments of a Wiener process are independent of one another, it also is common to assume that the weak EMH holds at minimum, in addition to the normality of log returns. Using this equation as a basis for the derivation, assuming a riskless options portfolio must earn the risk‐free rate, and rearranging terms, the Black‐Scholes equation follows: (1.11) where is the price of a European call (with a dependence on and ), is the price of the stock (with a dependence on ), is the risk‐free rate, and is the volatility of the stock. The Black‐Scholes formula can be calculated by solving the Black‐Scholes equation according to boundary conditions given by the payoff at expiration of European options. The formula, which provides the value of a European call option for a non‐dividend‐paying stock, is given by the following equation: (1.12) where is the value of the standard normal cumulative distribution function at and similarly for , T is the time that the option will expire ( is the duration of the contract), is the price of the stock at time t , K is the strike price of the option, and and are given by the following: (1.13) (1.14) where is the volatility of the stock. If the equations seem gross, it's because they are. Again, the purpose of this section is not to describe the underlying mechanics of the Black‐Scholes model in detail. Rather, Equations (1.10) through (1.14) are included to emphasize three important points. There is inherent uncertainty in the price of stock. Stock price movements are also assumed to be independent of one another and log‐normally distributed. 12 An estimate for the fair price of an option can be calculated according to the price of the stock, the volatility of the stock, the risk‐free rate, the duration of the contract, and the strike price. The volatility of a stock, which plays an important role in estimating the risk of an asset and the valuation of an option, cannot be directly observed. This suggests that the “true risk” of an instrument can never be exactly known. Risk can only be approximated using a metric, such as historical volatility or the standard deviation of the historical returns over some timescale, typically matching the duration of the contract. Other than using a past‐looking metric, such as historical volatility to estimate the risk of an asset, one can also infer the risk of an asset from the price of its options. As stated previously, the Black‐Scholes model only gives a theoretical estimate for the fair price of an option. Once the contract is traded on the options market, the price of the contract is often driven up or down depending on speculation and perceived risk. The deviation of an option's price from its theoretical value as a result of these external factors is indicative of implied volatility . When initially valuing an option, the historical volatility of the stock has been priced into the model. However, when the price of the option trades higher or lower than its theoretical value, this indicates that the perceived volatility of the underlying deviates from what is estimated by historical returns. Implied volatility may be the most important metric in options trading. It is effectively a measure of the sentiment of risk for a given underlying according to the supply and demand for options contracts. For an example, suppose a non‐dividend‐paying stock currently trading at $100 per share has a historical 45‐day returns volatility of 20%. Suppose its call option with a 45‐day duration and a strike price of $105 is trading at $2 per share. Plugging these parameters into the Black‐Scholes model, this call option should theoretically be trading at $1 per share. However, demand for this position has increased the contract price significantly. For the model to return a call price of $2 per share, the volatility of this underlying would have to be 28% (assuming all else is constant). Therefore, although the historical volatility of the underlying is only 20%, the perceived risk of that underlying (i.e., the implied volatility) is actually 28%. To conclude, the primary purpose of this section was not to dive into the math of the Black‐Scholes. These concepts were, instead, introduced to justify the following axioms that are foundational to this book: Profits cannot be made without risk. Stock log returns have inherent uncertainty and are assumed to follow a normal distribution. Stock price movements are independent across time (i.e., future price changes are independent of past price changes, requiring a minimum of the weak EMH). Options can theoretically be priced fairly based on the price of the stock, the volatility of the stock, the risk‐free rate, the duration of the contract, and the strike price. The volatility of an asset cannot be directly observed, only estimated using metrics like historical volatility or implied volatility. The Greeks Other than implied volatility, the Greeks are the most relevant metrics derived from the Black‐Scholes model. The Greeks are a set of risk measures, and each describes the sensitivity of an option's price with respect to changes in some variable. The most essential Greeks for options traders are delta , gamma , and theta . Delta is one of the most important and widely used Greeks. It is a first‐order 13 Greek that measures the expected change in the option price given a $1 increase in the price of the underlying (assuming all other variables stay constant). The equation is as follows: (1.15) where V is the price of the option (a call or a put) and S is the price of the underlying stock, noting that ∂ is the partial derivative. The value of delta ranges from –1 to 1, and the sign of delta depends on the type of position: Long stock: is 1. Long call and short put: is between 0 and 1. Long put and short call: is between –1 and 0. For example, the price of a long call option with a delta of 0.50 (denoted 50 because that is the total for a one lot, or 100 shares of underlying) will increase by approximately $0.50 per share when the price of the underlying increases by $1. This makes intuitive sense because a long stock, a long call, and a short put are all bullish strategies, meaning they will profit when the underlying price increases. Similarly, because long puts and short calls are bearish, they will take a loss when the underlying price increases. Delta has a sign and magnitude, so it is a measure of the degree of directional risk of a position. The sign of delta indicates the direction of the risk, and the magnitude of delta indicates the severity of exposure. The larger the magnitude of delta, the larger the profit and loss potential of the contract. This is because positions with larger deltas are closer to/deeper ITM and more sensitive to changes in the underlying price. A contract with a delta of 1.0 (100 ) has maximal directional exposure and is maximally ITM. 100 options behave like the stock price, as a $1 increase in the underlying creates a $1 increase in the option's price per share. A contract with a delta of 0.0 has no directional exposure and is maximally OTM. A 50 contract is defined as having the ATM strike. 14 Because delta is a measure of directional exposure, it plays a large role when hedging directional risks. For instance, if a trader currently has a 50 position on and wants the position to be relatively insensitive to directional moves in the underlying, the trader could offset that exposure with the addition of 50 negative deltas (e.g., two 25 long puts). The composite position is called delta neutral. Gamma is a second‐order Greek and a measure of the expected change in the option delta given a $1 change in the underlying price. Gamma is mathematically represented as follows: (1.16) As with delta, the sign of gamma depends on the type of position: Long call and long put: . Short call and short put: . In other words, if there is a $1 increase in the underlying price, then the delta for all long positions will become more positive, and the delta for all short positions will become more negative. This makes intuitive sense because a $1 increase in the underlying pushes long calls further ITM, increasing the directional exposure of the contract, and it pushes long puts further OTM, decreasing the inverse directional exposure of the contract and bringing the negative delta closer to zero. The magnitude of gamma is highest for ATM positions and lower for ITM and OTM positions, meaning that delta is most sensitive to underlying price movements at –50 and 50 . Awareness of gamma is critical when trading options, particularly when aiming for specific directional exposure. The delta of a contract is typically transient, so the gamma of a position gives a better indication of the long‐term directional exposure. Suppose traders wanted to construct a delta neutral position by pairing a short call (negative delta) with a short put (positive delta), and they are considering using 20 or 40 contracts (all other parameters identical). The 40 contracts are much closer to ATM (50 ) and have more profit potential than the 20 positions, but they also have significantly more gamma risk and are less likely to remain delta neutral in the long term. The optimal choice would then depend on how much risk traders are willing to accept and their profit goals. For traders with high profit goals and a large enough account to handle the large P/L swings and loss potential of the trade, the 40 contracts are more suitable. Theta is a first‐order Greek that measures the expected P/L changes resulting from the decay of the option's extrinsic value (the difference between the current market price for the option and the intrinsic value of the option) per day. It is also commonly referred to as the time decay of the option. Theta is mathematically represented as follows: (1.17) where V is the price of the option (a call or a put) and t is time. The sign of theta depends on the type of position and is opposite gamma: Long call and long put: . Short call and short put: . In other words, the time decay of the extrinsic value decreases the value of the long position and increases the value of the short position. For instance, a long call with a theta of –5 per one lot is expected to decline in value by $5 per day. This makes intuitive sense because the holders of the contract take gradual losses as their asset depreciates with time, a result of the value of the option converging to its intrinsic value as uncertainty dissipates. Because the extrinsic value of a contract decreases with time, the short side of the position profits with time and experiences positive time decay. The magnitude of theta is highest for ATM options and lower for ITM and OTM positions, all else constant. There is a trade‐off between the gamma and theta of a position. For instance, a long call with the benefit of a large, positive gamma will also be subjected to a large amount of negative time decay. Consider these examples: Position 1: A 45 DTE, 16 call with a strike price of $50 is trading on a $45 underlying. The long position has a gamma of 5.4 and a theta of –1.3. Position 2: A 45 DTE, 44 call with a strike price of $50 is trading on a $49 underlying. The long position has a gamma of 7.9 and a theta of –2.2. Compared to the first position, the second position has more gamma exposure, meaning that the contract delta (and the contract price) is more sensitive to changes in the underlying price and is more likely to move ITM. However, this position also comes with more theta decay, meaning that the extrinsic value also decreases more rapidly with time. To conclude this discussion of the Black‐Scholes model and its risk measures, note that the outputs of all options pricing models should be taken with a grain of salt. Pricing models are founded on simplified assumptions of real financial markets. Those assumptions tend to become less representative in highly volatile market conditions when potential profits and losses become much larger. The assumptions and Greeks of the Black‐Scholes model can be used to form reasonable expectations around risk and return in most market conditions , but it's also important to supplement that framework with model‐free statistics. Covariance and Correlation Up until now we have discussed trading with respect to a single position, but quantifying the relationships between multiple positions is equally important. Covariance quantifies how two signals move relative to their means with respect to one another. It is an effective way to measure the variability between two variables. For one signal, X , with observations and mean , and another, Y , with observations and mean the covariance between the two signals is given by the following: (1.18) Represented in terms of random variables X and Y, this is equivalent to the following: 15 (1.19) Simplified, covariance quantifies the tendency of the linear relationship between two variables: A positive covariance indicates that the high values of one signal coincide with the high values of the other and likewise for the low values of each signal. A negative covariance indicates that the high values of one signal coincide with the low values of the other and vice versa. A covariance of zero indicates that no linear trend was observed between the two variables. Covariance can be best understood with a graphical example. Consider the following ETFs with daily returns shown in the following figures: SPY (S&P 500), QQQ (Nasdaq 100), and GLD (Gold), TLT (20+ Year Treasury Bonds). Figure 1.9 (a) QQQ returns versus SPY returns. The covariance between these assets is 1.25, indicating that these instruments tend to move similarly. (b) TLT returns versus SPY returns. The covariance between these assets is –0.48, indicating that they tend to move inversely of one another. (c) GLD returns versus SPY returns. The covariance between these assets is 0.02, indicating that there is not a strong linear relationship between these variables. Covariance measures the direction of the linear relationship between two variables, but it does not give a clear notion of the strength of that relationship. Because the covariance between two variables is specific to the scale of those variables, the covariances between two sets of pairs are not comparable. Correlation, however, is a normalized covariance that indicates the direction and strength of the linear relationship, and it is also invariant to scale. For signals with standard deviations and covariance , the correlation coefficient (rho) is given by the following: (1.20) The correlation coefficient ranges from –1 to 1, with 1 corresponding to a perfect positive linear relationship, –1 corresponding to a perfect negative linear relationship, and 0 corresponding to no measured linear relationship. Revisiting the example pairs shown in Figure 1.9 , the strength of the linear relationship in each case can now be evaluated and compared. For Figure 1.9 (a), QQQ returns versus SPY returns, the correlation between these assets is 0.88, indicating a strong, positive linear relationship. For Figure 1.9 (b), TLT returns versus SPY returns, the correlation between these assets is –0.43, indicating a moderate, negative linear relationship. And for Figure 1.9 (c), GLD returns versus SPY returns, the correlation between these assets is 0.00, indicating no measurable linear relationship between these variables. According to the correlation values for the pairs shown, the strongest linear relationship is between SPY and QQQ because the magnitude of the correlation coefficient is largest. The correlation coefficient plays a huge role in portfolio construction, particularly from a risk management perspective. Correlation quantifies the relationship between the directional tendencies of two assets. If portfolio assets have highly correlated returns (either positively or negatively), the portfolio is highly exposed to directional risk. To understand how correlation impacts risk, consider the additive property of variance. For two random variables with individual variances and covariance , the combined variance is given by the following: (1.21) When combining two assets, the overall impact on the uncertainty of the portfolio depends on the uncertainties of the individual assets as well as the covariance between them. Therefore, for every new position that occupies additional portfolio capital, the covariance will increase portfolio uncertainty (high correlation), have little effect on portfolio uncertainty (correlation near zero), or reduce portfolio uncertainty (negative correlation). Additional Measures of Risk This chapter has introduced several measures for risk including historical volatility, implied volatility, and the option Greeks. Two additional metrics are worth noting and will appear throughout this text: beta and conditional value at risk (CVaR). Beta is a measure of systematic risk and specifically quantifies the volatility of the stock relative to that of the overall market, which is typically estimated with a reference asset, such as SPY. Given the market's returns, , a stock with returns has the following beta: (1.22) The volatility of a stock relative to the market can then be evaluated according to the following: : The asset tends to move more than the market. (For example, if the beta of a stock is 1.5, then the asset will tend to move $1.50 for every $1 the market moves.) : The asset movements tend to match those of the market. : The asset is less volatile than the market. (For example, if the beta of a stock is 0.5, then the asset will be 50% less volatile than the market.) : The asset has no systematic risk (market risk). : The asset tends to move inversely to the market as a whole. This metric is essential for portfolio management, where it is used in the formulation of beta‐weighted delta. This will be covered in more detail in Chapter 7 . Value at risk (VaR) is another distribution statistic that is especially useful when dealing with heavily skewed distributions. VaR is an estimate of the potential losses for a portfolio or position over a given time frame at a specific likelihood level based on historical behavior. For example, a position with a daily VaR of –$100 at the 5% likelihood level can expect to lose $100 (or more) in a single day at most 5% of the time. This means that the bottom 5% of occurrences on the historical daily P/L distribution are –$100 or worse. For a visualization, see the historical daily returns distribution for SPY in Figure 1.10 . Figure 1.10 SPY daily returns distribution from 2010–2021. Included is the VaR at the 5% likelihood level, indicating that SPY lost at most 1.65% of its value on 95% of all days. For strategies with significant negative tail skew, VaR gives a numerical estimate for the extreme loss potential according to past tendencies. To place more emphasis on the negative tail of a distribution and determine a more extreme loss estimate, traders may use CVaR, otherwise known as expected shortfall. CVaR is an estimate for the expected loss of portfolio or position if the extreme loss threshold (VaR) is crossed. This is calculated by taking the average of the distribution losses past the VaR benchmark. To see how VaR and CVaR compare for SPY returns, refer to Figure 1.11 . Figure 1.11 SPY daily returns distribution from 2010–2021. Included are VaR and CVaR at the 5% likelihood level. A CVaR of 2.7% indicates that SPY can expect an average daily loss of roughly 2.7% on the worst 5% of days. The choice between using VaR and CVaR depends on the risk profile of the portfolio or position considered. CVaR is more sensitive to tail losses and provides a metric that is more conservative from the perspective of risk, which is more suitable for the kind of instruments focused on in this book. Notes 1 In liquid markets, which will be discussed in Chapter 5 , American and European options are mathematically very similar. 2 The future value of the option should be used, but for simplicity, this approximates the future value as the current price of the option. The future value of the option premium is the current value of the option multiplied by the time‐adjusted interest rate factor. 3 Population calculations are used for all the moments introduced throughout this chapter. 4 This is the sum of the squared differences between each data point and the distribution mean, normalized by the number of data points in the set. 5 The skew of the returns distribution is also used to estimate the directional risk of an asset. The fourth moment (kurtosis) quantifies how heavy the tails of a returns distribution are and is commonly used to estimate the outlier risk of an asset. 6 Dividends can be accounted for in variants of the original model. 7 This application of Wiener processes as well as their use in financial mathematics are due to them arising as the scaling limit of simple random walk. A simple random walk is a discrete process that takes independent steps with probability . The scaling limit is reached by shrinking the size of the steps while speeding up their rate in such a way that the process neither sits at its initial location nor runs off to infinity immediately. 8 Note that, unless stated or shown otherwise, the date ranges throughout this book generally end on the first of the final year. For the range shown here, the data begins on January 1, 2010 and ends on January 1, 2015. 9 Displacement along the X‐axis is the difference between the current horizontal location of the particle and the previous horizontal location of the particle for each step. 10 Simple returns will also be approximated as normally distributed throughout this book. Although this is not explicitly implied by the Black‐Scholes model, it is a fair and intuitive approximation in most cases because the difference between log returns and simple returns is typically negligible on daily timescales. 11 d is a symbol used in calculus to represent a mathematical derivative. It equivalently represents an infinitesimal change in the variable it's applied to. dS ( t ) is merely a very small, incremental movement of the stock price at time t . ∂ is the partial derivative, which also represents a very small change in one variable with respect to variations in another. 12 The log function and log‐normal distribution are both covered in the appendix. 13 Order refers to the number of mathematical derivatives taken on the price of the option. Delta has a single derivative of V and is first‐order. Greeks of second‐order are reached by taking a derivative of first‐order Greeks. 14 In practice, the strike and underlying prices for 50Δ contracts tend to differ slightly due to strike skew. 15 The covariance of a variable with itself (e.g., Cov(X, X)) is merely the variance of the signal itself. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c02.xhtml SCORE: 323.50 ================================================================================ Chapter 2 The Nature of Volatility Trading and Implied Volatility Traders often hedge against periods of extreme market volatility (either to the upside or the downside) using options. Options are effectively financial insurance, and they are priced according to similar principles as other forms of insurance. Premiums increase or decrease according to the perceived risk of a given underlying (a result of supply and demand for those contracts), just as the cost of hurricane insurance increases or decreases depending on the perceived risk of hurricanes in a given area. To quantify the perceived risk in the market, traders use implied volatility (IV). Implied volatility is the value of volatility that would make the current market price for an option be the fair price for that option in a given model, such as Black‐Scholes. 1 When options prices increase (i.e., there is more demand for insurance), IV increases accordingly, and when options prices decrease, IV decreases. IV is, thus, a proxy for the sentiment of market risk as it relates to supply and demand for financial insurance. IV gives the perceived magnitude of expected price movements; it is not directional. 2 Table 2.1 gives a numerical example. Table 2.1 Two underlyings with the same price and put contracts on each underlying with identical parameters (number of shares, put strike, contract duration). The contract prices differ, indicating that these two instruments have different implied volatilities. 45‐day Put Contract Underlying A Underlying B Underlying Price $101 $101 Strike Price $100 $100 Contract Price $10 $5 The price of the put is around 10% of the stock price for underlying A and 5% of the stock price for underlying B. This suggests that there is more perceived uncertainty associated with the price of underlying A compared to underlying B. Equivalently, this indicates that the anticipated magnitude of future moves in the underlying price is larger for underlying A compared to underlying B. Demand for options tends to increase when the historical volatility of an underlying increases unexpectedly, particularly with large moves to the downside. This means that IV tends to be positively correlated with historical volatility and negatively correlated with price. However, there are exceptions to this rule, as IV is based on the perceived risk and not on historical risk directly. IV may increase due to factors that are not directly related to price movements, such as company‐specific uncertainty (earnings reports, silly tweets from the CEO) or larger‐scale macroeconomic uncertainty (political conflict, proposed legislative measures). This also means that volatility profiles vary significantly from instrument to instrument, which will be discussed more later in the chapter. Similar to historical volatility, IV gives a one standard deviation range of annual returns for an instrument. Though historical volatility represents the realized past volatility of returns , IV is the approximation for future volatility of returns because it is based on how the market is using options to hedge against future price changes. While each option for an underlying has its own implied volatility, the “overall” IV of an asset is normally calculated from 30‐day options and is a rough annualized volatility forecast. 3 Example: An asset has a price of $100 and an IV of 0.10 (10%). Therefore, the asset is expected to move about 10% to the upside or the downside by the end of the following year. This means the ending price will most likely be between $90 and $110. The volatility forecast can also be scaled to approximate the expected price across days, weeks, months, or longer. The equations used to calculate the expected price ranges of an asset over some forecasting period are given below. 4 (2.1) (2.2) These estimates of expected range will be used to formulate options strategies in future chapters. The time frame for the expected range is often scaled to match the contract duration. Most examples in this book will have a duration of 45 days to expiration (DTE) (or 33 trading days), so implied volatilities are typically multiplied by 0.35 to ensure forecasts match the duration of the contract. The expected move cone is helpful to visualize this likely price range for an instrument according to market speculation. The width of the cone is calculated using Equation (2.2) and scales with the IV of the underlying. More specifically, the cones are wider in higher volatility environments and narrower when volatility is low and the expected range is tighter. Consider the expected move cones shown in Figure 2.1 , corresponding to the expected price ranges for SPY. Figure 2.1 (c) shows the realized price trajectory for SPY in December 2019, which stayed within its expected price range for the majority of the 45‐day duration. Prices tend to stay within their expected range more often than not, and the assumptions of the Black‐Scholes model can be used to develop a theoretical estimate for how often that should be. Trading Volatility An inconceivable number of factors affect prices in financial markets, which makes precisely forecasting price movements extremely difficult. Arguably, the most reliable way to form expectations around future price trends is using statistics from past price data and financial models. IV is derived from current options prices and the Black‐Scholes options pricing model, meaning that the Black‐Scholes assumptions can be used to add statistical context to the expected price range. More specifically, one can infer the likelihood of a stock price remaining within its IV‐derived price range because stock returns are assumed to be normally distributed. The one standard deviation range of the normal distribution encompasses 68.2% of event outcomes, so there is theoretically a 68.2% chance the price of an equity lands within its expected range. This probability can also be generalized over any timescale using Equation (2.1) . Figure 2.1 (a) The 45‐day expected move cone for SPY in early 2019. The price of SPY was roughly $275, and the IV was around 19%, corresponding to a 45‐day expected price range of ±6.7% ( Equation (2.1) ) or ±$18 ( Equation (2.2) ). (b) The 45‐day expected move cone for SPY when IV was 12%. (c) The same expected move cone as (b) with the realized price over 45 days. Example: An asset has a price of $100 and an IV of 0.10 (10%). The asset price is expected to remain between $90 and $110 by the end of the following year with 68% certainty. Equivalently, the asset price is expected to remain between $96 and $104 58 days from today with 68% certainty (calculated using Equation (2.2) ). However, historical data show that perceived uncertainty in the market (IV) tends to overstate the realized underlying price move more often than theory suggests. Though theory predicts that IV should overstate the realized move roughly only 68% of the time, market IV (estimated using the IV for SPY) overstated the realized move 87% of the time between 2016 and 2021. This means the price for SPY stayed within its expected price range more often than estimated. Realized moves were larger just 13% of the time, indicating that IV rarely understates the realized risk in the market. The exact degree to which IV tends to overstate realized volatility depends on the instrument. For example, consider the IV overstatement rates of the stocks and exchange‐traded funds (ETFs) in Table 2.2 . Table 2.2 IV overstatement of realized moves for six assets from 2016–2021. Assets include SPY (S&P 500 ETF), GLD (gold commodity ETF), SLV (silver commodity ETF), AAPL (Apple stock), GOOGL (Google stock), AMZN (Amazon stock). Volatility Data (2016–2021) Asset IV Overstatement Rate SPY 87% GLD 79% SLV 89% AAPL 70% GOOGL 79% AMZN 77% Different assets are more or less prone to stay within their expected move range depending on their unique risk profile. Stocks are subject to single‐company risk factors and tend to be more volatile. ETFs, which contain a variety of assets, are inherently diversified and tend to be less prone to dramatic price swings. For example, the S&P 500 includes Apple, but it also includes around 499 other companies. This means that a tech‐sector specific event will have a bigger impact on APPL compared to SPY. Commodities like gold and silver also tend to be less volatile than individual stocks, meaning they are less prone to spikes in IV and have more predictable returns. Although the IV overstatement rates differ between instruments, one can conclude that fear of large price moves is usually greater than realized price moves in the market. So, how exactly can options traders capitalize on this knowledge of IV and IV overstatement? Let's revisit the example of hurricane insurance. The price for hurricane insurance is proportional to the expected cost of potential hurricane damage in the area. These prices are based on historical hurricane activity and forecasts of future events, which may underestimate, overestimate, or match the realized outcomes. People who sell hurricane insurance initially collect premiums, with the value depending on the perceived risk of home damage. During uneventful hurricane seasons, most policies go unused, and insurers keep the majority of premiums initially collected. In the unlikely event that hurricane damage is significantly worse than expected in an area dense with policyholders, insurers take very large losses. Insurance companies essentially make small, consistent profits the majority of the time while being exposed to large, infrequent losses. Financial insurance carries a similar risk‐reward trade‐off as sellers make small, consistent profits most of the time but run the risk of large losses in extreme circumstances. IV yields an approximate price range forecast for a given underlying with 68% certainty. This means there is a 68% chance that the calls with strikes at the upper end of the expected range and puts with strikes at the lower end will both expire with no intrinsic value. For example, if traders sold one call and one put with strikes along the expected move cone, they would theoretically profit with 68% certainty. If the underlying price were to move unexpectedly to the upside or the downside, however, the traders may take substantial losses. Unlike sellers of hurricane insurance, options sellers have more room to strategize and more control over their risk‐reward profile. Premium sellers can choose when to sell insurance and how to construct contracts most likely to be profitable. Because IV is a proxy for the demand for options and the inflation of premium, it can be used to identify opportune times to sell insurance. Additionally, because IV can be used to estimate the most likely price range for a specific asset, premium sellers can use IV to structure those positions so they likely expire worthless, like in the previous example. Options sellers (or short premium traders) have the long‐term statistical advantage over options buyers, with the trade‐off of exposure to unlikely, potentially significant losses. Because of that long‐term statistical advantage, short premium trading is the focus of this book, with the next chapter detailing the mechanics of trading based on implied volatility. The States of VIX SPY is frequently used as a proxy for the broader market. It is also a baseline underlying for the short options strategies in this book because it is highly diversified across market sectors and has minimal idiosyncratic risk factors. The CBOE Volatility Index (VIX) is meant to track the annualized IV for SPY and is derived from 30‐day index options. As SPY is a proxy for the broader market, the VIX, therefore, gauges the perceived risk of the broader market. For context, from 1990 to 2021, the VIX ranged from roughly 10 to a peak of just over 80 in March 2020 during the COVID‐19 pandemic. 5 Unlike equities, whose prices typically drift from their starting values over time, IV tends to revert back to a long‐term value following a cyclic trend. This is because equities are used to estimate the perceived value of a company, sector, or commodity, but IV tracks the uncertainty sentiment of the market, which can only stay elevated for so long. During typical bull market conditions, the VIX hovers at a relatively low value at or below its average of 18.5. This is known as a lull state. When market uncertainty rapidly increases for whatever reason, often in response to large sudden price changes, the VIX expands and spikes far above its steady‐state value. Once the market adjusts to the new volatility conditions or the volatile conditions dissipate, the VIX gradually contracts back to a lull state. To see an example of this cycle, refer to Figure 2.2 . Figure 2.2 The three phases of the VIX, using data from early 2017 to late 2018. When comparing how often the VIX is in each state, one finds the following approximate rates: Lull (70%): IV consistently remains below or near its long‐term average. This state occurs when market prices trend upward gradually and market uncertainty is consistently low. Expansion (10%): IV expansion usually follows a prolonged lull period and is marked by expanding market uncertainty and typically large price moves in the underlying equity. Contraction (20%): IV contraction follows an expansion and is marked by a continued decline in IV. A contraction turns into a lull when IV reverts back to its long‐term average. Lull periods are most common and tend to be much longer than the average expansion or contraction period. Since 2000, the average lull period was more than three times the length of the average expansion or contraction. When expansions do happen, the higher the IV peak, the faster the VIX contracts. For example, according to data from 2005 to 2020, when the VIX contracted from 20 to 16 points (20% decrease), it took an average of 75.3 trading days to do so. However, when the VIX contracted from 70 to 56 points (also a 20% decrease), it only took an average of four trading days. Spikes in the VIX are generally caused by unprecedented market or worldwide events. For example, the VIX reached over 80 in November 2008 during the peak of the worldwide financial crisis and hit its all‐time high of 82.69 in March 2020 during the COVID‐19 pandemic. The VIX peak of 2020 was especially unprecedented as the first major spike due to COVID‐19 happened on February 28, 2020 when the VIX hit 40.11. This VIX high in 2020 had not been reached since February 2018, and it followed a 96‐day lull. On March 16, 2020, the VIX hit 82.69, making the 2020 VIX expansion one of the most rapid ever recorded. Though contraction periods tend to be longer than expansions but much shorter than lulls, fairly long contractions tend to follow major sell‐offs or corrections. For example, the VIX contraction following the 2008 sell‐off lasted well over a year, and the contraction following the 2020 sell‐off lasted more than 10 months. This is normally because it takes time for the market (and specific subsectors) to revert to regular conditions following such broad macroeconomic shocks. Premium sellers can potentially profit in any type of market, whether it be during volatility expansions (bearish), contractions (bullish/neutral), or lulls (neutral) if adopting an appropriate strategy for the volatility conditions. Generally, the most favorable trading state for selling premium is when IV contracts. This is because IV contracts when premium prices deflate, meaning that options traders who sold positions in high IV 6 are able to buy identical positions back in low IV at a lower price, thus profiting from the difference. Volatility expansions, on the other hand, have the potential to generate significant losses for short premium traders. Volatility expansions tend to occur when there are large movements in the underlying price and uncertainty increases, causing options on that underlying to become more expensive. If traders sell premium during an expansion period once IV is already elevated , then the traders can capitalize on higher premium prices and the increased likelihood of a volatility contraction. However, if traders sell premium during a lull period, when the expected range is tight, and volatility transitions into an expansion period, then those traders will likely take large losses from the underlying price moving far outside the expected range. Additionally, to close their positions early, traders must buy back their options for more than they received in initial credit and incur a loss from the difference. Short premium traders can profit in any type of market, but the risk of significant losses for short premium traders is highest when volatility is low . Unexpected transitions from a volatility lull to an expansion do not happen often, but when they do happen, they can be detrimental to an account. It is still necessary to trade during these low‐IV periods because IV spends the majority of the time in this state, but risk management during this period is crucial. These risk management techniques will be outlined in the upcoming chapters. This cyclic trend (lull, expansion, contraction, lull) is easily observable when looking at a relatively stable volatility index, such as the VIX. However, this trend, which we will describe as IV reversion, is present in some capacity for all IV signals. IV Reversion Certain types of signals tend to revert back to a long‐term value following a significant divergence. Although this concept cannot be empirically proven or disproven, the reversion of IV is a core assumption in options trading. 7 The reversion dynamics and the minimum IV level vary across instruments, but reversion is assumed to be present in all IV signals to some extent. To understand this, first consider the probability of large magnitude returns for four assets with different risk profiles: SPY, GLD, AAPL, and AMZN. A comparison of these probabilities is shown in Table 2.3 . Table 2.3 Rates thats different assets experienced daily returns larger than 1%, 3%, and 5% in magnitude. For example, there is a 22% chance that SPY returns more than 1% or less than –1% in a single day (according to past data). Probability of Surpassing Daily Returns Magnitude (2015–2021) Asset > 1% Magnitude > 3% Magnitude > 5% Magnitude SPY 22% 3% 0.8% GLD 19% 1% 0.1% AAPL 43% 9% 2% AMZN 45% 10% 3% Compared to assets like SPY and GLD, AMZN and AAPL are more volatile. These tech stocks experience large daily returns roughly three times as often as SPY and roughly 10 times as often as GLD. Each of these assets is subject to unique risk factors, but all are expected to have reverting IV signals nonetheless. Figure 2.3 shows these volatility profiles graphically. Figure 2.3 demonstrates how IV has tended to revert back to a long‐term baseline for each of the different assets, and it also demonstrates that elevated uncertainty is unsustainable in financial markets. Events may occur that spark fear in the market and drive up the demand for insurance, but as fear inevitably dissipates and the market adapts to the new conditions, IV deflates back down. This phenomenon has significant implications for short options traders. As stated in Chapter 1 , it is controversial whether directional price assumptions are statistically valid or not as trading according to pricing forecasts has never been proven to consistently outperform the market. IV is assumed to eventually revert down following inflations from its stable volatility state unlike asset prices, which drift from their initial value with time. The timescale for these contractions is unpredictable, but this nonetheless indicates some statistical validity to make downward directional assumptions about volatility once it is elevated. Figure 2.3 also shows how volatility profiles vary greatly across instruments. More volatile assets like Apple and Amazon stocks have higher IV averages, twice that of SPY and gold in this case, and experience expansion events more often. Single‐company factors, such as quarterly earnings reports, pending mergers, acquisitions, and executive changes can all cause volatility spikes not seen in diversified assets and portfolios. However, this increased volatility also comes with higher credits and more volatility contraction opportunities for premium sellers. 8 For an example of how the propensity for expansions and contractions differs between stocks with earnings and a diversified ETF, refer to Figures 2.4 (a)–(c). Marked are the earnings report dates for each stock or the date when the company reported its quarterly profits (after‐tax net income). Figure 2.3 IV indexes for different assets with their respective averages (dashed) from 2015–2021. Assets include (a) SPY (S&P 500 ETF), (b) GLD (gold commodity ETF), (c) AAPL (Apple stock), and (d) AMZN (Amazon stock). Figure 2.4 Implied volatility indexes for different equities from 2017–2020 with earnings dates marked (if applicable). Assets include (a) AMZN (Amazon stock), (b) AAPL (Apple stock), and (c) SPY (S&P 500 ETF). With tech stocks like AMZN and AAPL, it's common for IV to increase sharply prior to earnings and contract almost immediately afterward. The previous graphs show that sharp IV expansions happen less frequently with a more diversified market ETF, such as SPY. These figures indicate that when SPY does experience a volatility expansion, it generally takes much longer to contract. From 2017 to 2020, the VIX only rose above 35 two times and, in both situations, took roughly half a month to contract down to its original level. Meanwhile, volatility levels of AMZN and AAPL rose above 40 many times and even had a few spikes above 50, or in the case of AMZN, almost 60. Takeaways IV is a proxy for the sentiment of market risk derived from supply and demand. When options prices increase, IV increases; when options prices decrease, IV decreases. IV also gives the perceived magnitude of future movement, and it is not directional. Demand for options tends to increase when the historical volatility of an underlying increases unexpectedly, particularly with large moves to the downside. IV tends to be positively correlated with historical volatility and negatively correlated with price, but it is ultimately based on the perceived market risk and not directly on price information. IV can be used to estimate the expected price range of an instrument. IV gives a one standard deviation expected range because it is based on how the market is using options to hedge against future periods of volatility. Because stock returns are assumed to be normally distributed, theoretically, there is a 68.2% chance the price of an equity lands within its expected range over a given time frame. However, historical data show that prices stay within their expected ranges more often than theoretically estimated. For example, market IV (estimated using the IV for SPY) overstated the realized move 87% of the time between 2016 and 2021. Options sellers have the long‐term statistical advantage over options buyers, with the trade‐off of exposure to unlikely, potentially significant losses. Because IV is a proxy for the demand for options and the inflation of premium, it can be used to identify opportune times to sell insurance. Premium sellers can also use IV to structure positions so they are likely to expire worthless, the ideal outcome for the short position. Volatility profiles differ significantly between assets, but all IV signals are assumed to revert back to some long‐term value following significant diversions. Stated differently, IV tends to contract back to a long‐term value following significant expansions from its lull volatility state. This phenomenon indicates that there is some degree of statistical validity when making downward directional assumptions about volatility once it's inflated. Notes 1 Implied volatility (IV), like historical volatility, is a percentage and pertains to log returns. It is common to represent IV as either a decimal (0.X) or percentage (X%). An IV index, which is an instrument that tracks IV and will be introduced later in this chapter, is typically represented using points (X) but should be understood as a percentage (X%). 2 It is possible to get directional expected move information about an underlying by analyzing the IV across various strikes. This will be elaborated on more in the appendix. 3 IV yields a rough approximation for the expected price range, but this is not how the expected range is typically calculated on most trading platforms. Refer to the appendix for more information about how expected range is calculated more precisely. For the time being, we are using this simplified formula since it is most intuitive. 4 When ignoring the risk‐free rate, the expected price range over T days for a stock with price S and volatility σ can be estimated by . The formula in Equation (2.2) is an approximation because, for small x values, e x ≈ 1 + x . This approximation becomes less valid when x is large, meaning this expected range calculation is less accurate when IV is high. This will be explored more in the appendix. 5 Note that volatility indices, such as the VIX, will be represented using points but are meant to be understood as a percentage. For example, a VIX of 30 corresponds to an annualized implied volatility of 30%. 6 It's important to note that the threshold for high IV is different for every asset because each instrument is subject to unique risk factors. Evaluating IV can be difficult because there is so much variability between assets, but there will be a more in‐depth discussion of this in the following chapter. 7 The value that the signal reverts back to is roughly the long‐term mode of the distribution, or the volatility that has occurred most often historically. 8 Such underlyings can be used for earnings plays, which will be discussed in a Chapter 9 . ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c03.xhtml SCORE: 616.00 ================================================================================ Chapter 3 Trading Short Premium Options are highly versatile instruments. They can be used to hedge the directional risk of a stock, or they can be used as a source of profits. As alluded to in the example of hurricane insurance, short premium positions can be used to generate small, consistent profits for those willing to accept the tail risk. The mechanics of short premium trading are subtle, but many of the core concepts can be introduced in an intuitive way with some simple gambling analogies. For example, when using options for profit generation (i.e., not risk mitigation), the long‐term performance of long and short options can be analogized with slot machines. Buying Options for profit is like playing the slot machines. Gamblers who play enough times may hit the jackpot and receive a huge payout. However, despite the potential payouts, most players average a loss in the long run because they are taking small losses the majority of the time. Investors who buy options are betting on large, often directional moves in the underlying asset. Those assumptions may be correct and yield significant profits occasionally, but underlying prices ultimately stay within their expected ranges most of the time. This results in small, frequent losses on unused contracts and an average loss over time. Selling Options for profit is like owning the slot machines. Casino owners have the long‐run statistical advantage for every game, an edge particularly high for slots. Owners may occasionally pay out large jackpots, but as long as people play enough and the payouts are manageable, they are compensated for taking on this risk with nearly guaranteed profit in the long term. Similarly, because short options carry tail risk but provide small, consistent profits from implied volatility (IV) overstatement, then they should average a profit in the long run if risk is managed appropriately. Long premium strategies have a high profit potential but cannot be consistently timed to ensure profit in the long term. This is because outlier underlying moves and IV expansions that benefit long premium positions are strongly linked to external events (such as natural disasters or political conflict), which are relatively difficult to reliably predict. Short premium strategies, on the other hand, profit more often and have the long‐term statistical advantage if investors manage risks appropriately. Similar to the slot machine owner, a short premium trader must reduce the impact of outlier losses to reach a large number of occurrences (trades) and realize the positive long‐term averages. This is most effectively done by limiting position size and by adjusting portfolio exposure according to current market conditions. This chapter will, therefore, cover the following broader concepts in volatility trading: Trading in high IV: Identifying favorable conditions for opening short premium trades. Number of occurrences: Reaching the minimum number of trades required to achieve long‐term averages. Portfolio allocation and position sizing: Establishing an appropriate level of risk for the given market conditions. Active management and efficient capital allocation: Understanding the benefits of managing trades prior to expiration. IV plays a crucial role in trading short premium. Remember that IV is a measure of the sentiment of uncertainty in the market. It is a proxy for the amount of fear among premium buyers (or excitement , depending on your personality) and a measure of opportunity for premium sellers. When market uncertainty increases, premium prices also increase, and premium sellers receive more compensation for being exposed to large losses. However, IV is also instrumental when managing exposure to extreme losses and establishing appropriate position sizes. Background: A Note on Visualizing Option Risk When discussing the risk‐reward trade‐off of trading short premium, it is helpful to contextualize concepts and statistics with respect to a specific strategy. The next few chapters will focus on a short strangle , an options strategy consisting of a short out‐of‐the‐money (OTM) call and a short OTM put: A short OTM call (the right to buy an asset at a certain price) has a bearish directional assumption. The seller profits when the underlying price stays below the specified strike price. A short OTM put (the right to sell an asset at a certain price) has a bullish directional assumption. The seller profits when the underlying price stays above the specified strike price. These two contracts combine to form a strangle. This is an example of an undefined risk strategy, where the loss is theoretically unlimited. The short call has undefined risk because stock prices can increase indefinitely, meaning the potential loss to the upside is unknown. Though short puts technically cannot lose more than 100 times the strike price, this potential loss is large enough that they are also considered undefined risk. Defined risk strategies, where the maximum loss is limited by the construction of the trade, have pros and cons that will be discussed in Chapter 5 . For simplicity, the strangle is used to formulate most examples in this book. Strangles have a neutral directional assumption for the contract seller, meaning it is typically profitable when the price of the underlying stays within the range defined by the short call strike and short put strike. Investors often define the strikes of a strangle according to the expected range of the underlying price (or some multiple of the expected range) over the contract duration. The one standard deviation expected range can be approximated with the current implied volatility of the underlying, as shown in Chapter 2 . Figure 3.1 The price of SPY in the last five months of 2019. Included is the 45‐day expected move cone calculated from the IV of SPY in December 2019. The edges of the cones are labeled according to appropriate strikes for an example strangle. Figure 3.1 shows that SPY was priced at roughly $315 around December 2019, when the current IV for SPY was 12% (corresponding to a VIX level of 12). This means the price for SPY was forecasted to move between –4.2% and +4.2% over the next 45 days with a 68% certainty. This is equivalent to a 45‐day forecast of the price of SPY staying between $302 and $328 approximately. A contract with a strike price corresponding to the expected move range is approximately a 16 contract. In this scenario, a 45 days to expiration (DTE) short SPY call with a strike price of $328 is a –16 contract roughly, and a 45 DTE short SPY put with a strike price of $302 is approximately a 16 contract. The two positions combined form a delta‐neutral position known as a 45 DTE 16 SPY strangle. 1 The strangle buyer and seller are making different bets: The strangle buyer assumes that SPY's price will move beyond expectation within the next 45 days, either to the upside or the downside. More specifically, the long strangle yields profit if the price of SPY significantly increases above $328 or decreases below $302 prior to expiration. The strangle seller profits if the position expires when the underlying price is within or near its expected range or if the position is closed when the contract is trading for a cheaper price than when it was opened (IV contraction). Because there is a 68% chance the underlying will stay within its expected range, the short position theoretically has a 68% chance of being profitable. However, since the underlying price tends to stay in its expected range more often than theoretically predicted, this results in the probability of profit (POP) of short strangles held to expiration being much higher. For example, consider the profit and loss (P/L) distributions for the short 45 DTE 16 SPY strangle in Figures 3.2 (a)–(c). These distributions were generated using historical options data and are useful for visualizing the long‐term risk‐reward profile and likely trade‐by‐trade outcomes for this type of contract. Each occurrence in the histogram corresponds to the final P/L of a short strangle held to expiration. 2 P/L can be represented as a raw dollar amount or as a percentage of initial credit (the fraction of option premium that the seller ultimately kept). 3 Figure 3.2 (a) Historical P/L distribution (% of initial credit) for short 45 DTE 16 SPY strangles, held to expiration from 2005–2021. (b) Historical P/L distribution ($) for short 45 DTE 16 SPY strangles, held to expiration from 2005–2021. (c) The same distribution as in (b) but zoomed in near $0. The percentage of occurrences on either side of $0 have been labeled. Figure 3.2 (c) shows that 81% of occurrences are positive and only 19% are negative . This means this strategy has historically profited 81% of the time and only taken losses 19% of the time, significantly higher than the 68% POP that the simplified theory suggests. Over the long run, this strategy was profitable and averaged a P/L of $44 (or 28% of the initial credit) per trade. However, notice the P/L distributions for this strategy are highly skewed and carry significant tail risk. As shown in Figure 3.2 (a), these tail losses are unlikely but could potentially amount to –1,000% or even –4,000% of the initial credit. In other words, if a trader receives $100 in initial credit for selling a SPY strangle, there is a slim chance of losing upward of $4,000 on that trade according to historical behavior. This is the trade‐off for the high POPs of short premium strategies. The possibility of outlier losses should not be surprising because placing a short premium trade is betting against large, unexpected price swings. For a relatively stable asset like SPY, these types of swings rarely happen. When they do, things can fly off the handle rapidly, such as during the 2008 recession or 2020 sell‐off. Consequently, the most important goals for a short premium trader are to profit consistently enough to cover moderate, more likely losses and to construct a portfolio that can survive those unlikely extreme losses. Background: A Note on Quantifying Option Risk Approximating the historical risk of a stock or exchange-traded fund (ETF) is relatively straightforward. Equity log returns distributions are fairly symmetric and resemble a normal distribution, thus justifying that standard deviation of returns (historical volatility) be used to approximate historical risk. However, a short option P/L distribution is highly skewed and subject to substantial outlier risk. Due to this more complex risk profile, using option P/L standard deviation as a lone proxy for risk significantly misrepresents the true risk of the strategy. Therefore, the following metrics will be used to more thoroughly discuss the risk of short options: standard deviation of P/L, skew, and conditional value at risk (CVaR). 4 The standard deviation of P/L encompasses the range that the majority of endings P/Ls fall within for a given strategy historically. The standard deviation for financial strategies is commonly interpreted relative to the normal distribution, where one standard deviation accounts for 34% of the distribution on either side of the mean. For options P/L distributions, however, the one standard deviation of P/L typically accounts for more than 68% of the total occurrences and the density of occurrences is not symmetric about the mean. Again, consider the P/L distribution for the short 45 DTE 16 SPY strangle. Figure 3.3 Historical P/L distribution ($) for 45 DTE 16 SPY strangles, held to expiration from 2005–2021. The distribution has been zoomed in near the mean (solid line), and the percentage of occurrences within of the mean has been labeled. For 45 DTE 16 SPY strangles from 2005–2021, the average P/L was $44, and the standard deviation of P/L was $614. As shown in Figure 3.3 , the one standard deviation range accounts for nearly 96% of all occurrences, significantly higher than the range for the normal distribution. Additionally, because the distribution is highly asymmetric, the P/Ls in the range are less likely than the P/Ls in the range. Due to these factors, the interpretation of standard deviation as a measure of risk must be adjusted. Standard deviation overestimates the magnitude of the most likely losses (e.g., a $500 loss is unlikely, but the standard deviation range does not clarify that) and does not account negative tail risk. It does yield a range for the most likely profits and losses on a trade‐by‐trade basis for a given strategy. Therefore, traders can generally form more reliable P/L expectations for strategies with a lower P/L standard deviation. Skew and CVaR are used to estimate the historical tail risk of a strategy. As covered in Chapter 1 , skew is a measure of the asymmetry of a distribution. Strategies with a larger magnitude of negative skew in their P/L distribution have more historical outlier loss exposure. CVaR gives an estimate of the potential loss of a position over a given time frame at a specific likelihood level based on historical behavior. CVaR can be used to approximate the magnitude of an expected worst‐case loss and contextualize skew. For example, consider the two example short strangles outlined in Table 3.1 . Table 3.1 Two example short strangles. For Strangle A, CVaR estimates losing at least $200 at most 5% of the time. In this example, the time frame for this loss has not been specified, but one may assume the time frame is identical for both strategies. Risk Factors Strangle A Strangle B Skew –5.0 –1.0 CVaR (5%) –$200 –$2,000 Strangle A has a larger magnitude of negative skew, indicating that this strategy is more susceptible to tail risk and outlier losses compared to Strangle B. However, there is 10 times more capital at risk in an extreme loss scenario for Strangle B compared to Strangle A perhaps because the underlying for Strangle B is more expensive. Generally speaking, strategies with less skew are preferable because those strategies are less susceptible to large, unpredictable losses and perform more consistently. However, the optimal trade ultimately depends on the acceptable amount of per‐trade capital at risk according to the trader's personal preferences. Also note it is difficult to accurately model outlier loss events because they happen rarely. P/L distributions can give an idea of the magnitude of extreme losses, but these statistics are averaged over a broad range of market conditions and volatility environments. They are not necessarily representative of outlier risk at the present time. Buying power reduction (BPR), which will be covered in the next chapter, yields an estimate for the worst‐case loss of a trade according to current market conditions. Similar to implied volatility, BPR is a forward‐looking metric designed to encompass the most likely scope of losses for an undefined risk position. Trading in High IV Selling premium once IV is elevated comes with several advantages. Before that discussion, there are subtleties to note when evaluating “how high” the IV of an asset is. Contextualizing the current IV for an asset like SPY is somewhat straightforward because it has a well‐known and widely available IV index. The VIX has historically ranged from approximately 10 to 90, has an average of roughly 18, is typically below 20, and rarely surpasses 40. Therefore, a trader can intuitively interpret a level of 15 as fairly low and a level of 35 as fairly high relative to the long‐term behavior of the VIX. But how do traders contextualize the current IV relative to a shorter timescale, such as the last year? And how do traders contextualize the current IV for a less popular IV index with a totally different risk profile? For example, is 35 high for VXAZN, the IV index for AMZN? One way to gauge the degree of IV elevation with respect to some timescale is by converting raw implied volatility into a relative measure such as IV percentile (IVP). IVP is the percentage of days in the past year where the IV was below the current IV level, calculated with the following equation. Note that 252 is the number of trading days in a year. (3.1) IVP ranges from 0% to 100%, with a higher number indicating a higher relative IV. This metric normalizes raw IV to put the current level in context, and unlike raw IV, it is comparable between assets. For example, consider the raw IV indexes and the corresponding IVP values for SPY and AMZN shown in Figure 3.4 . Figure 3.4 The VIX (solid) and VXAZN (dashed) from 2015–2016. Labeled are the IVP values for each index at the end of 2015. When the VIX was roughly 18 SPY had an IVP of 74%, and VXAZN was roughly 36 AMZN had an IVP of 67%. At the end of 2015, the VIX was near its long‐term average of 18 and would have been considered low. However, market IV was below average for the majority of 2015, and a VIX level of 18 was higher than nearly 74% of occurrences from the previous year. A SPY IVP of 74% indicates that IV is fairly elevated relative to the recent market conditions, suggesting that volatility may contract following this expansion period. Comparatively, the volatility index for AMZN at the end of 2015 was 37. This is significantly higher than the VIX at the time but is actually less elevated relative to its volatility history from the past year according to the AMZN IVP of 67%. SPY and AMZN have dramatically different volatility profiles, with VXAZN frequently exceeding 35 and the VIX rarely doing so. This makes raw IV a poor metric for comparing relative volatility and a metric like IVP necessary. Another commonly used relative volatility metric is IV rank (IVR), which compares the current IV level to the historical implied volatility range for that underlying. It is calculated according to the following formula: (3.2) Similar to IVP, IVR normalizes raw IV on a 0% to 100% scale and is comparable between assets. IVR gives a better direct metric for evaluating the price of an option compared to IVP. However, IVP is more robust than IVR because IVR is more sensitive to outlier moves and prone to skew. Both metrics are suitable for practical decision making because they assist traders with evaluating current volatility levels and selecting a suitable strategy/underlying for those conditions. They are also useful for identifying suitable, high IV underlyings for a portfolio because most assets do not have well‐known volatility indices. However, both metrics are fairly unstable, sensitive to timescale, and can be skewed by prolonged outlier events such as sell‐offs. Raw IV, assuming that the characteristics of the volatility profile are well understood, is generally a more stable and reliable metric for analyzing long‐term trends. Because most studies throughout this book use SPY as a baseline underlying and span several years, raw IV will be used rather than a relative metric. As previously mentioned, trading short premium when IV is elevated comes with the added benefits of higher credits and more profit potential for sellers. This is shown in Figure 3.5 , which includes average credits for 16 SPY strangles from 2010–2020 in different volatility environments. Trading short premium in elevated IV is an effective way to capitalize on higher premium prices and the increased likelihood of a significant volatility contraction. Trading when credits are higher also means common losses tend to be larger (as a dollar amount), but the exposure to outlier risk actually tends to be lower when IV is elevated compared to when it's closer to equilibrium. This may seem counterintuitive: If market uncertainty is elevated and there is higher perceived risk, wouldn't short premium strategies carry more outlier risk? Although moves in the underlying tend to be more dramatic when IV is high, the expected range adjusts to account for the new volatility almost immediately, which in many cases reduces the risk of an outlier loss. To understand this, consider Figures 3.6 (a) and (b), showing extreme losses for 16 SPY strangles from 2005–2021, with an emphasis on the 2008 recession. Figure 3.5 SPY IV from 2010–2020. The average prices for 45 DTE 16 SPY strangles are labeled at different VIX levels: 10–20, 20–30, and 30–40. When the VIX was between 30 and 40, the average initial credit per one lot for the 16 SPY strangle was roughly 42% higher than when the VIX was between 10 and 20. A short 16 SPY strangle rarely incurs a loss over $1,000. From 2005–2021, this occurred less than 1% of the time. However, 84% of these losses occurred when the VIX was below 25. During the initial IV expansion of the 2008 recession (late August to early October), strangles incurred these large losses approximately 56% of the time. Notice in Figure 3.6 that these extreme losses were confined to the initial IV expansion (when the VIX increased from roughly 20 to 35). This is because the market was not anticipating the large downside moves of the recession, as reflected by the VIX being near its long‐term average of 18. Because these large swings happened when the expected move range was tight, the historical volatility of the market well exceeded its expected range, and long strangles were highly profitable. Once market uncertainty adjusted to the new conditions and initial credits and expected ranges increased to reflect the perceived risks, the outlier losses for short strangles diminished. Figure 3.6 (a) SPY IV from 2005–2021. Labeled are the extreme losses for 45 DTE 16 SPY strangles held to expiration, meaning losses that are worse than $1,000. (b) The same figure as shown in (a) but zoomed in to 2008–2010, during the 2008 recession. These unexpected periods of high market volatility are the primary source of extreme loss for short premium positions. These events typically happen when there are large price swings in the underlying and the expected move range is tight (low IV). These extreme expansion events are rare, and trading short premium once IV is elevated tends to reduce this type of exposure. Another way to demonstrate this concept is to consider the amount of skew in the P/L distribution of the 16 SPY strangle at different IV levels. Figures 3.7 (a)–(d) illustrate that strangle P/L distributions have less negative skew and smaller tail losses as IV increases. This means that, historically, the exposure to negative tail risk was much higher when the VIX was closer to the lower end of its range compared to when the VIX already expanded. The P/L distribution becomes more symmetric as IV increases, indicated by the decreasing magnitude of negative skew. This means that higher IV conditions facilitate more dependable profit and loss expectations than lower IV conditions. As an important note, observe that there are significantly fewer occurrences when the VIX was over 35 (a few hundred occurrences) compared to when the VIX was between 0 and 25 (thousands of occurrences). This brings us to the next point to consider: How often should one trade? Figure 3.7 Historical P/L distributions for 45 DTE 16 SPY strangles, held to expiration from 2005–2021: (a) Occurrences when the VIX is between 0 and 15 (1,603 occurrences total), (b) Occurrences when the VIX is between 15 and 25 (1,506 occurrences total). (c) Occurrences when the VIX is between 25 and 35 (416 occurrences total). (d) Occurrences when the VIX is above 35 (228 occurrences total). Number of Occurrences Table games at a casino typically have maximum bet sizes. The house has the statistical edge for every game in the casino, but the house will not necessarily profit from that edge unless patrons bet often . In blackjack, the house has an edge of 0.5% if the player's strategy is statistically optimized. So, if gamblers wager $100,000 on blackjack throughout the night, they should lose approximately $500 to the house after a sufficiently large number of hands. If the opponent plays 10 hands at $10,000 per hand, they may win eight hands, three hands, or even all 10 hands. In this case, the variance of potential outcomes is fairly large, and the casino may have to pay fairly large payouts. However, if the opponent plays 1,000 hands at $100 per hand, it is more likely the player's loss will amount to the expected $500. By capping bet sizes, the casino aims to increase the number of occurrences from a single gambler so the house is more likely to reach long‐run averages for each game, a consequence of the law of large numbers and the central limit theorem. When a small number of events is randomly sampled from a probability distribution repeatedly and the averages of those samples are compared, the variance of those averages tends to be quite large. But as the number of occurrences increases, the variance of the averages decreases and the sampled means converge to the expected value of the distribution. 5 Just as the casino aims to realize the long‐term edge of table games by capping bet sizes and increasing the number of plays, short premium traders should make many small trades to maximize their chances of realizing the positive long‐run expected averages of short premium strategies. For an example of why this is crucial, refer again to the P/L distribution of the 16 SPY strangle. Figure 3.8 Historical P/L distribution for 45 DTE 16 SPY strangles, held to expiration from 2005–2021. The dotted line is the long‐term average P/L of this strategy. This strategy, shown in Figure 3.8 , has an average P/L per trade of roughly $44 and a POP of 81%. However, these long‐term averages were calculated using roughly 3,750 trades. Calculating averages with a large pool of data provides the least amount of statistical error but does not model the occurrences retail traders can realistically achieve. What P/L would short premium traders have averaged if they only placed 10 trades from 2005 to 2021? 100 trades? 500 trades? Figure 3.9 shows a plot of average P/Ls for a collection of sample portfolios, each with a different number of trades randomly selected from the P/L distribution of the 16 SPY strangle. Figure 3.9 P/L averages for portfolios with N number of trades, randomly sampled from the historical P/L distribution for 45 DTE 16 SPY strangles, held to expiration from 2005–2021. The variance among these portfolio averages is very large when a small number of trades are sampled. As more trades are sampled, the averages converge to the long‐term average P/L of this strategy. As you can see, when a small number of trades is sampled, 10 for example, the average P/L ranges from roughly –$900 to $200. This means that if two traders randomly traded 10 short strangles from 2005 to 2021, one trader may have profited by $2,000, and the other may have lost $9,000. As the number of occurrences increases, the variance of P/L averages among these sample portfolios decreases, and the averages converge toward the long‐run expected value of this strategy. In other words, if two traders randomly traded 1,000 short strangles from 2005 to 2021, it would be fairly likely for both to average a P/L near $44 per trade, the historical long‐term average P/L of this strategy. Number of occurrences is a critical factor in achieving long‐term averages, and the minimum number of occurrences needed varies with the specific strategy's standard deviation of P/L. For practical purposes, a minimum of roughly 200 occurrences is necessary to reach long‐run averages, and more is better. This puts short premium traders in a bit of a predicament because, although trading short premium in high IV is ideal, high IV environments are very uncommon as shown in Table 3.2 . Table 3.2 How often the VIX fell in a given range from 2005–2021. VIX Data (2005–2021) VIX Range % of Occurrences 0–15 43% 15–25 40% 25–35 11% 35+ 6% The VIX is at the low end of its range 43% of the time and below 18.5, its long‐term average, the majority of the time. From 2005–2021, the VIX was only above 35 roughly 6% of the time, which does not leave much opportunity for trading short premium in very high IV. To optimize the likelihood of reaching the favorable long‐term expected values of this strategy, it is clearly necessary to trade in non‐ideal, low volatility conditions. The next section covers how to trade in all market conditions while mitigating the outlier risk in low volatility environments, specifically by maintaining small position sizes and limiting the capital exposed to outlier losses. Portfolio Allocation and Position Sizing In practice, short premium traders must strike a balance between being exposed to large losses and reaching a sufficient number of occurrences. Trading in high IV tends to carry less exposure to outlier risk compared to trading in low IV, but trading in low IV is still profitable on average. Unlike long stocks, which are only profitable during bullish conditions, short options may be profitable in bullish, bearish, or neutral conditions and spanning all volatility environments. For the 16 SPY strangle from 2005–2021, for example, the majority of occurrences were profitable in all IV ranges. (See Table 3.3 .) Table 3.3 The POPs and average P/Ls in different IV ranges for 45 DTE 16 SPY strangles, held to expiration from 2005–2021. 16 SPY Strangle Data (2005–2021) VIX Range POP Average P/L 0–15 82% $20 15–25 78% $7 25–35 86% $159 35+ 89% $255 By trading short options strategies in all IV environments, profits accumulate more consistently, and the minimum number of occurrences is more achievable. To manage exposure to outlier risk throughout these environments, it's essential to keep position sizes small and limit the total amount of portfolio capital allocated to short premium positions, which can be scaled according to the current outlier risk. The percentage of portfolio capital allocated to short premium strategies should generally range from 25% to 50%, with the remaining capital either kept in cash or a low‐risk passive investment. 6 This is because allocating less than 25% severely limits upside growth, while allocating more than 50% may not leave enough capital for a portfolio to recover from an outlier loss event. Because the exposure to outlier risk tends to be higher when IV is low, scaling allocation down in low IV protects portfolio capital from the tail exposure of unexpected market volatility. Once IV increases, scaling short premium capital allocation up increases the potential to profit from higher credits, larger profits, and reduced outlier risk. Table 3.4 Guidelines for allocating portfolio capital according to market IV. VIX Range Max Portfolio Allocation 0–15 25% 15–20 30% 20–30 35% 30–40 40% 40+ 50% A portfolio should not be overly concentrated in short options strategies for the given market conditions, and the capital allocated to short premium should also not be overly concentrated in a single position. An appropriately sized position should not occupy more than 5% to 7% of portfolio capital. The exact percentage varies depending on the POP of the strategies used, and this will be covered in more detail in Chapter 8 . To understand why it's crucial to limit capital exposure and beneficial to scale portfolio allocation according to IV, look at a worst‐case scenario: the 2020 sell‐off. The 2020 sell‐off produced historic losses for short premium positions. From late February to late March 2020, the price of SPY crashed by roughly 34%. For 45 DTE 16 SPY strangles, the most extreme losses recorded for this position occurred throughout this time. A 16 SPY strangle opening on February 14, 2020, and expiring on March 20, 2020, had a P/L per one lot of roughly –$8,974, the worst recorded loss in 16 years for this type of contract. If traders allocated different percentages of a $100,000 portfolio to short SPY strangles beginning with this worst‐case loss, how would those portfolios perform in regular market conditions compared to highly volatile conditions like the 2020 sell‐off? Compare three portfolio allocation strategies: allocation by IV guidelines (25–50%), a more conservative allocation (constant 15%), and a more aggressive allocation (constant 65%). 7 Unsurprisingly, the portfolios perform markedly differently in regular conditions compared to the 2020 sell‐off. From 2017 to February of 2020, the aggressive portfolio dramatically outperformed the conservative and IV‐allocated portfolios. Throughout this three‐year period, the conservative portfolio grew by 13% and the IV‐allocated portfolio by 28%, and the aggressive portfolio increased by 78%. Comparatively, from 2017–2020, SPY grew by 50%. This means that a $100,000 portfolio fully allocated to SPY shares would have outperformed the conservative and IV-allocated portfolios but underperformed the aggressive portfolio, though it would have required significantly more capital than any of them. Figure 3.10 (a) Performances from 2017 to 2021, through the 2020 sell‐off. Each portfolio has different amounts of capital allocated to approximately 45 DTE 16 SPY strangles that are closed at expiration and reopened at the beginning of the expiration cycle. The portfolios are (a) IV‐allocated (solid), conservative (dashed), and aggressive (hashed). (b) SPY price from 2017 to 2021. (c) VIX throughout the same time frame. Upon the onset of the highly volatile market conditions of 2020, the highly exposed aggressive portfolio was immediately wiped out. The conservative and IV‐allocated portfolios were also impacted by significant losses and declined by 35% and 24%, respectively, from February to March 2020. In all the previous scenarios, each portfolio experienced some degree of loss during the extreme market conditions of the 2020 sell‐off. The important thing to note is that portfolios with less capital exposure and position concentration ultimately had the capital to recover following these losses. Following the 2020 sell‐off, the conservative portfolio recovered by 7% and the IV‐allocated by 20% because this portfolio was able to capitalize on the high IV and higher credits of the sell‐off recovery. For profit goals to be reached consistently , it's crucial to construct a portfolio that is robust in every type of market. A highly exposed portfolio takes extraordinary profits in more regular market conditions, but there is a high risk of going under in the rare event of a sell‐off or major correction. A more conservative portfolio is well suited for extreme market conditions, but upside profits are limited the majority of the time. Comparatively, scaling capital allocation according to market IV is an effective way to capitalize on higher profits when IV is high, protect capital from outlier losses when IV is low, and achieve reasonable growth with lower capital requirements than purchasing equities directly. More importantly, limiting capital exposure and maintaining appropriate position sizes are arguably the most effective ways to minimize the impact from extreme events. These concepts will be explored in more detail in Chapter 7 . Active Management and Efficient Capital Allocation Up until now, this book has discussed option risk and profitability for contracts held to expiration. However, short premium traders can also close, or manage, their positions early by purchasing long options with the same underlying, strike, and date of expiration. This can often be profitable as a result of partial theta decay and IV contractions, and it also tends to reduce P/L variability per trade. Options tend to have more P/L fluctuations in the second half of the contract duration compared to the first half, a result of increasing gamma risk. Gamma, as discussed in earlier chapters, is a measure of how sensitive a contract's delta is to changes in the price of the underlying. Gamma increases for near‐the‐money options as expiration approaches, meaning that delta (and, therefore, the price sensitivity of the option) becomes more unstable in response to moves in the underlying toward the end of the contract. Managing short positions actively, such as closing a trade prior to expiration and redeploying capital to new positions, is one way to reduce the P/L swings throughout the trade duration, as well as the per‐trade loss potential and ending P/L standard deviation. Early management strategies will not necessarily reduce risk in the long term because the cumulative losses of many shorter‐term trades may exceed the single loss of a longer‐term trade, but they do make per‐trade loss potentials more reasonable. This strategy effectively allows traders to assess the viability of a trade before P/L swings become more extreme and assess whether it is an efficient use of portfolio capital to remain in the trade. Compare how the P/Ls of 45 DTE 16 SPY strangles are distributed when the contracts are held to expiration versus managed around halfway to expiration (21 DTE). Table 3.5 Comparison of management strategies for 45 DTE 16 SPY strangles from 2005–2021 that are held to expiration and managed early. Statistics include POP, average P/L, standard deviation of P/L, and CVaR at the 5% likelihood level. 16 SPY Strangle Statistics (2005–2021) Statistics Held to Expiration Managed at 21 DTE POP 81% 79% Average P/L $44 $30 Average Daily P/L $1.29 $1.60 Standard Deviation of P/L $614 $260 CVaR (5%) –$1,535 –$695 According to the statistics in Table 3.5 , strangles managed at 21 DTE carry significantly less negative tail risk and P/L standard deviation on a trade‐by‐trade basis than strangles held to expiration. Additionally, although early‐managed contracts collect less on average per trade, they actually average more profit on a daily basis and allow for more occurrences due to the shorter duration. Managing trades early has several benefits, most of which will be covered in Chapter 6 . Much of this decision depends on the acceptable amount of capital to risk on a single trade and whether it is an efficient use of capital to remain in the existing trade. Notice from this example that managed trades take 24 days (21 days remaining on a 45‐day duration trade corresponds to an elapsed duration of 24 days) to profit $30 on average and held contracts 45 days to make $44 on average. Trades may accumulate the majority of their profit potential well before expiration, depending on the market and staying in the position for the remainder of the duration may limit upside potential. Closing trades prior to expiration and redeploying capital to a new position in the same underlying is an effective method for increasing the number of occurrences in a given time frame. Redeploying that capital to a position in a different underlying with more favorable characteristics (such as higher IV) can be a more efficient use of capital and can offer elements of risk reduction in certain situations. Taking an active approach to investing and trade management provides more control over portfolio capital allocation and the flexibility to modify trades given new information. Takeaways Compared to long premium strategies, short premium strategies yield more consistent profits and have the long‐term statistical advantage. The trade‐off for receiving consistent profits is exposure to large and sometimes undefined losses, which is why the most important goals of a short premium trader are to (1) profit consistently enough to cover moderate and more likely losses and (2) to construct a portfolio that can survive unlikely extreme losses. Unexpected periods of high market volatility are the primary source of extreme loss for short premium positions. These events are highly unlikely but typically happen when large price swings occur in the underlying while the expected move range is tight (low IV). Trading short premium once IV is elevated is one way to consistently reduce this exposure. The profitability of short options strategies depends on having a large number of occurrences to reach positive statistical averages. At minimum, approximately 200 occurrences are needed for the average P/L of a strategy to converge to long‐term profit targets and more is better. Although trading short premium in high IV is ideal, high IV environments are somewhat uncommon. This means that short premium traders must strike a balance between being exposed to large losses and reaching a sufficient number of occurrences. Trading short options strategies in all IV environments accumulates profits more consistently and makes it more likely to reach the minimum number of occurrences. To manage exposure to outlier risk when adopting this strategy, it's essential to maintain small position sizes and limit the amount of capital allocated to short premium positions. This strategy can also be improved by scaling the amount of capital allocated to short premium according to the current market conditions. Managing positions actively is one way to reduce P/L uncertainty on a trade‐by‐trade basis, use capital more efficiently, and achieve more occurrences in a given time frame. The choice of whether to close a position early and redeploy capital depends on the acceptable amount of capital to risk on a single trade and whether it is an efficient use of capital to remain in the existing trade. These concepts will be explored more in Chapter 6 . Notes 1 These are approximate strikes for the 16Δ SPY strangle calculated using the equation from Chapter 2 . The actual strikes for a 16Δ SPY strangle are calculated using more complex estimations for expected range, which will be touched on in the appendix. 2 It is difficult to make a one‐to‐one comparison between equity returns and option P/Ls because these instruments operate over different timescales. The closest option analog to an equity returns distribution is a distribution for the ending P/Ls of a particular strategy. 3 Statistics represented as a percentage of initial credit are more representative of long‐term values than those represented with dollars. Equity prices drift with time, meaning the prices for their options do as well. Normalizing P/L statistics by the initial credit makes them more robust to changes in time but also makes comparisons between strategies less intuitive. This book will often represent option statistics in dollars, but remember these statistics are averaged over fairly long time frames. 4 These are past‐looking risk metrics. Metrics of forward‐looking risk include implied volatility and buying power reduction (BPR), which will be covered in the following chapter. Forward‐looking metrics are the focus of this book and more relevant in applied trading, but past‐looking metrics are still included for the sake of completeness and education. 5 Specifically, the standard deviation of the average of n independent occurrences is times the standard deviation of a single occurrence. 6 More specifically, the portfolio capital being referred to here is the portfolio buying power, which we will introduce in the following chapter. 7 This is a highly simplified backtest and should be taken with a grain of salt. These portfolios are highly concentrated in a single position and do not incorporate any complex management strategies. Options are highly sensitive to changes in timescale, meaning that a concurrent portfolio with strangles opened on slightly different days, closed on slightly different days, or with slightly different durations may have performed quite differently than the ones shown here. These backtests show one specific outcome and serve to compare the risk of different allocation percentages in a one‐to‐one fashion. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c04.xhtml SCORE: 279.50 ================================================================================ Chapter 4 Buying Power Reduction Having discussed the nature of implied volatility (IV) and the general risk‐reward profile of short premium positions, it's time to introduce some elements of short volatility trading in practice. Because short options are subject to significant tail risk, brokers must reserve a certain amount of capital to cover the potential losses of each position. The capital required to place and maintain a short premium trade is called the buying power reduction (BPR), and the total amount of portfolio capital available for trading is the portfolio buying power. BPR is the amount of capital required to be set aside in the account to insure a short option position, similar to escrow. BPR is used to evaluate short premium risk on a trade‐by‐trade basis in two ways: BPR acts as a fairly reliable metric for the worst‐case loss for an undefined risk position in current market conditions. BPR is used to determine if a position is appropriate for a portfolio with a certain buying power. Though BPR is the option counterpart of stock margin, the distinction between the two cannot be overstated , as short options positions can never be traded with borrowed money. BPR is not borrowed money nor does it accrue interest. It is your capital that is out of play for the duration of the short option trade. Margin, mostly used for stock trading, is money borrowed from brokers to purchase stock valued beyond the cash in an account. Interest does accrue on margin (usually between a 5% to 7% annual rate), and traders are required to pay back the margin plus interest regardless of whether the stock trade was profitable. Margin and BPR are conceptually different: Margin amplifies stock purchasing power, and BPR lowers purchasing power to account for the additional risk of short options. The definition of BPR and its usage differs depending on whether the strategy is long or short and whether the strategy has defined or undefined risk. For long options, the maximum loss is simply the cost of the option, so that is the BPR. Defining the BPR for short options is more complicated, particularly for undefined risk positions, because the loss is theoretically unlimited. Defined risk trades, which will be covered in the next chapter, are short premium trades with a known maximum loss. These are simply short premium contracts (undefined risk trades) combined with cheaper, long premium contracts that will cap the excess losses when the underlying price moves past the further strike. BPR is the maximum loss for a defined risk strategy, but only an estimate for maximum loss for an undefined risk trade. Because the undefined risk case is more complicated, this chapter explains the BPR as it relates to undefined risk strategies, specifically short strangles. Up until now, options trading has predominantly been discussed within the context of strangles, an undefined risk strategy with limited gain and theoretically unlimited loss. In this case, the BPR is calculated such that it is unlikely that the loss of a position will exceed that threshold. More specifically, BPR is intended to account for roughly 95% of potential losses with exchange-traded fund (ETF) underlyings and 90% of potential losses with stock underlyings. 1 The historical effectiveness of BPR for an ETF underlying is seen in Figure 4.1 by looking at losses for 45 days to expiration (DTE) 16 SPY strangle from 2005–2021. Figure 4.1 Loss as a % of BPR for 45 DTE 16 SPY strangles held to expiration from 2005–2021. In this example, most losses ranged from 0% to 20% of the BPR. Roughly 95% of all these losses were accounted for by the BPR when this position was held to expiration, as expected. Though BPR did not always capture the full extent of realized losses, it is an effective proxy for worst‐case loss on a trade‐by‐trade basis in most cases. This metric works fairly well for SPY strangles, but strangles with more volatile underlyings and strangles with tighter strikes may be more likely to have losses that breach BPR (hence the 90% efficacy rate for stocks). BPR corresponds to the capital required to place a trade, and that quantity varies depending on the specific strategy. The BPR for short strangles can be approximated as 20% of the price of the underlying, but mathematically, BPR depends on three variables: the stock price, put/call prices, and the put/call strike prices. 2 Because the strangle is composed of the short out‐of‐the‐money (OTM) call and short OTM put, the BPR required to sell a strangle is simply the larger of the short put BPR and the short call BPR. The short call/put BPR is the largest of three different values: , which is the expected loss from a 20% move in the underlying price. , which is the expected loss from a 10% strike breach. , which ensures that there is a minimum BPR for cheap options. As BPR is intended to encompass the largest likely loss for an undefined risk contract, the largest of these values is taken. This can be mathematically represented using the max function, which takes the largest of the given values: (4.1) (4.2) Combining these formulas, the BPR of the strangle is given by: (4.3) Clearly, this equation is hairy, but using some numerical examples, one can infer how strangle BPR and, therefore, option risk changes with more intuitive variables, such as the historical and implied volatility of the underlying. Consider three potential strangle trades outlined in Table 4.1 . Table 4.1 Three examples of approximate 45 DTE 16 strangle trades with different parameters and the resulting BPR. Scenario A Scenario B Scenario C Stock Price $150 $150 $300 Call Strike $160 $175 $320 Put Strike $140 $130 $280 Call Price $1 $2 $2 Put Price $1 $2 $2 BPR $2,000 $1,750 $4,000 IV 20% 45% 20% The underlying in Scenario B is priced the same as that of Scenario A, but the strikes for the 16 strangle are further apart (consistent with a higher implied volatility). The underlying in Scenario C is twice as expensive as the underlyings in Scenarios A and B, but the IV in Scenario C is the same as that of Scenario A. Because the BPR is higher in Scenario C compared to Scenario A (but the implied volatility and contract delta are the same), traders can deduce that strangle BPR tends to increase with the price of the underlying. Technically , BPR is inversely correlated with option price, but the BPR still tends to increase with the price of the underlying because more expensive instruments have larger volatilities (as a dollar amount) and, therefore, higher potential losses. BPR also decreases as the IV of the underlying increases, and both relationships can be seen in Figure 4.2 looking at BPR for 45 DTE 16 SPY strangles from 2005–2021. These charts show a strong linear relationship between BPR and underlying price and a slightly messier inverse relationship between BPR and underlying IV. This relationship is largely driven by the strikes moving further OTM for a fixed as IV increases. BPR tends to decrease exponentially as the IV of the underlying increases, and because BPR is a rough estimate for worst‐case loss, this relationship illustrates how the magnitude of potential outlier losses tends to decrease when IV increases. 3 Figure 4.2 Data from 45 DTE 16 SPY strangles from 2005–2021. (a) BPR as a function of underlying price. (b) BPR as a function of underlying IV. Short premium positions carry higher credits and larger profit potentials when IV is high, but the reduction in BPR also allows more short premium positions to be placed compared to when IV is low. Because average profit and loss (P/L) is higher on a trade‐by‐trade basis and more potentially profitable positions can be opened, it is essential to reserve a large percentage of portfolio buying power for high IV conditions. This additionally justifies increasing the percentage of portfolio capital allocated to short premium BPR as IV increases. These crucial high‐IV profits improve portfolio performance but also cushion potential future losses. Historically, when the VIX has been over 40 compared to under 15, the same amount of capital has covered the BPR of roughly twice as many 16Δ SPY strangles. The difference between the number of short premium trades allowed in these two volatility environments is even larger when taking portfolio allocation guidelines into account. For context, consider the scenarios outlined in Table 4.2 . Table 4.2 Two portfolios with the same net liquidity but different amounts of market volatility, using SPY strangle data from 2005–2021. Scenario A Scenario B Net Portfolio Liquidity $100,000 $100,000 Current VIX > 40 < 15 Portfolio Allocation $50,000 $25,000 Approx. 16 SPY Strangle BPR $1,500 $3,300 Max Number of Strangles 33 7 It's important to note that BPR can be used to compare the capital at risk for variations of the same type of strategy, but it cannot be used to compare the risk between defined risk strategies and undefined risk strategies. For example, if the BPR required to trade a short strangle with underlying A was twice the BPR required to trade a short strangle with underlying B and otherwise had identical parameters, we can conclude that A is twice as risky as B. This is a valid comparison because we are considering two trades with the same risk profile, but BPR cannot be used to compare strategies with different risk profiles (say, a short strangle versus a short put) because it does not account for factors like the probability of profit or the probability of incurring a large loss. This subtlety will be discussed in more detail in the following chapter. Understanding BPR is crucial when transitioning from options theory to applied options trading because it corresponds to the actual capital requirements of trading short options. BPR is also necessary to discuss the capital efficiency of options (option leverage) in entirety. Consider a stock trading at $100 with a volatility of 20%, and suppose a trader wanted to invest in this asset with a bullish directional assumption. The trader could achieve a bullish directional exposure to this underlying in a few different ways as shown with the examples in Table 4.3 . Table 4.3 Example trades that offer bullish directional exposure. Assume that the 50 (ATM) call and put contracts have 45 DTE durations and cover 100 shares of stock. Strategy Capital Required Max Profit Max Loss Probability of Profit (POP) 50 Shares of Long Stock $5,000 ∞ $5,000 50% Long 50 Call $280 ∞ $280 30% Short 50 Put $2,000 (BPR) $280 $9,720 60% In this one‐to‐one comparison, the effects of option leverage are clear because the long call position achieves the same profit potential as the long stock position with 94% less capital at risk. The short put position is capable of losing several times the initial investment of the trade but has a higher POP than the long stock position and requires 60% less capital. Suppose that the price of the stock increases to $105 after 45 days. The resulting profits and corresponding returns for these different positions is given below: Long stock: Long ATM call: Short ATM put: In this example, the long call position was able to achieve 88% of the long stock profit with 94% less capital, and the short put position was able to achieve 12% more profit than the long stock position with 60% less capital. Takeaways Because short premiums are subject to significant tail risk, brokers must reserve capital to cover the potential losses of each position. This capital is called BPR. The total amount of portfolio capital available for trading is called portfolio buying power. BPR is used to evaluate short premium risk on a trade‐by‐trade basis in two ways: BPR is a fairly reliable metric for worst‐case loss of an undefined risk position, and BPR is used to determine if a position is appropriate for a portfolio based on its buying power. For long options, BPR is the cost of the option. For short strangles, the BPR is roughly 20% of the price of the underlying. BPR for short options encompasses roughly 95% of potential losses for ETF underlyings and 90% of losses for stock underlyings. Strangle BPR tends to increase linearly with the price of the underlying because more expensive instruments have larger volatilities (as a dollar amount) and, therefore, higher potential losses. There is an inverse relationship between strangle BPR and underlying IV; more specifically, it approximately decreases exponentially as the IV of the underlying increases. This demonstrates the advantages of trading short when IV is high because more short strangles can be opened with the same amount of capital as in low IV, and the outlier loss potential is generally lower. BPR can be used to compare capital at risk for variations of the same strategy, but it cannot be used to compare the risk of different strategies with different risk profiles. The leveraged nature of options allows traders to achieve a desired risk‐return profile with significantly less capital than an equivalent stock position. Notes 1 This statistic will vary with the IV of the underlying, but this is a suitable approximation for general cases. 2 This is the FINRA (Financial Industry Regulatory Authority) regulatory minimum. Brokers typically follow this formula, but occasionally (especially when IV is very high) they will increase the capital requirements for contracts on specific underlyings. 3 This relationship between BPR and IV is specific to strangles. The next chapter discusses how these relationships may differ for certain defined risk strategies. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c05.xhtml SCORE: 879.50 ================================================================================ Chapter 5 Constructing a Trade This book has covered a number of topics but how does one tie all these concepts together and actually build a trade? Options are unique in that they have tunable risk‐reward profiles, and the type of strategy and choice of contract parameters hugely impact the characteristics of that profile. This chapter describes some common short premium strategies and how varying each contract feature tends to alter the risk‐reward properties of a short position. Some basic guidelines are also included, but the ideal trade selection ultimately depends on personal profit goals, loss tolerances, account size, and the existing positions in a portfolio. Each new trade should complement existing positions, ideally contributing some degree of diversification to the overall risk profile. However, first this chapter outlines the mechanics of building individual trades; portfolio management will be discussed later. The general procedure for constructing a trade can be summarized as follows: Choose an asset universe. Choose an underlying. Choose a contract duration. Choose a defined or undefined risk strategy. Choose a directional assumption. Choose a delta. All these factors impact the overall profile of a trade, and strategies are rarely constructed in a linear manner. Traders build trades according to their personal preferences and the size of their account, making the process of constructing a position unique. For instance, if the priority is an undefined risk trade, the choice of underlying will have more constraints. If the priority is trading a particular underlying under a certain directional assumption , the delta and the risk definition will have more constraints. Choose an Asset Universe Before choosing an underlying, it's important to start with an appropriate asset universe or a set of tradable securities with desirable characteristics. The assets suitable for retail options trading must have highly liquid options markets, meaning the contracts for the security can be easily converted into cash without significantly affecting market price. To understand why liquidity is crucial, consider an example of an illiquid asset, such as a house. Selling a home at fair market value in a saturated housing market requires significant time and effort. Sellers run the additional risk of having to reduce the asking price significantly to secure a buyer quickly. Options illiquidity carries risk for similar reasons, and selectively trading assets with liquid options markets ensures that contract orders will be filled efficiently and at a fair market price. Options liquidity is not equivalent to underlying liquidity. An underlying is considered liquid if it has the following characteristics: A high daily volume, meaning many shares traded daily (>1 million). A tight bid‐ask spread, meaning a small difference between the maximum a buyer is willing to pay and the minimum a seller is willing to take (<0.1% of the asset price). Some examples of liquid underlyings include AMZN, IBM, SPY, and TSLA, as shown in Table 5.1 below. Table 5.1 Pricing, bid‐ask spread, and daily volume data for different equities collected on February 10, 2020, at 1 p.m. Asset Previous Closing Price Bid‐Ask Spread Spread/Close (% of Closing Price) Daily Trading Volume AMZN $3,322.94 $0.32 0.01% 1,240,935 IBM $121.98 $0.05 0.04% 2,484,505 SPY $390.51 $0.02 0.005% 16,619,920 TSLA $863.42 $0.51 0.06% 9,371,760 It is relatively straightforward to verify underlying liquidity using daily volume and bid‐ask spread as a percentage of closing price. However, a liquid underlying may not have an equally liquid options market. Sufficiently liquid options underlyings must have contract prices with tight bid‐ask spreads and high daily volumes. The options selection should also offer flexible time frames and strike prices. An underlying with a liquid options market is thus classified by the following properties: A high open interest or volume across strikes (at least a few hundred per strike). A tight bid‐ask spread (<1% of the contract price). Available contracts with several strike prices and expiration dates. Options liquidity ensures that traders have a wide selection of contracts to choose from and that short premium positions can be opened (i.e., contracts can be sold to a buyer) easily. Additionally, liquidity minimizes the risk of being stuck in a position because it allows traders to close short premium positions (i.e., identical contracts can be bought back) quickly. The asset universe presented in this book is equity‐based and mostly consists of stock and exchange‐traded fund (ETF) underlyings, recalling that a stock represents a share of ownership for a single company, and an ETF tracks a specific set of securities, such as a sector, commodity, or market index. However, asset universes are generally product indifferent and can include any instruments with liquid options that present opportunities, such as commodities, digital currencies, and futures. Choose an Underlying The choice of underlying from a universe of sufficiently liquid assets is somewhat arbitrary, but traders often choose to trade short options on instruments for a preferred company, sector, or market under specific directional beliefs. Though this is a perfectly fine way to trade, it's also important to select an underlying with an appropriate amount of risk for a given account size. The two broad classes of instruments in the example asset universe, stocks and ETFs generally have different volatility profiles, and there are pros and cons to trading each, summarized in Table 5.2 . Table 5.2 General pros and cons for stock and ETF underlyings. Stocks ETFs Pros Cons Pros Cons Tend to have options with higher credits and higher profit potentials Frequent high implied volatility (IV) conditions Single‐company risk factors Earnings and dividend risk Tend to have options with higher buying power reductions (BPRs) Inherently diversified across sectors or markets Tend to have options with lower BPRs and are still highly liquid Limited selection compared to stocks High IV conditions are not common When choosing an underlying, the capital requirement of the trade is a limiting factor. A single position should generally occupy no more than 5% to 7% of portfolio capital, meaning that stock underlyings may not be suitable for small accounts because they are more expensive to trade. However, since selling premium when IV is elevated has several benefits, stock underlyings may be preferable underlyings in certain circumstances. As stocks are subject to company‐ and sector‐specific risks, they tend to have higher IVs compared to ETFs and tend to present elevated IV opportunities more often. Note that if trading stock options, investors should also be aware of the contextual information (e.g., earnings reports dates, company announcements) that may be driving these periods of IV inflation because it may impact the strategy choice. 1 This practice is less important when trading options with ETF underlyings. The additional risk factors (coupled with the fact that liquid stocks are often more expensive than ETFs) result in stock options generally having much larger profit and loss (P/L) swings throughout the contract duration, more ending P/L variability, and more tail risk. If the capital requirements of the trade are not excessive and the IV of the underlying is favorable, then these will be the next factors to consider. Overall, stock options are usually riskier but also carry a higher profit potential than ETF options. Consider the statistics outlined in Table 5.3 . Table 5.3 Options P/L and probability of profit (POP) statistics 45 days to expiration (DTE) 16 strangles with six different underlyings, held to expiration, from 2009–2020. Assets include SPY (S&P 500 ETF), GLD (gold commodity ETF), SLV (silver commodity ETF), AAPL (Apple stock), GOOGL (Google stock), and AMZN (Amazon stock). 16 Strangle Statistics, Held to Expiration (2009–2020) Underlying Average Profit Average Loss POP ETFs SPY $160 –$297 82% GLD $125 –$424 83% SLV $33 –$103 81% Stocks AAPL $431 –$1,425 76% GOOGL $1,108 –$2,886 80% AMZN $1,041 –$2,215 78% The tolerance for P/L swings, ending P/L variability, and tail exposure depends mostly on account size and personal risk preferences. If a trade approximately satisfies those preferences and the constraints previously stated, then the choice of underlying is somewhat irrelevant because of a concept called product indifference. Because IV is derived from option price, if two assets have the same IV, their options will have roughly the same price (as a percentage of underlying price). Consequently, one underlying will not give more edge with respect to options pricing inefficiencies compared to another, provided they have similarly liquid options markets. To visualize this, consider the example in Table 5.4 . Table 5.4 Two sample options underlyings with the same IV but differing stock and put prices. Option Parameters Scenario A Scenario B Stock Price $100 $200 IV 33% 33% 45 DTE 16 Put Price $1 $2 In Scenario A, the put is $1 (1% of the underlying price). Due to the efficient nature of options pricing, the short put in Scenario B will also cost 1% of the underlying price, as both assets have the same IV. Product indifference suggests that no one (liquid) underlying is inherently superior to another, merely that there are proportional trade‐offs among different assets. The high‐risk, high‐reward nature of stocks is not inherently better or worse than the relatively stable nature of ETFs, but some assets may be more suitable for an individual trader than others. We can, thus, conclude that the choice of an underlying essentially depends on five main factors (in order of significance): The liquidity of the options market The BPR of the trade relative to account size 2 The IV of the underlying 3 The preferred magnitude of P/L swings, ending P/L variability, and tail exposure per trade The preferred company, sector, or market exposure Choose a Contract Duration There are many ways to choose a contract duration, but this book approaches this process from a qualitative perspective. The three primary goals when choosing a contract duration are summarized as follows: Using portfolio buying power effectively. Maintaining consistency and reaching a large number of occurrences. Selecting a suitable time frame given contextual information. It is essential to determine what contract duration is the most effective use of portfolio buying power without exceeding risk tolerances. Premium prices tend to be more sensitive to changes in underlying price (higher gamma) for contracts that are near expiration (5 DTE) compared to contracts that are far from expiration (120 DTE). Consequently, short‐term contracts tend to have significant P/Ls swings for a larger portion of their duration compared to longer‐term contracts, which initially have more moderate P/L swings and gradually become more volatile. Most contracts also tend to exhibit an increase in P/L instability as they near expiration, which is also a consequence of higher gamma. The gamma of a contract tends to increase throughout a contract's duration, usually the result of the underlying price drifting closer to one of the strangle strikes over time. Figure 5.1 illustrates these concepts by comparing the standard deviation of daily P/Ls for different durations of the same type of contract. All of these strangles exhibit a decrease in P/L swings right before expiration. This is because options rapidly lose their extrinsic value near expiration, presuming they are not in‐the‐money (ITM), which is usually the case because 16Δ options often expire worthless. Near expiration, this exponential decline in premium from theta decay outweighs the magnitude of the P/L swings. The P/L swings at the beginning of the contract vary greatly based on the contract duration. On day seven, the daily P/L for the 15 DTE contract has a high variance, and the 30 DTE, 45 DTE, and 60 DTE contracts have much lower P/L swings around the seven‐day mark. This is because the 16 strikes in the 15 DTE contract are much closer to the at‐the‐money (ATM) than the 16 strikes in the 30+ DTE contracts. This is shown numerically in Table 5.5 . 4 Figure 5.1 Standard deviation of daily P/Ls (in dollars) for 16 SPY strangles with various durations from 2005–2021. Included are durations of (a) 15 DTE, (b) 30 DTE, (c) 45 DTE and (d) 60 DTE. Table 5.5 illustrates how the 16 strikes are closer to the stock price for the 15 DTE contract compared to longer duration strangles. Therefore, small changes in the price of the underlying will have a larger impact on the option's delta compared to contracts with longer durations and further out strike prices. The 30+ DTE contracts tend to experience larger P/L swings once they near expiration because the underlying price often drifts toward one of the strikes over time. Longer contract durations, because their P/L swings are manageable for a longer period of time, give traders more time to assess the trade and adjust to changes in market conditions. However, trade durations that are too long are not necessarily effective uses of buying power because they do not allow for as many occurrences and take a longer time to generate profits. To summarize, longer‐term contracts, which don't typically experience large changes in P/L until the latter half of their duration, tie up buying power for a long time without generating significant profit most of that time. By comparison, shorter‐term contracts exhibit volatile P/L swings for the majority of their duration and leave little time to react to new conditions. A middle ground contract duration, one between 30 and 60 days on a monthly expiration cycle, 5 is considered a suitable use of buying power. Middle ground durations offer a period of manageable P/L swings while providing a fair amount of daily premium decay and a reasonable timescale for profit. This buffer time allows traders to evaluate the viability of a trade before P/L swings become more volatile. It also allows traders to incorporate different trade management strategies, which will be covered in the next chapter. Table 5.5 Data for 16 SPY strangles with different durations from April 20, 2021. The first row is the distance between the strike for a 16 put and the price of the underlying for different contract durations (i.e., if the price of the underlying is $100 and the strike for a 16 put is $95, then the put distance is ($100 – $95)/$100 = 5%). The second row is the distance between the strike for a 16 call and the price of the underlying for different contract durations. 16 SPY Option Distance from ATM Option Type 15 DTE 30 DTE 45 DTE Put Distance 3.9% 6.5% 8.0% Call Distance 2.4% 3.9% 4.9% Another important factor to consider when choosing a contract duration is consistency and the number of occurrences. Consistently choosing similar contract time frames increases the number of occurrences and simplifies portfolio management because expiration and management times will roughly align for the majority of short premium trades in a portfolio. As discussed in Chapter 3 , a large number of occurrences is required to reduce the variance of portfolio averages and maximize the likelihood of realizing long‐term expected values. For profit and risk expectations to be dependable, it is essential to choose contract durations (and management strategies) that allow for a reasonable number of occurrences and to do so consistently. Therefore, it's good practice to choose a contract time frame that is convenient to maintain and short enough to allow for several trades to be placed throughout the trading year, presuming the duration maintains a manageable amount of tail risk exposure. The final major factor when choosing a contract duration is contextual information, particularly when trading stock options. Contextual information, such as an approaching election, earnings report date, or forecasted natural disaster cannot necessarily be used to consistently forecast price direction, but it may indicate a predictable change in price volatility. There is, therefore, utility in taking contextual information into account when choosing a contract time frame. This will be discussed in more detail in Chapter 9 . Choose Defined or Undefined Risk Long options strategies are defined risk trades, as the maximum loss is capped by the price of the contract. Short options positions may have defined or undefined risk profiles. Defined risk strategies have a fixed maximum loss, but capping downside risk has drawbacks. Undefined risk strategies have unlimited downside risk, meaning the maximum loss on a trade-by-trade basis is potentially unlimited. The pros and cons of defined and undefined risk strategies are outlined in Table 5.6 . Table 5.6 Comparison of defined and undefined risk strategies. Undefined Risk Defined Risk Pros Cons Pros Cons Higher POPs Higher profit potentials Unlimited downside risk Higher BPRs (more expensive to trade) Limited downside risk Lower BPRs (less expensive to trade) Lower POPs Lower profit potentials Can run into liquidity issues a a Defined risk trades, because they consist of short premium and long premium contracts, require more contracts to be filled than equivalent undefined risk trades. There is, therefore, a higher risk that a defined risk order will be unable to close at a good price compared to an equivalent undefined risk position. Defined risk strategies have a known maximum loss (i.e., the BPR of the trade) and will typically have a lower BPR than an undefined risk strategy with similar parameters (underlying, contract duration, strikes). Although defined risk positions expose less capital than equivalent undefined risk positions, this does not imply they carry less risk. Recall from the discussion of option risk in Chapter 3 that there are several ways to quantify the risk of an options strategy. Though defined risk strategies avoid carrying outlier risk , they are more likely to lose most or all their BPR when losses do occur. It's, therefore, essential to recognize that BPR is mathematically and functionally different for defined and undefined risk trades, and it cannot be used as a comparative risk metric between them. This will be discussed later in the chapter. Due to the differences in POP and profit potential between risk profiles, the maximum amount of portfolio capital allocated should differ depending on whether the strategy is defined or undefined risk. For undefined risk strategies, traders are compensated for the significant tail risk with high profit potentials and high POPs. It is generally recommended that undefined risk strategies constitute the majority of portfolio capital allocated to short premium strategies. More specifically, at least 75% of allocated capital should be in undefined risk strategies (with a maximum of 7% allocated per trade) and at most 25% of allocated capital should be in defined risk strategies (with a maximum of 5% allocated per trade). For a numerical example, consider the allocation scenarios for a $100,000 portfolio described in Table 5.7 . Table 5.7 Portfolio allocation for defined and undefined risk strategies with a $100,000 portfolio at different VIX levels. VIX Level Maximum Portfolio Allocation Minimum Undefined Risk Allocation Maximum Defined Risk Allocation 20 $30,000 $22,500 ($7,000 max BPR per trade) $7,500 ($5,000 max BPR per trade) 40 $50,000 $37,500 ($7,000 max BPR per trade) $12,500 ($5,000 max BPR per trade) These differences will be elaborated on in the next section, but to summarize, the following five factors are generally the most important to consider when comparing defined and undefined risk trades: The amount of BPR required for a trade relative to the net liquidity of the portfolio. The likelihood of profiting from a position. The preferred amount of downside risk. The preferred ending P/L variability and preferred magnitude of P/L swings throughout the contract duration. The profit targets. Defined risk trades typically require less capital, have more moderate P/L swings throughout the trade, and have less ending P/L standard deviation compared to undefined risk trades. Consequently, defined risk trades may be preferable for small accounts and relatively new traders. Undefined risk trades are statistically favorable and have, therefore, been the focus of this book. However, the following section discusses how to construct defined risk trades that behave like undefined risk trades while offering protection against extreme losses. For these types of strategies, and only these types of strategies, defined risk trades can be substituted for undefined risk trades in the portfolio allocation guidelines. Choose a Directional Assumption After choosing a contract underlying, duration, and risk profile, the next steps are determining the directional assumption for the price of the underlying asset and selecting a strategy consistent with that belief and the preferred risk profile. The directional assumption may be bullish, bearish or neutral, and the optimal choice is subjective and depends on one's interpretation of the efficient market hypothesis (EMH). Recall that the EMH assumes that current prices reflect some degree of available information and comes in three main forms: Weak EMH: Current prices reflect all past price information. Semi‐strong EMH: Current prices reflect all publicly available information. Strong EMH: Current prices reflect all possible information. Each form of the EMH implies some degree of limitation with respect to price predictability: Weak EMH: Past price information cannot be used to consistently predict future price information, which invalidates technical analysis. Semi‐strong EMH: Any publicly available information cannot be used to consistently predict future price information, which invalidates fundamental analysis. Strong EMH: No information can be used to consistently predict future price information, which invalidates insider trading. No form of the EMH is universally accepted or rejected, and the ideal form to trade under (if any) depends on personal preference. This book takes a semi‐strong approach to market predictability, assuming equity and option prices effectively reflect available information and that few directional assumptions are valid (e.g., the market trends bullish in the long term). As volatility reverts back to a long‐term value following significant deviations, it is more valid to make directional assumptions on IV once it's inflated rather than directional assumptions around equity prices. This book, therefore, typically focuses on directionally neutral strategies, such as the short strangle, because these types of positions profit from changes in volatility and time and are relatively insensitive to price changes. However, that is a personal choice. Multiple strategies are outlined in Table 5.8 . For reasons discussed in earlier chapters, all these strategies perform best in high IV. However, the POPs of these trades remain relatively high in all volatility environments, justifying that some percentage of capital should be allocated in all IV conditions. To elaborate on the differences between defined and undefined risk, compare statistics for the two neutral strategies: the iron condor and the strangle. An iron condor consists of a short out-of-the-money (OTM) vertical call spread and a short OTM vertical put spread (introduced in Table 5.8 ). This trade is effectively a short strangle paired with a long strangle having strikes that are further OTM (typically called wings). As with strangles, iron condors are profitable when the underlying price stays within the range defined by the short strikes or when there is a significant IV contraction or time decay. For example, a 16 strangle can be turned into a 16 iron condor with 10 wings 6 with the addition of a long call and a long put with the same duration, further from OTM (the long contracts are 10 in this case). An example of an iron condor is shown in Table 5.9 and Figure 5.2 . Table 5.8 Examples of popular short options strategies with the same delta of approximately 20. a Strategy Composition Defined or Undefined Risk Directional Assumption POP b Naked Option Short OTM put Undefined Bullish 80% Short OTM call Undefined Bearish 80% Vertical Spread Short OTM put, long further OTM put Defined Bullish 77% Short OTM call, long further OTM put Defined Bearish 77% Strangle Short OTM put, short OTM call Undefined Neutral 70% Iron Condor Short OTM vertical call spread, short OTM vertical put spread Defined Neutral 60% a The directional assumption will be flipped for the long side of a non‐neutral position. For a long neutral position, the assumption is that the underlying price will move outside of the price range defined by the contract strikes. The POP of the long side is given by 1 – (short POP). b These POPs are approximate. The POP of a defined risk strategy depends heavily on the choice of long delta(s). Contracts with wider long deltas will generally have higher POPs. This will be explored more later in the chapter. The long wings of the iron condor cap the maximum loss as either the difference between the strike prices of the vertical put spread or vertical call spread (whichever is greater) times the number of shares in the contract (typically 100) minus the net credit. The maximum loss of the short iron condor is equivalently the BPR required to open the trade. It can be summarized by the following formula: (5.1) Continuing with the same example as shown in Table 5.9 , we apply this formula to calculate some statistics for these two trades in Table 5.10 . Table 5.9 Example of a 16 SPY strangle and a 16 SPY iron condor with 10 wings when the price of SPY is $315 and its IV is 12%. All contracts must have the same duration. Contract Strikes 16 Strangle 16 Iron Condor with 10 Wings Long Call Strike ‐‐‐ $332 Short Call Strike $328 $328 Short Put Strike $302 $302 Long Put Strike ‐‐‐ $298 The short strikes were approximated with the expected range formula and the long strikes for the iron condor wings were approximated with the Black‐Scholes formula. Underlyings are often subject to strike skew, not to be confused with distribution skew, which neither of these methods really consider. This means that the strikes (both long and short) are typically not equidistant (as a dollar amount) from the price of the underlying although they were approximated in this example as such. This concept will be explored more later in the chapter. Figure 5.2 Graphical representation of the iron condor described in Table 5.9 . The 10 wings correspond to long strikes that are $17 from ATM, which is further OTM than the 16 short strikes that are $13 from ATM. Table 5.10 Initial credits for the 16 SPY strangle and the 16 SPY iron condor with 10 wings outlined in Table 5.9 . Because the difference between the vertical call spread strikes ($332–$328) and the vertical put spread strikes ($302–$298) is the same ($4), this value is used when calculating the maximum loss. Contract Credits 16 Strangle 16 Iron Condor with 10 Wings Long Call Debit ‐‐‐ −$69 Short Call Credit $122 $122 Short Put Credit $108 $108 Long Put Debit ‐‐‐ −$57 Net Credit $230 $104 Max Loss ∞ BPR $5,000 $296 The choice of wing width depends on personal profit targets and the threshold for extreme loss. Large losses generally occur once the long put or call strikes are breached by the price of the underlying, so wings that are further from ATM are exposed to larger outlier moves but are more likely to be profitable. Wings that are closer to ATM are more expensive but also reduce the maximum loss of a trade. To summarize, wings that are further out yield iron condors with a larger profit potential and a higher probability of profit but also larger possible losses. For some numerical examples, refer to the statistics in Table 5.11 . Table 5.11 Statistical comparison of 45 DTE 16 SPY iron condors with different wing widths, held to expiration from 2005–2021. Wings that have a smaller delta are further from ATM compared to wings with a larger delta. Included are 45 DTE 16 SPY strangle statistics held to expiration from 2005–2021 for comparison. 16 Iron Condor Statistics (2005–2021) 16 Strangle Statistics (2005–2021) Statistics 5 Wings 10 Wings 13 Wings POP 79% 75% 73% 81% Average P/L $35 $15 $6 $44 Standard Deviation of P/L $251 $132 $74 $614 Conditional Value at Risk (CVaR) (5%) −$771 −$399 −$220 −$1,535 If the account size allows for it, it is preferable to trade iron condors with wide wings , which have more tail risk than narrow iron condors but are historically more profitable. While iron condors with narrow wings have POPs near 70%, wide iron condors may have POPs of nearly 80%, as shown in Table 5.11 . Wider iron condors, although they have higher BPR requirements, are also less likely to reach max loss than tighter iron condors when losses do occur. Defined risk strategies tend to have lower POPs and profit potentials compared to undefined risk strategies as shown by the strangle statistics included for reference. The iron condor has roughly a third of the profit potential as the strangle on average (in the case of 10Δ wings), but it also has roughly a third of the P/L standard deviation and significantly less tail exposure. Also, as in the wide iron condor example, defined risk trades can be constructed to have similar POPs as an undefined risk strategy while still offering protection from outlier losses. Defining risk in low IV, particularly with strategies that have high POPs, is one way to manage the outlier loss exposure while capitalizing on the benefits of short premium. Defined risk strategies also come with the added benefit of being significantly cheaper to trade, which is another reason they may be a more effective use of portfolio buying power when IV is low. For a numeric reference, consider the BPR statistics in Table 5.12 . Table 5.12 Average BPR comparison of 45 DTE 16 SPY strangles and 45 DTE 16 SPY iron condors with 10 wings when held to expiration using data from 2005–2021. SPY Strangle and Iron Condor BPRs (2005–2021) VIX Range Strangle BPR Iron Condor BPR a 0–15 $3,270 $363 15–25 $2,641 $426 25–35 $2,261 $585 35–45 $1,648 $553 45+ $1,445 $615 a Iron condors with static dollar wings (e.g., $10 wings, $20 wings) have BPRs that decrease with IV as seen with strangles. Iron condors with dynamic wings that change with variables, such as IV (e.g., 10 , 5 ) have BPRs that increase with IV. Recall that the iron condor BPR is the widest short spread width minus the initial credit. Therefore, as IV increases, the widest width increases faster than the initial credit, so the BPR increases with IV. Defined risk strategies with high POPs can account for a greater percentage of portfolio allocation than defined risk strategies with lower POPs. Previously, we stated that at least 75% of allocated capital should be in undefined risk strategies (with a maximum of 7% allocated per trade) and at most 25% of allocated capital should be in defined risk strategies (with a maximum of 5% allocated per trade). However, a defined risk strategy with a POP comparable to an undefined risk strategy can share undefined risk portfolio buying power, which protects capital from extreme losses while still allowing for consistent profits. Once IV expands, traders can then transition to strangles to capitalize on the higher credits and reduced outlier risk. It's crucial to reiterate that BPR cannot be used to compare risk between strategies with different risk profiles. For instance, refer back to the example in Table 5.10 . The strangle requires roughly 17 times more buying power than the iron condor, but this is not to say that the risk of the strangle is equivalent to the risk of 17 iron condors. The strangle is more likely to be profitable and much less likely to lose the entire BPR because that would require a much larger move in the underlying (20%) compared to the iron condor (5%). Very wide iron condors have similar risk profile to strangles, but it is generally good practice to avoid directly comparing defined and undefined risk strategies using buying power. Choosing a Delta Recall that delta is a measure of directional exposure . According to the mathematical definition derived from the Black‐Scholes model, it represents the expected change in the option price given a $1 increase in the price of the underlying (assuming all other variables stay constant). 7 For example, if the price of an underlying increases by $1, the price for a long call option with a delta of 0.50 (denoted as 50 ) will increase by approximately $0.50 per share, and the price for a long put option with a delta of –0.50 (denoted as –50 , or just 50 when the sign is clear from context) will decrease by approximately $0.50 per share. 8 The delta of a contract additionally represents the perceived risk of that option in terms of shares of equity. More specifically, delta corresponds to the number of shares required to hedge the directional exposure of that option according to market sentiment. This book frequently references the 16 SPY strangle, which is a delta neutral trade consisting of a short 16 put directionally hedged with a short 16 call. Delta neutral positions profit from factors such as decreases in IV and time decay rather than directional changes in the underlying. When originally presented in Chapter 3 , the short strike prices were related to the expected range, and therefore, strike prices were shown to be equidistant from the price of the underlying as in Figure 5.3 . The strikes in this example were derived from the expected move range approximation shown in Chapter 2 . However, in practice the strikes for a 16 SPY put/call are calculated from real‐time supply and demand and are often subject to strike skew . Revisit the example from Table 5.5 to see an example of this. Table 5.5 shows that the put strikes are much further from the price of the underlying compared to the call strikes even though the call and put contracts are both 16 . According to market demand, put contracts further OTM have equivalent risk as call contracts less OTM. This skew results from market fear to the downside , meaning the market fears larger extreme moves to the downside more than extreme moves to the upside. 9 As delta is based on the market's perception of risk, strikes for a given delta are skewed according to that perception. But not all instruments will have the same degree of skew. Stocks like AAPL and GOOGL have fairly equidistant strikes, but market indexes and commodities (e.g., gold and oil) tend to have downside skew, otherwise known as put skew. Assets like GME (GameStop) and AMC (entertainment company) developed upside skew, otherwise known as call skew, during 2020. Figure 5.3 The price of SPY in the last 5 months of 2019. Included is the 45‐day expected move cone calculated from the IV of SPY in December 2019, where the strike for the 16 call is $328 and the strike for the 16 put is $302. Because delta is a measure of perceived risk in terms of share equivalency, the chosen delta is going to significantly impact the risk‐reward profile of a trade. Positions with larger deltas (closer to −100 or +100 ) are more sensitive to changes in the price of the underlying compared to positions with smaller deltas (closer to 0). To observe how this impacts per‐trade performance, consider the statistics for 45 DTE SPY strangles with different deltas outlined in Tables 5.13 – 5.15 . Table 5.13 Statistical comparison of 45 DTE SPY strangles of different deltas, held to expiration from 2005–2021. SPY Strangle Statistics (2005–2021) Statistics 16 20 30 POP 81% 76% 68% Average P/L $44 $49 $54 Standard Deviation of P/L $614 $659 $747 CVaR (5%) −$1,535 −$1,673 −1,931 Table 5.14 Average BPRs of 45 DTE SPY strangles with different deltas, sorted by IV from 2005–2021. SPY Strangle BPRs (2005–2021) VIX Range 16 20 30 0–15 $3,270 $3,366 $3,573 15–25 $2,641 $2,756 $3,014 25–35 $2,261 $2,415 $2,794 35–45 $1,648 $1,715 $2,058 45+ $1,445 $1,421 $1,520 Table 5.15 Probability of incurring a loss exceeding the BPR for 45 DTE SPY strangles of different deltas, held to expiration from 2005–2021. SPY Strangle Statistics (2005–2021) Strangle Delta Probability of Loss Greater Than BPR 16 0.90% 20 0.93% 30 1.0% Positions with higher deltas have larger P/L swings throughout the contract duration, more ending P/L variability, higher BPRs and lower POPs compared to positions with lower deltas. However, higher delta positions also carry higher credits and larger profit potentials overall. Positions with lower deltas achieve smaller profits more often and are lower risk than higher delta trades. Positions with lower deltas also tend to have higher thetas as a percentage of the option value, meaning they may reach profit targets more quickly than positions with higher deltas (not shown in these tables). The optimal choice of delta depends on the personal profit goals and, most importantly, personal risk tolerances. ITM options (options with a delta magnitude larger than 50) generally carry more directional risk and an insufficient amount of theta (expected daily profits due to time decay) than what is suitable for a short premium trade. OTM options are typically better candidates. When trading short premium, contract deltas between 10 and 40 are typically large enough to achieve reasonable growth but small enough to have manageable P/L swings, moderate standard deviation of ending P/L, and moderate outlier risk. More risk‐tolerant traders generally trade options over 25 and more risk‐averse traders will trade under 25 . When IV increases and options become cheaper to trade, more risk‐tolerant traders may also scale delta up to capitalize on the larger credits across the entire options chain. It is also good practice to re‐center the deltas of existing positions when IV increases because increases in IV cause the strike price for a given delta to move further away from the spot price. To see an example of this, consider Table 5.16 . Table 5.16 Comparison of strike prices for two 30 DTE 16 call options with the same underlying price but different IVs. Example Parameters for a 30 DTE 16 Call Option IV Underlying Price Strike Price 10% $100 $103 50% $100 $117 The strike price for a 16 call is $17 away from the price of the underlying when the IV is 50%, compared to $3 away when the IV is 10%. This is because an increase in IV indicates an increase in the expected range for the underlying price. When this expected range becomes larger, contracts with strikes further away from the current price of the underlying are in higher demand than in lower IV conditions. This demand increases the premiums of those contracts and consequently the perceived risk. When IV increases, it is good practice to close existing positions and reopen them with adjusted strikes that better reflect the new volatility conditions. Takeaways Constructing a trade has six major steps, and the ideal choices are based on account size and the personal profit goals, risk tolerances, and market assumptions. The primary factors to consider are the asset universe, the underlying, the contract duration, the risk profile of the strategy, the directional assumption, and the delta. Traders should choose assets with highly liquid options markets, consisting of contracts that can be easily converted into cash without a significant impact on market price. Liquid options markets have a high volume across strikes, tight bid‐ask spreads, and available contracts with several strike prices and expiration dates. In an equity‐focused asset universe, traders have two main choices of equity underlyings: stocks and ETFs. Options with stock underlyings tend to have higher credits, higher profit potentials, and more frequent high IV conditions, but they also have single‐company risks and cost more to trade than options with ETF underlyings. ETFs are inherently diversified and are cheaper than stocks while being very liquid, but fewer choices are available and high IV conditions are less common. A suitable contract duration should use buying power effectively, allow for consistency and a reasonable number of occurrences, and reflect the timescale of contextual events, such as upcoming earnings reports and forecasted natural disasters. Contract durations ranging from 30 to 60 days are generally a suitable use of portfolio buying power, offering manageable P/L volatility and a reasonable timescale for profit. Short premium strategies may have defined or undefined risk. Undefined risk trades have higher POPs and higher profit potentials but also unlimited downside risk and higher BPRs, making them more expensive to trade. Defined risk strategies have limited downside risk and lower BPRs but also lower POPs and lower profit potentials with possible liquidity issues. High‐POP defined risk strategies, such as wide iron condors, can occupy the capital reserved for undefined risk trades, and this is a particularly good strategy when IV is low. Trading high‐POP defined risk trades in low IV and transitioning to undefined risk in high IV is an effective way to protect capital from outlier moves while profiting consistently. Traders must choose one of three directional assumptions for the underlying price: bullish, bearish, and neutral. The optimal choice is subjective and depends on individual interpretation of the EMH, which assumes current prices reflect some degree of available information. The delta of a contract represents the perceived risk of the option in terms of shares of equity, making the choice of delta based on personal risk tolerances and profit goals. A higher delta OTM contract is closer to ATM and more sensitive to changes in underlying price, meaning that these positions are generally riskier but have higher profit potentials. Lower delta OTM contracts are further from ATM and have more moderate P/L swings throughout the contract with lower ending P/L standard deviation generally. When trading short premium, ITM contracts are generally not suitable due to their high directional risks and low thetas. Contracts between 10 and 40 are generally large enough to achieve a reasonable amount of growth but small enough to have manageable P/L swings and moderate ending P/L variability. Notes 1 IV inflation specifically due to earnings is the basis for a type of strategy called an earnings play. Earnings plays will be discussed in Chapter 9 and for now will not be part of stock options discussions. 2 This will be explored more later in this chapter and in Chapter 7 , when covering the portfolio allocation guidelines in more detail. 3 In practice, IV is often interpreted according to the IV percentile or IV rank of the underlying. This is a more common trading metric because traders are rarely deeply familiar with the IV dynamics of different assets, and it is essential to include a range of assets in a balanced portfolio. 4 The put distance and call distance are not symmetric. This is due to strike skew, which will be discussed later in this chapter and in the appendix. 5 Common options expiration dates are divided into weekly, monthly, and quarterly cycles. Contracts with monthly expirations cycles are preferable because they are consistently liquid across liquid underlyings. For highly liquid assets, any expiration cycle is acceptable. 6 Recall that smaller deltas are further from ATM than larger deltas. 7 For contracts with deltas between approximately 10 and 40, delta can also be used as a very rough proxy for the probability that an option will expire ITM. For instance, a 25 put has about a 25% chance of expiring ITM, meaning that there is a 75% POP for the short put. A 16 strangle is composed of a 16 put and a 16 call, so there is approximately a 32% chance that it will expire ITM (consistent with the 68% POP for the short strangle). 8 Delta is between 0 and 1 for long calls and between –1 and 0 for long puts. For short calls and short puts, the numbers are flipped. 9 This is mainly the result of the history of extreme market crashes, such as the 1987 Black Monday crash, the 2008 housing crisis, and the 2020 sell‐off. Prior to 1987, the put and call strikes of the same delta were much closer to equidistant. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c06.xhtml SCORE: 192.50 ================================================================================ Chapter 6 Managing Trades Options traders can hold a position to expiration or close it prior to expiration (active management). Compared to holding a contract until expiration, an active management strategy should be considered for the following reasons: It allows for more occurrences over a given time frame (if capital is redeployed). It may allow for a more efficient use of portfolio buying power (if capital is redeployed). It tends to reduce risk on a trade‐by‐trade basis. Trades can be managed in any number of ways, but similar to choosing a contract duration, consistency is essential for reaching a large number of occurrences and realizing favorable long‐term averages. This book advocates for adopting a simple management strategy that is easily maintainable: Closing a trade at a fixed point in the contract duration. Closing a trade at a fixed profit or loss target. Some combination of these strategies. This chapter discusses different management strategies, compares trade‐by‐trade performance, and elaborates on the major factors to consider when choosing appropriate position management. Because management strategies impact the proportion of initial credit traders ultimately collect, the statistics will often be represented as an initial credit percentage rather than dollars. This chapter also predominantly focuses on undefined risk strategy management. Many of these principles also apply to defined risk positions, but defined risk positions are generally more forgiving from the perspective of trade management because they occupy a smaller percentage of portfolio buying power and have limited loss potential. Managing According to DTE As mentioned in Chapters 3 and 5 , trade profit and loss (P/L) swings tend to become more volatile as options approach expiration. For a strangle, this increase generally results from the price of the underlying drifting toward one of the strikes throughout the contract duration. Consequently, closing a trade prior to expiration, whether at a fixed point in the contract duration or at a specific profit or loss target, tends to reduce ending P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis. Managing trades actively also frees portfolio buying power from existing positions, which can then be allocated more strategically as opportunities arise. The freed capital can be redeployed to the same type of initial position (increasing the number of occurrences) 1 or to a new position with more favorable short premium conditions (which may be a more efficient use of buying power). Managing a trade according to days to expiration (DTE), such as closing a position halfway to expiration, offers the benefits described previously and is straightforward to execute. This technique has a clear management timeline and requires minimal portfolio supervision, particularly when portfolio positions have comparable durations. The choice of management time greatly affects the profit potential and outlier risk exposure of a trade because trades managed closer to expiration are more likely to be profitable and have larger profits on average but are generally exposed to more tail risk. The trade‐by‐trade statistics shown in Table 6.1 compare the performance of different management times for 45 DTE 16 SPY strangles. Table 6.1 Statistics for 45 DTE 16 SPY strangles from 2005–2021 managed at different times in the contract duration. 16 SPY Strangle Statistics (2005–2021) Management DTE Probability of Profit (POP) Average P/L Average Daily P/L P/L Standard Deviation Conditional Value at Risk (CVaR) (5%) 40 DTE 67% 2.3% $0.23 73% –206% 30 DTE 73% 10% $1.75 88% –212% 21 DTE 79% 21% $1.60 96% –283% 15 DTE 78% 25% $1.51 105% –304% 5 DTE a 82% 33% $1.34 185% –514% Expiration 81% 28% $1.29 247% –708% a Strangles managed at 5 DTE seem to outperform strangles held to expiration because they have a higher POP and average P/L but lower P/L volatility and less tail risk. These results are specific to this strategy and data set, and were likely skewed by significant historical events. This trend is not generalizable across strategies, including the one presented in this table. Table 6.1 shows that managing a trade prior to expiration is less likely to profit but also has less P/L standard deviation and less tail risk, and it also collects more daily, on average, compared to holding to expiration. These statistics also demonstrate that management time generally carries a trade‐off among profit potential, loss potential, and the number of occurrences. Compared to trades managed earlier in the contract duration, trades managed later have larger profits and losses and also allow for fewer occurrences. As early‐managed positions accommodate more occurrences and average more P/L per day than positions held to expiration, closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more extrinsic value from an existing position. If adopting this strategy, choose a management time that satisfies individual trade‐by‐trade risk tolerances, offers a suitable profit potential, and occupies buying power for a reasonable amount of time. Remember that selling premium in any capacity carries tail risk exposure even when a position is closed almost immediately (see the 40 DTE results in Table 6.1 ). To achieve a decent amount of long‐term profit and justify the tail loss exposure, consider closing trades around the contract duration midpoint. Managing According to a Profit or Loss Target Compared to allowing a trade to expire, managing a position according to a profit target simplifies profit expectations and tends to reduce per‐trade P/L variance. Closing limit orders can be set by a trader and automatically executed by the broker, but this management strategy still requires some active maintenance. This is because trades may never reach the predetermined profit benchmark and may require alternative management prior to expiration. Additionally, there is some subtlety in choosing the profit target because that choice significantly impacts the profit and loss potential of a trade, as shown in Tables 6.2 and 6.3 . Managing at a profit threshold or expiration generally carries more P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis than managing at 21 DTE, although it also comes with higher POPs and higher per‐trade profit potentials depending on the profit benchmark. Short options are highly likely to reach low profit targets early in the contract duration when P/L swings and tail risk are both fairly low. Therefore, managing a trade according to a low profit target yields a higher strategy POP, lower P/L standard deviation, and less outlier risk compared to managing at a high profit target. However, despite the higher average daily P/Ls, setting the profit threshold too low does not allow traders to collect a sufficient credit to justify the inherent tail risk of the position. Average P/Ls are well below the given profit target in all cases due to the tail loss potential. When using a 25% target, for example, the contract failed to reach the target only 4% of the time. Still, those losses were significant enough to bring down the P/L average by more than half. If this management strategy is adopted, a profit threshold between 50% and 75% of the initial credit is suitable to realize a reasonable amount of long‐term average profit and reduce the impact of outlier losses. Additionally, because these mid‐range profit targets tend to be reached near the contract midpoint or shortly after, these benchmarks also allow for a reasonable number of occurrences. 2 Table 6.2 Statistics for 45 DTE 16 SPY strangles from 2005–2021 managed at different profit targets. If the profit target is not reached during the contract duration, the strangle expires. The final row includes statistics for 45 DTE 16 SPY strangles managed around halfway to expiration (21 DTE) as a reference. 16 SPY Strangle Statistics (2005–2021) Profit Target POP Average P/L P/L Standard Deviation Probability of Reaching Target CVaR (5%) 25% or Exp. 96% 11% 191% 96% −522% 50% or Exp. 91% 16% 236% 90% −654% 75% or Exp. 84% 22% 245% 80% −699% 100% (Exp.) 81% 28% 247% 52% −708% 21 DTE 79% 21% 96% N/A −283% These tests did not account for whether a P/L target was reached throughout the trading day, but rather whether a target was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique. Table 6.3 Average daily P/L and average duration for the contracts and management strategies described in Table 6.2 . 16 SPY Strangle Statistics (2005–2021) Profit Target Average Daily P/L Over Average Duration Average Duration (Days) 25% or Exp. $1.75 15 50% or Exp. $1.67 24 75% or Exp. $1.49 34 100% (Exp.) $1.29 44 21 DTE $1.60 24 These tests did not account for whether a P/L target was reached throughout the trading day, but rather whether a target was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique. Additionally, because there can be significant variability in when a contract reaches a certain profit threshold, daily P/L estimates were derived from data over the average duration of the trade. Just as trades can be managed according to a fixed profit target, they can also be managed according to a fixed loss limit (a stop loss). Defining a loss limit is trickier because option P/L swings are highly volatile. Small loss limits are reached commonly, but trades are also likely to recover. Implementing a very small loss limit may significantly limit upside growth and make losses more likely. To understand this, see Table 6.4 . Table 6.4 Statistics for 45 DTE 16 SPY strangles from 2005–2021 managed at different loss limits. If the loss limit is not reached during the contract duration, the strangle expires. The final two rows reference other management strategies for comparison. 16 SPY Strangle Statistics (2005–2021) Loss Limits POP Avg P/L P/L Standard Deviation Prob. of Reaching Target CVaR (5%) −50% or Exp. 58% 21% 90% 40% −168% −100% or Exp. 69% 25% 110% 25% −238% −200% or Exp. 76% 27% 131% 13% −338% −300% or Exp. 79% 27% 149% 8% −450% −400% or Exp. 79% 27% 160% 6% –536% None (Exp.) 81% 28% 247% N/A −708% 21 DTE 79% 21% 96% N/A −283% 50% Profit or Exp. 91% 16% 236% 90% −654% These tests did not account for whether or not a P/L amount was reached throughout the trading day, but rather whether it was reached by the end of the trading day. Therefore, these statistics are not entirely representative of this management technique. Using a low stop loss threshold, –50% for example, results in lower P/L standard deviation and outlier risk compared to holding the contract to expiration. However, in this case, losses are more common and occur roughly 42% of the time since it is not uncommon for options to reach this loss threshold, although many positions ultimately recover prior to expiration (note the higher POPs for larger limits). Implementing a stop loss also does not necessarily eliminate all tail risk exceeding that threshold. For example, despite having a stop loss of –50%, a sudden implied volatility (IV) expansion or underlying price change may cause daily loss to increase from –25% to –75%, resulting in the closure of the trade but with a final P/L past the loss threshold. Because upside potential is limited and some degree of tail exposure exists with a very small stop loss, a mid‐range stop loss of at least –200% is practical. 3 Using a stop loss and otherwise holding to expiration generally has a higher profit and larger loss potential than managing at the duration midpoint but tends to carry less tail risk than managing at a reasonable profit target. For more active trading, stop losses are not typically used alone but rather combined with another management strategy. Comparing Management Techniques and Choosing a Strategy The strangle management strategies presented thus far are relatively straightforward. These techniques can be ranked according to loss potential (from highest to lowest) and quantified using CVaR and P/L standard deviation of the positions studied: Hold until expiration. Manage at a profit target between 50% and 75%. Manage at a loss limit of –200%. Manage at 21 DTE (halfway to expiration). Remember that consistency and ease of implementation are important factors to consider when choosing a management strategy. For traders who are comfortable with active trading, strategies can be combined and more precisely tuned according to individual preferences. For instance, suppose a trader of 45 DTE 16 SPY strangles wants a management strategy with a high POP, moderate P/L standard deviation, and moderate outlier exposure. One possibility is managing at 50% of the initial credit or at 21 DTE, whichever occurs first. The statistics for this strategy are outlined in Table 6.5 . Table 6.5 Statistics for 45 DTE 16 SPY strangles from 2005–2021 managed either at 50% of the initial credit or 21 DTE, whichever comes first. Statistics for other strategies are given for comparison and ranked by CVaR. 16 SPY Strangle Statistics (2005–2021) Management Strategy POP Average P/L Average Daily P/L P/L Standard Deviation CVaR (5%) 21 DTE 79% 21% $1.60 96% –283% 21 DTE or 50% Profit 81% 18% $1.67 96% –288% –200% Loss or Exp. 76% 27% N/A 131% –338% 50% Profit or Exp. 91% 16% $1.67 236% –654% None (Exp.) 81% 28% $1.29 247% –708% In this example, the duration and profit targets are moderate, resulting in a combined strategy with smaller but slightly more likely profits than 21 DTE management and significantly less loss potential than 50% profit management. This may be appealing to risk‐averse traders because it eliminates a large fraction of the historic losses and significantly reduces tail exposure with the benefit of a slightly higher POP and higher average daily P/L. When choosing a management strategy, know that all management strategies come with trade‐offs among POP, average P/L, P/L standard deviation, and loss potential. How these factors are weighted depends on individual goals: For likely profits, profit potential must be smaller or exposure to outlier losses must be larger. For large profits, there must be fewer occurrences or more exposure to outlier losses. For a small loss potential, profit potential must be smaller or profits must be less likely. For a qualitative comparison of the different strategies, see Table 6.6 . As mentioned, a suitable management strategy depends on individual preferences for trading engagement, per‐trade P/L potential, P/L likelihood and number of occurrences. Following are example scenarios highlighting different management profiles: Table 6.6 Qualitative comparison of different management strategies. Management Strategy 21 DTE 50% or Exp. –200% or Exp. Exp. Convenience Med High a High High POP Med High Med Med Per‐Trade Loss Potential Low High Low High Per‐Trade Profit Potential Med Low High High Number of Occurrences Med Med Low Low a If limit orders are used, profit target management is very convenient. For passive traders with portfolios that can accommodate more outlier risk, it may make more sense to use only a stop loss and otherwise hold trades to expiration to extract as much extrinsic value from existing positions as possible. Active traders with portfolios that can accommodate more outlier risk may manage general positions at a fixed profit target and close higher‐risk, higher‐reward trades halfway to expiration. Very active traders may manage all undefined risk contracts at either 50% of the initial credit or halfway through the contract duration because this method prioritizes moderating outlier risk and achieving likely profits of reasonable size. Generally speaking, an active management approach is more suitable for retail traders because more occurrences can be achieved in a given time frame, it is a more efficient use of capital, average daily profits are higher, and the per‐trade loss potential is lower. It's critical to reiterate that this risk is on a trade‐by‐trade basis. Short premium losses happen infrequently and are often caused by unexpected events, making it difficult to precisely compare long‐term performance of strategies of varying timescales. The next section discusses in more detail why comparing the long‐term risks for management strategies is not straightforward. A Note about Long‐Term Risk As mentioned previously, contracts tend to have more volatile P/L swings as the contract approaches expiration. Managing trades prior to expiration, therefore, tends to have lower P/L standard deviation and outlier risk exposure on a trade‐by‐trade basis compared to holding the contract to expiration. But it's critical to note that this reduction in risk on a trade‐by‐trade basis does not necessarily translate to a reduction in risk on a long‐term basis . Though early management techniques reduce loss magnitude per trade , inherent risk factors arise from a larger number of occurrences. Consequently, one management strategy may have lower per‐trade exposure compared to another, but it may have more cumulative long‐term risk. Consider the scenarios outlined in Figures 6.1 and 6.2 . Each scenario compares the performances of two portfolios, each with $100,000 of capital invested. Both portfolios consist of short 45 DTE 16 SPY strangles continuously traded, but the trades in one portfolio are managed halfway to expiration (21 DTE) and the trades in the other are managed at expiration. The unique market conditions in each scenario affect the performance of each management strategy. 4 The IV expansion during the 2020 sell‐off was one of the largest and most rapid expansions recorded in the past 20 years, producing historic losses for SPY strangles. Due to the timing and duration of this volatility expansion, 45 DTE contracts opened in February and closed at the end of the March expiration cycle experienced the majority of the expansion and were especially affected. Shown in Figure 6.1 , the portfolio of contracts held to expiration was immediately wiped out by this extreme market volatility, and the portfolio of early‐managed contracts incurred a large drawdown of roughly 40% but ultimately survived. This scenario demonstrates how the loss potential for contracts held to expiration is significantly larger than for contracts managed early. However, this does not necessarily mean that holding to expiration results in more cumulative loss long term. Figure 6.1 (a) Two portfolios, each with $100,000 in capital invested, trading short 45 DTE 16 SPY strangles from February 2020 to January 2021. One portfolio consists of strangles managed at 21 DTE (dashed line), and the other consists of strangles held until expiration (solid line). (b) The VIX from February 2020 to January 2021. Figure 6.2 (a) Two portfolios, each with $100,000 in capital invested, trading short 45 DTE 16 SPY strangles from September 2018 to September 2019. One portfolio consists of strangles managed at 21 DTE (dashed line), and the other consists of strangles held until expiration (solid line). (b) The VIX from September 2018 to September 2019. These same strategies perform quite differently near the end of 2018 when the market experienced smaller, more frequent IV expansions. During this period, the 21 DTE management time for 45 DTE contracts consistently landed on IV peaks during this cycle of market volatility, causing the early‐managed portfolio to incur several consecutive losses. Comparatively, the 45 DTE expiration cycles were just long enough to evade these smaller peaks and the portfolio of contracts held to expiration had much stronger performance overall. This scenario demonstrates how having lower per‐trade loss potential does not guarantee stronger long‐term performance or smaller drawdowns. Comparing the long‐term risks of strategies that occur over different timescales is complicated. These examples show potential trading strategies during unique macroeconomic conditions, but any number of factors could have impacted the realized experience of someone trading during these periods. For instance, if people began trading short 45 DTE 16 SPY strangles on February 3, 2020, they would have had a final P/L of –$717 if they managed at 21 DTE and a final P/L of –$8,087 if they held the contract to expiration. If they instead began trading the same strategy one month later on March 4, 2020, they would have had a final P/L of –$2,271 if they managed at 21 DTE and a final P/L of $518 if they held the contract to expiration. Strangle risk and performance, particularly during periods of extreme market volatility, are highly sensitive to changes in timescale and IV. There is as much variation in how people choose contract duration, manage positions, and apply stop losses as there are traders. This makes it difficult to model how people would realistically trade in a statistically rigorous way and, consequently, creates complications when evaluating the long‐term risk of different management strategies. Rather than factor in long‐term risk when selecting a management strategy, the choice should ultimately be based on the following criteria: Convenience/consistency. Capital allocation preferences and desired number of occurrences. Average P/L and outlier loss exposure per trade . Takeaways Traders should choose a consistent management strategy to increase the number of occurrences and the chances of achieving favorable long‐term averages. Some management strategies include closing a trade at a fixed point in the contract duration, closing a trade at a fixed profit or loss target, or some combination of the two. Compared to trades managed early in the contract duration, trades managed later have larger profits and losses, higher POPs, and allow for fewer occurrences. Early‐managed positions accommodate more occurrences and average more P/L per day than positions held to expiration. Closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more extrinsic value from an existing position. If managing according to DTE, consider closing trades around the contract duration midpoint to achieve a decent amount of long‐term profit and justify the tail loss exposure of short premium. To realize reasonable profits and reduce outlier losses, consider a profit threshold between 50% and 75% of the initial credit. A profit or loss target that is too small (say 25% of initial credit) reduces average P/L and per‐trade profit potential, and a profit or loss target that is too large does little to mitigate outlier risk. If implementing a stop loss, a mid‐range stop loss threshold of at least −200% is practical because there is limited upside potential and still some degree of tail exposure with a very low stop loss. A suitable management strategy depends on an individual's preferences for trade engagement, per‐trade average P/L, per‐trade outlier risk exposure, and the number of occurrences. Managing undefined risk contracts at 50% of the initial credit or halfway through the contract duration generally achieves reasonable, consistent profits and moderate outlier risk for those more comfortable with active trading. This policy of trading small and trading often also allows for more occurrences. Comparing long‐term risks of trade management strategies is complicated because unexpected events, such as the 2020 sell‐off, affect short premium strategies differently depending on the contract duration. For this reason, compare the risk and rewards of different strategies on a trade‐by‐trade basis and choose one based on convenience and consistency, capital allocation preferences, tail exposure preferences, and profit goals. The concepts outlined in this chapter are specific to undefined risk positions. These management principles can also be applied to defined risk positions, but defined risk positions are generally more forgiving because they have limited loss potential. It is not as essential to manage defined risk losses because the maximum loss is known, and in some cases, it may be better to allow a defined risk trade more time to recover rather than close the position at a loss. Notes 1 This technique is commonly known as rolling. 2 For defined risk positions, a profit target of roughly 50% or lower is more suitable because P/L swings are less volatile and higher profit targets are less likely to be reached. 3 Stop losses are not suitable for defined risk strategies. As defined risk strategies have a fixed maximum loss, it is best to allow defined risk losers to expire rather than manage them at a specific loss threshold. This gives the position more opportunity to recover. 4 Options portfolio backtests should be taken with a grain of salt. Options are highly sensitive to changes in timescale, meaning that a concurrent portfolio with strangles opened on slightly different days, closed on slightly different days, or with slightly different durations may have performed quite differently than the ones shown here. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c07.xhtml SCORE: 473.50 ================================================================================ Chapter 7 Basic Portfolio Management Whether adopting an equity, option, or hybrid portfolio, building a portfolio is nontrivial. Identifying a suitable collection of elements, calculating optimal portfolio weights, and maintaining that balance easily becomes hairy. Though countless ways to approach this process exist, the portfolio management tactics discussed in this book are fairly back‐of‐the‐envelope and divided between two chapters. This chapter covers necessary guidelines in portfolio management, and the following chapter covers advanced portfolio management including supplementary techniques for portfolio optimization. Basic portfolio management includes the following concepts: Capital allocation guidelines Diversification Maintaining portfolio Greeks Capital Allocation and Position Sizing The purpose of the dynamic allocation guidelines first introduced in Chapter 3 is to limit portfolio tail exposure while also allowing for reasonable long‐term growth by scaling capital allocation according to the current risks and opportunities in the market. Recall that the amount of portfolio buying power allotted to short premium positions, such as short strangles and short iron condors, should range from 25% to 50%, depending on the current market volatility, with the remaining capital either kept in cash or a low‐risk passive investment. Of the amount allocated to short premium, at least 75% should be reserved for undefined risk trades (with less than 7% of portfolio buying power allocated to a single position) and at most 25% reserved for defined risk strategies (with less than 5% of portfolio buying power allocated to a single position), although there are exceptions for high probability of profit (POP), defined risk strategies. It's worth mentioning that it is not always feasible to strictly abide by the position size caps of 5% to 7%. If a portfolio has only $10,000 in buying power and implied volatility (IV) is low (i.e., VIX<15), this rule limits the maximum per‐trade buying power reduction (BPR) to $700 for an undefined risk trade at a time when BPRs tend to be high. This guideline would severely limit the opportunities available for small accounts. Though total portfolio allocation guidelines must be followed, there is more leniency for the per‐trade allocation guidelines in smaller accounts. These guidelines limit the amount of capital exposed to outlier losses, but how capital is allocated depends on personal profit goals and loss tolerances. An options portfolio is typically composed of two types of positions: core and supplemental. Core positions are usually high‐POP trades with moderate profit and loss (P/L) standard deviation. These types of positions should offer consistent, fairly reliable profits and reasonable outlier exposure although they will vary by risk tolerance. Consider the following examples: Riskier core position: a 45 days to expiration (DTE) 20 strangle (undefined risk trade) with a diversified exchange‐traded fund (ETF) underlying, such as SPY or QQQ. More conservative core position: a 45 DTE 16 SPY iron condor with 6 wings (high‐POP, defined risk trade) with a diversified ETF underlying, such as SPY or QQQ. Core positions should comprise the majority of a portfolio and be diversified across sectors to develop more reliable portfolio profit and loss expectations and resilience to market volatility. Supplemental positions are not necessarily dependable sources of profit but rather tools for market engagement. These positions are typically higher‐risk, higher‐reward trades meant to capitalize on dynamic opportunities in the market. Some examples of supplemental positions include earnings trades (which will be discussed in more detail in Chapter 9 ) or strangles with stock underlyings, such as a 45 DTE 16 AAPL strangle. When trading stock underlyings, defined risk supplemental positions would be suitable for more risk‐averse traders. These types of positions have significantly more P/L variability than positions with ETF underlyings, resulting in more per‐trade profit potential and more loss potential with less dependable profit and loss expectations. The expected returns, P/L variability, and tail exposure of a portfolio overall primarily depend on the types of core positions, types of supplemental positions, and the ratio of core positions to supplemental positions. Portfolios for more risk‐tolerant traders may include a larger percentage of supplemental positions. However, mitigating tail risk remains the highest priority, particularly if the portfolio underlyings are not diversified well. This is why, generally speaking, at most 25% of the capital allocated to short premium should go toward supplemental positions. For example, if the VIX is valued at 45 and 50% of portfolio buying power is allotted to short premium positions (per the allocation guidelines), then at most 25% of the 50% portfolio buying power (or 12.5%) should be allocated to supplemental positions. See Table 7.1 for some numerical context. Compared to core positions, such as SPY or QQQ strangles, the supplemental positions above have significantly more profit potential, loss potential, and tail risk exposure. The average profit is larger partially as the result of supplemental underlying assets having higher per share prices. This was the case with GOOGL and AMZN, which cost more than the other equity underlyings throughout the entire backtest period. However, these instruments also carry larger profit potentials as option underlyings because they are subject to company‐specific risk factors that often inflate the values of their respective options. This was particularly the case with AAPL, which had a lower per share value than SPY, QQQ, and GLD throughout this backtest period but more option volatility. Table 7.1 Statistics for 45 DTE 16 strangles from 2011–2020, managed at expiration. Included are examples for core and supplemental position underlyings. 16 Strangle Statistics (2011–2020) Underlying POP Average Profit Average Loss Conditional Value at Risk (CVaR) (5%) Core SLV 84% $32 −$88 −$201 QQQ 74% $109 −$183 −$454 SPY 80% $162 −$320 −$800 GLD 81% $119 −$456 −$1,100 Supplemental AAPL 74% $425 −$1,443 −$4,771 GOOGL 80% $1,174 −$2,955 −$6,593 AMZN 77% $1,235 −$2,513 −$6,810 These statistics do not account for IV or stock‐specific factors, such as earnings or dividends. Due to these single‐stock risk factors and the variance reflected in the option P/Ls, stocks are generally unsuitable underlyings for core positions. Their high profit potentials make them appealing supplemental position underlyings for opportunistic investors, but mitigating the tail risk exposure from supplemental positions is key for portfolio longevity. The most effective way to accomplish this is by strictly limiting the portfolio capital allocated to high‐risk positions. To summarize, core positions should provide somewhat reliable expectations around P/L and be diversified across sectors. Supplemental positions should comprise a smaller percent of a portfolio because they bring higher profit potentials but also more risk. Diversification, particularly when trading options, is another crucial risk management strategy that can significantly reduce portfolio P/L variability and outlier exposure. The Basics of Diversification All financial instruments are subject to some degree of risk, with the risk profiles of some instruments being more flexible than others. A single equity has an immutable risk profile, and an option's risk profile can be adjusted according to multiple parameters. However in either scenario, traders are subject to the risk factors of the particular position. When trading a portfolio of assets, a trader may offset the risks of individual positions using complementary positions. Spreading portfolio capital across a variety of assets is known as diversification. Risk is divided into two broad categories: idiosyncratic and systemic. Idiosyncratic risk is specific to an individual asset, sector, or position and can be minimized using diversification. For example, a portfolio containing only Apple stock is subject to risk factors specific to Apple and the tech sector. Some of those risks can be offset with the addition of an uncorrelated or inversely correlated asset, such as a commodity ETF like GLD. In this more diversified scenario, some hypothetical company‐specific risk factors causing AAPL stock to depreciate may be reduced by the performance of GLD, which has relatively independent dynamics. Comparatively, systemic risk is inherent to the market as a whole and cannot be diversified away. All traded assets are subject to systemic risk because every economy, market, sector, and company has the potential to fail. No amount of diversification will ever remove that element of uncertainty. Instead, the purpose of diversification is to construct a robust portfolio with minimal sensitivity to company‐, sector‐, or market‐specific risk factors. The process of building a diversified portfolio depends on the types of assets comprising the target portfolio. For an equity portfolio, the most effective way to diversify against idiosyncratic risk is to distribute portfolio capital across assets that have low or inversely correlated price movements. This is because the primary concern when trading equities is the directional movement of the underlying, specifically to the downside. Diversifying portfolio assets, typically using instruments for a variety of companies, sectors, and markets, reduces some of this directional concentration and improves the stability of the portfolio. To understand the effectiveness of diversification by this method, consider the example outlined next. Table 7.2 shows different portfolio allocation percentages for two equity portfolios, Table 7.3 shows the correlation of the assets in both portfolios, and Figure 7.1 shows the comparative performance of the two portfolios. The historical directional tendencies are often estimated using the correlation coefficient, which quantifies the strength of the historical linear relationship between two variables. Recall that the correlation coefficient ranges from –1 to 1, with 1 corresponding to perfect positive correlation, –1 corresponding to perfect inverse correlation, and 0 corresponding to no measured correlation. Table 7.2 Two sample portfolios, each containing some percentage of market ETFs for reliable portfolio growth (SPY, QQQ), low volatility assets for diversification (GLD, TLT), and high volatility assets for increased profit potential (AMZN, AAPL). % Portfolio Allocation Portfolio A Portfolio B Market ETFs 40% 50% Low Volatility Assets 50% 0 High Volatility Assets 10% 50% These portfolio weights were determined intuitively and not by any particular quantitative methodology. This example demonstrates the effectiveness of diversification rather than providing a specific framework for achieving diversification in equity portfolios. Table 7.3 The five‐year correlation history for the assets in Portfolios A and B. Though these relationships fluctuate with time over short timescales, they are assumed to remain relatively constant long term. Correlation (2015–2020) SPY QQQ GLD TLT AMZN AAPL Market SPY 1.0 0.89 −0.13 −0.33 0.62 0.64 ETFs QQQ 0.89 1.0 −0.12 −0.26 0.75 0.74 Low Volatility GLD −0.13 −0.12 1.0 0.39 −0.12 −0.11 Assets TLT −0.33 −0.26 0.39 1.0 −0.18 −0.22 High Volatility AMZN 0.62 0.75 −0.12 −0.18 1.0 0.50 Assets AAPL 0.64 0.74 −0.11 −0.22 0.50 1.0 Table 7.2 outlines two portfolios: Portfolio A is a relatively diversified portfolio with conservative risk tolerances and moderate profit expectations, while Portfolio B is a risk tolerant and fairly concentrated portfolio. Table 7.3 shows how the elements in Portfolio B (SPY, QQQ, AMZN, AAPL) have fairly high mutual historic correlations and therefore similar directional tendencies. Comparatively, half of Portfolio A is allocated to low volatility assets that are uncorrelated or inversely correlated with the market ETFs and high volatility assets. Therefore, due to the diversifying contributions of those relatively independent assets, Portfolio A is less sensitive to outlier market events. Figure 7.1 shows how these portfolios would have performed from 2020–2021, importantly including the 2020 sell‐off and subsequent recovery. Figure 7.1 Performance comparison for Portfolios A and B from 2020 to 2021. Each portfolio begins with $100,000 in initial capital. Historic correlations have become stronger during financial crashes and sell‐offs. Stated differently, assets have become more correlated or more inversely correlated during volatile market periods. The correlations in Table 7.2 , therefore, underestimate the correlation magnitudes that would have been measured from 2020–2021. As a result of the COVID‐19 pandemic, market ETFs and highly correlated assets, such as large cap tech stocks incurred significant drawdowns. Portfolio B, half of which was high volatile tech stocks, crashed by roughly 25% from February to late March 2020. Comparatively, Portfolio A still experienced massive drawdowns but only declined by 14% during the same period. Portfolio B is significantly more exposed to market volatility than Portfolio A, resulting in a more rapid, but unstable recovery following the 2020 sell‐off. Throughout this year, Portfolio B grew by roughly 90% from its minimum in March while Portfolio A was growing by 44%, but Portfolio B was nearly twice as volatile. Nondiversified portfolios are generally more sensitive to sector‐ or market‐specific fluctuations compared to diversified portfolios. Diversifying a portfolio across asset classes reduces position concentration risk and tends to reduce loss potential in the event of turbulent market conditions. However, Figure 7.1 shows how more volatile, higher‐risk portfolios can pay off with higher profits. Due to their complex risk profiles, options are inherently more diversified relative to one another compared to their equity counterparts. Unlike equities, where the primary concern is directional risk, several factors may affect option P/L: Directional movement in the underlying price. Changes in IV. Changes in time to expiration. Because exposure to each of these variables can be controlled according to the contract parameters, varying factors, such as duration/management time, underlying, and strategy creates an additional reduction in P/L correlation that is not possible when trading equities exclusively. However, diversifying against directional risk of the underlyings remains most essential from the perspective of risk management, particularly outlier risk management. Diversifying against nondirectional risk by varying strategy or contract duration is supplemental. To understand why it is so essential to diversify the option underlyings of a portfolio, consider two market ETFs: SPY and QQQ. These assets have historically had highly correlated price dynamics and IV dynamics, as shown in the correlation matrix in Table 7.4 . The equity underlyings and IV indices are highly correlated, meaning that IV expansion events and outlier price moves tend to happen simultaneously for these two assets. When such events do occur, short premium positions with these two underlyings may experience simultaneous tail losses. To get an idea of how often these positions have incurred simultaneous outlier losses historically, refer to the strangle statistics shown in Table 7.5 . Table 7.4 Historic correlations between two market ETFs (SPY, QQQ) and the correlations between their implied volatility indices (VIX, VXN) from 2011 to 2020. Also included is the correlation between each market index and the respective VIX, for reference. Equity Price and IV Index Correlation (2011–2020) SPY QQQ VIX VXN Equities SPY 1.0 0.89 −0.80 QQQ 0.89 1.0 −0.76 Volatility VIX −0.80 1.0 0.89 Indices VXN −0.76 0.89 1.0 Table 7.5 The probability of outlier losses (worse than 200% of the initial credit) occurring simultaneously for 16 SPY strangles and 16 QQQ strangles from 2011 to 2020. All contracts have approximately the same duration (45 DTE), start date, and expiration date. The diagonal entries (SPY Strangle‐SPY Strangle, QQQ Strangle‐QQQ Strangle) indicate the probability of a strategy incurring an outlier loss individually, and the off‐diagonal entries correspond to the probability of the pair incurring outlier losses simultaneously. Probability of Loss Worse than 200% (2011–2020) SPY Strangle QQQ Strangle SPY Strangle 5.8% 3.9% QQQ Strangle 3.9% 8.7% Table 7.5 shows that it is reasonably unlikely for the pair of strategies to incur outlier losses simultaneously having occurred only 3.9% of the time. However, if these events were completely independent, then these compound losses would have occurred less than 1% of the time: . Additionally, when considering the outlier loss probability for each strategy on an individual basis, the effects of trading strangles with correlated underlyings becomes a bit clearer. For example, the probability of a SPY strangle incurring an outlier loss is 5.8%. What is the probability a QQQ strangle will incur a simultaneous outlier loss given that a SPY strangle has taken an outlier loss? To calculate this, one can use conditional probability. 1 In other words, SPY strangles and QQQ strangles may only have simultaneous outlier losses 3.9% of the time, but when a SPY strangle incurs an outlier loss, there is a 67% chance that a QQQ strangle also will. 2 Generally, the probability of a compound loss is fairly low, but when one short premium position takes a loss there is often a high likelihood an equivalent position with a correlated underlying will experience a loss of comparable magnitude. Because the loss potential of these compound occurrences is so large, it is essential to diversify underlying equities and maintain appropriate position sizes for correlated options to reduce the likelihood and impact of compounding outlier losses. Now consider two market ETFs (SPY and QQQ) and two diversifying ETFs that have been uncorrelated or inversely correlated to the market (GLD, TLT). The historic correlations are shown in Table 7.6 and the probability of outlier losses occurring simultaneously are shown in Table 7.7 . Table 7.6 Historic correlations among two market ETFs (SPY and QQQ), a gold ETF (GLD), and a bond ETF (TLT) from 2011 to 2020. Equity Price Correlation (2011–2020) SPY QQQ GLD TLT SPY 1.0 0.89 −0.03 −0.41 QQQ 0.89 1.0 −0.04 −0.34 GLD −0.03 −0.04 1.0 0.23 TLT −0.41 −0.34 0.23 1.0 Table 7.7 The probability of outlier losses (worse than 200% of the initial credit) occurring simultaneously for different types of 16 strangles held to expiration from 2011 to 2020. All contracts have approximately the same duration (45 DTE), open and close dates. The diagonal entries correspond to the probability of the specific strategy incurring an outlier loss individually, and the off‐diagonal entries correspond to the probability of the pair incurring outlier losses simultaneously. Probability of Loss Worse than 200% for Different Strangles (2011–2020) SPY QQQ GLD TLT SPY 5.8% 3.9% 2.1% 1.9% QQQ 3.9% 8.7% 1.9% 1.7% GLD 2.1% 1.9% 12% 4.8% TLT 1.9% 1.7% 4.8% 12% Again, it is relatively unlikely for any pair to incur simultaneous outlier losses, but this table shows the significant reduction in the conditional outlier probability when the underlying assets are uncorrelated or inversely correlated. Consider the following: If a SPY strangle incurs an outlier loss, there is a 67% chance of a compounding loss with a QQQ strangle. If a SPY strangle incurs an outlier loss, there is a 36% chance of a compounding loss with a GLD strangle. If a QQQ strangle incurs an outlier loss, there is a 20% chance of a compounding loss with a TLT strangle. Compound losses still occur when the underlying assets have low or inversely correlated price movements, but this reduction in likelihood is crucial nonetheless. Having a portfolio that includes uncorrelated or inversely correlated assets is particularly meaningful during periods of unexpected market volatility when most assets develop a stronger correlation to the market and there are widespread expansions in IV. Though options can be diversified with respect to several variables, diversifying the underlying assets is one of the most effective ways to reduce the impact of outlier events on a portfolio. Because diversification does not entirely remove the risk of compounding outlier losses, so maintaining small position sizes (at most 5% to 7% of portfolio capital allocated to a single position) remains critical. Maintaining Portfolio Greeks The Greeks form a set of risk measures that quantify different dimensions of exposure for options. Each contract has its own specific set of Greeks, but some Greeks have the convenient property of being additive across positions with different underlyings. Consequently, these metrics can be used to summarize the various sources of risk for a portfolio and guide adjustments. The following portfolio Greeks will be the focus of this section: Beta‐weighted delta ( ): Recall from Chapter 1 that beta is a measure of systematic risk and specifically quantifies the directional tendency of the stock relative to that of the overall market. Stocks with positive correlation to the market have positive beta and stocks with negative correlation have negative beta. is similar to delta, which is the expected change in the option price given a $1 change in the price of the underlying. When delta is beta‐weighted, the adjusted value corresponds to the expected change in the option price given a $1 change in some reference index, such as SPY. Theta ( ): The decline in an option's value due to the passage of time, all else being equal. This is generally represented as the expected decrease in an option's value per day. Maintaining the balance of these two variables is crucial for the long‐term health of a short options portfolio. represents the amount of directional exposure a position has relative to some index rather than the underlying itself. The cumulative portfolio delta represents the overall directional exposure of the portfolio relative to the market assuming that the beta index is a market ETF like SPY. Normalizing delta according to a standard underlying allows delta to be additive across all portfolio positions. This cannot be done with unweighted delta because $1 moves across different underlyings are not comparable, i.e., trying to add deltas of different positions is like adding inches and ounces. For example, a 50 sensitivity to underlying A and a 25 sensitivity to underlying B does not imply a 75 sensitivity to anything, unless A and B happen to be perfectly correlated. neutral portfolios are attractive to short premium traders because the portfolio is relatively insensitive to changes in the market, and profit is primarily driven by changes in IV and time. Adopting neutrality also simplifies aspects of the diversification process because a near‐zero indicates low directional market exposure. As the delta of a position drifts throughout the contract duration, the overall delta of the portfolio is skewed. To maintain neutrality, existing positions can be re‐centered (where the current trade is closed and reopened with a new delta), existing positions can be closed entirely, or new positions can be added. The most appropriate strategy depends on the current portfolio theta. Theta is also additive across positions because the units of theta are identical for all options ($/day). Because short premium traders consistently profit from time decay, the total theta across positions gives a reliable estimate for the expected daily growth of the portfolio. The theta ratio ( ) estimates the expected daily profit per unit of capital for a short premium portfolio. Options portfolios are subject to significant tail risk, so the expected daily profit should be significantly higher than a portfolio passively invested in the market to justify that risk. Therefore, one can determine the benchmark profit goals of an equivalent short options portfolio by referring to the daily P/L performance of a passively invested SPY portfolio as shown below in Table 7.8 . Table 7.8 Daily performance statistics for five portfolios passively invested in SPY from 2011–2021. Each portfolio has $100,000 in initial capital, and the amount of capital allocated in each portfolio ranges from 25% to 50%. SPY Allocation Percentage Daily Portfolio P/L (2011–2021) 25% 0.013% 30% 0.015% 35% 0.017% 40% 0.020% 50% 0.025% From 2011–2021, a passively invested SPY portfolio collected between 0.013% and 0.025% daily depending on the percentage of capital allocated. In other words, these portfolios had daily profits between $13 and $25 per $100,000 of capital over the past 10 years ( ). However, the expected daily profit per unit of capital for a short options portfolio should be significantly higher than this benchmark. For most traders, the minimum theta ratio should range from 0.05% to 0.1% of portfolio net liquidity to justify the tail risks of short premium. In other words, short premium portfolios should have a daily expected profit between $50 and $100 per $100,000 of portfolio buying power from decay. The theta ratio should not exceed 0.2%. A higher theta ratio is preferable, but it should not be too high due to hidden gamma risk. Gamma ( ) is the expected change in the option's delta given a $1 change in the price of the underlying. Delta neutral positions are rarely gamma neutral, and if the gamma of a position is especially high, then the delta of the trade is highly sensitive to changes in the underlying price and is generally unstable. A position with high delta sensitivity can easily affect the overall neutrality of a portfolio. The gammas of different derivatives cannot be compared across underlyings for similar reasons as to why raw delta cannot be compared across underlyings. Gamma cannot be accurately beta‐weighted as delta can; however, a positive relationship between gamma and theta presents a solution to this problem. Positions with large amounts of theta, such as trades with strikes that are close to at‐the‐money (ATM) or trades that are near expiration, typically also have large amounts of gamma risk. Because theta is additive across portfolio positions, the theta ratio is the most direct indicator of excessive gamma risk. This relationship between gamma and theta also demonstrates how short premium traders must balance the profitability of time decay with the P/L fluctuations resulting from gamma. To summarize, the theta ratio for an options portfolio should range from 0.05% to 0.1% and should not exceed 0.2%. Based on the theta ratio and the amount of capital currently allocated, existing positions should then be re‐centered, short premium positions should be added, or short premium positions should be removed. Given these benchmarks for expected daily profits, the procedure for modifying portfolio positions can be summarized as follows: If a properly allocated, a well‐diversified portfolio is neutral but does not provide a sufficient amount of theta, then the positions in the portfolio should be reevaluated. In this case, perhaps some defined risk trades should be replaced with undefined risk trades or undefined risk positions should be rolled to higher deltas. New delta neutral positions can also be added, such as strangles and iron condors, for example. IV and theta are also highly correlated, meaning that higher IV underlyings could also be considered if theta is too low. These measures can be reversed if the portfolio has too much theta exposure while being neutral. If the theta ratio is too low (<0.1%), then either existing positions should be re‐centered/tightened or new short premium positions should be added. If the is too large and positive (bullish), then add new negative positions (e.g., add short calls on positive beta underlyings or add short puts on negative beta underlyings). If the is too large and negative (bearish), then add new positive positions (e.g., add short puts on positive beta underlyings). If the theta ratio is too large (>0.2%), then either existing positions should be re‐centered/widened or short premium positions should be removed. If the is too large and positive (bullish), then remove positive positions (e.g., remove short puts on positive beta underlyings). If the is too large and negative (bearish), then remove negative positions (e.g., remove short calls on positive beta underlyings). If a properly allocated, well-diversified portfolio provides a sufficient amount of theta but is not neutral, then existing positions should be reevaluated. For example, skewed positions could be closed and re‐centered or replaced with new delta-neutral positions that offer comparable amounts of theta. Takeaways The amount of portfolio buying power allotted to short premium positions should range from 25% to 50% depending on the current market volatility, with the remaining capital either kept in cash or a low‐risk passive investment. Of the amount allocated, at least 75% should be reserved for undefined risk trades (with no more than 7% allocated to a single position), and at most 25% should be reserved for defined risk strategies (with no more than 5% allocated to a single position). The total portfolio allocation guidelines must be followed, but there is more leniency for the per‐trade allocation guidelines, especially in smaller accounts. An options portfolio is typically composed of two types of positions: core and supplemental. Core positions are usually high‐POP trades with moderate P/L variance that offer consistent profits and reasonable outlier exposure. Supplemental positions are not necessarily dependable sources of profit but rather tools for market engagement. At most 25% of the capital allocated to short premium should go toward supplemental positions. Unlike equity portfolios, options portfolios can be diversified with respect to multiple variables, such as duration/management time, underlying, and strategy. Diversifying the underlyings of an options portfolio remains the most essential diversification tool for portfolio risk management, particularly outlier risk management. Beta‐weighted delta ( ) represents the amount of directional exposure a position has relative to some index rather than the underlying itself. Portfolio theta ( ) represents the expected daily growth of the portfolio. The minimum theta ratio for an options portfolio should range from 0.05% to 0.1% and should not exceed 0.2%. Maintaining the balance of these two Greeks ensures the risk‐reward profile of an options portfolio remains as close to the target as possible. Notes 1 For an introduction to conditional probability, refer to the appendix. 2 A 67% conditional probability of a compound loss is very high but lower than the compound loss probability when trading the equivalent equities. SPY and QQQ are highly correlated and experience near‐identical drawdowns in periods of market turbulence. Therefore, that these options incur compound outlier losses only 70% of the time demonstrates the inherent diversification of options alluded to earlier. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c08.xhtml SCORE: 201.00 ================================================================================ Chapter 8 Advanced Portfolio Management Having covered the necessary basics of portfolio management, this chapter discusses supplemental optimization techniques for traders who can accommodate more active trading. The capital allocation guidelines, underlying diversification, and Greeks of a portfolio are essential to maintain and are relatively straightforward to employ. This chapter will introduce some less essential strategies: Additional option diversification techniques. Weighting assets according to probability of profit (POP). Advanced Diversification As stated in the previous chapter, one of the biggest strategic differences between equity portfolios and options portfolios is the ability to diversify risk with respect to factors other than price. Diversifying with respect to the underlying is the most effective way to reduce the effect of outlier events on a portfolio. Diversifying with respect to other variables, such as time and strategy, requires more active management but tends to reduce the profit and loss (P/L) correlation between positions. For example, consider the per‐day standard deviation of P/L for SPY strangles with different durations as shown in Figure 8.1 . Figure 8.1 Standard deviation of daily P/Ls (in dollars) for 16 SPY strangles with various durations from 2005–2021. Included are durations of (a) 15 days to expiration (DTE), (b) 30 DTE, (c) 45 DTE, and (d) 60 DTE. Short premium trades tend to have more volatile P/L swings as they approach expiration, a result of the position becoming more sensitive to changes in time and underlying price (larger gamma and theta). Because contracts with different durations have varying sensitivities to these factors at a given time, diversifying the timescales of portfolio positions reduces the correlations among their P/L dynamics. Because trading consistent contract durations is important for reaching many occurrences, the most effective way to diversify with respect to time is by trading contracts with consistent durations but a variety of expiration dates. This strategy achieves an assortment of contract durations in a portfolio at a given time without compromising the number of occurrences. Despite its efficacy, diversification with respect to time will not be thoroughly covered in this chapter because it is difficult to maintain conveniently and consistently. Strategy diversification, while not as essential as underlying diversification, is another risk management technique that is more straightforward than time diversification. This method effectively spreads portfolio capital across different risk profiles while maintaining the same directional assumption for a given underlying (or a highly correlated underlying). This lets traders capitalize on the directional dynamics of an asset while protecting a proportion of portfolio capital from outlier losses. To see an example of the diversification potential for this method, consider a backtest of three different portfolios. Each portfolio contains some combination of two directionally neutral SPY strategies: strangles and iron condors. The performance of these portfolios in this long‐term backtest is shown in Figure 8.2 and analyzed in Table 8.1 . The purpose of this backtest is not to demonstrate the profit or loss potential associated with combining SPY strangles and iron condors but rather to illustrate the possible effects of strategy diversification on portfolio risk according to one sample of outcomes. The impact of diversification is immediately clear, particularly when emphasizing the drawdowns of the 2020 sell‐off. Strangles and iron condors experienced massive drawdowns in early 2020 even though defined risk trades are lower‐risk, lower‐reward trades. The cumulative drawdowns as a percentage of portfolio capital are approximately the same across all three portfolios (roughly 150%). However, the drawdowns as a raw dollar amount were significantly larger for the strangle portfolio compared to the combined portfolio. During more regular market conditions, the combined portfolio also had a much larger POP and profit potential than the iron condor portfolio and less P/L variability and outlier risk than the strangle portfolio. Figure 8.2 Cumulative P/L of three different portfolios containing some combination of SPY strangles and SPY iron condors, held to expiration from 2005–2021. The strangle portfolio contains 10 strangles, the combined portfolio contains five strangles and five iron condors, and the iron condor portfolio contains 10 iron condors. All contracts are traded once per expiration cycle, opened at the beginning of the expiration cycle and closed at expiration. These positions have the same short delta (16 ), approximately the same duration (45 DTE), and the same open and close dates. The long strikes of the iron condors are roughly 10 . This example demonstrates how diversifying portfolio capital across defined and undefined risk strategies lets a trader capitalize on the directional tendencies of an underlying asset (or several highly correlated underlyings) while protecting a fraction of capital from unlikely outlier events. However, this example combines strategies in a highly simplified way as market implied volatility (IV), capital allocation guidelines, alternative management techniques, and strategy‐specific factors are not considered. In practice, defined and undefined risk strategies reach P/L targets at different rates and often require different management strategies. The percentage of capital allocated to a single position also depends on a number of factors, including the buying power reduction (BPR) of the trade (maximum of 5% for defined risk trades and 7% for undefined risk) and the correlation with the existing positions in a portfolio. For traders interested in a more quantitative approach to positional capital allocation, allocation weights can be estimated from the probability of profit of the strategy. Table 8.1 Statistical analysis of the three portfolios illustrated in Figure 8.2 . The first four statistics (POP, average P/L, standard deviation of P/L, and conditional value at risk (CVaR)) gauge portfolio performance during more regular market conditions (2005–2020). The final column gives the worst‐case drawdown from the 2020 sell‐off (the cumulative losses from February to March 2020). 2005–2020 2020 Sell‐Off Portfolio Type POP Average P/L Standard Deviation of P/L CVaR (5%) Worst‐Case Drawdowns Strangle 76% $379 $1,803 −$5,174 −$77,520 Combined 75% $221 $1,275 −$3,648 −$45,080 Iron Condor 67% $64 $799 −$2,324 −$12,640 Balancing Capital According to POP The proportion of capital to allocate to a position can be estimated from the POP of the strategy. An appropriate percentage of buying power can be estimated using the following formula, derived from the Kelly Criterion: 1 (8.1) where r is the annualized risk‐free rate of return, DTE is days to expiration or the contract duration (in calendar days), and POP is the probability of profit of the strategy. 2 Approximating the risk‐free rate is not straightforward because it is an unobservable market‐wide constant, but the long‐term bond rate is commonly used as a conservative estimate. For the remainder of this chapter, the risk‐free rate will be estimated at roughly 3% for the sake of simplicity. To see some examples of portfolio allocation percentages calculated using this equation, see Table 8.2 . Table 8.2 POPs and allocation percentages of buying power for 45 DTE 16 SPY, QQQ, and GLD strangles from 2011–2018. Strangle Statistics (2011–2018) POP Allocation Percentages SPY Strangle 79% 1.4% QQQ Strangle 73% 1.0% GLD Strangle 84% 1.9% The equation above suggests that the amount of portfolio buying power allocated to these positions should range from 1.0% to 1.9%, but those calculations don't take correlations between positions into account. Strategies with perfectly correlated underlyings should be counted against the same percentage of portfolio capital because Equation (8.1) requires that trades be independent of one another. In this example, because SPY and QQQ are highly correlated to each other but mutually uncorrelated with GLD, GLD strangles can occupy an entire 1.9% of portfolio buying power, and SPY strangles and QQQ strangles combined should occupy around 1.4% (the larger of the two allocation percentages). Because SPY and QQQ are not perfectly correlated, this is a conservative lower bound. Overall, these allocation percentages are fairly low because the Kelly Criterion advocates for placing many small, uncorrelated bets. When aiming to allocate between 25% and 50% of portfolio buying power, strictly abiding by these bet sizes is somewhat impractical; there just aren't enough uncorrelated underlyings. The value of the risk‐free rate provides a conservative estimate for the ideal capital allocation, so scaling these percentages up and adopting a more aggressive approach is justified. To scale up these percentages without violating the capital allocation guidelines, these bet sizes can be used as a heuristic to estimate proportions of capital allocation rather than the explicit percentages. For example, rather than allocating according to POP weights, a more heuristic approach would be as follows: According to initial estimates, 1.4% of portfolio buying power should be allocated to SPY strangles and 1.9% to GLD strangles. Dividing by 1.9, these weights correspond to a ratio of approximately 0.74:1.0. This means that SPY strangles should occupy roughly 0.74 times the portfolio buying power of GLD strangles. If the maximum per‐trade allocation of 7% goes toward GLD strangles, then approximately 5.2% (derived from ) should be allocated to SPY strangles. To continue this example, suppose that the capital allocated to SPY strangles is further split between SPY strangles and QQQ strangles. Although these underlyings are correlated, splitting capital between these positions achieves more diversification than allocating the entire 5.2% to one underlying. This process can also be estimated using the POP weights: According to initial estimates, 1.4% of portfolio buying power should be allocated to SPY strangles and 1.0% to QQQ strangles. Dividing by 2.4% (from ), these weights correspond to a ratio of approximately 0.58:0.42. This means that SPY strangles should occupy 58% of the capital allocation and QQQ strangles should occupy 42%. If a maximum of 5.2% can be allocated toward these positions, then 3.0% of portfolio capital should go toward SPY strangles and 2.2% to QQQ strangles. This scaling formula, when combined with position sizing caps of the capital allocation guidelines, allows traders to construct portfolio weights that scale with the POP of a strategy without overexposing capital to outlier risk. These two concepts form a simple but effective basis for options portfolio construction. Constructing a Sample Portfolio Throughout this section, simplified capital allocation guidelines, option diversification, and POP‐weighting are combined to create a sample portfolio. The sample portfolio shown here will be constructed using data from January 2011 to January 01, 2018 and backtested with data from January 02, 2018 to September 2019. This backtest will focus on implementing some of the portfolio construction techniques outlined in Chapters 7 and 8. This sample portfolio has six different core positions (all strangles), each occupying a constant amount of portfolio capital determined by the POP‐weight scaling method described in the previous section. The following three simplifications are made for ease of analysis and understanding: Neither market IV nor underlying IV will be considered. Scaling portfolio allocation up when market IV increases is an effective way to capitalize on higher premium prices, as is focusing on underlyings with inflated implied volatilities. Because a constant 30% of portfolio capital will be allotted to the same short premium positions throughout this backtest, profit potential will be significantly limited. Therefore, the focus of this analysis is risk management. This study only uses strangles with exchange‐traded fund (ETF) underlyings instead of a combination of strategies. This makes the portfolio approximately delta neutral and eliminates the need to justify specific directional assumptions or risk profiles for individual assets. By disregarding stock underlyings, stock‐specific binary events, such as earnings and dividends do not apply. This also means that the added profit potential from supplemental positions (which tend to be higher risk and include stock underlyings) will not be accounted for in this backtest. Rather than managing trades at fixed profit targets, all the trades shown in this backtest will be approximately opened on the first of the month and closed at the end of the month. Step 1: Identify suitable underlyings using past data. Core positions should have moderate P/L standard deviations and well‐diversified underlying assets. ETFs, such as the ones in Table 8.3 , are viable candidates for core position underlyings. Though the market ETFs are highly correlated, a sufficient number of uncorrelated and inversely correlated assets can achieve a reasonable reduction in idiosyncratic risk. Table 8.3 Correlations between different ETFs from 2011–2018. Included are two market ETFs (SPY, QQQ), a gold ETF (GLD), a bond ETF (TLT), a currency ETF (FXE ‐ Euro), and a utilities ETF (XLU). Correlation (2011–2018) SPY QQQ GLD TLT FXE XLU Market ETFs SPY 1.0 0.88 −0.02 −0.44 0.16 0.49 QQQ 0.88 1.0 −0.03 −0.36 0.12 0.35 Diversifying ETFs GLD −0.02 −0.03 1.0 0.19 0.34 0.08 TLT −0.44 −0.36 0.19 1.0 −0.03 −0.04 FXE 0.16 0.12 0.34 −0.03 1.0 0.18 XLU 0.49 0.35 0.08 −0.04 0.18 1.0 Step 2: Calculate the percentage of portfolio capital that should be allocated to each position. These percentages can be estimated with Equation (8.1) and scaled according to the methodology described in the previous section, as shown in Table 8.4 . The core positions shown in Table 8.4 are high‐POP, have moderate P/L standard deviation, and have well‐diversified underlyings, and the allocation amounts are below the 7% per‐trade buying power maximum. The total portfolio buying power allocated to short premium amounts to 30%, which is close enough to the minimum 25% to suffice for this backtest. With the portfolio initialized using data from 2011 to early 2018, it can now be backtested on new data from early 2018 to late 2019, bearing in mind that this test does not take dynamic management or implied volatility into account. The results of backtesting this sample portfolio are shown in Figure 8.3 and Table 8.5 . 3 Interestingly, Table 8.5 shows that the equity portfolio was the most volatile of the three and experienced the largest worst‐case drawdown despite having less tail exposure than the options portfolios. The POP‐weighted portfolio performed more consistently and had significantly less per‐trade standard deviation than either of the other two, with per‐trade POP matching the equal‐weight portfolio and average P/L comparable to the equity portfolio. Despite consisting of undefined risk strategies, the POP‐weighted portfolio had nearly half the P/L variability and worst‐case loss as the equity portfolio throughout the backtest period. The equal‐weight strangle portfolio also underperformed compared to the POP‐weighted portfolio although not experiencing any more P/L variance or severe drawdowns compared to a comparable portfolio of equities. To reiterate, the performance of both strangle portfolios can be further optimized by increasing the allocation percentage according to market volatility (which can be done with the addition of uncorrelated short premium positions) or by incorporating more complex management strategies. Still, this simplified backtest illustrates the impact of incorporating the risk management techniques of capital allocation, diversification, and POP‐weighted allocation. Table 8.4 Core position statistics for 45 DTE 16 strangles from 2011–2018. The allocation ratio is the allocation percentages normalized such that the largest bet size is set to 1.0. The portfolio weights are determined by multiplying the allocation ratio by 7% (the maximum per‐trade allocation percentage). The adjusted portfolio weights show how portfolio capital is split across assets that are highly correlated. Core Position Statistics (2011–2018) POP Allocation Percentages SPY Strangle 79% 1.4% QQQ Strangle 73% 1.0% GLD Strangle 84% 1.9% TLT Strangle 78% 1.3% FXE Strangle 83% 1.8% XLU Strangle 81% 1.6% Allocation Ratio SPY/QQQ:GLD:TLT:FXE:XLU 0.74:1.0:0.68:0.95:0.84 Portfolio Weights SPY/QQQ:GLD:TLT:FXE:XLU 5.2%:7.0%:4.8%:6.7%:5.9% Adjusted Portfolio Weights SPY:QQQ:GLD:TLT:FXE:XLU 3.0%:2.2%:7.0%:4.8%:6.7%:5.9% Figure 8.3 Portfolio performance of three different portfolios from early 2018 until September of 2019. Each portfolio has $200,000 in initial capital with 30% of the portfolio capital allocated. This initial amount of $200,000 allows at least one trade for each type of position, as $100,000 in initial capital does not. The 30% SPY equity portfolio (a) has 30% allocated to shares of SPY. The 30% equally‐weighted strangle portfolio (b) has 5% allocated to each of the six types of strangles, and the 30% POP‐weighted portfolio (c) has the 30% weighted according to the percentages in Table 8.4 . All contracts have the same delta (16 ), identical durations (roughly 45 DTE), and the same open and close dates. For the sake of comparison, the trades in the equity portfolio are opened on the first of each month and closed at the end of each month. Table 8.5 Portfolio backtest performance statistics for the three portfolios described in Figure 8.3 from 2018–2019. Portfolio Performance Comparison (2018–2019) Portfolio Type POP Average P/L Standard Deviation of P/L Worst Loss SPY Equity 60% $285 $2,879 −$6,319 Equal‐Weight 67% $26 $2,440 −$6,117 POP‐Weighted 67% $268 $1,610 −$3,561 The heuristic derived from the Kelly Criterion provides a good guide for how much capital should be allocated to a trade when initializing a portfolio, indicating that more capital should be allocated to higher POP trades and less capital should be allocated to less reliable trades. However, this method does not provide a thorough structure for dynamic portfolio management. At different points in time, trades often reach profit or loss targets, require strike re‐centering, or present new opportunities. Traders can simplify the complex management process by, for example, choosing the same contract duration or management strategy for all trades in a portfolio. However, a framework for navigating these dynamic circumstances is still necessary, and this is where the portfolio Greeks and the re‐balancing protocol outlined in Chapter 7 are particularly useful. Takeaways Options can be diversified with respect to a number of variables, but diversifying the equity underlyings of an options portfolio remains the most essential for portfolio risk management. Traders who can accommodate more involvement and are interested in further diversification can also diversify positions with respect to time and strategy. Diversification with respect to time tends to reduce the correlations between portfolio positions because contracts respond differently to changes in time, volatility, and underlying price depending on their duration. The most effective way to diversify with respect to time without compromising occurrences is by trading contracts with consistent durations but a variety of expiration dates. This strategy is difficult to maintain consistently, however, particularly when multiple management strategies are used. Diversifying portfolio capital across defined and undefined risk strategies allows traders to capitalize on the directional tendencies of an underlying asset while protecting a fraction of capital from unlikely outlier events. If implementing this diversification technique, note that defined and undefined risk strategies typically reach P/L targets at different rates and often require different management strategies. The percentage of capital allocated to a single position can be calculated from the POP of the strategy and the correlation between existing portfolio positions. The percentage of portfolio capital allocated to a single position can be estimated using Equation (8.1) ; however, this percentage can also be scaled up because the risk‐free rate yields a very conservative estimate. Notes 1 For an introduction to the Kelly Criterion, refer to the appendix. 2 The POPs used throughout this chapter are calculated from historic options data. Options data are ideal for statistical analyses but inaccessible to most people. Trading platforms often provide the theoretical POP of a strategy, which can substitute measured POP for these calculations. 3 This backtest demonstrates one specific outcome out of many possible when trading short premium. The goal of this backtest is to demonstrate how one sample portfolio performs relative to other portfolios with similar characteristics under these specific circumstances. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c09.xhtml SCORE: 60.50 ================================================================================ Chapter 9 Binary Events To this point, this book has highlighted unpredictable implied volatility (IV) expansions and their impact on short premium portfolios. However, traders can expect a certain class of IV expansions and contractions with near certainty. These expected volatility dynamics are the result of binary events . A binary event is a known upcoming event affecting a specific asset (or group of assets) that is anticipated to create a large price move. Though price variance is expected to increase, it may or may not actually do so depending on the outcome of the binary event. 1 Some examples of binary events include company earnings reports (motivating earnings trades), new product announcements, oil market reports, elections, and Federal Reserve announcements pertaining to the broader market. Because the date of the anticipated price swing is known, there is typically significant demand for contracts expiring on or after the binary event for that underlying asset. This increased demand results in an increase in the asset's IV, which usually contracts back to nonevent levels immediately after the outcome is known. This trend is shown in Figure 9.1 . The impact from a binary event volatility expansion differs from that of unexpected periods of market volatility because the options approaching binary events are priced to reflect the expectation of large moves in the underlying. However, the high credits and immediate volatility contractions that often result from binary events do not necessarily translate into higher (or even likely) profits for short premium positions. This is because the magnitude of the price move following the outcome of the binary event is unpredictable, and it may meet or diverge from expectations. On average, the market response to a binary event tends to be quite large, causing the short options strategies that capitalize on these conditions to be highly volatile and not necessarily profitable in the long run. This phenomenon also follows from the efficient market hypothesis (EMH), as the well‐understood nature of binary events challenges any consistent edge for these types of strategies. There is no strong evidence that buying or selling premium around binary events provides a consistent edge with respect to probability of profit (POP) or average profit and loss (P/L) because a lot of the IV overstatement edge is lost in the large moves following a binary event. However, binary event trades are a very time‐efficient use of capital because volatility contractions happen more rapidly and predictably than in more regular market conditions. Binary event trades may also be attractive to risk‐tolerant traders as a source of market engagement. During earnings season, a single week may present up to 20 high‐risk/high‐reward opportunities for earnings trades. Binary event trades can also be educational for new traders wanting to learn how to adjust positions in rapidly changing, high volatility conditions outside of sell‐offs. These types of trades, as they take place under unique circumstances, are structured and managed differently than typical core or supplemental positions. Figure 9.1 IV indexes for different stocks from 2017–2020. Assets include (a) AMZN (Amazon stock) and (b) AAPL (Apple stock). Option Strategies for Binary Events Because binary event trades are highly volatile and have no strong evidence of a long‐term statistical edge, they should only occupy spare portfolio capital and their position size should be kept exceptionally small. For example, if a trader's usual position size for an AAPL strangle is a five‐lot (five calls and five puts, each written for 100 shares of stock), then an AAPL earnings strangle may comprise a one‐ or two‐lot. Additionally, underlyings for binary event trades are typically stocks, with quarterly earnings reports being the most common type of binary event. Binary event trades take place over much shorter timescales than more typical trades and must be carefully monitored. Earnings trades, for example, are typically opened the day before earnings and closed the day following earnings. This strategy limits downside risk and capitalizes on the majority of the volatility contraction, which tends to occur immediately after the binary event. The long‐term success of binary event trades is difficult to verify because there are relatively few occurrences, resulting in high statistical uncertainty. AAPL, for example, has only reported earnings roughly 100 times since the mid 1990s. The Federal Reserve holds press conferences just eight times per year, and large‐scale elections take place once every two or four years. For trading strategies not built around earnings, there are thousands of data points and the statistics are more representative of long‐term expectations (the central limit theorem at work). Therefore, working with this small number of data points can yield an idea of how binary events trades have performed in the past, but they should be taken with a large grain of salt. Tables 9.1 – 9.3 demonstrate how earnings trades for three different tech companies have performed over 15 years. There is clearly significant variability in strategy performance for these three different underlyings. To reiterate, high statistical uncertainty makes it difficult to make definitive conclusions about the success of earnings trades, but some consistent trends are observable. Earnings trades are highly sensitive to changes in time. This is evidenced by the significant differences in the per‐trade statistics further from the earnings announcement and demonstrates why binary event trades must be closely monitored. The majority of earnings trades are usually profitable, but do not necessarily average a profit in the long term because of the high per‐trade standard deviation. Per‐trade variance and tail exposure also tend to increase the longer the trade is held, indicating why these types of trades should be relatively short term. This is why generally, binary event trades, such as earning trades, are closed the day following the binary event. Table 9.1 Statistics for 45 days to expiration (DTE) 16 AAPL strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings. AAPL Strangle Statistics (2005–2020) Day Position Is Closed Relative to Earnings POP Average P/L Standard Deviation of P/L Conditional Value at Risk (CVaR) (5%) Day After 72% $85 $203 –$405 5 Days After 70% $43 $400 –$1,027 10 Days After 61% $60 $408 –$1,025 20 Days After 56% −$34 $660 –$1,976 Table 9.2 Statistics for 45 DTE 16 AMZN strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings. AMZN Strangle Statistics (2005–2020) Day Position Is Closed Relative to Earnings POP Average P/L Standard Deviation of P/L CVaR (5%) Day After 65% $99 $803 –$1,927 5 Days After 65% $85 $842 –$2,154 10 Days After 72% $1 $1,446 –$4,416 20 Days After 76% $78 $1,540 –$4,477 Table 9.3 Statistics for 45 DTE 16 GOOGL strangles from 2005–2020. Trades are opened the day before an earnings report and closed either one, five, 10, or 20 days after earnings. GOOGL Strangle Statistics (2005–2020) Day Position Is Closed Relative to Earnings POP Average P/L Standard Deviation of P/L CVaR (5%) Day After 75% –$60 $1,320 –$4,639 5 Days After 67% –$113 $1,358 –$4,724 10 Days After 65% –$122 $1,275 –$3,675 20 Days After 71% –$2 $1,584 –$4,909 Takeaways A binary event is a known upcoming event affecting a specific asset (or group of assets) that is anticipated to create a large price move. This anticipation creates demand for options contracts expiring on or after the binary event and an increase in the IV of the asset. IV typically contracts back to nonevent levels immediately after the outcome is known. The high credits and immediate volatility contractions resulting from binary events do not necessarily translate to large or consistent short premium profits because the magnitude of the market response is unpredictable. Binary events trades are generally highly volatile and undependable sources of profit but can be used for market engagement or an educational experience for new traders. Binary event trades should only occupy spare portfolio capital and their position size should be kept exceptionally small. Binary event trades should also take place over much shorter timescales than more typical trades, and they must be carefully monitored. Note 1 The term binary is used to describe systems that can exist in one of two possible states (on/off, yes/no). In this context, a binary event is a type of event where price changes either remain within expectations or exceed expectations. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:c10.xhtml SCORE: 216.50 ================================================================================ Chapter 10 Conclusion and Key Takeaways Successful traders do not rely on luck. Rather, the long‐term success of traders depends on their ability to obtain a consistent, statistical edge from the tools, strategies, and information available. This book introduces the core concepts of options trading and teaches new traders how to capitalize on the versatility and capital efficiency of options in a personalized and responsible way. Options are fairly complicated instruments, but this book aims to lessen the learning curve by focusing on the most essential aspects of applied options trading. The detailed framework laid out in this book can be summarized succinctly in the following key takeaways: Implied volatility (IV) is a proxy for the sentiment of market risk derived from supply and demand for financial insurance. When options prices increase, IV increases; when options prices decrease, IV decreases. IV gives the perceived magnitude of future movements and is not directional. It can also be used to approximate the one standard deviation expected price range of an asset (although this does not take strike skew into account). The CBOE Volatility Index (VIX) is meant to track the IV for the S&P 500 and is used as a proxy for the perceived risk of the broader market. The VIX, like all volatility signals, is assumed to revert down following significant expansions, which indicates some statistical validity in making downward directional assumptions about volatility once it is inflated. Compared to long premium strategies, short premium strategies yield more consistent profits and have the long‐term statistical advantage. The trade‐off for receiving consistent profits is exposure to large and sometimes undefined losses, which is why the two most important goals of a short premium trader are to profit consistently enough to cover moderate, more likely losses and to construct a portfolio that can survive unlikely extreme losses. The profitability of short options strategies depends on having a large number of occurrences to reach positive statistical averages, a consequence of the law of large numbers and the central limit theorem. At minimum, approximately 200 occurrences are needed for the average profit and loss (P/L) of a strategy to converge to long‐term profit targets and more is better. Extreme losses for short premium positions are highly unlikely but typically happen when price swings in the underlying are large while the expected move range is tight (low IV). Because large price movements in low IV are rare and difficult to reliably model, the most effective way to reduce this exposure is to trade short premium once IV is elevated. Although high volatility environments are ideal for short premium positions, short premium positions have high probability of profits (POPs) and some statistical edge in all volatility environments. Additionally, because volatility is low the majority of the time, trading short options strategies in all IV environments allows traders to profit more consistently and increases the number of occurrences. To manage exposure to outlier risk when adopting this strategy, it is essential to maintain small position sizes and limit the amount of capital allocated to short premium positions, especially when IV is low. This strategy can be further improved by scaling the amount of capital allocated to short premium according to the current market conditions. VIX Range Maximum Portfolio Allocation 0–15 25% 15–20 30% 20–30 35% 30–40 40% 40+ 50% Buying power reduction (BPR) is the amount of portfolio capital required to place and maintain an option trade. The BPR for long options is merely the cost of the contract, and the BPR for short options is meant to encompass at least 95% of the potential losses for exchange‐traded fund (ETF) underlyings and 90% of the potential losses for stock underlyings. BPR is used to evaluate short premium risk on a trade‐by‐trade basis in two ways: BPR is a fairly reliable metric for the worst‐case loss of an undefined risk position, and BPR is used to determine if a position is appropriate for a portfolio based on its buying power. A defined risk trade should not occupy more than 5% of portfolio buying power and an undefined risk trade should not occupy more than 7%, with exceptions allowed for small accounts. The formulae for BPR are complicated and specific to the type of strategy, but the BPR for short strangles is approximately 20% of the price of the underlying. BPR can be used to compare the risk for variations of the same strategy (e.g., strangle on underlying A versus strangle on underlying B), but it cannot be used to compare risk for strategies with different risk profiles (e.g., strangle on underlying A versus iron condor on underlying A). Traders trade according to their personal profit goals, risk tolerances, and market beliefs, but it is generally good practice to be aware of the following: Only trade underlyings with liquid options markets to minimize illiquidity risk. The choice of underlying is somewhat arbitrary, but it's important to select an underlying with an appropriate level of risk. Stock underlyings tend to be higher‐risk, higher‐reward than ETF underlyings. This means stock underlyings present high IV opportunities more frequently, but they have more tail loss exposure and are more expensive to trade. Choose a contract duration that is an efficient use of buying power, allows for consistency, offers a reasonable number of occurrences, has manageable P/L swings throughout the duration, and has moderate ending P/L variability. Durations between 30 and 60 days are suitable for most traders. Compared to defined risk trades, undefined risk trades have higher POPs, higher profit potentials, unlimited downside risk, and higher BPRs. High‐POP defined risk trades, such as wide iron condors, have comparable risk profiles to undefined risk trades while also offering protection from extreme losses. Such trades can be better suited for low IV conditions compared to undefined risk trades and are allowed to occupy undefined risk portfolio capital. Contracts with higher deltas are higher-risk, higher-reward than contracts with lower deltas. When trading premium, consider contracts between 10Δ and 40Δ, which is large enough to achieve a reasonable amount of growth but small enough to have manageable P/L swings and ending P/L variability. When choosing a management strategy, the primary factors to consider are convenience and consistency, capital allocation preferences, desired number of occurrences, per‐trade average P/L, and per‐trade exposure. Early‐managed positions have lower per‐trade P/Ls but less tail risk than positions held to expiration. Because managing early also accommodates more occurrences and averages more P/L per day, closing positions prior to expiration and redeploying capital to new positions is generally a more efficient use of capital compared to extracting more value from an existing position. If managing according to days to expiration (DTE), consider closing trades around the contract duration midpoint to achieve a decent amount of long‐term profit and justify the tail loss exposure. If managing an undefined position according to a profit target, choosing a target between 50% and 75% of the initial credit allows for reasonable profits while also reducing the potential magnitude of outlier losses. Choosing a profit target that is too low reduces average P/L, and choosing a profit target that is too high does little to mitigate outlier risk. Profit targets for defined risk positions can be lower because they are generally less volatile. If combining strategies, managing undefined risk contracts at either 50% of the initial credit or halfway through the contract duration generally achieves reasonable, consistent profits and moderates outlier risk. If implementing a stop loss, a mid‐range stop loss threshold of at least −200% of the initial credit is practical. If the stop loss is too small (−50% for example), losses are more likely since options have significant P/L variance, although they often recover. It's also important to note that stop losses do not guarantee a maximum loss in cases of rapid price movements, so stop losses are typically paired with another management strategy unless trading passively. Stop losses are generally not suitable for defined risk strategies. Maintaining the capital allocation guidelines is crucial for limiting tail exposure and achieving a reasonable amount of long‐term growth: The amount of portfolio buying power allotted to short premium positions, such as short strangles and short iron condors, should range from 25% to 50% depending on the current market volatility, with the remaining capital either kept in cash or a low‐risk passive investment. [refer to Takeaway 5]. Of the amount allocated to short premium, at least 75% should be reserved for undefined risk trades (with less than 7% of portfolio buying power allocated to a single position) and at most 25% reserved for defined risk strategies (with less than 5% of portfolio buying power allocated to a single position) [refer to Takeaway 6]. Generally speaking, at most 25% of the capital allocated to short premium should go toward supplemental positions, or higher-risk, higher-reward trades that are tools for market engagement. The remainder should go toward core positions or trades with high POPs and moderate P/L variation that offer consistent profits and reasonable outlier exposure. Diversifying the underlyings of an options portfolio (i.e., trading a collection of assets with low correlations) is one of the most essential diversification tools for portfolio risk management, particularly outlier risk management. Strategy diversification and duration diversification, though not as essential as underlying diversification, are other straightforward risk management techniques. The Greeks form a set of risk measures that quantify different dimensions of exposure for options. Each contract has its own specific set of Greeks, but some Greeks are additive across positions with different underlyings. Consequently, these metrics can be used to summarize the various sources of risk for a portfolio and guide adjustments. Two key Greeks are beta‐weighted delta ( ) and theta ( ). Beta‐weighted delta represents the amount of directional exposure a position has relative to some index rather than the underlying itself. Theta represents the expected decrease in an option's value per day. neutral portfolios are attractive to investors because they are relatively insensitive to directional moves in the market and profit from changes in IV and time. Because short‐premium traders consistently profit from time decay, the total theta across positions gives a reliable estimate for the expected daily growth of a short options portfolio. The minimum theta ratio ( ) for an options portfolio should range from 0.05% to 0.1% and should not exceed 0.2% because this indicates excessive risk. If a portfolio is not meeting these theta ratio guidelines, then the positions should be adjusted as follows: If a properly allocated, well‐diversified portfolio is neutral but does not provide a sufficient amount of theta, then the positions in the portfolio should be reevaluated. In this case, perhaps some defined risk trades should be replaced with undefined risk trades or undefined risk positions be rolled to higher deltas. New delta neutral positions can also be added, such as strangles and iron condors, for example. IV and theta are also highly correlated, meaning that higher IV underlyings could also be considered if theta is too low. These measures can be reversed if the portfolio has too much theta exposure while being neutral. If the theta ratio is too low (<0.1%) and the portfolio is not neutral, then either existing positions should be re‐centered or tightened or new short premium positions should be added. If the is too large and positive (bullish), then add new negative positions (e.g., add short calls on positive beta underlyings or add short puts on negative beta underlyings). If the is too large and negative (bearish), then add new positive positions (e.g., add short puts on positive beta underlyings). If the theta ratio is too large (>0.2%) and the portfolio is not neutral, then either existing positions should be re‐centered or widened or short premium positions should be removed. If the is too large and positive (bullish), then remove positive positions (e.g., remove short puts on positive beta underlyings). If the is too large and negative (bearish), then remove negative positions (e.g., remove short calls on positive beta underlyings). If a properly allocated, well‐diversified portfolio provides a sufficient amount of theta but is not βΔ neutral, then existing positions should be reevaluated. For example, skewed positions could be closed and re‐centered or replaced with new delta-neutral positions that offer comparable amounts of theta. Binary event trades, such as trades around quarterly earnings reports, should be traded cautiously, only occupy spare portfolio capital, and their position size should be kept exceptionally small. Binary event trades must be carefully monitored and typically take place over much shorter timescales than more typical trades. They are often opened the day before a binary event and closed the day after. Options trading is not for everyone. However, for traders who are prepared to understand the complex risk profiles of options, comfortable accepting a certain level of exposure, and willing to commit the time to active trading, short premium strategies can offer a probabilistic edge and the potential to profit in any type of market. There is no “right” way to trade these instruments; all traders have unique profit goals and risk tolerances. It is our hope that this book will guide traders to make informed decisions that best align with their personal objectives. ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:b01.xhtml SCORE: 127.50 ================================================================================ Appendix I. The Logarithm, Log‐Normal Distribution, and Geometric Brownian Motion, with contributions from Jacob Perlman For the following section, let be the initial value of some asset or collection of assets and the value at time . Given the goals of investing, the most obvious statistic to evaluate an investment or portfolio is the profit or loss: . However, according to the efficient market hypothesis (EMH), assets should be judged relative to their initial size, represented using returns, . The returns of the asset from time 0 to time can also be written in terms of each individual return over that time frame. More specifically, for an integer , if then the returns, , can be split into a telescoping 1 product. (A.1) The EMH states that each term in this product should be independent and similarly distributed. The central limit theorem, and many other powerful tools in probability theory, concern long sums of independent random variables. To apply these tools to this telescoping product of random variables, it first must be converted into a sum of random variables. Logarithms offer a convenient way to accomplish this. Logarithmic functions are a class of functions with wide applications in science and mathematics. Though there are several equivalent definitions, the simplest is as the inverse of exponentiation. If and are positive numbers, and , then (read as “the log base of ”) is the number such that . For example, can be equivalently written as . The choice of base is largely arbitrary, only affecting the logarithm by a constant multiple. If is another possible base, then . In mathematics, the most common choice is Euler's constant, a special number: . Using this constant as a base results in the natural logarithm , denoted . The justification for this choice largely comes down to notational convenience, such as when taking derivatives: . In this example, as , using avoids the accumulation of cumbersome and not particularly meaningful constant factors. As , logarithms have the useful property 2 given by: (A.2) This property transforms the telescoping product given above into a sum of small independent pieces, given by the following equation: (A.3) The central limit theorem states that if a random variable is made by adding together many independently random pieces, then the result will be normally distributed. One can, therefore, conclude that log returns are normally distributed. Observe the following: (A.4) This suggests that stock prices follow a log‐normal distribution or a distribution where the logarithm of a random variable is normally distributed. Within the context of Black‐Scholes, this implies that stock log‐returns evolve as Brownian motion (normally distributed), and stock prices evolve as geometric Brownian motion (log‐normally distributed). The log‐normal distribution is more appropriate to describe stock prices because the log‐normal distribution cannot have negative values and is skewed according to the volatility of price, as shown in the comparisons in Figure A.1 . II. Expected Range, Strike Skew, and the Volatility Smile The majority of this book refers to expected range approximated with the following equation: (A.5) For a stock trading at current price with volatility and risk‐free rate , the Black‐Scholes theoretical price range at a future time for this asset is given by the following equation: (A.6) The equation in ( A.5 ) is a valid approximation of this formula when is small, which follows from the mathematical relation . Generally speaking, ( A.5 ) is a very rough approximation for expected range, and it becomes less accurate in high volatility conditions, when is larger. Though ( A.5 ) still yields a reasonable, back‐of‐the‐envelope estimate for expected range, the one standard deviation expected move range is calculated on most trading platforms according to the following: (A.7) Figure A.1 Comparison of the log‐normal distribution (a) and the normal distribution (b). The mean and standard deviation of the normal distribution are the exponentiated parameters of the log‐normal distribution. According to the EMH, this is simply the expected future price displacement, i.e., price of at‐the‐money (ATM) straddle, with additional terms (prices of near ATM strangles) to counterbalance the heavy tails pulling the expected value beyond the central 68%. To see how this formula compares with the ( A.5 ) approximation, consider the statistics in Table A.1 . Table A.1 Expected 30‐day price range approximations for an underlying with a price of $100 and implied volatility (IV) of 20%. According to the Black‐Scholes model, the per‐share prices for the 30‐day options are $4.58 for the straddle, $3.64 for the strangle one strike from ATM, and $2.85 for the strangle two strikes from ATM. 30‐Day Expected Price Range Comparison Equation (A.5) Equation (A.7) $5.73 $4.13 Compared to Equation (A.5) , Equation (A.7) is a more attractive way to calculate expected range on trading platforms because it is computationally simpler and independent of a rigid mathematical model. However, neither of these expected range calculations take skew into account. When comparing contracts across the options chain, an interesting phenomenon commonly observed is the volatility smile . According to the Black‐Scholes model, options with the same underlying and duration should have the same implied volatility, regardless of strike price (as volatility is a property of the underlying). However, because the market values each contract differently and implied volatility is derived from from options prices, the implied volatilities across strikes often vary. A volatility smile appears when the implied volatility is lowest for contracts near ATM and increases as the strikes move further out‐of‐the‐money (OTM). Similarly, a volatility smirk (also known as volatility skew) is a weighted volatility smile, where the options with lower strikes tend to have higher IV than options with higher strikes. The opposite of the volatility smirk is described as forward skew, which is relatively rare, having occurred, for example, with GME in early 2021. For an example of volatility skew, consider the SPY 30 days to expiration (DTE) OTM option data shown in Figure A.2 . Figure A.2 Volatility curve for OTM 30 DTE SPY calls and puts, collected on November 15, 2021, after the close. The volatility curve in Figure A.2 is clearly asymmetric around the ATM strike, with the options with lower strikes (OTM puts) having higher IVs than options with higher strikes (OTM calls). This type of curve is useful for analyzing the perceived value of OTM contracts. Compared to ATM volatility, OTM puts are generally overvalued while OTM calls are generally undervalued until very far OTM (near $510). This suggests that traders are willing to pay a higher premium to protect against downside risk compared to upside risk. This is an example of put skew, a consequence of put contracts further from ATM being perceived as equivalently risky as call contracts closer to ATM. Table A.2 reproduces data from Chapter 5 . Table A.2 Data for 16 SPY strangles with different durations from April 20, 2021. The first row is the distance between the strike for a 16 put and the price of the underlying for different DTEs (i.e., if the price of the underlying is $100 and the strike for a 16 put is $95, then the put distance is [$100 – $95]/$100 = 5%). The second row is the distance between the strike for a 16 call and the price of the underlying for different contract durations. 16 SPY Option Distance from ATM Option Type 15 DTE 30 DTE 45 DTE Put Distance 3.9% 6.5% 8.0% Call Distance 2.4% 3.9% 4.9% This skew results from market fear to the downside , meaning the market fears larger extreme moves to the downside more than extreme moves to the upside. According to the EMH, the skew has already been priced into the current value of the underlying. Hence, the put skew implies that the market views large moves to the downside as more likely than large moves to the upside but small moves to the upside as being the most likely outcome overall. For a given duration, the strikes for the 16 puts and calls approximately correspond to the one standard deviation expected range of that asset over that time frame. For example, since SPY was trading at approximately $413 on April 20, 2021, the 30‐day expected price move to the upside was $16 and the expected price move to the downside was $27 according to the 16 options. III. Conditional Probability Conditional probability is mentioned briefly in this book, but it is an interesting concept in probability theory worthy of a short discussion. Conditional probability is the probability that an event will occur, given that another event occurred. Consider the following examples: Given that the ground is wet, what is the probability that it rained? Given that the last roll of a fair die was six, what is the probability that the next roll will also be a six? Given that SPY had an up day yesterday, what is the probability it will have an up day tomorrow? Analyzing probabilities conditionally looks at the likelihood of a given outcome within the context of known information. For events and the conditional probability (read as the probability of , given ) is calculated as follows: (A.8) where is the probability that event occurs and is the probability that and occur. For example, suppose is the event that it rains on any given day and (20% chance of rain). Suppose is the event that there is a tornado on any given day, there is a 1% chance of a tornado occurring on any given day, and tornados never happen without rain, meaning that . Therefore, given that it is a rainy day, we have the following probability that a tornado will appear: In other words, a tornado is five times more likely to appear if it is raining than under regular circumstances. IV. The Kelly Criterion, derivation courtesy of Jacob Perlman The Kelly Criterion is a concept from information theory and was originally created to analyze signal transmission through noisy communication channels. It can be used to determine the optimal theoretical bet size for a repeated game, presuming the odds and payouts are known. The Kelly bet size is the fraction of the bankroll that maximizes the expected long‐term growth rate of the game, more specifically the logarithm of wealth. For a game with probability of winning and a probability of losing 1 (the full wager), the Kelly bet size is given as follows: (A.9) This is the theoretically optimal fraction of the bankroll to maximize the expected growth rate of the game. A brief justification for this formula follows from the paper listed in Reference 4. Consider a game with probability of winning and a probability of losing the full wager. If a player has in starting wealth and bets a fraction of that wealth, , on this game, the player's goal is to choose a value of that maximizes their wealth growth after bets. If the player has wins and losses in the plays of this game, then: Over many bets of this game, the log‐growth rate is then given by the following: following from the law of large numbers The bet size that maximizes the long‐term growth rate corresponds to . The Kelly Criterion can also be applied to asset management to determine the theoretically optimal allocation percentage for a trade with known (or approximated) probability of profit (POP) and edge. More specifically, for an option with a given duration and POP, the optimal fraction of the bankroll to allocate to this trade is approximately: (A.10) where is the risk‐free rate and is the duration of the trade in years. The derivation for this equation is outlined as follows: For a game with probability of winning and a probability of losing 1 unit, the expected change in bankroll after one play is given by . For an investment of time with the risk‐free rate given by , the expected change in value is estimated by , derived from the future value of the game with continuous compounding. Assuming that is small, then . For the bet to be fairly priced, the change in the bankroll should also equal . Therefore, if , the odds for this trade can be estimated as . Using this value for in the Kelly Criterion formula, one arrives at the following: This then yields the approximate optimal proportion of bankroll to allocate to a given trade, substituting for and POP for . Notes 1 So called because adjacent numerators and denominators cancel, allowing the long product to be collapsed like a telescope. 2 Stated abstractly, logarithms are the group homomorphisms between and . ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:b02.xhtml SCORE: 71.50 ================================================================================ Glossary of Common Tickers, Acronyms, Variables, and Math Equations Ticker Full Name SPY SPDR S&P 500 XLE Energy Select Sector SPDR Fund GLD SPDR Gold Trust QQQ Invesco QQQ ETF (NASDAQ‐100) TLT iShares 20+ Year Treasury Bond ETF SLV iShares Silver Trust FXE Euro Currency ETF XLU Utilities ETF AAPL Apple Stock GOOGL Google Stock IBM IBM Stock AMZN Amazon Stock TSLA Tesla Stock VIX CBOE Volatility Index (implied volatility for the S&P 500) GVZ CBOE Gold Volatility Index VXAPL CBOE Equity VIX On Apple VXAZN CBOE Equity VIX On Amazon VXN CBOE NASDAQ‐100 Volatility Index Acronym Full Name NYSE New York Stock Exchange ETF Exchange‐Traded Fund DTE Days to Expiration EMH Efficient Market Hypothesis ITM In‐the‐Money OTM Out‐of‐the‐Money ATM At‐the‐Money P/L Profit and Loss IV Implied Volatility VaR Value at Risk CVaR Conditional Value at Risk POP Probability of Profit BPR Buying Power Reduction IVP IV Percentile IVR IV Rank NFT Non‐Fungible Tokens Variable Symbol Variable Name/Definition Spot/stock price: the price of the underlying Contract price: the price of the option, noting that C is used if the contract is a call and P is used in the case of puts Strike price: the price at which the holder of an option can buy or sell an asset on or before a future date Risk‐free rate of return: the theoretical rate of return of a riskless asset Mean: the central tendency of a distribution Standard deviation: the spread of a distribution; also used as a measure of uncertainty or risk Volatility: the standard deviation of log‐returns for an asset; a key input in options pricing Delta: the expected change in an option's price given a $1 increase in the price of the underlying Gamma: the expected change in an option's delta given a $1 change in the price of the underlying Theta: the expected time decay of an option's extrinsic value in dollars per day Beta: the volatility of the stock relative to that of the overall market Beta‐weighted delta: the expected change in an option's price given a $1 change in some reference index Equation Number Equation 1.1 Simple Returns 1.2 Log Returns 1.3 Long Call P/L 1.4 Long Put P/L 1.5 Population Mean 1.6 Expected Value 1.7 Population Variance 1.8 Variance 1.9 Skew 1.15 Delta 1.16 Gamma 1.17 Theta 1.18 Population Covariance 1.19 Covariance 1.20 Correlation Coefficient 1.21 Additive Property of Variance 1.22 Beta 2.1 ±1σ Expected Range Approximation (%) 2.2 ±1σ Expected Range Approximation ($) 3.1 IV Percentile (IVP) 3.2 IV Rank (IVR) 4.1 Short Put BPR 4.2 Short Call BPR 4.3 Short Strangle BPR 5.1 Short Iron Condor BPR 8.1 Approximate Kelly Allocation Percentage ================================================================================ SOURCE: eBooks\The Unlucky Investor_s Guide to Options Trading\The Unlucky Investor_s Guide to Options Trading.epub#section:b04.xhtml SCORE: 417.00 ================================================================================ Index Active management, 117 , 125 –126, 150 capital allocation, relationship, 79 –81 volatility trading concept, 58 Active traders, 125 Active trading, 2 –3, 123 , 149 Advanced portfolio management, 3 , 133 , 149 advanced diversification, 149 –153 capital (balancing), POP (usage), 153 –156 market/underlying IV, consideration (absence), 156 portfolio construction, 156 –160 positions, POP‐weighting, 156 straddle, price, 181 strategy diversification, 151 American options, exercise, 7 Assets combination, 38 correlation history, 138t illiquid asset, 94 management, Kelly Criterion (application), 185 portfolio, trading, 137 rates, experience, 52t realized moves, IV overstatement, 46t trading, 94 , 173 –174 universe, selection, 94 –95 volatility, 31 weighting, POP (usage), 149 At‐the‐money (ATM) contract description, 9 positions, 33 straddle, 181 strikes, 32 closeness, 99 –100, 146 Autocorrelation, 26 Backtest period, usage, 158 Beta ( β ) beta‐weighted delta, 38 , 144 –145, 148 , 174 index, assumption, 145 metric, 38 Bid‐ask spread, 94 , 95t Binary events, 3 EMH, relationship, 164 examples, 163 option strategies, 166 –167 outcomes, predictability (absence), 164 premium, buying/selling result (evidence), 164 stock‐specific binary events, 156 trades, 166 –167, 175 volatility expansion, impact, 164 Black‐Scholes assumptions, usage, 44 –45 Black‐Scholes equation, 29 European‐style option price evolution, relationship, 23 Black‐Scholes model, 22 –31, 35 , 42 , 179 , 181t assumptions, 23 , 27 , 35 , 44 , 45 Brownian motion (Wiener process), relationship, 23 –26 geometric Brownian motion, relationship, 27 –28 mathematical definition, derivation, 111 mechanics, 30 options fair price, estimate, 30 , 42 price dynamics approximation, 24 Black‐Scholes option pricing formalism, impact, 22 –23 Black‐Scholes options pricing model, 44 –45 Black‐Scholes theoretical price range, 179 Brownian motion Black‐Scholes model, relationship, 23 –26 cumulative horizontal displacements, 24 –25, 25f particle, 2D position, 25f price dynamics, comparison, 25 –26 stock log‐returns, evolution, 179 Bullish directional exposure, 90t Buying power, allocation percentages, 154t Buying Power Reduction (BPR), 3 , 66 , 83 , 153 average BPR comparison, 110t , 113t calculation, 84 capital coverage, 89 requirement, correspondence, 85 –86 definition, variation, 84 historical effectiveness, 84 IV comparison, 66 inverse relationship, 87 loss percentage, 85f margin, contrast, 84 maximum per‐trade BPR, limitation, 134 option price, inverse correlation, 87 options, capital efficiency (relationship), 90 portfolio capital amount, 171 reduction, impact, 89 result, 87t short call/put BPR, 86 short strangle BPR, 86 stock margin, option counterpart, 84 undefined risk strategies, relationship, 84 underlying IV function/underlying price function, 88f understanding, importance, 90 usage, 83 , 89 variables, dependence, 85 –86 Call option, 7 , 9 strike prices, comparison, 114t trading level (determination), Black‐Scholes model (usage), 31 Call skew, 112 Call strikes, comparison, 111 –112 Capital balancing, POP (usage), 153 –156 requirement, BPR (correspondence), 85 –86 Capital allocation amounts, differences, 78f control, 81 efficiency, active management (relationship), 79 –81 estimate, risk‐free rate value (usage), 154 –155 guidelines, 133 , 152 , 155 , 156 maintenance, 149 , 173 market IV, impact, 76t violation, avoidance, 155 position sizing, relationship, 134 –136 positional capital allocation, quantitative approach, 153 preferences, 129 , 131 , 172 proportions, estimation, 155 risk management techniques, incorporation (impact), 158 scaling, 79 , 134 short premium capital allocation, scaling up, 76 undefined risk capital allocation, sharing, 110 undefined risk strategy, usage, 110 volatility trading concept, 58 Capital at risk (comparison), BPR (usage), 89 Casinos long‐run statistical advantage, 58 , 72 –73 options trading, 1 –2 CBOE volatility index. See Volatility index Central limit theorem, 20 , 72 , 166 , 170 , 178 Company exposure, 98 Company‐specific risk, 96 Company‐specific uncertainty, 43 Conditional probability, 183 –184 calculation, 184 usage, 142 Conditional value at risk (CVaR), 63 inclusion, 40f metric, 38 usage, 39 –40, 65 –66, 123 VaR, contrast, 40 Contract delta, 33 –35, 79 , 111 , 114 implied volatility (IV), equivalence, 87 risk, 172 Contract duration middle ground contract duration, 101 selection, 94 , 99 –102 trading, importance, 151 Contracts average daily P/L and average duration, 121t extrinsic value, decrease, 34 prices, differences, 42t Core positions, 134 P/L standard deviations, presence, 156 –157 Covariance correlation, relationship, 35 –38 measures, 37 negative covariance, 36 positive covariance, 35 Cumulative horizontal displacement, 25f Cumulative horizontal displacements, 24 Daily P/Ls, standard deviation, 150f Daily returns, distribution, 39f , 40f Days to expiration (DTE), management usage, 118 –120 Defined risk, selection, 102 –104 Defined risk strategies, 152 maximum loss, 102 BPR, usage, 84 limitation, 59 P/L targets, attainment, 153 POP, usage, 110 portfolio allocation, 103t risk, comparison, 89 selection, 94 short premium allocation, 173 stop losses, unsuitability, 173 undefined risk strategies, comparison, 102t , 109 avoidance, 110 Delta (Δ), 31 –32, 106t basis, 112 beta‐weighted delta, 38 , 144 –145, 148 , 174 contract delta, 33 –35, 79 , 111 , 114 implied volatility (IV), equivalence, 87 contract risk, 172 contract usage, 32 directional exposure measurement, 111 drift, 145 level, 114 magnitude, 32 , 114 negative delta/positive delta, 33 neutral position, 33 , 61 , 146 , 156 neutral positions profit, 111 normalization, 145 perceived risk measure, 112 –113 raw delta, comparisons (impossibility), 146 –147 re‐centering, 114 scaling up, 114 selection, 94 , 111 –115 optimum, factors, 114 sensitivity, 146 sign, 32 value, range, 32 Derivatives, gamma comparison (impossibility), 146 –147 Deterministic price trends, 28 –29 Dice rolls, histogram, 13 , 14f , 17f , 19f , 21f Directional assumption, selection, 94 , 104 –110 Directional exposure (measurement), delta (usage), 111 Directional risk, degree (measure), 32 Distributions asymmetry (measure), skew (usage), 65 mean (histogram), 17e normal distribution, 22f , 44 –45, 180f skew, 16 –18, 20 , 39 statistics, understanding, 21 –22 Diversification, 136 –144, 158 effectiveness, understanding, 137 –138 time diversification, 151 tools, 173 Dividends payment, avoidance, 23 Downside risk amount, preference, 104 limitation, absence, 102 Downside skew, 112 Early‐managed contracts, 126 , 129 occurrences allowance, 80 Early‐managed portfolio, losses, 129 Early‐management strategies, 80 Earnings dates, marking, 54f Earnings report, 115 dates, 53 , 96 , 102 impact, 43 inclusion, 163 quarterly earnings report (single‐company factors), 52 , 166 , 175 Efficient market hypothesis (EMH), 11 –13, 177 –178, 183 binary events, relationship, 164 forms, 11 –12, 104 –105 interpretation, 104 , 116 Equities implied volatility indexes, 54f pricing/bid‐ask spread/volume data, 95t trading, 137 , 140 European call options, 29 European options, expiration (payoff), 29 European‐style option (price evolution), Black‐Scholes equation (relationship), 23 Events outcomes, 44 –45 sampling, probability distribution (usage), 72 Exchange‐traded funds (ETFs), 5 –7, 36 , 157 BPR, historical effectiveness, 84 correlations, 157t diversification, 53 –54, 134 historical risk, approximation, 63 IV overstatement rates, 46 market ETFs, 139 –142, 145 , 157 volatility assets, correlation, 139 skewed returns distribution, 22 stability, 98 underlyings, 95 , 135 , 137 , 172 advantages/disadvantages, 96t losses, 84 , 171 strangles, usage, 156 usage, 97 volatility profiles, differences, 96 Expected move cones, 44 , 45f , 60f Expected move range, 179 Expected price range, 45f Expected range, 58 , 179 –183 adjustment, 68 –69 calculation, 43 –45, 47 , 179 , 181 estimates, 44 increase, 115 short strike prices, relationship, 111 tightness, 51 underlying price expected range, 60 –61 External events, outlier underlying moves/IV expansions (relationship), 58 Financial derivative, options (comparison), 7 Financial insurance, risk‐reward trade‐off, 47 Gamma ( Γ ), 31 , 33 comparison, impossibility, 146 –147 increase, 79 magnitude, 33 risk, 146 –147 Gaussian distribution (bell curve), 20 Geometric Brownian motion, Black‐Scholes model (relationship), 27 –28 GLD returns, SPY returns (contrast), 36f Greeks, 31 –35. See also Delta ; Gamma ; Sigma ; Theta assumptions, 35 balance, 148 option Greeks, 38 portfolio Greeks, 160 maintenance, 133 , 144 –147 risk measures, 174 Heteroscedasticity, 26 High implied volatility (high IV) short premium trading, 75 trading, 66 –72, 75 Histogram daily returns/prices, 27f dice rolls, 14f , 17f , 19f , 21f Historical distribution, 73f Historical P/L distribution, 62f , 64f , 71f Historical returns, standard deviation, 28 , 30 Historical tail risk, estimation, 65 Historical volatility, 21 –22, 38 increase, 42 market historical volatility, 69 representation, 43 stock historical volatility, 30 underlying historical volatility, 31 usage, 30 , 63 Historic risk, estimation, 21 –22 Horizontal displacements, distribution, 26f Hurricane insurance price, proportion, 47 sellers, strategic room, 47 –48 Idiosyncratic risk, 137 Illiquid asset, example, 94 Illiquidity risk, minimization, 171 Implied volatility (IV), 3 , 38 , 41 , 83 , 169 –170, 181 basis, 48 BPR comparison, 66 inverse volatility, 87 contract delta, equivalence, 87 contraction, 50 conversion, 66 correlation, 42 –43 decrease/increase, 42 –43, 87 , 89 derivation, 44 –45 differences, 42t environments, short option strategies (trading), 76 expansion, 58 , 122 –123, 163 indexes, 53f , 54f , 165f indication, 30 IV‐derived price range, 44 –45 long‐term baseline reversion, 52 metric, importance, 30 –31 overstatement, 46 , 46t , 164 profits, 58 rates, 47 peak, increase, 49 price range forecast, 47 ranges, 76t realized risk measurement, 46 reversion, 51 –54 signals, capacity, 51 source, 23 SPY annualized implied volatility (tracking), 48 SPY implied volatility, 69f standard deviation range, 43 tracking, 48 trading (volatility trading concept), 58 underlying IV, 60 , 86 , 88f usage, 41 , 134 Implied volatility percentile (IVP), 66 –68 Implied volatility rank (IVR), 68 Increments, distribution, 26f Insider trading, 12 , 105 In‐the‐money (ITM), 99 contract description, 9 ITM put, price, 10 long calls ITM, 33 movement, 34 –35 options, directional risk, 114 positions, 34 relationship, 32 Iron condors, 105 , 110t , 151 cap, long wings, 106 , 108 drawdowns, experience, 151 narrow wings, POP (presence), 109 neutral SPY strategies, 151 profit potential, 109 representation, 107f risk, 110 short iron condor BPR, 108 short iron condors, range, 134 , 173 statistical comparison, 109t underlying strangle, contrast, 171 wide iron condors, 116 , 172 wide wings, inclusion (trading), 109 wings, inclusion, 106 Kelly Criterion application, 185 buying power percentage, 153 derivation, 184 –186 formula, 186 heuristic derivation, 160 uncorrelated bets, 154 Law of large numbers, 72 , 170 , 185 Liquidity importance, understanding, 94 net liquidity, 89t options liquidity, 94 –95 portfolio net liquidity, 104 , 145 theta ratio/net portfolio liquidity, 145 Log‐normal distribution, 177 comparison, 180f skew, 179 stock prices, relationship, 179 Log returns equation, 7 standard deviation, 23 Long call, 32 , 34 addition, 106 directional assumption, 8t option, price, 32 , 111 P/L, 10 –11 position, 33 profit potential, 90 Long premium contracts, impact, 84 positions, profit yield (comparison), 12 strategies, 58 , 170 trade, 8 Long put, 32 , 34 addition, 106 directional assumption, 8t option, price, 111 P/L, 10 –11 position, 33 Long stock, 32 Long strikes, 207f Loss incurring, probability, 113t targets, 122t , 123 Low‐loss targets, attainment, 122 Management P/L target, usage, 120 –124 techniques, 123 –126, 152 timeline, usage, 118 –119 Management strategies, 121t , 122t , 158 average daily P/L and average duration, 121t impact/comparison, 79 –80, 80t , 102 long‐term risks, 126 , 129 performance, scenarios (impact), 126 qualitative comparison, 125t selection, 172 usage, 117 –118 Management time, selection, 119 , 129 Margin, BPR (contrast), 84 Market conditions, risk/return expectations, 35 exposure, 98 frictionlessness, 23 historical volatility, 69 implied volatility (IV), 76t , 152 perceived uncertainty, 46 trader beliefs, 171 –172 uncertainty sentiment, IV tracking, 48 volatility amounts, differences, 89t Market ETFs, 139 –142, 145 , 157 historic correlations, 141t , 143t percentage, 138t volatility assets, correlation, 139 Market risk sentiment, IV proxy, 42 sentiment, IV proxy (usage), 169 –170 Maximum per‐trade BPR, limitation, 134 Mean (moment), 14 –15 Middle ground contract duration, 101 Mid‐range stop loss, 123 , 130 , 173 Moments, 14 –22 Near‐the‐money options, gamma (increase), 79 Negative covariance, 36 Non‐dividend‐paying stock, trading, 30 –31 Non‐fungible tokens (NFTs), 5 Normal distribution comparison, 180f mean/standard deviation, 180f plot, 22f standard deviation range, 44 –45 Occurrences, 62f , 71f , 101 compound occurrences, loss potential, 142 concentration, 20 consistency, 117 density, 64 early‐managed contract allowance, 80 final P/L, correspondence, 61 goal, 125 –126, 151 increase, 117 P/L distribution, 39 reduction/increase, 72 , 89 , 124 standard deviation range, 64 VIX level, contrast, 67 Occurrences, number, 58 , 72 –76, 99 attainment, 99 compromise, absence, 151 increase, 81 , 101 –102, 118 presence, 15 , 126 , 129 trade‐off, 119 volatility trading concept, 58 Off‐diagonal entries, 141t Options, 5 –6 buying, profit, 57 –58 capital efficiency, BPR (relationship), 90 demand, 42 –43 fair price (estimation), Black‐Scholes model (usage), 30 , 42 financial derivative, comparison, 7 Greeks, 38 illiquidity, risk, 94 leverage, effects (clarity), 90 liquidity, 94 –95 market, liquidity, 98 P/L standard deviation, usage, 73 P/L statistics, 97t price, BPR (inverse correlation), 87 profitability, 10 risk, visualization, 59 –63 traders, assumptions, 11 types, 7 underlyings, sample, 98t Options trading, 84 , 97 , 102 , 169 , 175 casinos, usage, 1 –2 diversification, importance, 136 ETF underlyings, usage, 97 gamma, awareness (importance), 33 implied volatility metric, 30 –31 reversion, 51 learning curve/math knowledge, 3 option theory, transition, 90 profitability, option pricing (impact), 11 quantitative options trading, 3 retail options trading, assets (suitability), 94 risk management, relationship, 2 usage, market performance, 12 Outlier losses, 142 capital exposure, limitation, 134 probability, 141t Outlier risk carrying, avoidance, 103 reduction, 76 Out‐of‐the‐money (OTM) contract description, 9 positions, 34 volatility curve, 182f Over‐the‐counter (OTC) options, 7 Passive investment, daily performance statistics, 146t Passive traders, 125 Perceived risk (measurement), delta (usage), 112 –113 Personal profit goals, 171 –172 Per‐trade allocation percentage, 158t Per‐trade standard deviation, 158 , 166 Per‐trade statistics, differences, 166 Per‐trade variance, 167 P/L targets, attainment, 153 Portfolio averages, variance, 74f backtest performance statistics, 159t concentration excess, avoidance, 77 construction, 12 , 156 –160 cumulative P/L, 152f delta skew, 145 expected loss, CVaR estimate, 40 Greeks, 149 , 160 maintenance, 133 , 144 –147 net liquidity, 89t , 104 , 146 passive investment, daily performance statistics, 146t performance, 159f comparison, 139f P/L averages, 74f POP‐weighted portfolio, 157 –158 risk management, diversification tools, 173 statistical analysis, 153t Portfolio allocation, 109 defined/undefined risk strategies, 103t guidelines, usage, 89 , 104 , 134 percentages, 137 –138, 138t , 154 , 154t position sizing, relationship, 75 –79 scaling, 77 , 156 strategies, comparison, 77 usage, 103 volatility trading concept, 58 Portfolio buying power, 83 , 89 , 134 allotment/allocation, 134 –135, 154 –155, 157 defined risk position occupation, 118 expected profit, 146 undefined risk strategy occupation, 110 usage, 99 , 109 , 117 Portfolio capital allocation control, 81 guidelines, market IV (impact), 76t amount, BPR (relationship), 171 diversification, 152 investment, 127f , 128f Portfolio management, 3 , 93 , 149 back‐of‐the‐envelope tactics, 133 beta ( β ) metric, importance, 38 capital allocation, 134 –136 capital balancing, POP (usage), 153 –156 concepts, 133 construction, 156 –160 diversification, usage, 136 –144, 149 –153 portfolio Greeks, maintenance, 144 –147 position sizing, 134 –136 simplification, 101 Positional capital allocation, quantitative approach, 153 Positions core position statistics, 158t delta drift, 145 delta level, 114 expected loss, CVaR estimate, 40 intrinsic value, 9 ITM, relationship, 32 long side/short side, adoption, 8 management, 118 P/L correlation, reduction, 150 POP‐weighting, 156 profiting, likelihood, 104 sizing capital allocation, relationship, 134 –136 portfolio allocation, relationship, 75 –79 volatility trading concept, 58 Positive covariance, 35 Premium sellers, profit, 50 Premium, trading, 172 Price dynamics Black‐Scholes model approximation, 24 Brownian motion, comparison, 25 –26 Price predictability (limitation), EMH implications, 105 Probabilistic system, probability distribution, 14 Probability distribution, 13 –22 asymmetry, 16 events sampling, 72 Gaussian distribution (bell curve), 20 mean (moment), 14 –15 normal distribution, 20 skew (moment), 16 –22 variance (moment), 15 –16 Probability of profit (POP), 89 , 164 , 185 asset weighting, 149 buying power, allocation percentages, 154t capital, balancing, 153 –156 decrease, 114 dependence, 77 heuristic, 160 IV ranges, 76t level, elevation, 61 , 90 , 105 , 108 –109, 120 , 123 –124, 151 percentage, 62 , 73 , 109 POP‐weighted allocation, 158 POP‐weighted portfolio, 157 –158, 159t POP‐weight scaling method, 156 positions, POP‐weighting, 156 profit potential, differences, 103 selection, 2 statistics, 80t , 97t , 153t trade‐off, 63 trades, level (elevation), 134 usage, 110 , 149 , 153 , 185 –186 weights, usage, 155 yield, 121 Product indifference, 97 –98 Profitability, considerations, 8t Profit and loss (P/L) average daily P/L, 121t average P/L, 76t , 164 averages, 74f cumulative P/L, 152f daily P/Ls, standard deviation, 150f distribution skew, 62 –63 expectations, 135 frequency, 124 historical distribution, 73f historical P/L distribution, 62f , 64f , 71f IV ranges, 76t per‐day standard deviation, 150 standard deviation, 134 , 153t , 157 carrying, 120 –121 core position usage, 156 –157 reduction, 118 –119, 122 , 126 trade‐offs, 124 usage, 63 –65, 74 –75, 80t , 99 , 100t , 123 swings, 79 , 97 magnitude, 98 tolerance, 97 –98 Profit potential, POP differences, 103 level, elevation, 151 Profit targets, 104 , 120t , 123 Put options, 9 Put prices, differences, 98t Put skew, 112 Puts (option type), 7 QQQ returns, SPY returns (contrast), 36f , 37 strangles, outlier losses, 142 Quantitative options trading, 3 Quarterly earnings report (single‐company factors), 52 , 166 , 175 Random variable, probability distribution, 13 Realized moves, IV overstatement, 46t Realized risk (measurement), IV (usage), 46 Realized volatility, IV overstatement, 46 Reference index, usage, 144 Relative volatility, metrics, 66 –68 Retail options trading, assets (suitability), 94 Returns distributions skews, 22 past volatility/future volatility, 43 standard deviation, 21 –22 usage, 63 Risk approximation, 30 categories, 137 measures, 38 –40 minimization, liquidity (impact), 95 reduction, trade‐by‐trade basis, 117 sentiment, measure, 30 –31 tolerances, 171 –172 trade‐off, 12 Risk‐free rate, 29 approximation, 154 value, usage, 154 –155 Risk management, 2 –3, 37 , 140 , 156 importance, 51 strategy/technique, 136 , 151 , 158 , 174 Risk‐reward trade‐off, 59 Sector exposure, 98 Sector‐specific risk, 96 Sell‐offs 2020 sell‐off, performances (2017‐2021), 78f volatility conditions, 164 Semi‐strong EMH, 12 , 104 –105 Short call, 32 , 34 addition, 147 , 175 BPR, 86 directional assumption, 8t P/L, 10 –11 position, 33 removal, 175 short put, pairing, 33 strike, 60 undefined risk, 59 Short‐call/put BPR, 86 Short iron condors, range, 134 , 173 Short options P/L distribution skew, 63 trading, capital requirements, 90 Short option strategies, 106t profitability, factors, 170 trading, 76 , 170 Short premium allocation, 173 capital allocation, scaling up, 76 positions, losses (unlikelihood), 170 risk (evaluation), BPR (usage), 83 strategies, POP trade‐off, 63 traders, profit, 51 Short premium trading, 48 , 114 benefits, 68 implied volatility elevation, impact, 71 importance, 59 mechanics, 57 risk‐reward trade‐off, 59 Short put, 34 addition, 147 , 174 –175 BPR, 86 bullish strategy, 32 directional assumption, 8t position, 33 removal, 175 strike, 60 Short strangles, POP level (elevation), 61 Short strike prices, expected range (relationship), 111 Short volatility trading, 83 Sigma ( σ ), 15 Single‐company factors, 52 –53 Single company risk factors, impact, 46 Skew, 68 amount, consideration, 71 contextualization, 65 distribution skew, 16 –18, 20 , 39 log‐normal distribution skew, 179 magnitude, decrease, 72 moment, 16 –22 P/L distribution skew, 62 –63 portfolio delta skew, 145 pure number, 17 reduction, 71 –72 returns distribution skews, 22 strike skew, 111 –112, 179 –183 tail skew, usage, 39 usage, 65 –66 volatility skew (volatility smirk), 181 SPDR S&P 500 (SPY) annualized implied volatility, tracking, 48 daily returns distribution, 39f , 40f expected move cone, 45f expected price ranges, 44 histogram, daily returns/prices, 27f implied volatility (IV), 69f , 70f iron condors, wings (inclusion), 107t –110t neutral SPY strategies, 151 price, 112f change, 60f , 78f trends, 24 returns, QQQ/TLT/GLD returns (contrast), 36f , 37 trading level, 183 SPDR S&P 500 (SPY) strangles, 64f , 73f BPR loss, 85f data (2005‐2021), 88f , 89t deltas (differences), statistical comparison, 113t durations, differences, 183t example, 107t initial credits, 108t management statistics, 119t , 120t , 122t , 124t , 125t strategies, comparison, 80t outlier losses, 142 P/L per‐day standard deviation, 150 stability, 63 VIX level labeling, 69f Standard deviation, 20 –21 daily P/Ls, standard deviation, 150 estimates, 16 expected move range, 179 expected range, 60 strikes, correspondence, 183 histogram, 17f historical returns, standard deviation, 28 , 30 indication, 16 interpretation, 18 –19, 64 –65 log returns, standard deviation, 23 normal distribution usage, 180f per‐trade standard deviation, 158 , 166 P/L per‐day standard deviation, 150 P/L standard deviation, 63 –65, 74 –75, 80t , 99 , 100t , 134 , 153t , 157 carrying, 120 –121 reduction, 118 –119, 122 , 126 trade‐offs, 124 usage, 123 probabilities, 22f range, sigma ( σ ), 37 , 43 –45, 64 –65 representation, 15 returns, standard deviation, 21 –22 sigma ( σ ), 15 usage, 63 –65 Steady‐state value, 48 Stocks, 5 –6 historical risk, approximation, 63 historical volatility, 30 IV overstatement rates, 46 liquidity, 94 –95 log returns, 23 options, trading, 96 –97 prices differences, 98t log‐normal distribution, relationship, 179 skewed returns distributions, 22 stock‐specific binary events, 156 trading, 90 , 179 margin, usage, 84 underlyings advantages/disadvantages, 96t trading, 135 volatility profiles, differences, 96 Stop loss, 122 application, 129 implementation, 122 , 130 , 173 mid‐range stop loss, 123 , 130 , 173 threshold, usage, 122 –123 usage, 123 –125 Straddles ATM straddle, price, 181 trades, BPR result, 87t Strangles, 105 buyer assumption, 61 drawdowns, experience, 151 durations, differences, 101t magnitude, 65 management strategies, 123 neutral SPY strategies, 151 P/L distributions, skew/tail losses, 71 –72 sale, BPR requirement, 86 seller, profit, 61 short strangle BPR, 86 statistics, 167t management, 122t , 136t trades, examples, 87t trading, effects, 142 usage, 156 Strategy‐specific factors, 152 –153 Strike skew, 111 –112, 179 –183 Strikes long strikes, 107f prices, comparison, 114t range, 104 standard deviation, expected range (correspondence), 183 Strong EMH, 12 , 104 –105 Supplemental positions, 134 Swaptions, 5 Systemic risk, 137 Tail exposure limitation, capital allocation guidelines (maintenance), 173 magnitude, 98 Tail losses CVaR sensitivity, 40 reduction, 71 –72 Tail risk, 83 , 103 , 121 , 145 acceptance, 57 carrying, 58 , 62 , 120 elimination, 122 –123 exposure, 102 , 135 historical tail risk, estimation, 65 increase, 97 , 108 –109, 119 inherent tail risk, justification, 121 mitigation, 135 –136 negative tail risk, 65 , 72 , 80 Tail skew, usage, 39 Theta ( Θ ), 31 , 34 , 144 , 174 additivity, 145 –147 ratio, size (reaction), 147 theta ratio/net liquidity, 174 theta ratio/net portfolio liquidity, 145 Time diversification, 151 TLT returns, SPY returns (contrast), 36f Trade‐by‐trade basis, 79 –80, 117 , 125 –126 Trade‐by‐trade performance, comparison, 118 Trade‐by‐trade risk tolerances, 119 –120 Trades BPR, 98 bullish directional exposure, 90t management, 3 , 80 –81, 117 –118 strategies, usage, 101 maximum loss, reduction, 108 Trades, construction, 93 asset universe, selection, 94 –95 contract duration, selection, 99 –102 defined risk, selection, 102 –104 delta, selection, 111 –115 directional assumption, selection, 104 –110 procedure, 94 undefined risk, selection, 102 –104 underlying, selection, 96 –98 Trading engagement, preferences, 124 mechanics, 48 platforms, usage, 179 , 181 strategies, 129 , 166 Uncertainty sentiment, IV tracking, 48 Undefined risk capital allocation, sharing, 110 selection, 102 –104 Undefined risk strategies, 59 , 152 BPR, relationship, 84 , 103 defined risk strategies, comparison, 102t , 109 avoidance, 110 downside risk, limitation (absence), 102 gain, limitation, 84 loss, limitation (absence), 59 , 84 management, focus, 118 P/L targets, attainment, 153 portfolio allocation, 103t risk, comparison, 89 selection, 94 short premium allocation, 173 trader compensation, 103 Underlying historical volatility, 31 increase, 42 implied volatility (IV), 98 option underlyings, sample, 98t selection, 94 , 96 –98 strangle, iron condor (contrast), 171 Underlying price BPR function, 88f expected range, 60 –61, 181t Upside skew, 112 Value at risk (VaR). See Conditional value at risk CVaR, contrast, 40 distribution statistic, 39 inclusion, 39f , 40f Variance moment, 15 –16 per‐trade variance, 166 –167 Volatility curve, 182 expansions, 50 –51 forecast, 43 realized volatility, IV overstatement, 46 reversion, 105 smile, 179 –183 smirk (volatility skew), 181 trading, 41 , 44 –48, 58 Volatility assets, market ETFs (correlation), 139 Volatility index (VIX) (CBOE volatility index), 51 , 60 , 78f 2008 sell‐off, 50 , 63 2020 sell‐off, 50 , 63 , 77 , 78f comparison, 89 contraction, 50 contracts, acceleration, 49 correlations, 141t expansion, 48 increase, 54 IVP labeling, 67f levels, 127f , 128f differences, 103t SPY strangles, labeling, 69f long‐term average, 67 , 69 long‐term behavior, 66 lull/expansion/contraction, 49 occurrences, relationship, 71f phases, 49f range, 48 , 66 , 72 , 171 reduction/increase, 69 , 134 frequency, 75t spikes, causes, 50 states, 48 –51 valuation, 135 VXAZN IVP values labeling, 67f level, 66 Weak EMH, 11 , 29 , 31 , 104 –105 Wide iron condors, 116 , 172 Wide wings, usage, 109 Wiener process, 29 Black‐Scholes model, relationship, 23 –26 increments, distribution, 26f Wings, 105 ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00003.html SCORE: 12.00 ================================================================================ Copyright © 2012 by Dan Passarelli. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. First edition was published in 2008 by Bloomberg Press. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com . Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at www.wiley.com/go/permissions . Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Long-Term AnticiPation Securities ® (LEAPS) is a registered trademark of the Chicago Board Options Exchange. Standard & Poor’s 500 ® (S&P 500) and Standard & Poor’s Depository Receipts™ (SPDRs) are registered trademarks of the McGraw-Hill Companies, Inc. Power Shares QQQ™ is a registered trademark of Invesco PowerShares Capital Management LLC. NASDAQ-100 Index ® is a registered trademark of The NASDAQ Stock Market, Inc. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com . Library of Congress Cataloging-in-Publication Data : Passarelli, Dan, 1971- Trading options Greeks : how time, volatility, and other pricing factors drive profits / Dan Passarelli. – 2nd ed. p. cm. – (Bloomberg financial series) Includes index. ISBN 978-1-118-13316-3 (cloth); ISBN 978-1-118-22512-7 (ebk); ISBN 978-1-118-26322-8 (ebk); ISBN 978-1-118-23861-5 (ebk) 1. Options (Finance) 2. Stock options. 3. Derivative securities. I. Title. HG6024.A3P36 2012 332.64′53—dc23 2012019462 ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00005.html SCORE: 20.00 ================================================================================ Disclaimer This book is intended to be educational in nature, both theoretically and practically. It is meant to generally explore the factors that influence option prices so that the reader may gain an understanding of how options work in the real world. This book does not prescribe a specific trading system or method. This book makes no guarantees. Any strategies discussed, including examples using actual securities and price data, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. Examples may or may not be based on factual or historical data. In order to simplify the computations, examples may not include commissions, fees, margin, interest, taxes, or other transaction costs. Commissions and other costs will impact the outcome of all stock and options transactions and must be considered prior to entering into any transactions. Investors should consult their tax adviser about potential tax consequences. Past performance is not a guarantee of future results. Options involve risks and are not suitable for everyone. While much of this book focuses on the risks involved in option trading, there are market situations and scenarios that involve unique risks that are not discussed. Prior to buying or selling an option, a person should read Characteristics and Risks of Standardized Options (ODD) . Copies of the ODD are available from your broker, by calling 1-888-OPTIONS, or from The Options Clearing Corporation, One North Wacker Drive, Chicago, Illinois 60606. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00006.html SCORE: 26.00 ================================================================================ Foreword The past several years have brought about a resurgence in market volatility and options volume unlike anything that has been seen since the close of the twentieth century. As markets have become more interdependent, interrelated, and international, the U.S. listed option markets have solidified their place as the most liquid and transparent venue for risk management and hedging activities of the world’s largest economy. Technology, competition, innovation, and reliability have become the hallmarks of the industry, and our customer base has benefited tremendously from this ongoing evolution. However, these advances can be properly tapped only when the users of the product continue to expand their knowledge of the options product and its unique features. Education has always been the driver of growth in our business, and it will be the steward of the next generation of options traders. Dan Passarelli’s new and updated book Trading Option Greeks is a necessity for customers and traders alike to ensure that they possess the knowledge to succeed and attain their objectives in the high-speed, highly technical arena that the options market has become. The retail trader of the past has given way to a new retail trader of the present—one with an increased level of technology, support, capital treatment, and product selection. The impact of the staggering growth in such products as the CBOE Holdings’ VIX options and futures, and the literally dozens of other products tied to it, have made the volatility asset class a new, unique, and permanent pillar of today’s option markets. Dan’s updated book continues his mission of supporting, preparing, and reinforcing the trader’s understanding of pricing, volatility, market terminology, and strategy, in a way that few other books have been able. Using a perspective forged from years as an options market maker, professional trader, and customer, Dan has once again provided a resource for those who wish to know best how the option markets behave today, and how they are likely to continue to behave in the future. It is important to understand not only what happens in the options space, but also why it happens. This book is intended to provide those answers. I wish you all the best in your trading! William J. Brodsky Chairman and CEO Chicago Board Options Exchange ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00007.html SCORE: 132.00 ================================================================================ Preface I’ve always been fascinated by trading. When I was young, I’d see traders on television, in their brightly colored jackets, shouting on the seemingly chaotic trading floor, and I’d marvel at them. What a wonderful job that must be! These traders seemed to me to be very different from the rest of us. It’s all so very esoteric. It is easy to assume that professional traders have closely kept secrets to their ways of trading—something that secures success in trading for them, but is out of reach for everyone else. In fact, nothing could be further from the truth. If there are any “secrets” of professional traders, this book will expose them. True enough, in years past there have been some barriers to entry to trading success that did indeed make it difficult for nonprofessionals to succeed. For example, commissions, bid-ask spreads, margin requirements, and information flow all favored the professional trader. Now, these barriers are gone. Competition among brokers and exchanges—as well as the ubiquity of information as propagated on the Internet—has torn down those walls. The only barrier left between the Average Joe and the options pro is that of knowledge. Those who have it will succeed; those who do not will fail. To be sure, the knowledge held by successful traders is not that of what will happen in the future; it is the knowledge of how to manage the uncertainty. No matter what our instincts tell us, we do not know what will happen in the future with regard to the market. As Socrates put it, “The only true wisdom is in knowing you know nothing.” The masters of option trading are masters of managing the risk associated with what they don’t know—the risk of uncertainty. As an instructor, I’ve talked to many traders who were new to options who told me, “I made a trade based on what I thought was going to happen. I was right, but my position lost money!” Choosing the right strategy makes all the difference when it comes to mastery of risk management and ultimate trading success. Knowing which option strategy is the right strategy for a given situation comes with knowledge and experience. All option strategies are differentiated by their unique risk characteristics. Some are more sensitive to directional movement of the underlying asset than others; some are more affected by time passing than others. The exact exposure positions have to these market influences determines the success of individual trades and, indeed, the long-term success of the trader who knows how to exploit these risk characteristics. These option-value sensitivities can be controlled when a trader understands the option greeks. Option greeks are metrics used to measure an option’s sensitivity to influences on its price. This book will provide the reader with an understanding of these metrics, to help the reader truly master the risk of uncertainty associated with option trading. Successful traders strive to create option positions with risk-reward profiles that benefit them the most in a given situation. A trader’s objectives will dictate the right strategy for the right situation. Traders can tailor a position to fit a specific forecast with respect to the time horizon; the degree of bullishness, bearishness, neutrality, or volatility in the underlying stock; and the desired amount of leverage. Furthermore, they can exploit opportunities unique to options. They can trade option greeks. This opens the door to many new opportunities. A New Direction Traders, both professional and retail, need ways to act on their forecasts without the constraints of convention. “Get long, or do nothing” is no longer a viable business model for people active in the market. “Up is good; down is bad” is burned into traders’ minds from the beginning of their market education. This concept has its place in the world of investing, but becoming an active trader in the option market requires thinking in a new direction. Market makers and other expert option traders look at the market differently from other traders. One fundamental difference is that these traders trade all four directions: up, down, sideways, and volatile. Trading Strategies Buying stock is a trading strategy that most people understand. In practical terms, traders who buy stock are generally not concerned with the literal ownership stake in a corporation, just the opportunity to profit if the stock rises. Although it’s important for traders to understand that the price of a stock is largely tied to the success or failure of the corporation, it’s essential to keep in mind exactly what the objective tends to be for trading a stock: to profit from changes in its price. A bullish position can also be taken in the options market. The most basic example is buying a call. A bearish position can be taken by trading stock or options, as well. If traders expect the value of a stock they own to fall, they will sell the stock. This eliminates the risk of losses from the stock’s falling. If the traders do not own the stock that they think will decline, they can take a more active stance and short it. The short-seller borrows the stock from a party that owns it and then sells the borrowed shares to another party. The goal of selling stock short is to later repurchase the shares at a lower price before returning the stock to its owner. It is simply reversing the order of “buy low/sell high.” The risk is that the stock rises and shares have to be bought at a higher price than that at which they were sold. Although shorting stock can lead to profits when the market cooperates, in the options market, there are alternative ways to profit from falling prices. The most basic example is buying a put. A trader can use options to take a bullish or bearish position, given a directional forecast. Sideways, nontrending stocks and their antithesis, volatile stocks, can be traded as well. In the later market conditions, profit or loss can be independent of whether the stock rises or falls. Opportunity in option trading is not necessarily black and white—not necessarily up and down. Option trading is nonlinear. Consequently, more opportunities can be exploited by trading options than by trading stock. Option traders must consider the time period in question, the volatility expected during this period, interest rates, and dividends. Along with the stock price, these factors make up the dynamic components of an option’s value. These individual factors can be isolated, measured, and exploited. Incremental changes in any of these elements as measured by option greeks provide opportunity for option traders. Because of these other influences, direction is not the only tradable element of a forecast. Time, volatility, interest rates—these can all be traded using option greeks. These factors and more will all be discussed at great length throughout this book. This Second Edition of Trading Option Greeks This book addresses the complex price behavior of options by discussing option greeks from both a theoretical and a practical standpoint. There is some tactical discussion throughout, although the objective of this book is to provide education to the reader. This book is meant to be less a how-to manual than a how-come tutorial. This informative guide will give the retail trader a look inside the mind of a professional trader. It will help the professional trader better understand the essential concepts of his craft. Even the novice trader will be able to apply these concepts to basic options strategies. Comprehensive knowledge of the greeks can help traders to avoid common pitfalls and increase profit potential. Much of this book is broken down into a discussion of individual strategies. Although the nuances of each specific strategy are not relevant, presenting the material this way allows for a discussion of very specific situations in which greeks come into play. Many of the concepts discussed in a section on one option strategy can be applied to other option strategies. As in the first edition of Trading Option Greeks , Chapter 1 discusses basic option concepts and definitions. It was written to be a review of the basics for the intermediate to advanced trader. For newcomers, it’s essential to understand these concepts before moving forward. A detailed explanation of option greeks begins in Chapter 2. Be sure to leave a bookmark in this chapter, as you will flip to it several times while reading the rest of the book and while studying the market thereafter. Chapter 3 introduces volatility. The same bookmark advice can be applied here, as well. Chapters 4 and 5 explore the minds of option traders. What are the risks they look out for? What are the opportunities they seek? These chapters also discuss direction-neutral and direction-indifferent trading. The remaining chapters take the reader from concept to application, discussing the strategies for nonlinear trading and the tactical considerations of a successful options trader. New material in this edition includes updated examples, with more current price information throughout many of the chapters. More detailed discussions are also included to give the reader a deeper understanding of important topics. For example, Chapter 8 has a more elaborate explanation of the effect of dividends on option prices. Chapter 17 of this edition has new material on strategy selection, position management, and adjusting, not featured in the first edition of the book. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00008.html SCORE: 16.00 ================================================================================ Acknowledgments A book like Trading Option Greeks is truly a collaboration of the efforts of many people. In my years as a trader, I had many teachers in the School of Hard Knocks. I have had the support of friends and family during the trials and tribulations throughout my trading career, as well as during the time spent writing this book, both the first edition and now this second edition. Surely, there are hundreds of people whose influences contributed to the creation of this book, but there are a few in particular to whom I’d like to give special thanks. I’d like to give a very special thanks to my mentor and friend from the CBOE’s Options Institute, Jim Bittman. Without his help this book would not have been written. Thanks to Marty Kearney and Joe Troccolo for looking over the manuscript. Their input was invaluable. Thanks to Debra Peters for her help during my career at the Options Institute. Thanks to Steve Fossett and Bob Kirkland for believing in me. Thanks to the staff at Bloomberg Press, especially Stephen Isaacs and Kevin Commins. Thanks to my friends at the Chicago Board Options Exchange, the Options Industry Council, and the CME group. Thanks to John Kmiecik for his diligent content editing. Thanks to those who contribute to sharing option ideas on my website, markettaker.com . Thanks to my wife, Kathleen, who has been more patient and supportive than anyone could reasonably ask for. And thanks, especially, to my students and those of you reading this book. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00010.html SCORE: 997.00 ================================================================================ CHAPTER 1 The Basics To understand how options work, one needs first to understand what an option is. An option is a contract that gives its owner the right to buy or the right to sell a fixed quantity of an underlying security at a specific price within a certain time constraint. There are two types of options: calls and puts. A call gives the owner of the option the right to buy the underlying security. A put gives the owner of the option the right to sell the underlying security. As in any transaction, there are two parties to an option contract—a buyer and a seller. Contractual Rights and Obligations The option buyer is the party who owns the right inherent in the contract. The buyer is referred to as having a long position and may also be called the holder, or owner, of the option. The right doesn’t last forever. At some point the option will expire. At expiration, the owner may exercise the right or, if the option has no value to the holder, let it expire without exercising it. But he need not hold the option until expiration. Options are transferable—they can be traded intraday in much the same way as stock is traded. Because it’s uncertain what the underlying stock price of the option will be at expiration, much of the time this right has value before it expires. The uncertainty of stock prices, after all, is the raison d’être of the option market. A long position in an option contract, however, is fundamentally different from a long position in a stock. Owning corporate stock affords the shareholder ownership rights, which may include the right to vote in corporate affairs and the right to receive dividends. Owning an option represents strictly the right either to buy the stock or to sell it, depending on whether it’s a call or a put. Option holders do not receive dividends that would be paid to the shareholders of the underlying stock, nor do they have voting rights. The corporation has no knowledge of the parties to the option contract. The contract is created by the buyer and seller of the option and made available by being listed on an exchange. The party to the contract who is referred to as the option seller, also called the option writer, has a short position in the option. Instead of having a right to take a position in the underlying stock, as the buyer does, the seller incurs an obligation to potentially either buy or sell the stock. When a trader who is long an option exercises, a trader with a short position gets assigned . Assignment means the trader with the short option position is called on to fulfill the obligation that was established when the contract was sold. Shorting an option is fundamentally different from shorting a stock. Corporations have a quantifiable number of outstanding shares available for trading, which must be borrowed to create a short position, but establishing a short position in an option does not require borrowing; the contract is simply created. The strategy of shorting stock is implemented statistically far less frequently than simply buying stock, but that is not at all the case with options. For every open long-option contract, there is an open short-option contract—they are equally common. Opening and Closing Traders’ option orders are either opening or closing transactions. When traders with no position in a particular option buy the option, they buy to open. If, in the future, the traders wish to eliminate the position by selling the option they own, the traders enter a sell to close order—they are closing the position. Likewise, if traders with no position in a particular option want to sell an option, thereby creating a short position, the traders execute a sell-to-open transaction. When the traders cover the short position by buying back the option, the traders enter a buy-to-close order. Open Interest and Volume Traders use many types of market data to make trading decisions. Two items that are often studied but sometimes misunderstood are volume and open interest. Volume, as the name implies, is the total number of contracts traded during a time period. Often, volume is stated on a one-day basis, but could be stated per week, month, year, or otherwise. Once a new period (day) begins, volume begins again at zero. Open interest is the number of contracts that have been created and remain outstanding. Open interest is a running total. When an option is first listed, there are no open contracts. If Trader A opens a long position in a newly listed option by buying a one-lot, or one contract, from Trader B, who by selling is also opening a position, a contract is created. One contract traded, so the volume is one. Since both parties opened a position and one contract was created, the open interest in this particular option is one contract as well. If, later that day, Trader B closes his short position by buying one contract from Trader C, who had no position to start with, the volume is now two contracts for that day, but open interest is still one. Only one contract exists; it was traded twice. If the next day, Trader C buys her contract back from Trader A, that day’s volume is one and the open interest is now zero. The Options Clearing Corporation Remember when Wimpy would tell Popeye, “I’ll gladly pay you Tuesday for a hamburger today.” Did Popeye ever get paid for those burgers? In a contract, it’s very important for each party to hold up his end of the bargain—especially when there is money at stake. How does a trader know the party on the other side of an option contract will in fact do that? That’s where the Options Clearing Corporation (OCC) comes into play. The OCC ultimately guarantees every options trade. In 2010, that was almost 3.9 billion listed-options contracts. The OCC accomplishes this through many clearing members. Here’s how it works: When Trader X buys an option through a broker, the broker submits the trade information to its clearing firm. The trader on the other side of this transaction, Trader Y, who is probably a market maker, submits the trade to his clearing firm. The two clearing firms (one representing Trader X’s buy, the other representing Trader Y’s sell) each submit the trade information to the OCC, which “matches up” the trade. If Trader Y buys back the option to close the position, how does that affect Trader X if he wants to exercise it? It doesn’t. The OCC, acting as an intermediary, assigns one of its clearing members with a customer that is short the option in question to deliver the stock to Trader X’s clearing firm, which in turn delivers the stock to Trader X. The clearing member then assigns one of its customers who is short the option. The clearing member will assign the trader either randomly or first in, first out. Effectively, the OCC is the ultimate counterparty to both the exercise and the assignment. Standardized Contracts Exchange-listed options contracts are standardized, meaning the terms of the contract, or the contract specifications, conform to a customary structure. Standardization makes the terms of the contracts intuitive to the experienced user. To understand the contract specifications in a typical equity option, consider an example: Buy 1 IBM December 170 call at 5.00 Quantity In this example, one contract is being purchased. More could have been purchased, but not less—options cannot be traded in fractional units. Option Series, Option Class, and Contract Size All calls or puts of the same class, the same expiration month, and the same strike price are called an option series . For example, the IBM December 170 calls are a series. Options series are displayed in an option chain on an online broker’s user interface. An option chain is a full or partial list of the options that are listed on an underlying. Option class means a group of options that represent the same underlying. Here, the option class is denoted by the symbol IBM—the contract represents rights on International Business Machines Corp. (IBM) shares. Buying one contract usually gives the holder the right to buy or to sell 100 shares of the underlying stock. This number is referred to as contract size . Though this is usually the case, there are times when the contract size is something other than 100 shares of a stock. This situation may occur after certain types of stock splits, spin-offs, or stock dividends, for example. In the minority of cases in which the one contract represents rights on something besides 100 shares, there may be more than one class of options listed on a stock. A fairly unusual example was presented by the Ford Motor Company options in the summer of 2000. In June 2000, Ford spun off Visteon Corporation. Then, in August 2000, Ford offered shareholders a choice of converting their shares into (a) new shares of Ford plus $20 cash per share, (b) new Ford stock plus fractional shares with an aggregate value of $20, or (c) new Ford stock plus a combination of more new Ford stock and cash. There were three classes of options listed on Ford after both of these changes: F represented 100 shares of the new Ford stock; XFO represented 100 shares of Ford plus $20 per share ($2,000) plus cash in lieu of $1.24; and FOD represented 100 shares of new Ford, 13 shares of Visteon, and $2,001.24. Sometimes these changes can get complicated. If there is ever a question as to what the underlying is for an option class, the authority is the OCC. A lot of time, money, and stress can be saved by calling the OCC at 888-OPTIONS and clarifying the matter. Expiration Month Options expire on the Saturday following the third Friday of the stated month, which in this case is December. The final trading day for an option is commonly the day before expiration—here, the third Friday of December. There are usually at least four months listed for trading on an option class. There may be a total of six months if Long-Term Equity AnticiPation Securities ® or LEAPS ® are listed on the class. LEAPS can have one year to about two-and-a-half years until expiration. Some underlyings have one-week options called Weeklys SM listed on them. Strike Price The price at which the option holder owns the right to buy or to sell the underlying is called the strike price, or exercise price. In this example, the holder owns the right to buy the stock at $170 per share. There is method to the madness regarding how strike prices are listed. Strike prices are generally listed in $1, $2.50, $5, or $10 increments, depending on the value of the strikes and the liquidity of the options. The relationship of the strike price to the stock price is important in pricing options. For calls, if the stock price is above the strike price, the call is in-the-money (ITM). If the stock and the strike prices are close, the call is at-the-money (ATM). If the stock price is below the strike price the call is out-of-the-money (OTM). This relationship is just the opposite for puts. If the stock price is below the strike price, the put is in-the-money. If the stock price and the strike price are about the same, the put is at-the-money. And, if the stock price is above the put strike, it is out-of-the-money. Option Type There are two types of options: calls and puts. Calls give the holder the right to buy the underlying and the writer the obligation to sell the underlying. Puts give the holder the right to sell the underlying and the writer the obligation to buy the underlying. Premium The price of an option is called its premium. The premium of this option is $5. Like stock prices, option premiums are stated in dollars and cents per share. Since the option represents 100 shares of IBM, the buyer of this option will pay $500 when the transaction occurs. Certain types of spreads may be quoted in fractions of a penny. An option’s premium is made up of two parts: intrinsic value and time value. Intrinsic value is the amount by which the option is in-the-money. For example, if IBM stock were trading at 171.30, this 170-strike call would be in-the-money by 1.30. It has 1.30 of intrinsic value. The remaining 3.70 of its $5 premium would be time value. Options that are out-of-the-money have no intrinsic value. Their values consist only of time premium. Sometimes options have no time value left. Options that consist of only intrinsic value are trading at what traders call parity . Time value is sometimes called premium over parity . Exercise Style One contract specification that is not specifically shown here is the exercise style. There are two main exercise styles: American and European. American-exercise options can be exercised, and therefore assigned, anytime after the contract is entered into until either the trader closes the position or it expires. European-exercise options can be exercised and assigned only at expiration. Exchange-listed equity options are all American-exercise style. Other kinds of options are commonly European exercise. Whether an option is American or European has nothing to with the country in which it’s listed. ETFs, Indexes, and HOLDRs So far, we’ve focused on equity options—options on individual stocks. But investors have other choices for trading securities options. Options on baskets of stocks can be traded, too. This can be accomplished using options on exchange-traded funds (ETFs), index options, or options on holding company depositary receipts (HOLDRs). ETF Options Exchange-traded funds are vehicles that represent ownership in a fund or investment trust. This fund is made up of a basket of an underlying index’s securities—usually equities. The contract specifications of ETF options are similar to those of equity options. Let’s look at an example. One actively traded optionable ETF is the Standard & Poor’s Depositary Receipts (SPDRs or Spiders). Spider shares and options trade under the symbol SPY. Exercising one SPY call gives the exerciser a long position of 100 shares of Spiders at the strike price of the option. Expiration for ETF options typically falls on the same day as for equity options—the Saturday following the third Friday of the month. The last trading day is the Friday before. ETF options are American exercise. Traders of ETFs should be aware of the relationship between the price of the ETF shares and the value of the underlying index. For example, the stated value of the Spiders is about one tenth the stated value of the S&P 500. The PowerShares QQQ ETF, representing the Nasdaq 100, is about one fortieth the stated value of the Nasdaq 100. Index Options Trading options on the Spiders ETF is a convenient way to trade the Standard & Poor’s (S&P) 500. But it’s not the only way. There are other option contracts listed on the S&P 500. The SPX is one of the major ones. The SPX is an index option contract. There are some very important differences between ETF options like SPY and index options like SPX. The first difference is the underlying. The underlying for ETF options is 100 shares of the ETF. The underlying for index options is the numerical value of the index. So if the S&P 500 is at 1303.50, the underlying for SPX options is 1303.50. When an SPX call option is exercised, instead of getting 100 shares of something, the exerciser gets the ITM cash value of the option times $100. Again, with SPX at 1303.50, if a 1300 call is exercised, the exerciser gets $350—that’s 1303.50 minus 1300, times $100. This is called cash settlement . Many index options are European, which means no early exercise. At expiration, any long ITM options in a trader’s inventory result in an account credit; any short ITMs result in a debit of the ITM value times $100. The settlement process for determining whether a European-style index option is in-the-money at expiration is a little different, too. Often, these indexes are a.m. settled. A.m.-settled index options will have actual expiration on the conventional Saturday following the third Friday of the month. But the final trading day is the Thursday before the expiration day. The final settlement value of the index is determined by the opening prices of the components of the index on Friday morning. HOLDR Options Like ETFs, holding company depositary receipts also represent ownership in a basket of stocks. The main difference is that investors owning HOLDRs retain the ownership rights of the individual stocks in the fund, such as the right to vote shares and the right to receive dividends. Options on HOLDRs, for all intents and purposes, function much like options on ETFs. Strategies and At-Expiration Diagrams One of the great strengths of options is that there are so many different ways to use them. There are simple, straightforward strategies like buying a call. And there are complex spreads with creative names like jelly roll, guts, and iron butterfly. A spread is a strategy that involves combining an option with one or more other options or stock. Each component of the spread is referred to as a leg. Each spread has its own unique risk and reward characteristics that make it appropriate for certain market outlooks. Throughout this book, many different spreads will be discussed in depth. For now, it’s important to understand that all spreads are made up of a combination of four basic option positions: buy call, sell call, buy put, and sell put. Understanding complex option strategies requires understanding these basic positions and their common, practical uses. When learning options, it’s helpful to see what the option’s payout is if it is held until expiration. Buy Call Why buy the right to buy the stock when you can simply buy the stock? All option strategies have trade-offs, and the long call is no different. Whether the stock or the call is preferable depends greatly on the trader’s forecast and motivations. Consider a long call example: Buy 1 INTC June 22.50 call at 0.85. In this example, a trader is bullish on Intel (INTC). He believes Intel will rise at least 20 percent, from $22.25 per share to around $27 by June expiration, about two months from now. He is concerned, however, about downside risk and wants to limit his exposure. Instead of buying 100 shares of Intel at $22.25—a total investment of $2,225—the trader buys 1 INTC June 22.50 call at 0.85, for a total of $85. The trader is paying 0.85 for the right to buy 100 shares of Intel at $22.50 per share. If Intel is trading below the strike price of $22.50 at expiration, the call will expire and the total premium of 0.85 will be lost. Why? The trader will not exercise the right to buy the stock at a $22.50 if he can buy it cheaper in the market. Therefore, if Intel is below $22.50 at expiration, this call will expire with no value. However, if the stock is trading above the strike price at expiration, the call can be exercised, in which case the trader may purchase the stock below its trading price. Here, the call has value to the trader. The higher the stock, the more the call is worth. For the trade to be profitable, at expiration the stock must be trading above the trader’s break-even price. The break-even price for a long call is the strike price plus the premium paid—in this example, $23.35 per share. The point here is that if the call is exercised, the effective purchase price of the stock upon exercise is $23.35. The stock is literally bought at the strike price, which is $22.50, but the premium of 0.85 that the trader has paid must be taken into account. Exhibit 1.1 illustrates this example. EXHIBIT 1.1 Long Intel call. Exhibit 1.1 is an at-expiration diagram for the Intel 22.50 call. It shows the profit and loss, or P&(L), of the option if it is held until expiration. The X-axis represents the prices at which INTC could be trading at expiration. The Y-axis represents the associated profit or loss on the position. The at-expiration diagram of any long call position will always have this same hockey-stick shape, regardless of the stock or strike. There is always a limit of loss, represented by the horizontal line, which in this case is drawn at −0.85. And there is always a line extending upward and to the right, which represents effectively a long stock position stemming from the strike. The trade-offs between a long stock position and a long call position are shown in Exhibit 1.2 . EXHIBIT 1.2 Long Intel call vs. long Intel stock. The thin dotted line represents owning 100 shares of Intel at $22.25. Profits are unlimited, but the risk is substantial—the stock can go to zero. Herein lies the trade-off. The long call has unlimited profit potential with limited risk. Whenever an option is purchased, the most that can be lost is the premium paid for the option. But the benefit of reduced risk comes at a cost. If the stock is above the strike at expiration, the call will always underperform the stock by the amount of the premium. Because of this trade-off, conservative traders will sometimes buy a call rather than the associated stock and sometimes buy the stock rather than the call. Buying a call can be considered more conservative when the volatility of the stock is expected to rise. Traders are willing to risk a comparatively small premium when a large price decline is feared possible. Instead, in an interest-bearing vehicle, they harbor the capital that would otherwise have been used to purchase the stock. The cost of this protection is acceptable to the trader if high-enough price advances are anticipated. In terms of percentage, much higher returns and losses are possible with the long call. If the stock is trading at $27 at expiration, as the trader in this example expected, the trader reaps a 429 percent profit on the $0.85 investment ([$27 − 23.35] / $0.85). If Intel is below the strike price at expiration, the trader loses 100 percent. This makes call buying an excellent speculative alternative. Those willing to accept bigger risk can further increase returns by purchasing more calls. In this example, around 26 Intel calls—representing the rights on 2,600 shares—can be purchased at 85 cents for the cost of 100 shares at $22.25. This is the kind of leverage that allows for either a lower cash outlay than buying the stock—reducing risk—or the same cash outlay as buying the stock but with much greater exposure—creating risk in pursuit of higher returns. Sell Call Selling a call creates the obligation to sell the stock at the strike price. Why is a trader willing to accept this obligation? The answer is option premium. If the position is held until expiration without getting assigned, the entire premium represents a profit for the trader. If assignment occurs, the trader will be obliged to sell stock at the strike price. If the trader does not have a long position in the underlying stock (a naked call), a short stock position will be created. Otherwise, if stock is owned (a covered call), that stock is sold. Whether the trader has a profit or a loss depends on the movement of the stock price and how the short call position was constructed. Consider a naked call example: Sell 1 TGT October 50 call at 1.45 In this example, Target Corporation (TGT) is trading at $49.42. A trader, Sam, believes Target will continue to be trading below $50 by October expiration, about two months from now. Sam sells 1 Target two-month 50 call at 1.45, opening a short position in that series. Exhibit 1.3 will help explain the expected payout of this naked call position if it is held until expiration. EXHIBIT 1.3 Naked Target call. If TGT is trading below the exercise price of 50, the call will expire worthless. Sam keeps the 1.45 premium, and the obligation to sell the stock ceases to exist. If Target is trading above the strike price, the call will be in-the-money. The higher the stock is above the strike price, the more intrinsic value the call will have. As a seller, Sam wants the call to have little or no intrinsic value at expiration. If the stock is below the break-even price at expiration, Sam will still have a profit. Here, the break-even price is $51.45—the strike price plus the call premium. Above the break-even, Sam has a loss. Since stock prices can rise to infinity (although, for the record, I have never seen this happen), the naked call position has unlimited risk of loss. Because a short stock position may be created, a naked call position must be done in a margin account. For retail traders, many brokerage firms require different levels of approval for different types of option strategies. Because the naked call position has unlimited risk, establishing it will generally require the highest level of approval—and a high margin requirement. Another tactical consideration is what Sam’s objective was when he entered the trade. His goal was to profit from the stock’s being below $50 during this two-month period—not to short the stock. Because equity options are American exercise and can be exercised/assigned any time from the moment the call is sold until expiration, a short stock position cannot always be avoided. If assigned, the short stock position will extend Sam’s period of risk—because stock doesn’t expire. Here, he will pay one commission shorting the stock when assignment occurs and one more when he buys back the unwanted position. Many traders choose to close the naked call position before expiration rather than risk assignment. It is important to understand the fundamental difference between buying calls and selling calls. Buying a call option offers limited risk and unlimited reward. Selling a naked call option, however, has limited reward—the call premium—and unlimited risk. This naked call position is not so much bearish as not bullish . If Sam thought the stock was going to zero, he would have chosen a different strategy. Now consider a covered call example: Buy 100 shares TGT at $49.42 Sell 1 TGT October 50 call at 1.45 Unlimited and risk are two words that don’t sit well together with many traders. For that reason, traders often prefer to sell calls as part of a spread. But since spreads are strategies that involve multiple components, they have different risk characteristics from an outright option. Perhaps the most commonly used call-selling spread strategy is the covered call (sometimes called a covered write or a buy-write ). While selling a call naked is a way to take advantage of a “not bullish” forecast, the covered call achieves a different set of objectives. After studying Target Corporation, another trader, Isabel, has a neutral to slightly bullish forecast. With Target at $49.42, she believes the stock will be range-bound between $47 and $51.50 over the next two months, ending with October expiration. Isabel buys 100 shares of Target at $49.42 and sells 1 TGT October 50 call at 1.45. The implications for the covered-call strategy are twofold: Isabel must be content to own the stock at current levels, and—since she sold the right to buy the stock at $50, that is, a 50 call, to another party—she must be willing to sell the stock if the price rises to or through $50 per share. Exhibit 1.4 shows how this covered call performs if it is held until the call expires. EXHIBIT 1.4 Target covered call. The solid kinked line represents the covered call position, and the thin, straight dotted line represents owning the stock outright. At the expiration of the call option, if Target is trading below $50 per share—the strike price—the call expires and Isabel is left with a long position of 100 shares plus $1.45 per share of expired-option premium. Below the strike, the buy-write always outperforms simply owning the stock by the amount of the premium. The call premium provides limited downside protection; the stock Isabel owns can decline $1.45 in value to $47.97 before the trade is a loser. In the unlikely event the stock collapses and becomes worthless, this limited downside protection is not so comforting. Ultimately, Isabel has $47.97 per share at risk. The trade-off comes if Target is above $50 at expiration. Here, assignment will likely occur, in which case the stock will be sold. The call can be assigned before expiration, too, causing the stock to be called away early. Because the covered call involves this obligation to sell the sock at the strike price, upside potential is limited. In this case, Isabel’s profit potential is $2.03. The stock can rise from $49.42 to $50—a $0.58 profit—plus $1.45 of option premium. Isabel does not want the stock to decline too much. Below $47.97, the trade is a loser. If the stock rises too much, the stock is sold prematurely and upside opportunity is lost. Limited reward and unlimited risk. (Technically, the risk is not unlimited—the stock can only go to zero. But if the stock drops from $49.42 to zero in a short time, the risk will certainly feel unlimited.) The covered call strategy is for a neutral to moderately bullish outlook. Sell Put Selling a put has many similarities to the covered call strategy. We’ll discuss the two positions and highlight the likenesses. Chapter 6 will detail the nuts and bolts of why these similarities exist. Consider an example of selling a put: Sell 1 BA January 65 put at 1.20 In this example, trader Sam is neutral to moderately bullish on Boeing (BA) between now and January expiration. He is not bullish enough to buy BA at the current market price of $69.77 per share. But if the shares dropped below $65, he’d gladly scoop some up. Sam sells 1 BA January 65 put at 1.20. The at-expiration diagram in Exhibit 1.5 shows the P&(L) of this trade if it is held until expiration. EXHIBIT 1.5 Boeing short put. At the expiration of this option, if Boeing is above $65, the put expires and Sam retains the premium of $1.20. The obligation to buy stock expires with the option. Below the strike, put owners will be inclined to exercise their option to sell the stock at $65. Therefore, those short the put, as Sam is in this example, can expect assignment. The break-even price for the position is $63.80. That is the strike price minus the option premium. If assigned, this is the effective purchase price of the stock. The obligation to buy at $65 is fulfilled, but the $1.20 premium collected makes the purchase effectively $63.80. Here, again, there is limited profit opportunity ($1.20 if the stock is above the strike price) and seemingly unlimited risk (the risk of potential stock ownership at $63.80) if Boeing is below the strike price. Why would a trader short a put and willingly assume this substantial risk with comparatively limited reward? There are a number of motivations that may warrant the short put strategy. In this example, Sam had the twin goals of profiting from a neutral to moderately bullish outlook on Boeing and buying it if it traded below $65. The short put helps him achieve both objectives. Much like the covered call, if the stock is above the strike at expiration, this trader reaches his maximum profit potential—in this case 1.20. And if the price of Boeing is below the strike at expiration, Sam has ownership of the stock from assignment. Here, a strike price that is lower than the current stock level is used. The stock needs to decline in order for Sam to get assigned and become long the stock. With this strategy, he was able to establish a target price at which he would buy the stock. Why not use a limit order? If the put is assigned, the effective purchase price is $63.80 even if the stock price is above this price. If the put is not assigned, the premium is kept. A consideration every trader must make before entering the short put position is how the purchase of the stock will be financed in the event the put is assigned. Traders hoping to acquire the stock will often hold enough cash in their trading account to secure the purchase of the stock. This is called a cash-secured put . In this example, Sam would hold $6,380 in his account in addition to the $120 of option premium received. This affords him enough free capital to fund the $6,500 purchase of stock the short put dictates. More speculative traders may be willing to buy the stock on margin, in which case the trader will likely need around 50 percent of the stock’s value. Some traders sell puts without the intent of ever owning the stock. They hope to profit from a low-volatility environment. Just as the short call is a not-bullish stance on the underlying, the short put is a not-bearish play. As long as the underlying is above the strike price at expiration, the option premium is all profit. The trader must actively manage the position for fear of being assigned. Buying the put back to close the position eliminates the risk of assignment. Buy Put Buying a put gives the holder the right to sell stock at the strike price. Of course, puts can be a part of a host of different spreads, but this chapter discusses the two most basic and common put-buying strategies: the long put and the protective put. The long put is a way to speculate on a bearish move in the underlying security, and the protective put is a way to protect a long position in the underlying security. Consider a long put example: Buy 1 SPY May 139 put at 2.30 In this example, the Spiders have had a good run up to $140.35. Trader Isabel is looking for a 10 percent correction in SPY between now and the end of May, about three months away. She buys 1 SPY May 139 put at 2.30. This put gives her the right to sell 100 shares of SPY at $139 per share. Exhibit 1.6 shows Isabel’s P&(L) if the put is held until expiration. EXHIBIT 1.6 SPY long put. If SPY is above the strike price of 139 at expiration, the put will expire and the entire premium of 2.30 will be lost. If SPY is below the strike price at expiration, the put will have value. It can be exercised, creating a short position in the Spiders at an effective price of $136.70 per share. This price is found by subtracting the premium paid, 2.30, from the strike price, 139. This is the point at which the position breaks even. If SPY is below $136.70 at expiration, Isabel has a profit. Profits will increase on a tick-for-tick basis, with downward movements in SPY down to zero. The long put has limited risk and substantial reward potential. An alternative for Isabel is to short the ETF at the current price of $140.35. But a short position in the underlying may not be as attractive to her as a long put. The margin requirements for short stock are significantly higher than for a long put. Put buyers must post only the premium of the put—that is the most that can be lost, after all. The margin requirement for short stock reflects unlimited loss potential. Margin requirements aside, risk is a very real consideration for a trader deciding between shorting stock and buying a put. If the trader expects high volatility, he or she may be more inclined to limit upside risk while leveraging downside profit potential by buying a put. In general, traders buy options when they expect volatility to increase and sell them when they expect volatility to decrease. This will be a common theme throughout this book. Consider a protective put example: This is an example of a situation in which volatility is expected to increase. Own 100 shares SPY at 140.35 Buy 1 SPY May139 put at 2.30 Although Isabel bought a put because she was bearish on the Spiders, a different trader, Kathleen, may buy a put for a different reason—she’s bullish but concerned about increasing volatility. In this example, Kathleen has owned 100 shares of Spiders for some time. SPY is currently at $140.35. She is bullish on the market but has concerns about volatility over the next two or three months. She wants to protect her investment. Kathleen buys 1 SPY May 139 put at 2.30. (If Kathleen bought the shares of SPY and the put at the same time, as a spread, the position would be called a married put.) Kathleen is buying the right to sell the shares she owns at $139. Effectively, it is an insurance policy on this asset. Exhibit 1.7 shows the risk profile of this new position. EXHIBIT 1.7 SPY protective put. The solid kinked line is the protective put (put and stock), and the thin dotted line is the outright position in SPY alone, without the put. The most Kathleen stands to lose with the protective put is $3.65 per share. SPY can decline from $140.35 to $139, creating a loss of $1.35, plus the $2.30 premium spent on the put. If the stock does not fall and the insuring put hence does not come into play, the cost of the put must be recouped to justify its expense. The break-even point is $142.65. This position implies that Kathleen is still bullish on the Spiders. When traders believe a stock or ETF is going to decline, they sell the shares. Instead, Kathleen sacrifices 1.6 percent of her investment up front by purchasing the put for $2.30. She defers the sale of SPY until the period of perceived risk ends. Her motivation is not to sell the ETF; it is to hedge volatility. Once the anticipated volatility is no longer a concern, Kathleen has a choice to make. She can let the option run its course, holding it to expiration, at which point it will either expire or be exercised; or she can sell the option before expiration. If the option is out-of-the-money, it may have residual time value prior to expiration that can be recouped. If it is in-the-money, it will have intrinsic value and maybe time value as well. In this situation, Kathleen can look at this spread as two trades—one that has declined in price, the SPY shares, and one that has risen in price, the put. Losses on the ETF shares are to some degree offset by gains on the put. Measuring Incremental Changes in Factors Affecting Option Prices At-expiration diagrams are very helpful in learning how a particular option strategy works. They show what the option’s price will ultimately be at various prices of the underlying. There is, however, a caveat when using at-expiration diagrams. According to the Options Industry Council, most options are closed before they reach expiration. Traders not planning to hold an option until it expires need to have a way to develop reasonable expectations as to what the option’s price will be given changes that can occur in factors affecting the option’s price. The tool option traders use to aid them in this process is option greeks. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00011.html SCORE: 1871.00 ================================================================================ CHAPTER 2 Greek Philosophy My wife, Kathleen, is not an options trader. Au contraire. However, she, like just about everyone, uses them from time to time—though without really thinking about it. She was on eBay the other day bidding on a pair of shoes. The bid was $45 with three days left to go. She was concerned about the price rising too much and missing the chance to buy them at what she thought was a good price. She noticed, though, that someone else was selling the same shoes with a buy-it-now price of $49—a good-enough price in her opinion. Kathleen was effectively afforded a call option. She had the opportunity to buy the shoes at (the strike price of) $49, a right she could exercise until the offer expired. The biggest difference between the option in the eBay scenario and the sort of options discussed in this book is transferability. Actual options are tradable—they can be bought and sold. And it is the contract itself that has value—there is one more iteration of pricing. For example, imagine the $49 opportunity was a coupon or certificate that guaranteed the price of $49, which could be passed along from one person to another. And there was the chance that the $49-price guarantee could represent a discount on the price paid for the shoes—maybe a big discount—should the price of the shoes rise in the eBay auction. The certificate guaranteeing the $49 would have value. Anyone planning to buy the shoes would want the safety of knowing they were guaranteed not to pay more than $49 for the shoes. In fact, some people would even consider paying to buy the certificate itself if they thought the price of the shoes might rise significantly. Price vs. Value: How Traders Use Option-Pricing Models Like in the common-life example just discussed, the right to buy or sell an underlying security—that is, an option—can have value, too. The specific value of an option is determined by supply and demand. There are several variables in an option contract, however, that can influence a trader’s willingness to demand (desire to buy) or supply (desire to sell) an option at a given price. For example, a trader would rather own—that is, there would be higher demand for—an option that has more time until expiration than a shorter-dated option, all else held constant. And a trader would rather own a call with a lower strike than a higher strike, all else kept constant, because it would give the right to buy at a lower price. Several elements contribute to the value of an option. It took academics many years to figure out exactly what those elements are. Fischer Black and Myron Scholes together pioneered research in this area at the University of Chicago. Ultimately, their work led to a Nobel Prize for Myron Scholes. Fischer Black died before he could be honored. In 1973, Black and Scholes published a paper called “The Pricing of Options and Corporate Liabilities” in the Journal of Political Economy , that introduced the Black-Scholes option-pricing model to the world. The Black-Scholes model values European call options on non-dividend-paying stocks. Here, for the first time, was a widely accepted model illustrating what goes into the pricing of an option. Option prices were no longer wild guesswork. They could now be rationalized. Soon, additional models and alterations to the Black-Scholes model were developed for options on indexes, dividend-paying stocks, bonds, commodities, and other optionable instruments. All the option-pricing models commonly in use today have slightly different means but achieve the same end: the option’s theoretical value. For American-exercise equity options, six inputs are entered into any option-pricing model to generate a theoretical value: stock price, strike price, time until expiration, interest rate, dividends, and volatility. Theoretical value—what a concept! A trader plugs six numbers into a pricing model, and it tells him what the option is worth, right? Well, in practical terms, that’s not exactly how it works. An option is worth what the market bears. Economists call this price discovery. The price of an option is determined by the forces of supply and demand working in a free and open market. Herein lies an important concept for option traders: the difference between price and value. Price can be observed rather easily from any source that offers option quotes (web sites, your broker, quote vendors, and so on). Value is calculated by a pricing model. But, in practice, the theoretical value is really not an output at all. It is already known: the market determines it. The trader rectifies price and value by setting the theoretical value to fall between the bid and the offer of the option by adjusting the inputs to the model. Professional traders often refer to the theoretical value as the fair value of the option. At this point, please note the absence of the mathematical formula for the Black-Scholes model (or any other pricing model, for that matter). Although the foundation of trading option greeks is mathematical, this book will keep the math to a minimum—which is still quite a bit. The focus of this book is on practical applications, not academic theory. It’s about learning to drive the car, not mastering its engineering. The trader has an equation with six inputs equaling one known output. What good is this equation? An option-pricing model helps a trader understand how market forces affect the value of an option. Five of the six inputs are dynamic; the only constant is the strike price of the option in question. If the price of the option changes, it’s because one or more of the five variable inputs has changed. These variables are independent of each other, but they can change in harmony, having either a cumulative or net effect on the option’s value. An option trader needs to be concerned with the relationship of these variables (price, time, volatility, interest). This multidimensional view of asset pricing is unique to option traders. Delta The five figures commonly used by option traders are represented by Greek letters: delta, gamma, theta, vega, rho. The figures are referred to as option greeks. Vega, of course, is not an actual letter of the greek alphabet, but in the options vernacular, it is considered one of the greeks. The greeks are a derivation of an option-pricing model, and each Greek letter represents a specific sensitivity to influences on the option’s value. To understand concepts represented by these five figures, we’ll start with delta, which is defined in four ways: 1. The rate of change of an option value relative to a change in the underlying stock price. 2. The derivative of the graph of an option value in relation to the stock price. 3. The equivalent of underlying shares represented by an option position. 4. The estimate of the likelihood of an option expiring in-the-money. 1 Definition 1 : Delta (Δ) is the rate of change of an option’s value relative to a change in the price of the underlying security. A trader who is bullish on a particular stock may choose to buy a call instead of buying the underlying security. If the price of the stock rises by $1, the trader would expect to profit on the call—but by how much? To answer that question, the trader must consider the delta of the option. Delta is stated as a percentage. If an option has a 50 delta, its price will change by 50 percent of the change of the underlying stock price. Delta is generally written as either a whole number, without the percent sign, or as a decimal. So if an option has a 50 percent delta, this will be indicated as 0.50, or 50. For the most part, we’ll use the former convention in our discussion. Call values increase when the underlying stock price increases and vice versa. Because calls have this positive correlation with the underlying, they have positive deltas. Here is a simplified example of the effect of delta on an option: Consider a $60 stock with a call option that has a 0.50 delta and is trading for 3.00. Considering only the delta, if the stock price increases by $1, the theoretical value of the call will rise by 0.50. That’s 50 percent of the stock price change. The new call value will be 3.50. If the stock price decreases by $1, the 0.50 delta will cause the call to decrease in value by 0.50, from 3.00 to 2.50. Puts have a negative correlation to the underlying. That is, put values decrease when the stock price rises and vice versa. Puts, therefore, have negative deltas. Here is a simplified example of the delta effect on a −0.40-delta put: As the stock rises from $60 to $61, the delta of −0.40 causes the put value to go from $2.25 to $1.85. The put decreases by 40 percent of the stock price increase. If the stock price instead declined by $1, the put value would increase by $0.40, to $2.65. Unfortunately, real life is a bit more complicated than the simplified examples of delta used here. In reality, the value of both the call and the put will likely be higher with the stock at $61 than was shown in these examples. We’ll expand on this concept later when we tackle the topic of gamma. Definition 2 : Delta can also be described another way. Exhibit 2.1 shows the value of a call option with three months to expiration at a variable stock price. As the stock price rises, the call is worth more; as the stock price declines, the call value moves toward zero. Mathematically, for any given point on the graph, the derivative will show the rate of change of the option price. The delta is the first derivative of the graph of the option price relative to the stock price . EXHIBIT 2.1 Call value compared with stock price. Definition 3 : In terms of absolute value (meaning that plus and minus signs are ignored), the delta of an option is between 1.00 and 0. Its price can change in tandem with the stock, as with a 1.00 delta; or it cannot change at all as the stock moves, as with a 0 delta; or anything in between. By definition, stock has a 1.00 delta—it is the underlying security. A $1 rise in the stock yields a $100 profit on a round lot of 100 shares. A call with a 0.60 delta rises by $0.60 with a $1 increase in the stock. The owner of a call representing rights on 100 shares earns $60 for a $1 increase in the underlying. It’s as if the call owner in this example is long 60 shares of the underlying stock. Delta is the option’s equivalent of a position in the underlying shares . A trader who buys five 0.43-delta calls has a position that is effectively long 215 shares—that’s 5 contracts × 0.43 deltas × 100 shares. In option lingo, the trader is long 215 deltas. Likewise, if the trader were short five 0.43-delta calls, the trader would be short 215 deltas. The same principles apply to puts. Being long 10 0.59-delta puts makes the trader short a total of 590 deltas, a position that profits or loses like being short 590 shares of the underlying stock. Conversely, if the trader were short 10 0.59-delta puts, the trader would theoretically make $590 if the stock were to rise $1 and lose $590 if the stock fell by $1—just like being long 590 shares. Definition 4 : The final definition of delta is considered the trader’s definition. It’s mathematically imprecise but is used nonetheless as a general rule of thumb by option traders. A trader would say the delta is a statistical approximation of the likelihood of the option expiring in-the-money . An option with a 0.75 delta would have a 75 percent chance of being in-the-money at expiration under this definition. An option with a 0.20 delta would be thought of having a 20 percent chance of expiring in-the-money. Dynamic Inputs Option deltas are not constants. They are calculated from the dynamic inputs of the pricing model—stock price, time to expiration, volatility, and so on. When these variables change, the changes affect the delta. These changes can be mathematically quantified—they are systematic. Understanding these patterns and other quirks as to how delta behaves can help traders use this tool more effectively. Let’s discuss a few observations about the characteristics of delta. First, call and put deltas are closely related. Exhibit 2.2 is a partial option chain of 70-day calls and puts in Rambus Incorporated (RMBS). The stock was trading at $21.30 when this table was created. In Exhibit 2.2 , the 20 calls have a 0.66 delta. EXHIBIT 2.2 RMBS Option chain with deltas. Notice the deltas of the put-call pairs in this exhibit. As a general rule, the absolute value of the call delta plus the absolute value of the put delta add up to close to 1.00. The reason for this has to do with a mathematical relationship called put-call parity, which is briefly discussed later in this chapter and described in detail in Chapter 6. But with equity options, the put-call pair doesn’t always add up to exactly 1.00. Sometimes the difference is simply due to rounding. But sometimes there are other reasons. For example, the 30-strike calls and puts in Exhibit 2.2 have deltas of 0.14 and −0.89, respectively. The absolute values of the deltas add up to 1.03. Because of the possibility of early exercise of American options, the put delta is a bit higher than the call delta would imply. When puts have a greater chance of early exercise, they begin to act more like short stock and consequently will have a greater delta. Often, dividend-paying stocks will have higher deltas on some in-the-money calls than the put in the pair would imply. As the ex-dividend date—the date the stock begins trading without the dividend—approaches, an in-the-money call can become more apt to be exercised, because traders will want to own stock to capture the dividend. Here, the call begins to act more like long stock, leading to a higher delta. Moneyness and Delta The next observation is the effect of moneyness on the option’s delta. Moneyness describes the degree to which the option is in- or out-of-the-money. As a general rule, options that are in-the-money (ITM) have deltas greater than 0.50. Options that are out-of-the-money (OTM) have deltas less than 0.50. Finally, options that are at-the-money (ATM) have deltas that are about 0.50. The more in-the-money the option is, the closer to 1.00 the delta is. The more out-of-the-money, the closer the delta is to 0. But ATM options are usually not exactly 0.50. For ATMs, both the call and the put deltas are generally systematically a value other than 0.50. Typically, the call has a higher delta than 0.50 and the put has a lower absolute value than 0.50. Incidentally, the call’s theoretical value is generally greater than the put’s when the options are right at-the-money as well. One reason for this disparity between exactly at-the-money calls and puts is the interest rate. The more time until expiration, the more effect the interest rate will have, and, therefore, the higher the call’s theoretical and delta will be relative to the put. Effect of Time on Delta In a close contest, the last few minutes of a football game are often the most exciting—not because the players run faster or knock heads harder but because one strategic element of the game becomes more and more important: time. The team that’s in the lead wants the game clock to run down with no interruption to solidify its position. The team that’s losing uses its precious time-outs strategically. The more playing time left, the less certain defeat is for the losing team. Although mathematically imprecise, the trader’s definition can help us gain insight into how time affects option deltas. The more time left until an option’s expiration, the less certain it is whether the option will be ITM or OTM at expiration. The deltas of both the ITM and the OTM options reflect that uncertainty. The more time left in the life of the option, the closer the deltas tend to gravitate to 0.50. A 0.50 delta represents the greatest level of uncertainty—a coin toss. Exhibit 2.3 shows the deltas of a hypothetical equity call with a strike price of 50 at various stock prices with different times until expiration. All other parameters are held constant. EXHIBIT 2.3 Estimated delta of 50-strike call—impact of time. As shown in Exhibit 2.3 , the more time until expiration, the closer ITMs and OTMs move to 0.50. At expiration, of course, the option is either a 100 delta or a 0 delta; it’s either stock or not. Effect of Volatility on Delta The level of volatility affects option deltas as well. We’ll discuss volatility in more detail in future chapters, but it’s important to address it here as it relates to the concept of delta. Exhibit 2.4 shows how changing the volatility percentage (explained further in Chapter 3), as opposed to the time to expiration, affects option deltas. In this table, the delta of a call with 91 days until expiration is studied. EXHIBIT 2.4 Estimated delta of 50-strike call—impact of volatility. Notice the effect that volatility has on the deltas of this option with the underlying stock at various prices. In this table, at a low volatility with the call deep in- or out-of-the-money, the delta is very large or very small, respectively. At 10 percent volatility with the stock at $58 a share, the delta is 1.00. At that same volatility level with the stock at $42 a share, the delta is 0. But at higher volatility levels, the deltas change. With the stock at $58, a 45 percent volatility gives the 50-strike call a 0.79 delta—much smaller than it was at the low volatility level. With the stock at $42, a 45-percent volatility returns a 0.30 delta for the call. Generally speaking, ITM option deltas are smaller given a higher volatility assumption, and OTM option deltas are bigger with a higher volatility. Effect of Stock Price on Delta An option that is $5 in-the-money on a $20 stock will have a higher delta than an option that is $5 in-the-money on a $200 stock. Proportionately, the former is more in-the-money. Comparing two options that are in-the-money by the same percentage yields similar results. As the stock price changes because the strike price remains stable, the option’s delta will change. This phenomenon is measured by the option’s gamma. Gamma The strike price is the only constant in the pricing model. When the stock price moves relative to this constant, the option in question becomes more in-the-money or out-of-the-money. This means the delta changes. This isolated change is measured by the option’s gamma, sometimes called curvature . Gamma (Γ) is the rate of change of an option’s delta given a change in the price of the underlying security . Gamma is conventionally stated in terms of deltas per dollar move. The simplified examples above under Definition 1 of delta, used to describe the effect of delta, had one important piece of the puzzle missing: gamma. As the stock price moved higher in those examples, the delta would not remain constant. It would change due to the effect of gamma. The following example shows how the delta would change given a 0.04 gamma attributed to the call option. The call in this example starts as a 0.50-delta option. When the stock price increases by $1, the delta increases by the amount of the gamma. In this example, delta increases from 0.50 to 0.54, adding 0.04 deltas. As the stock price continues to rise, the delta continues to move higher. At $62, the call’s delta is 0.58. This increase in delta will affect the value of the call. When the stock price first begins to rise from $60, the option value is increasing at a rate of 50 percent—the call’s delta at that stock price. But by the time the stock is at $61, the option value is increasing at a rate of 54 percent of the stock price. To estimate the theoretical value of the call at $61, we must first estimate the average change in the delta between $60 and $61. The average delta between $60 and $61 is roughly 0.52. It’s difficult to calculate the average delta exactly because gamma is not constant; this is discussed in more detail later in the chapter. A more realistic example of call values in relation to the stock price would be as follows: Each $1 increase in the stock shows an increase in the call value about equal to the average delta value between the two stock prices. If the stock were to decline, the delta would get smaller at a decreasing rate. As the stock price declines from $60 to $59, the option delta decreases from 0.50 to 0.46. There is an average delta of about 0.48 between the two stock prices. At $59 the new theoretical value of the call is 2.52. The gamma continues to affect the option’s delta and thereby its theoretical value as the stock continues its decline to $58 and beyond. Puts work the same way, but because they have a negative delta, when there is a positive stock-price movement the gamma makes the put delta less negative, moving closer to 0. The following example clarifies this. As the stock price rises, this put moves more and more out-of-the-money. Its theoretical value is decreasing by the rate of the changing delta. At $60, the delta is −0.40. As the stock rises to $61, the delta changes to −0.36. The average delta during that move is about −0.38, which is reflected in the change in the value of the put. If the stock price declines and the put moves more toward being in-the-money, the delta becomes more negative—that is, the put acts more like a short stock position. Here, the put value rises by the average delta value between each incremental change in the stock price. These examples illustrate the effect of gamma on an option without discussing the impact on the trader’s position. When traders buy options, they acquire positive gamma. Since gamma causes options to gain value at a faster rate and lose value at a slower rate, (positive) gamma helps the option buyer. A trader buying one call or put in these examples would have +0.04 gamma. Buying 10 of these options would give the trader a +0.4 gamma. When traders sell options, gamma works against them. When options lose value, they move toward zero at a slower rate. When the underlying moves adversely, gamma speeds up losses. Selling options yields a negative gamma position. A trader selling one of the above calls or puts would have −0.04 gamma per option. The effect of gamma is less significant for small moves in the underlying than it is for bigger moves. On proportionately large moves, the delta can change quite a bit, making a big difference in the position’s P&(L). In Exhibit 2.1 , the left side of the diagram showed the call price not increasing at all with advances in the stock—a 0 delta. The right side showed the option advancing in price 1-to-1 with the stock—a 1.00 delta. Between the two extremes, the delta changes. From this diagram another definition for gamma can be inferred: gamma is the second derivative of the graph of the option price relative to the stock price. Put another way, gamma is the first derivative of a graph of the delta relative to the stock price. Exhibit 2.5 illustrates the delta of a call relative to the stock price. EXHIBIT 2.5 Call delta compared with stock price. Not only does the delta change, but it changes at a changing rate. Gamma is not constant. Moneyness, time to expiration, and volatility each have an effect on the gamma of an option. Dynamic Gamma When options are far in-the-money or out-of-the-money, they are either 1.00 delta or 0 delta. At the extremes, small changes in the stock price will not cause the delta to change much. When an option is at-the-money, it’s a different story. Its delta can change very quickly. ITM and OTM options have a low gamma. ATM options have a relatively high gamma. Exhibit 2.6 is an example of how moneyness translates into gamma on QQQ calls. EXHIBIT 2.6 Gamma of QQQ calls with QQQ at $44. With QQQ at $44, 92 days until expiration, and a constant volatility input of 19 percent, the 36- and 54-strike calls are far enough in- and out-of-the-money, respectively, that if the Qs move a small amount in either direction from the current price of $44, the movement won’t change their deltas much at all. The chances of their money status changing between now and expiration would not be significantly different statistically given a small stock price change. They have the smallest gammas in the table. The highest gammas shown here are around the ATM strike prices. (Note that because of factors not yet discussed, the strike that is exactly at-the-money may not have the highest gamma. The highest gamma is likely to occur at a slightly higher strike price.) Exhibit 2.7 shows a graph of the corresponding numbers in Exhibit 2.6 . EXHIBIT 2.7 Option gamma. A decrease in the time to expiration solidifies the likelihood of ITMs or OTMs remaining as such. But an ATM option’s moneyness at expiration remains to the very end uncertain. As expiration draws nearer, the gamma decreases for ITMs and OTMs and increases for the ATM strikes. Exhibit 2.8 shows the same 92-day QQQ calls plotted against 7-day QQQ calls. EXHIBIT 2.8 Gamma as time passes. At seven days until expiration, there is less time for price action in the stock to change the expected moneyness at expiration of ITMs or OTMs. ATM options, however, continue to be in play. Here, the ATM gamma is approaching 0.35. But the strikes below 41 and above 48 have 0 gamma. Similarly-priced securities that tend to experience bigger price swings may have strikes $3 away-from-the-money with seven-day gammas greater than zero. The volatility of the underlying will affect gamma, too. Exhibit 2.9 shows the same 19 percent volatility QQQ calls in contrast with a graph of the gamma if the volatility is doubled. EXHIBIT 2.9 Gamma as volatility changes. Raising the volatility assumption flattens the curve, causing ITM and OTM to have higher gamma while lowering the gamma for ATMs. Short-term ATM options with low volatility have the highest gamma. Lower gamma is found in ATMs when volatility is higher and it is lower for ITMs and OTMs and in longer-dated options. Theta Option prices can be broken down into two parts: intrinsic value and time value. Intrinsic value is easily measurable. It is simply the ITM part of the premium. Time value, or extrinsic value, is what’s left over—the premium paid over parity for the option. All else held constant, the more time left in the life of the option, the more valuable it is—there is more time for the stock to move. And as the useful life of an option decreases, so does its time value. The decline in the value of an option because of the passage of time is called time decay, or erosion. Incremental measurements of time decay are represented by the Greek letter theta (θ). Theta is the rate of change in an option’s price given a unit change in the time to expiration . What exactly is the unit involved here? That depends. Some providers of option greeks will display thetas that represent one day’s worth of time decay. Some will show thetas representing seven days of decay. In the case of a one-day theta, the figure may be based on a seven-day week or on a week counting only trading days. The most common and, arguably, most useful display of this figure is the one-day theta based on the seven-day week. There are, after all, seven days in a week, each day of which can see an occurrence with the potential to cause a revaluation in the stock price (that is, news can come out on Saturday or Sunday). The one-day theta based on a seven-day week will be used throughout this book. Taking the Day Out When the number of days to expiration used in the pricing model declines from, say, 32 days to 31 days, the price of the option decreases by the amount of the theta, all else held constant. But when is the day “taken out”? It is intuitive to think that after the market closes, the model is changed to reflect the passing of one day’s time. But, in fact, this change is logically anticipated and may be priced in early. In the earlier part of the week, option prices can often be observed getting cheaper relative to the stock price sometime in the middle of the day. This is because traders will commonly take the day out of their model during trading hours after the underlying stabilizes following the morning business. On Fridays and sometimes Thursdays, traders will take all or part of the weekend out. Commonly, by Friday afternoon, traders will be using Monday’s days to value their options. When option prices are seen getting cheaper on, say, a Friday, how can one tell whether this is the effect of the market taking the weekend out or a change in some other input, such as volatility? To some degree, it doesn’t matter. Remember, the model is used to reflect what the market is doing, not the other way around. In many cases, it’s logical to presume that small devaluations in option prices intraday can be attributed to the routine of the market taking the day out. Friend or Foe? Theta can be a good thing or a bad thing, depending on the position. Theta hurts long option positions; whereas it helps short option positions. Take an 80-strike call with a theoretical value of 3.16 on a stock at $82 a share. The 32-day 80 call has a theta of 0.03. If a trader owned one of these calls, the trader’s position would theoretically lose 0.03, or $0.03, as the time until expiration change from 32 to 31 days. This trader has a negative theta position. A trader short one of these calls would have an overnight theoretical profit of $0.03 attributed to theta. This trader would have a positive theta. Theta affects put traders as well. Using all the same modeling inputs, the 32-day 80-strike put would have a theta of 0.02. A put holder would theoretically lose $0.02 a day, and a put writer would theoretically make $0.02. Long options carry with them negative theta; short options carry positive theta. A higher theta for the call than for the put of the same strike price is common when an interest rate greater than zero is used in the pricing model. As will be discussed in greater detail in the section on rho, interest causes the time value of the call to be higher than that of the corresponding put. At expiration, there is no time value left in either option. Because the call begins with more time value, its premium must decline at a faster rate than that of the put. Most modeling software will attribute the disparate rates of decline in value all to theta, whereas some modeling interfaces will make clear the distinction between the effect of time decay and the effect of interest on the put-call pair. The Effect of Moneyness and Stock Price on Theta Theta is not a constant. As variables influencing option values change, theta can change, too. One such variable is the option’s moneyness. Exhibit 2.10 shows theoretical values (theos), time values, and thetas for 3-month options on Adobe (ADBE). In this example, Adobe is trading at $31.30 a share with three months until expiration. The more ITM a call or a put gets, the higher its theoretical value. But when studying an option’s time decay, one needs to be concerned only with the option’s time value, because intrinsic value is not subject to time decay. EXHIBIT 2.10 Adobe theos and thetas (Adobe at $31.30). The ATM options shown here have higher time value than ITM or OTM options. Hence, they have more time premium to lose in the same three-month period. ATM options have the highest rate of decay, which is reflected in higher thetas. As the stock price changes, the theta value will change to reflect its change in moneyness. If this were a higher-priced stock, say, 10 times the stock price used in this example, with all other inputs held constant, the option values, and therefore the thetas, would be higher. If this were a stock trading at $313, the 325-strike call would have a theoretical value of 16.39 and a one-day theta of 0.189, given inputs used otherwise identical to those in the Adobe example. The Effects of Volatility and Time on Theta Stock price is not the only factor that affects theta values. Volatility and time to expiration come into play here as well. The volatility input to the pricing model has a direct relationship to option values. The higher the volatility, the higher the value of the option. Higher-valued options decay at a faster rate than lower-valued options—they have to; their time values will both be zero at expiration. All else held constant, the higher the volatility assumption, the higher the theta. The days to expiration have a direct relationship to option values as well. As the number of days to expiration decreases, the rate at which an option decays may change, depending on the relationship of the stock price to the strike price. ATM options tend to decay at a nonlinear rate—that is, they lose value faster as expiration approaches—whereas the time values of ITM and OTM options decay at a steadier rate. Consider a hypothetical stock trading at $70 a share. Exhibit 2.11 shows how the theoretical values of the 75-strike call and the 70-strike call decline with the passage of time, holding all other parameters constant. EXHIBIT 2.11 Rate of decay: ATM vs. OTM. The OTM 75-strike call has a fairly steady rate of time decay over this 26-week period. The ATM 70-strike call, however, begins to lose its value at an increasing rate as expiration draws nearer. The acceleration of premium erosion continues until the option expires. Exhibit 2.12 shows the thetas for this ATM call during the last 10 days before expiration. EXHIBIT 2.12 Theta as expiration approaches. Days to Exp . ATM Theta 10 0.075 9 0.079 8 0.084 7 0.089 6 0.096 5 0.106 4 0.118 3 0.137 2 0.171 1 0.443 Incidentally, in this example, when there is one day to expiration, the theoretical value of this call is about 0.44. The final day before expiration ultimately sees the entire time premium erode. Vega Over the past decade or so, computers have revolutionized option trading. Options traded through an online broker are filled faster than you can say, “Oops! I meant to click on puts.” Now trading is facilitated almost entirely online by professional and retail traders alike. Market and trading information is disseminated worldwide in subseconds, making markets all the more efficient. And the tools now available to the common retail trader are very powerful as well. Many online brokers and other web sites offer high-powered tools like screeners, which allow traders to sift through thousands of options to find those that fit certain parameters. Using a screener to find ATM calls on same-priced stocks—say, stocks trading at $40 a share—can yield a result worth talking about here. One $40 stock can have a 40-strike call trading at around 0.50, while a different $40 stock can have a 40 call with the same time to expiration trading at more like 2.00. Why? The model doesn’t know the name of the company, what industry it’s in, or what its price-to-earnings ratio is. It is a mathematical equation with six inputs. If five of the inputs—the stock price, strike price, time to expiration, interest rate, and dividends—are identical for two different options but they’re trading at different prices, the difference must be the sixth variable, which is volatility. Implied Volatility (IV) and Vega The volatility component of option values is called implied volatility (IV). (For more on implied volatility and how it relates to vega, see Chapter 3.) IV is a percentage, although in practice the percent sign is often omitted. This is the value entered into a pricing model, in conjunction with the other variables, that returns the option’s theoretical value. The higher the volatility input, the higher the theoretical value, holding all other variables constant. The IV level can change and often does—sometimes dramatically. When IV rises or falls, option prices rise and fall in line with it. But by how much? The relationship between changes in IV and changes in an option’s value is measured by the option’s vega. Vega is the rate of change of an option’s theoretical value relative to a change in implied volatility . Specifically, if the IV rises or declines by one percentage point, the theoretical value of the option rises or declines by the amount of the option’s vega, respectively. For example, if a call with a theoretical value of 1.82 has a vega of 0.06 and IV rises one percentage point from, say, 17 percent to 18 percent, the new theoretical value of the call will be 1.88—it would rise by 0.06, the amount of the vega. If, conversely, the IV declines 1 percentage point, from 17 percent to 16 percent, the call value will drop to 1.76—that is, it would decline by the vega. A put with the same expiration month and the same strike on the same underlying will have the same vega value as its corresponding call. In this example, raising or lowering IV by one percentage point would cause the corresponding put value to rise or decline by $0.06, just like the call. An increase in IV and the consequent increase in option value helps the P&(L) of long option positions and hurts short option positions. Buying a call or a put establishes a long vega position. For short options, the opposite is true. Rising IV adversely affects P&(L), whereas falling IV helps. Shorting a call or put establishes a short vega position. The Effect of Moneyness on Vega Like the other greeks, vega is a snapshot that is a function of multiple facets of determinants influencing option value. The stock price’s relationship to the strike price is a major determining factor of an option’s vega. IV affects only the time value portion of an option. Because ATM options have the greatest amount of time value, they will naturally have higher vegas. ITM and OTM options have lower vega values than those of the ATM options. Exhibit 2.13 shows an example of 186-day options on AT&T Inc. (T), their time value, and the corresponding vegas. EXHIBIT 2.13 AT&T theos and vegas (T at $30, 186 days to Expry, 20% IV). Note that the 30-strike calls and puts have the highest time values. This strike boasts the highest vega value, at 0.085. The lower the time premium, the lower the vega—therefore, the less incremental IV changes affect the option. Since higher-priced stocks have higher time premium (in absolute terms, not necessarily in percentage terms) they will have higher vega. Incidentally, if this were a $300 stock instead of a $30 stock, the 186-day ATMs would have a 0.850 vega, if all other model inputs remain the same. The Effect of Implied Volatility on Vega The distribution of vega values among the strike prices shown in Exhibit 2.13 holds for a specific IV level. The vegas in Exhibit 2.13 were calculated using a 20 percent IV. If a different IV were used in the calculation, the relationship of the vegas to one another might change. Exhibit 2.14 shows what the vegas would be at different IV levels. EXHIBIT 2.14 Vega and IV. Note in Exhibit 2.14 that at all three IV levels, the ATM strike maintains a similar vega value. But the vegas of the ITM and OTM options can be significantly different. Lower IV inputs tend to cause ITM and OTM vegas to decline. Higher IV inputs tend to cause vegas to increase for ITMs and OTMs. The Effect of Time on Vega As time passes, there is less time premium in the option that can be affected by changes in IV. Consequently, vega gets smaller as expiration approaches. Exhibit 2.15 shows the decreasing vega of a 50-strike call on a $50 stock with a 25 percent IV as time to expiration decreases. Notice that as the value of this ATM option decreases at its nonlinear rate of decay, the vega decreases in a similar fashion. EXHIBIT 2.15 The effect of time on vega. Rho One of my early jobs in the options business was clerking on the floor of the Chicago Board of Trade in what was called the bond room. On one of my first days on the job, the trader I worked for asked me what his position was in a certain strike. I told him he was long 200 calls and long 300 puts. “I’m long 500 puts?” he asked. “No,” I corrected, “you’re long 200 calls and 300 puts.” At this point, he looked at me like I was from another planet and said, “That’s 500. A put is a call; a call is a put.” That lesson was the beginning of my journey into truly understanding options. Put-Call Parity Put and call values are mathematically bound together by an equation referred to as put-call parity. In its basic form, put-call parity states: where c = call value, PV(x) = present value of the strike price, p = put value, and s = stock price. The put-call parity assumes that options are not exercised before expiration (that is, that they are European style). This version of the put-call parity is for European options on non-dividend-paying stocks. Put-call parity can be modified to reflect the values of options on stocks that pay dividends. In practice, equity-option traders look at the equation in a slightly different way: Traders serious about learning to trade options must know put-call parity backward and forward. Why? First, by algebraically rearranging this equation, it can be inferred that synthetically equivalent positions can be established by simply adding stock to an option. Again, a put is a call; a call is a put. and For example, a long call is synthetically equal to a long stock position plus a long put on the same strike, once interest and dividends are figured in. A synthetic long stock position is created by buying a call and selling a put of the same month and strike. Understanding synthetic relationships is intrinsic to understanding options. A more comprehensive discussion of synthetic relationships and tactical considerations for creating synthetic positions is offered in Chapter 6. Put-call parity also aids in valuing options. If put-call parity shows a difference in the value of the call versus the value of the put with the same strike, there may be an arbitrage opportunity. That translates as “riskless profit.” Buying the call and selling it synthetically (short put and short stock) could allow a profit to be locked in if the prices are disparate. Arbitrageurs tend to hold synthetic put and call prices pretty close together. Generally, only professional traders can capture these types of profit opportunities, by trading big enough positions to make very small profits (a penny or less per contract sometimes) matter. Retail traders may be able to take advantage of a disparity in put and call values to some extent, however, by buying or selling the synthetic as a substitute for the actual option if the position can be established at a better price synthetically. Another reason that a working knowledge of put-call parity is essential is that it helps attain a better understanding of how changes in the interest rate affect option values. The greek rho measures this change. Rho is the rate of change in an option’s value relative to a change in the interest rate. Although some modeling programs may display this number differently, most display a rho for the call and a rho for the put, both illustrating the sensitivity to a one-percentage-point change in the interest rate. When the interest rate rises by one percentage point, the value of the call increases by the amount of its rho and the put decreases by the amount of its rho. Likewise, when the interest rate decrease by one percentage point, the value of the call decreases by its rho and the put increases by its rho. For example, a call with a rho of 0.12 will increase $0.12 in value if the interest rate used in the model is increased by one percentage point. Of course, interest rates usually don’t rise or fall one percentage point in one day. More commonly, rates will have incremental changes of 25 basis points. That means a call with a 0.12 rho will theoretically gain $0.03 given an increase of 0.25 percentage points. Mathematically, this change in option value as a product of a change in the interest rate makes sense when looking at the formula for put-call parity. and But the change makes sense intuitively, too, when a call is considered as a cheaper substitute for owning the stock. For example, compare a $100 stock with a three-month 60-strike call on that same stock. Being so far ITM, there would likely be no time value in the call. If the call can be purchased at parity, which alternative would be a superior investment, the call for $40 or the stock for $100? Certainly, the call would be. It costs less than half as much as the stock but has the same reward potential; and the $60 not spent on the stock can be invested in an interest-bearing account. This interest advantage adds value to the call. Raising the interest rate increases this value, and lowering it decreases the interest component of the value of the call. A similar concept holds for puts. Professional traders often get a short-stock rebate on proceeds from a short-stock sale. This is simply interest earned on the capital received when the stock is shorted. Is it better to pay interest on the price of a put for a position that gives short exposure or to receive interest on the credit from shorting the stock? There is an interest disadvantage to owning the put. Therefore, a rise in interest rates devalues puts. This interest effect becomes evident when comparing ATM call and put prices. For example, with interest at 5 percent, three-month options on an $80 stock that pays a $0.25 dividend before option expiration might look something like this: The ATM call is higher in theoretical value than the ATM put by $0.75. That amount can be justified using put-call parity: (Here, simple interest of $1 is calculated as 80 × 0.05 × [90 / 360] = 1.) Changes in market conditions are kept in line by the put-call parity. For example, if the price of the call rises because of an increase in IV, the price of the put will rise in step. If the interest rate rises by a quarter of a percentage point, from 5 percent to 5.25 percent, the interest calculated for three months on the 80-strike will increase from $1 to $1.05, causing the difference between the call and put price to widen. Another variable that affects the amount of interest and therefore option prices is the time until expiration. The Effect of Time on Rho The more time until expiration, the greater the effect interest rate changes will have on options. In the previous example, a 25-basis-point change in the interest rate on the 80-strike based on a three-month period caused a change of 0.05 to the interest component of put-call parity. That is, 80 × 0.0025 × (90/360) = 0.05. If a longer period were used in the example—say, one year—the effect would be more profound; it will be $0.20: 80 × 0.0025 × (360/360) = 0.20. This concept is evident when the rhos of options with different times to expiration are studied. Exhibit 2.16 shows the rhos of ATM Procter & Gamble Co. (PG) calls with various expiration months. The 750-day Long-Term Equity AnticiPation Securities (LEAPS) have a rho of 0.858. As the number of days until expiration decreases, rho decreases. The 22-day calls have a rho of only 0.015. Rho is usually a fairly insignificant factor in the value of short-term options, but it can come into play much more with long-term option strategies involving LEAPS. EXHIBIT 2.16 The effect of time on rho (Procter & Gamble @ $64.34) Why the Numbers Don’t Don’t Always Add Up There will be many times when studying the rho of options in an option chain will reveal seemingly counterintuitive results. To be sure, the numbers don’t always add up to what appears logical. One reason for this is rounding. Another is that traders are more likely to use simple interest in calculating value, whereas the model uses compound interest. Hard-to-borrow stocks and stocks involved in mergers and acquisitions may have put-call parities that don’t work out right. But another, more common and more significant fly in the ointment is early exercise. Since the interest input in put-call parity is a function of the strike price, it is reasonable to expect that the higher the strike price, the greater the effect of interest on option prices will be. For European options, this is true to a large extent, in terms of aggregate impact of interest on the call and put pair. Strikes below the price where the stock is trading have a higher rho associated with the call relative to the put, whereas strikes above the stock price have a higher rho associated with the put relative to the call. Essentially, the more in-the-money an option is, the higher its rho. But with European options, observing the aggregate of the absolute values of the call and put rhos would show a higher combined rho the higher the strike. With American options, the put can be exercised early. A trader will exercise a put before expiration if the alternative—being short stock and receiving a short stock rebate—is a wiser choice based on the price of the put. Professional traders may own stock as a hedge against a put. They may exercise deep ITM puts (1.00-delta puts) to avoid paying interest on capital charges related to the stock. The potential for early exercise is factored into models that price American options. Here, when puts get deeper in-the-money—that is, more apt to be exercised—the rho decreases. When the strike price is very high relative to the stock price—meaning the put is very deep ITM—and there is little or no time value left to the call or the put, the aggregate put-call rho can be zero. Rho is discussed in greater detail in Chapter 7. THE GREEKS DEFINED Delta (Δ) is: 1. The rate of change in an option’s value relative to a change in the underlying asset price. 2. The derivative of the graph of an option’s value in relation to the underlying asset price. 3. The equivalent of underlying asset represented by an option position. 4. The estimate of the likelihood of an option’s expiring in-the-money. Gamma (Γ) is the rate of change in an option’s delta given a change in the price of the underlying asset. Theta (θ) is the rate of change in an option’s value given a unit change in the time to expiration. Vega is the rate of change in an option’s value relative to a change in implied volatility. Rho (ρ) is the rate of change in an option’s value relative to a change in the interest rate. Where to Find Option Greeks There are many sources from which to obtain greeks. The Internet is an excellent resource. Googling “option greeks” will display links to over four million web pages, many of which have real-time greeks or an option calculator. An option calculator is a simple interface that accepts the input of the six variables to the model and yields a theoretical value and the greeks for a single option. Some web sites devoted to option education, such as MarketTaker.com/option_modeling , have free calculators that can be used for modeling positions and using the greeks. In practice, many of the option-trading platforms commonly in use have sophisticated analytics that involve greeks. Most options-friendly online brokers provide trading platforms that enable traders to conduct comprehensive manipulations of the greeks. For example, traders can look at the greeks for their positions up or down one, two, or three standard deviations. Or they can see what happens to their position greeks if IV or time changes. With many trading platforms, position greeks are updated in real time with changes in the stock price—an invaluable feature for active traders. Caveats with Regard to Online Greeks Often, online greeks are one click away, requiring little effort on the part of the trader. Having greeks calculated automatically online is a quick and convenient way to eyeball greeks for an option. But there is one major problem with online greeks: reliability. For active option traders, greeks are essential. There is no point in using these figures if their accuracy cannot be assured. Experienced traders can often spot these inaccuracies a proverbial mile away. When looking at greeks from an online source that does not require you to enter parameters into a model (as would be the case with professional option-trading platforms), special attention needs to be paid to the relationship of the option’s theoretical values to the bid and offer. One must be cautious if the theoretical value of the option lies outside the bid-ask spread. This scenario can exist for brief periods of time, but arbitrageurs tend to prevent this from occurring routinely. If several options in a chain all have theoretical values below the bid or above the offer, there is probably a problem with one or more of the inputs used in the model. Remember, an option-pricing model is just that: a model. It reflects what is occurring in the market. It doesn’t tell where an option should be trading. The complex changes that occur intraday in the market—taking the day or weekend out, changes in stock price, volatility, and the interest rate—are not always kept current. The user of the model must keep close watch. It’s not reasonable to expect the computer to do the thinking for you. Automatically calculated greeks can be used as a starting point. But before using these figures in the decision-making process, the trader may have to override the parameters that were used in the online calculation to make the theos line up with market prices. Professional traders will ignore online greeks altogether. They will use the greeks that are products of the inputs they entered in their trading software. It comes down to this: if you want something done right, do it yourself. Thinking Greek The challenge of trading option greeks is to adapt to thinking in terms of delta, gamma, theta, vega, and rho. One should develop a feel for how greeks react to changing market conditions. Greeks need to be monitored as closely as and in some cases more closely than the option’s price itself. This greek philosophy forms the foundation of option trading for active traders. It offers a logical way to monitor positions and provides a medium in and of itself to trade. Notes 1 . Please note that definition 4 is not necessarily mathematically accurate. This “trader’s definition” is included in the text because many option traders use delta as a quick rule of thumb for estimating probability without regard to the mathematical shortcomings of doing so. 2 . Note that the interest input in the equation is the interest, in dollars and cents, on the strike. Technically, this would be calculated as compounded interest, but in practice many traders use simple interest as a quick and convenient way to do the calculation. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00012.html SCORE: 624.50 ================================================================================ CHAPTER 3 Understanding Volatility Most option strategies involve trading volatility in one way or another. It’s easy to think of trading in terms of direction. But trading volatility? Volatility is an abstract concept; it’s a different animal than the linear trading paradigm used by most conventional market players. As an option trader, it is essential to understand and master volatility. Many traders trade without a solid understanding of volatility and its effect on option prices. These traders are often unhappily surprised when volatility moves against them. They mistake the adverse option price movements that result from volatility for getting ripped off by the market makers or some other market voodoo. Or worse, they surrender to the fact that they simply don’t understand why sometimes these unexpected price movements occur in options. They accept that that’s just the way it is. Part of what gets in the way of a ready understanding of volatility is context. The term volatility can have a few different meanings in the options business. There are three different uses of the word volatility that an option trader must be concerned with: historical volatility, implied volatility, and expected volatility. Historical Volatility Imagine there are two stocks: Stock A and Stock B. Both are trading at around $100 a share. Over the past month, a typical end-of-day net change in the price of Stock A has been up or down $5 to $7. During that same period, a typical daily move in Stock B has been something more like up or down $1 or $2. Stock A has tended to move more than Stock B as a percentage of its price, without regard to direction. Therefore, Stock A is more volatile—in the common usage of the word—than Stock B. In the options vernacular, Stock A has a higher historical volatility than Stock B. Historical volatility (HV) is the annualized standard deviation of daily returns. Also called realized volatility, statistical volatility , or stock volatility , HV is a measure of how volatile the price movement of a security has been during a certain period of time. But exactly how much higher is Stock A’s HV than Stock B’s? In order to objectively compare the volatilities of two stocks, historical volatility must be quantified. HV relates this volatility information in an objective numerical form. The volatility of a stock is expressed in terms of standard deviation. Standard Deviation Although knowing the mathematical formula behind standard deviation is not entirely necessary, understanding the concept is essential. Standard deviation, sometimes represented by the Greek letter sigma (σ), is a mathematical calculation that measures the dispersion of data from a mean value. In this case, the mean is the average stock price over a certain period of time. The farther from the mean the dispersion of occurrences (data) was during the period, the greater the standard deviation. Occurrences, in this context, are usually the closing prices of the stock. Some utilizers of volatility data may use other inputs (a weighted average of high, low, and closing prices, for example) in calculating standard deviation. Close-to-close price data are the most commonly used. The number of occurrences, a function of the time period, used in calculating standard deviation may vary. Many online purveyors of this data use the closing prices from the last 30 consecutive trading days to calculate HV. Weekends and holidays are not factored into the equation since there is no trading, and therefore no volatility, when the market isn’t open. After each day, the oldest price is taken out of the calculation and replaced by the most recent closing price. Using a shorter or longer period can yield different results and can be useful in studying a stock’s volatility. Knowing the number of days used in the calculation is crucial to understanding what the output represents. For example, if the last 5 trading days were extremely volatile, but the 25 days prior to that were comparatively calm, the 5-day standard deviation would be higher than the 30-day standard deviation. Standard deviation is stated as a percentage move in the price of the asset. If a $100 stock has a standard deviation of 15 percent, a one-standard-deviation move in the stock would be either $85 or $115—a 15 percent move in either direction. Standard deviation is used for comparison purposes. A stock with a standard deviation of 15 percent has experienced bigger moves—has been more volatile—during the relevant time period than a stock with a standard deviation of 6 percent. When the frequency of occurrences are graphed, the result is known as a distribution curve. There are many different shapes that a distribution curve can take, depending on the nature of the data being observed. In general, option-pricing models assume that stock prices adhere to a lognormal distribution. The shape of the distribution curve for stock prices has long been the topic of discussion among traders and academics alike. Regardless of what the true shape of the curve is, the concept of standard deviation applies just the same. For the purpose of illustrating standard deviation, a normal distribution is used here. When the graph of data adheres to a normal distribution, the result is a symmetrical bell-shaped curve. Standard deviation can be shown on the bell curve to either side of the mean. Exhibit 3.1 represents a typical bell curve with standard deviation. EXHIBIT 3.1 Standard deviation. Large moves in a security are typically less frequent than small ones. Events that cause big changes in the price of a stock, like a company’s being acquired by another or discovering its chief financial officer cooking the books, are not a daily occurrence. Comparatively smaller price fluctuations that reflect less extreme changes in the value of the corporation are more typically seen day to day. Statistically, the most probable outcome for a price change is found around the midpoint of the curve. What constitutes a large move or a small move, however, is unique to each individual security. For example, a two percent move in an index like the Standard & Poor’s (S&P) 500 may be considered a big one-day move, while a two percent move in a particularly active tech stock may be a daily occurrence. Standard deviation offers a statistical explanation of what constitutes a typical move. In Exhibit 3.1 , the lines to either side of the mean represent one standard deviation. About 68 percent of all occurrences will take place between up one standard deviation and down one standard deviation. Two- and three-standard-deviation values could be shown on the curve as well. About 95 percent of data occur between up and down two standard deviations and about 99.7 percent between up and down three standard deviations. One standard deviation is the relevant figure in determining historical volatility. Standard Deviation and Historical Volatility When standard deviation is used in the context of historical volatility, it is annualized to state what the one-year volatility would be. Historical volatility is the annualized standard deviation of daily returns. This means that if a stock is trading at $100 a share and its historical volatility is 10 percent, then about 68 percent of the occurrences (closing prices) are expected to fall between $90 and $110 during a one-year period (based on recent past performance). Simply put, historical volatility shows how volatile a stock has been based on price movements that have occurred in the past. Although option traders may study HV to make informed decisions as to the value of options traded on a stock, it is not a direct function of option prices. For this, we must look to implied volatility. Implied Volatility Volatility is one of the six inputs of an option-pricing model. Some of the other inputs—strike price, stock price, the number of days until expiration, and the current interest rate—are easily observable. Past dividend policy allows an educated guess as to what the dividend input should be. But where can volatility be found? As discussed in Chapter 2, the output of the pricing model—the option’s theoretical value—in practice is not necessarily an output at all. When option traders use the pricing model, they commonly substitute the actual price at which the option is trading for the theoretical value. A value in the middle of the bid-ask spread is often used. The pricing model can be considered to be a complex algebra equation in which any variable can be solved for. If the theoretical value is known—which it is—it along with the five known inputs can be combined to solve for the unknown volatility. Implied volatility (IV) is the volatility input in a pricing model that, in conjunction with the other inputs, returns the theoretical value of an option matching the market price. For a specific stock price, a given implied volatility will yield a unique option value. Take a stock trading at $44.22 that has the 60-day 45-strike call at a theoretical value of $1.10 with an 18 percent implied volatility level. If the stock price remains constant, but IV rises to 19 percent, the value of the call will rise by its vega, which in this case is about 0.07. The new value of the call will be $1.17. Raising IV another point, to 20 percent, raises the theoretical value by another $0.07, to $1.24. The question is: What would cause implied volatility to change? Supply and Demand: Not Just a Good Idea, It’s the Law! Options are an excellent vehicle for speculation. However, the existence of the options market is better justified by the primary economic purpose of options: as a risk management tool. Hedgers use options to protect their assets from adverse price movements, and when the perception of risk increases, so does demand for this protection. In this context, risk means volatility—the potential for larger moves to the upside and downside. The relative prices of options are driven higher by increased demand for protective options when the market anticipates greater volatility. And option prices are driven lower by greater supply—that is, selling of options—when the market expects lower volatility. Like those of all assets, option prices are subject to the law of supply and demand. When volatility is expected to rise, demand for options is not limited to hedgers. Speculative traders would arguably be more inclined to buy a call than to buy the stock if they are bullish but expect future volatility to be high. Calls require a lower cash outlay. If the stock moves adversely, there is less capital at risk, but still similar profit potential. When volatility is expected to be low, hedging investors are less inclined to pay for protection. They are more likely to sell back the options they may have bought previously to recoup some of the expense. Options are a decaying asset. Investors are more likely to write calls against stagnant stocks to generate income in anticipated low-volatility environments. Speculative traders will implement option-selling strategies, such as short strangles or iron condors, in an attempt to capitalize on stocks they believe won’t move much. The rising supply of options puts downward pressure on option prices. Many traders sum up IV in two words: fear and greed . When option prices rise and fall, not because of changes in the stock price, time to expiration, interest rates, or dividends, but because of pure supply and demand, it is implied volatility that is the varying factor. There are many contributing factors to traders’ willingness to demand or supply options. Anticipation of events such as earnings reports, Federal Reserve announcements, or the release of other news particular to an individual stock can cause anxiety, or fear, in traders and consequently increase demand for options that causes IV to rise. IV can fall when there is complacency in the market or when the anticipated news has been announced and anxiety wanes. “Buy the rumor, sell the news” is often reflected in option implied volatility. When there is little fear of market movement, traders use options to squeeze out more profits—greed. Arbitrageurs, such as market makers who trade delta neutral—a strategy that will be discussed further in Chapters 12 and 13—must be relentlessly conscious of implied volatility. When immediate directional risk is eliminated from a position, IV becomes the traded commodity. Arbitrageurs who focus their efforts on trading volatility (colloquially called vol traders ) tend to think about bids and offers in terms of IV. In the mind of a vol trader, option prices are translated into volatility levels. A trader may look at a particular option and say it is 30 bid at 31 offer. These values do not represent the prices of the options but rather the corresponding implied volatilities. The meaning behind the trader’s remark is that the market is willing to buy implied volatility at 30 percent and sell it at 31 percent. The actual prices of the options themselves are much less relevant to this type of trader. Should HV and IV Be the Same? Most option positions have exposure to volatility in two ways. First, the profitability of the position is usually somewhat dependent on movement (or lack of movement) of the underlying security. This is exposure to HV. Second, profitability can be affected by changes in supply and demand for the options. This is exposure to IV. In general, a long option position benefits when volatility—both historical and implied—increases. A short option position benefits when volatility—historical and implied—decreases. That said, buying options is buying volatility and selling options is selling volatility. The Relationship of HV and IV It’s intuitive that there should exist a direct relationship between the HV and IV. Empirically, this is often the case. Supply and demand for options, based on the market’s expectations for a security’s volatility, determines IV. It is easy to see why IV and HV often act in tandem. But, although HV and IV are related, they are not identical. There are times when IV and HV move in opposite directions. This is not so illogical, if one considers the key difference between the two: HV is calculated from past stock price movements; it is what has happened. IV is ultimately derived from the market’s expectation for future volatility. If a stock typically has an HV of 30 percent and nothing is expected to change, it can be reasonable to expect that in the future the stock will continue to trade at a 30 percent HV. By that logic, assuming that nothing is expected to change, IV should be fairly close to HV. Market conditions do change, however. These changes are often regular and predictable. Earnings reports are released once a quarter in many stocks, Federal Open Market Committee meetings happen regularly, and dates of other special announcements are often disclosed to the public in advance. Although the outcome of these events cannot be predicted, when they will occur often can be. It is around these widely anticipated events that HV-IV divergences often occur. HV-IV Divergence An HV-IV divergence occurs when HV declines and IV rises or vice versa. The classic example is often observed before a company’s quarterly earnings announcement, especially when there is lack of consensus among analysts’ estimates. This scenario often causes HV to remain constant or decline while IV rises. The reason? When there is a great deal of uncertainty as to what the quarterly earnings will be, investors are reluctant to buy or sell the stock until the number is released. When this happens, the stock price movement (volatility) consolidates, causing the calculated HV to decline. IV, however, can rise as traders scramble to buy up options—bidding up their prices. When the news is out, the feared (or hoped for) move in the stock takes place (or doesn’t), and HV and IV tend to converge again. Expected Volatility Whether trading options or stocks, simple or complex strategies, traders must consider volatility. For basic buy-and-hold investors, taking a potential investment’s volatility into account is innate behavior. Do I buy conservative (nonvolatile) stocks or more aggressive (volatile) stocks? Taking into account volatility, based not just on a gut feeling but on hard numbers, can lead to better, more objective trading decisions. Expected Stock Volatility Option traders must have an even greater focus on volatility, as it plays a much bigger role in their profitability—or lack thereof. Because options can create highly leveraged positions, small moves can yield big profits or losses. Option traders must monitor the likelihood of movement in the underlying closely. Estimating what historical volatility (standard deviation) will be in the future can help traders quantify the probability of movement beyond a certain price point. This leads to better decisions about whether to enter a trade, when to adjust a position, and when to exit. There is no way of knowing for certain what the future holds. But option data provide traders with tools to develop expectations for future stock volatility. IV is sometimes interpreted as the market’s estimate of the future volatility of the underlying security. That makes it a ready-made estimation tool, but there are two caveats to bear in mind when using IV to estimate future stock volatility. The first is that the market can be wrong. The market can wrongly price stocks. This mispricing can lead to a correction (up or down) in the prices of those stocks, which can lead to additional volatility, which may not be priced in to the options. Although there are traders and academics believe that the option market is fairly efficient in pricing volatility, there is a room for error. There is the possibility that the option market can be wrong. Another caveat is that volatility is an annualized figure—the annualized standard deviation. Unless the IV of a LEAPS option that has exactly one year until expiration is substituted for the expected volatility of the underlying stock over exactly one year, IV is an incongruent estimation for the future stock volatility. In practice, the IV of an option must be adjusted to represent the period of time desired. There is a common technique for deannualizing IV used by professional traders and retail traders alike. 1 The first step in this process to deannualize IV is to turn it into a one-day figure as opposed to one-year figure. This is accomplished by dividing IV by the square root of the number of trading days in a year. The number many traders use to approximate the number of trading days per year is 256, because its square root is a round number: 16. The formula is For example, a $100 stock that has an at-the-money (ATM) call trading at a 32 percent volatility implies that there is about a 68 percent chance that the underlying stock will be between $68 and $132 in one year’s time—that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for the volatility of the stock for one day in terms of standard deviation as a percentage of the price of the underlying is computed as follows: In one day’s time, based on an IV of 32 percent, there is a 68 percent chance of the stock’s being within 2 percent of the stock price—that’s between $98 and $102. There may be times when it is helpful for traders to have a volatility estimation for a period of time longer than one day—a week or a month, for example. This can be accomplished by multiplying the one-day volatility by the square root of the number of trading days in the relevant period. The equation is as follows: If the period in question is one month and there are 22 business days remaining in that month, the same $100 stock with the ATM call trading at a 32 percent implied volatility would have a one-month volatility of 9.38 percent. Based on this calculation for one month, it can be estimated that there is a 68 percent chance of the stock’s closing between $90.62 and $109.38 based on an IV of 32 percent. Expected Implied Volatility Although there is a great deal of science that can be applied to calculating expected actual volatility, developing expectations for implied volatility is more of an art. This element of an option’s price provides more risk and more opportunity. There are many traders who make their living distilling direction out of their positions and trading implied volatility. To be successful, a trader must forecast IV. Conceptually, trading IV is much like trading anything else. A trader who thinks a stock is going to rise will buy the stock. A trader who thinks IV is going to rise will buy options. Directional stock traders, however, have many more analysis tools available to them than do vol traders. Stock traders have both technical analysis (TA) and fundamental analysis at their disposal. Technical Analysis There are scores, perhaps hundreds, of technical tools for analyzing stocks, but there are not many that are available for analyzing IV. Technical analysis is the study of market data, such as past prices or volume, which is manipulated in such a way that it better illustrates market activity. TA studies are usually represented graphically on a chart. Developing TA tools for IV is more of a challenge than it is for stocks. One reason is that there is simply a lot more data to manage—for each stock, there may be hundreds of options listed on it. The only practical way of analyzing options from a TA standpoint is to use implied volatility. IV is more useful than raw historical option prices themselves. Information for both IV and HV is available in the form of volatility charts, or vol charts. (Vol charts are discussed in detail in Chapter 14.) Volatility charts are essential for analyzing options because they give more complete information. To get a clear picture of what is going on with the price of an option (the goal of technical analysis for any asset), just observing the option price does not supply enough information for a trader to work with. It’s incomplete. For example, if a call rises in value, why did it rise? What greek contributed to its value increase? Was it delta because the underlying stock rose? Or was it vega because volatility rose? How did time decay factor in? Using a volatility chart in conjunction with a conventional stock chart (and being aware of time decay) tells the whole, complete, story. Another reason historical option prices are not used in TA is the option bid-ask spread. For most stocks, the difference between the bid and the ask is equal to a very small percentage of the stock’s price. Because options are highly leveraged instruments, their bid-ask width can equal a much higher percentage of the price. If a trader uses the last trade to graph an option’s price, it could look as if a very large percentage move has occurred when in fact it has not. For example, if the option trades a small contract size on the bid (0.80), then on the offer (0.90) it would appear that the option rose 12.5 percent in value. This large percentage move is nothing more than market noise. Using volatility data based off the midpoint-of-the-market theoretical value eliminates such noise. Fundamental Analysis Fundamental analysis can have an important role in developing expectations for IV. Fundamental analysis is the study of economic factors that affect the value of an asset in order to determine what it is worth. With stocks, fundamental analysis may include studying income statements, balance sheets, and earnings reports. When the asset being studied is IV, there are fewer hard facts available. This is where the art of analyzing volatility comes into play. Essentially, the goal is to understand the psychology of the market in relation to supply and demand for options. Where is the fear? Where is the complacency? When are news events anticipated? How important are they? Ultimately, the question becomes: what is the potential for movement in the underlying? The greater the chance of stock movement, the more likely it is that IV will rise. When unexpected news is announced, IV can rise quickly. The determination of the fundamental relevance of surprise announcements must be made quickly. Unfortunately, these questions are subjective in nature. They require the trader to apply intuition and experience on a case-by-case basis. But there are a few observations to be made that can help a trader make better-educated decisions about IV. Reversion to the Mean The IVs of the options on many stocks and indexes tend to trade in a range unique to those option classes. This is referred to as the mean—or average—volatility level. Some securities will have smaller mean IV ranges than others. The range being observed should be established for a period long enough to confirm that it is a typical IV for the security, not just a temporary anomaly. Traders should study IV over the most recent 6-month period. When IV has changed significantly during that period, a 12-month study may be necessary. Deviations from this range, either above or below the established mean range, will occur from time to time. When following a breakout from the established range, it is common for IV to revert back to its normal range. This is commonly called reversion to the mean among volatility watchers. The challenge is recognizing when things change and when they stay the same. If the fundamentals of the stock change in such a way as to give the options market reason to believe the stock will now be more or less volatile on an ongoing basis than it typically has been in the recent past, the IV may not revert to the mean. Instead, a new mean volatility level may be established. When considering the likelihood of whether IV will revert to recent levels after it has deviated or find a new range, the time horizon and changes in the marketplace must be taken into account. For example, between 1998 and 2003 the mean volatility level of the SPX was around 20 percent to 30 percent. By the latter half of 2006, the mean IV was in the range of 10 percent to 13 percent. The difference was that between 1998 and 2003 was the buildup of “the tech bubble,” as it was called by the financial media. Market volatility ultimately leveled off in 2003. In a later era, between the fall of 2010 and late summer of 2011 SPX implied volatility settled in to trade mostly between 12 and 20 percent. But in August 2011, as the European debt crisis heated up, a new, more volatile range between 24 and 40 percent reigned for some time. No trader can accurately predict future IV any more than one can predict the future price of a stock. However, with IV there are often recurring patterns that traders can observe, like the ebb and flow of IV often associated with earnings or other regularly scheduled events. But be aware that the IV’s rising before the last 15 earnings reports doesn’t mean it will this time. CBOE Volatility Index ® Often traders look to the implied volatility of the market as a whole for guidance on the IV of individual stocks. Traders use the Chicago Board Options Exchange (CBOE) Volatility Index ® , or VIX ® , as an indicator of overall market volatility. When people talk about the market, they are talking about a broad-based index covering many stocks on many diverse industries. Usually, they are referring to the S&P 500. Just as the IV of a stock may offer insight about investors’ feelings about that stock’s future volatility, the volatility of options on the S&P 500—SPX options—may tell something about the expected volatility of the market as a whole. VIX is an index published by the Chicago Board Options Exchange that measures the IV of a hypothetical 30-day option on the SPX. A 30-day option on the SPX only truly exists once a month—30 days before expiration. CBOE computes a hypothetical 30-day option by means of a weighted average of the two nearest-term months. When the S&P 500 rises or falls, it is common to see individual stocks rise and fall in sympathy with the index. Most stocks have some degree of market risk. When there is a perception of higher risk in the market as a whole, there can consequently be a perception of higher risk in individual stocks. The rise or fall of the IV of SPX can translate into the IV of individual stocks rising or falling. Implied Volatility and Direction Who’s afraid of falling stock prices? Logically, declining stocks cause concern for investors in general. There is confirmation of that statement in the options market. Just look at IV. With most stocks and indexes, there is an inverse relationship between IV and the underlying price. Exhibit 3.2 shows the SPX plotted against its 30-day IV, or the VIX. EXHIBIT 3.2 SPX vs. 30-day IV (VIX). The heavier line is the SPX, and the lighter line is the VIX. Note that as the price of SPX rises, the VIX tends to decline and vice versa. When the market declines, the demand for options tends to increase. Investors hedge by buying puts. Traders speculate on momentum by buying puts and speculate on a turnaround by buying calls. When the market moves higher, investors tend to sell their protection back and write covered calls or cash-secured puts. Option speculators initiate option-selling strategies. There is less fear when the market is rallying. This inverse relationship of IV to the price of the underlying is not unique to the SPX; it applies to most individual stocks as well. When a stock moves lower, the market usually bids up IV, and when the stock rises, the market tends to offer IV creating downward pressure. Calculating Volatility Data Accurate data are essential for calculating volatility. Many of the volatility data that are readily available are useful, but unfortunately, some are not. HV is a value that is easily calculated from publicly accessible past closing prices of a stock. It’s rather straightforward. Traders can access HV from many sources. Retail traders often have access to HV from their brokerage firm. Trading firms or clearinghouses often provide professional traders with HV data. There are some excellent online resources for HV as well. HV is a calculation with little subjectivity—the numbers add up how they add up. IV, however, can be a bit more ambiguous. It can be calculated different ways to achieve different desired outcomes; it is user-centric. Most of the time, traders consider the theoretical value to be between the bid and the ask prices. On occasion, however, a trader will calculate IV for the bid, the ask, the last trade price, or, sometimes, another value altogether. There may be a valid reason for any of these different methods for calculating IV. For example, if a trader is long volatility and aspires to reduce his position, calculating the IV for the bid shows him what IV level can be sold to liquidate his position. Firms, online data providers, and most options-friendly brokers offer IV data. Past IV data is usually displayed graphically in what is known as a volatility chart or vol chart. Current IV is often displayed along with other data right in the option chain. One note of caution: when the current IV is displayed, however, it should always be scrutinized carefully. Was the bid used in calculating this figure? What about the ask? How long ago was this calculation made? There are many questions that determine the accuracy of a current IV, and rarely are there any answers to support the number. Traders should trust only IV data they knowingly generated themselves using a pricing model. Volatility Skew There are many platforms (software or Web-based) that enable traders to solve for volatility values of multiple options within the same option class. Values of options of the same class are interrelated. Many of the model parameters are shared among the different series within the same class. But IV can be different for different options within the same class. This is referred to as the volatility skew . There are two types of volatility skew: term structure of volatility and vertical skew. Term Structure of Volatility Term structure of volatility—also called monthly skew or horizontal skew —is the relationship among the IVs of options in the same class with the same strike but with different expiration months. IV, again, is often interpreted as the market’s estimate of future volatility. It is reasonable to assume that the market will expect some months to be more volatile than others. Because of this, different expiration cycles can trade at different IVs. For example, if a company involved in a major product-liability lawsuit is expecting a verdict on the case to be announced in two months, the one-month IV may be low, as the stock is not expected to move much until the suit is resolved. The two-month volatility may be much higher, however, reflecting the expectations of a big move in the stock up or down, depending on the outcome. The term structure of volatility also varies with the normal ebb and flow of volatility within the business cycle. In periods of declining volatility, it is common for the month with the least amount of time until expiration, also known as the front month, to trade at a lower volatility than the back months, or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have a higher IV than the back months. Exhibit 3.3 shows historical option prices and their corresponding IVs for 32.5-strike calls on General Motors (GM) during a period of low volatility. EXHIBIT 3.3 GM term structure of volatility. In this example, no major news is expected to be released on GM, and overall market volatility is relatively low. The February 32.5 call has the lowest IV, at 32 percent. Each consecutive month has a higher IV than the previous month. A graduated increasing or decreasing IV for each consecutive expiration cycle is typical of the term structure of volatility. Under normal circumstances, the front month is the most sensitive to changes in IV. There are two reasons for this. First, front-month options are typically the most actively traded. There is more buying and selling pressure. Their IV is subject to more activity. Second, vegas are smaller for options with fewer days until expiration. This means that for the same monetary change in an option’s value, the IV needs to move more for short-term options. Exhibit 3.4 shows the same GM options and their corresponding vegas. EXHIBIT 3.4 GM vegas. If the value of the September 32.5 calls increases by $0.10, IV must rise by 1 percentage point. If the February 32.5 calls increase by $0.10, IV must rise 3 percentage points. As expiration approaches, the vega gets even smaller. With seven days until expiration, the vega would be about 0.014. This means IV would have to change about 7 points to change the call value $0.10. Vertical Skew The second type of skew found in option IV is vertical skew, or strike skew. Vertical skew is the disparity in IV among the strike prices within the same month for an option class. The options on most stocks and indexes experience vertical skew. As a general rule, the IV of downside options—calls and puts with strike prices lower than the at-the-money (ATM) strike—trade at higher IVs than the ATM IV. The IV of upside options—calls and puts with strike prices higher than the ATM strike—typically trade at lower IVs than the ATM IV. The downside is often simply referred to as puts and the upside as calls. The rationale for this lingo is that OTM options (puts on the downside and calls on the upside) are usually more actively traded than the ITM options. By put-call parity, a put can be synthetically created from a call, and a call can be synthetically created from a put simply by adding the appropriate long or short stock position. Exhibit 3.5 shows the vertical skew for 86-day options on Citigroup Inc. (C) on a typical day, with IVs rounded to the nearest tenth. EXHIBIT 3.5 Citigroup vertical skew. Notice the IV of the puts (downside options) is higher than that of the calls (upside options), with the 31 strike’s volatility more than 10 points higher than that of the 38 strike. Also, the difference in IV per unit change in the strike price is higher for the downside options than it is for the upside ones. The difference between the IV of the 31 strike is 2 full points higher than the 32 strike, which is 1.8 points higher than the 33 strike. But the 36 strike’s IV is only 1.1 points higher than the 37 strike, which is also just 1.1 points higher than the 38 strike. This incremental difference in the IV per strike is often referred to as the slope. The puts of most underlyings tend to have a greater slope to their skew than the calls. Many models allow values to be entered for the upside slope and the downside slope that mathematically increase or decrease IVs of each strike incrementally. Some traders believe the slope should be a straight line, while others believe it should be an exponentially sloped line. If the IVs were graphed, the shape of the skew would vary among asset classes. This is sometimes referred to as the volatility smile or sneer, depending on the shape of the IV skew. Although Exhibit 3.5 is a typical paradigm for the slope for stock options, bond options and other commodity options would have differently shaped skews. For example, grain options commonly have calls with higher IVs than the put IVs. Volatility skew is dependent on supply and demand. Greater demand for downside protection may cause the overall IV to rise, but it can cause the IV of puts to rise more relative to the calls or vice versa. There are many traders who make their living trading volatility skew. Note 1 . This technique provides only an estimation of future volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00013.html SCORE: 1258.50 ================================================================================ CHAPTER 4 Option-Specific Risk and Opportunity New endeavors can be intimidating. The first day at a new job or new school is a challenge. Option trading is no different. When traders first venture into the world of options, they tend to start with what they know—trading direction. Buying stocks is at the heart of the comfort zone for many traders. Buying a call as a substitute for buying a stock is a logical progression. And for the most part, call buying is a pretty straightforward way to take a bullish position in a stock. But it’s not just a bullish position. The greeks come into play with the long call, providing both risk and opportunity. Long ATM Call Kim is a trader who is bullish on the Walt Disney Company (DIS) over the short term. The time horizon of her forecast is three weeks. Instead of buying 100 shares of Disney at $35.10 per share, Kim decides to buy one Disney March 35 call at $1.10. In this example, March options have 44 days until expiration. How can Kim profit from this position? How can she lose? Exhibit 4.1 shows the profit and loss (P&(L)) for the call at different time periods. The top line is when the trade is executed; the middle, dotted line is after three weeks have passed; and the bottom, darker line is at expiration. Kim wants Disney to rise in price, which is evident by looking at the graph for any of the three time horizons. She would anticipate a loss if the stock price declines. These expectations are related to the position’s delta, but that is not the only risk exposure Kim has. As indicated by the three different lines in Exhibit 4.1 , the call loses value over time. This is called theta risk . She has other risk exposure as well. Exhibit 4.2 lists the greeks for the DIS March 35 call. EXHIBIT 4.1 P&(L) of Disney 35 call. EXHIBIT 4.2 Greeks for 35 Disney call. Delta 0.57 Gamma 0.166 Theta −0.013 Vega 0.048 Rho 0.023 Kim’s immediate directional exposure is quantified by the delta, which is 0.57. Delta is immediate directional exposure because it’s subject to change by the amount of the gamma. The positive gamma of this position helps Kim by increasing the delta as Disney rises and decreasing it as it falls. Kim, however, has time working against her—theta. At this point, she theoretically loses $0.013 per day. Since her call is close to being at-the-money, she would anticipate her theta becoming more negative as expiration approaches if Disney’s share price remains unchanged. She also has positive vega exposure. A one-percentage-point increase in implied volatility (IV) earns Kim just under $0.05. A one-point decrease costs her about $0.05. With so few days until expiration, the 35-strike call has very little rho exposure. A full one-percentage-point change in the interest rate changes her call’s value by only $0.023. Delta Some of Kim’s risks warrant more concern than others. With this position, delta is of the greatest concern, followed by theta. Kim expects the call to rise in value and accepts the risk of decline. Delta exposure was her main rationale for establishing the position. She expects to hold it for about three weeks. Kim is willing to accept the trade-off of delta exposure for theta, which will cost her three weeks of erosion of option premium. If the anticipated delta move happens sooner than expected, Kim will have less decay. Exhibit 4.3 shows the value of her 35 call at various stock prices over time. The left column is the price of Disney. The top row is the number of days until expiration. EXHIBIT 4.3 Disney 35 call price–time matrix–value. The effect of delta is evident as the stock rises or falls. When the position is established (44 days until expiration), the change in the option price if the stock were to move from $35 to $36 is 0.62 (1.66 − 1.04). Between stock prices of $36 and $37, the option gains 0.78 (2.44 −1.66). If the stock were to decline in value from $35 to $34, the option loses 0.47 (1.04 − 0.57). The option gains value at a faster rate as the stock rises and loses value at a slower rate as the stock falls. This is the effect of gamma. Gamma With this type of position, gamma is an important but secondary consideration. Gamma is most helpful to Kim in developing expectations of what the delta will be as the stock price rises or falls. Exhibit 4.4 shows the delta at various stock prices over time. EXHIBIT 4.4 Disney call price–time matrix–delta. Kim pays attention to gamma only to gauge her delta. Why is this important to her? In this trade, Kim is focused on direction. Knowing how much her call will rise or fall in step with the stock is her main concern. Notice that her delta tends to get bigger as the stock rises and smaller as the stock falls. As time passes, the delta gravitates toward 1.00 or 0, depending on whether the call is in-the-money (ITM) or out-of-the-money (OTM). Theta Option buying is a veritable race against the clock. With each passing day, the option loses theoretical value. Refer back to Exhibit 4.3 . When three weeks pass and the time to expiration decreases from 44 days to 23, what happens to the call value? If the stock price stays around its original level, theta will be responsible for a loss of about 30 percent of the premium. If Disney is at $35 with 23 days to expiration, the call will be worth $0.73. With a big enough move in either direction, however, theta matters much less. With 23 days to expiration and Disney at $39, there is only 0.12 of time value—the premium paid over parity for the option. At that point, it is almost all delta exposure. Similarly, if the Disney stock price falls after three weeks to $33, the call will have only 0.10 of time value. Time decay is the least of Kim’s concerns if the stock makes a big move. Vega After delta and theta, vega is the next most influential contributor to Kim’s profit or peril. With Disney at $35.10, the 1.10 premium for the 35-strike call represents $1 of time value—all of which is vulnerable to changes in IV. The option’s 1.10 value returns an IV of about 19 percent, given the following inputs: Stock: $35.10 Strike: 35 Days to expiration: 44 Interest: 5.25 percent No dividend paid during this period Consequently, the vega is 0.048. What does the 0.048 vega tell Kim? Given the preceding inputs, for each point the IV rises or falls, the option’s value gains or loses about $0.05. Some of the inputs, however, will change. Kim anticipates that Disney will rise in price. She may be right or wrong. Either way, it is unlikely that the stock will remain exactly at $35.10 to option expiration. The only certainty is that time will pass. Both price and time will change Kim’s vega exposure. Exhibit 4.5 shows the changing vega of the 35 call as time and the underlying price change. EXHIBIT 4.5 Disney 35 call price–time matrix–vega. When comparing Exhibit 4.5 to Exhibit 4.3 , it’s easy to see that as the time value of the option declines, so does Kim’s exposure to vega. As time passes, vega gets smaller. And as the call becomes more in- or out-of-the-money, vega gets smaller. Since she plans to hold the position for around three weeks, she is not concerned about small fluctuations in IV in the interim. If indeed the rise in price that Kim anticipates comes to pass, vega becomes even less of a concern. With 23 days to expiration and DIS at $37, the call value is 2.21. The vega is $0.018. If IV decreases as the stock price rises—a common occurrence—the adverse effect of vega will be minimal. Even if IV declines by 5 points, to a historically low IV for DIS, the call loses less than $0.10. That’s less than 5 percent of the new value of the option. If dividend policy changes or the interest rate changes, the value of Kim’s call will be affected as well. Dividends are often fairly predictable. However, a large unexpected dividend payment can have a significant adverse impact on the value of the call. For example, if a surprise $3 dividend were announced, owning the stock would become greatly preferable to owning the call. This preference would be reflected in the call premium. This is a scenario that an experienced trader like Kim will realize is a possibility, although not a probability. Although she knows it can happen, she will not plan for such an event unless she believes it is likely to happen. Possible reasons for such a belief could be rumors or the company’s historically paying an irregular dividend. Rho For all intents and purposes, rho is of no concern to Kim. In recent years, interest rate changes have not been a major issue for option traders. In the Alan Greenspan years of Federal Reserve leadership, changes in the interest rate were usually announced at the regularly scheduled Federal Open Market Committee (FOMC) meetings, with but a few exceptions. Ben Bernanke, likewise, changed interest rates fairly predictably, when he made any rate changes at all. In these more stable periods, if there is no FOMC meeting scheduled during the life of the call, it’s unlikely that rates will change. Even if they do, the rho with 44 days to expiration is only 0.023. This means that if rates change by a whole percentage point—which is four times the most common incremental change—the call value will change by a little more than $0.02. In this case, this is an acceptable risk. With 23 days to expiration, the ATM 35 call has a rho of only 0.011. Tweaking Greeks With this position, some risks are of greater concern than others. Kim may want more exposure to some greeks and less to others. What if she is concerned that her forecasted price increase will take longer than three weeks? She may want less exposure to theta. What if she is particularly concerned about a decline in IV? She may want to decrease her vega. Conversely, she may believe IV will rise and therefore want to increase her vega. Kim has many ways at her disposal to customize her greeks. All of her alternatives come with trade-offs. She can buy more calls, increasing her greek positions in exact proportion. She can buy or sell stock or options against her call, creating a spread. The simplest way to alter her exposure to option greeks is to choose a different call to buy. Instead of buying the ATM call, Kim can buy a call with a different relationship to the current stock price. Long OTM Call Kim can reduce her exposure to theta and vega by buying an OTM call. The trade-off here is that she also reduces her immediate delta exposure. Depending on how much Kim believes Disney will rally, this may or may not be a viable trade-off. Imagine that instead of buying one Disney March 35 call, Kim buys one Disney March 37.50 call, for 0.20. There are a few observations to be made about this alternative position. First, the net premium, and therefore overall risk, is much lower, 0.20 instead of 1.10. From an expiration standpoint, the breakeven at expiration is $37.70 (the strike price plus the call premium). Since Kim plans on exiting the position after about three weeks, the exact break-even point at the expiration of the contract is irrelevant. But the concept is the same: the stock needs to rise significantly. Exhibit 4.6 shows how Kim’s concerns translate into greeks. EXHIBIT 4.6 Greeks for Disney 35 and 37.50 calls. 35 Call 37.50 Call Delta 0.57 0.185 Gamma 0.166 0.119 Theta −0.013 −0.007 Vega 0.048 0.032 Rho 0.023 0.007 This table compares the ATM call with the OTM call. Kim can reduce her theta to half that of the ATM call position by purchasing an OTM. This is certainly a favorable difference. Her vega is lower with the 37.50 call, too. This may or may not be a favorable difference. That depends on Kim’s opinion of IV. On the surface, the disparity in delta appears to be a highly unfavorable trade-off. The delta of the 37.50 call is less than one third of the delta of the 35 call, and the whole motive for entering into this trade is to trade direction! Although this strategy is very delta oriented, its core is more focused on gamma and theta. The gamma of the 37.50 call is about 72 percent that of the 35 call. But the theta of the 37.50 call is about half that of the 35 call. Kim is improving her gamma/theta relationship by buying the OTM, but with the call being so far out-of-the-money and so inexpensive, the theta needs to be taken with a grain of salt. It is ultimately gamma that will make or break this delta play. The price of the option is 0.20—a rather low premium. In order for the call to gain in value, delta has to go to work with help from gamma. At this point, the delta is small, only 0.185. If Kim’s forecast is correct and there is a big move upward, gamma will cause the delta to increase, and therefore also the premium to increase exponentially. The call’s sensitivity to gamma, however, is dynamic. Exhibit 4.7 shows how the gamma of the 37.50 call changes as the stock price moves over time. At any point in time, gamma is highest when the call is ATM. However, so is theta. Kim wants to reap as much benefit from gamma as possible while minimizing her exposure to theta. Ideally, she wants Disney to rally through the strike price—through the high gamma and back to the low theta. After three weeks pass, with 23 days until expiration, if Disney is at $37 a share, the gamma almost doubles, to 0.237. When the call is ATM, the delta increases at its fastest rate. As Disney rises above the strike, the gamma figures in the table begin to decline. EXHIBIT 4.7 Disney 37.50 call price–time matrix–gamma. Gamma helps as the stock price declines, too. Exhibit 4.8 shows the effect of time and gamma on the delta of the 37.50 call. EXHIBIT 4.8 Disney 37.50 call price–time matrix–delta. The effect of gamma is readily observable, as the delta at any point in time is always higher at higher stock prices and lower at lower stock prices. Kim benefits greatly when the delta grows from its initial level of 0.185 to above 0.50—above the point of being at-the-money. If the stock moves lower, gamma helps take away the pain of the price decline by decreasing the delta. While delta, gamma, and theta occupy Kim’s thoughts, it is ultimately dollars and cents that matter. She needs to translate her study of the greeks into cold, hard cash. Exhibit 4.9 shows the theoretical values of the 37.50 call. EXHIBIT 4.9 Disney 37.50 call price–time matrix–value. The sooner the price rise occurs, the better. It means less time for theta to eat away profits. If Kim must hold the position for the entire three weeks, she needs a good pop in the stock to make it worth her while. At a $37 share price, the call is worth about 0.50, assuming all other market influences remain constant. That’s about a 150 percent profit. At $38, Exhibit 4.9 reveals the call value to be 1.04. That’s a 420 percent profit. On one hand, it’s hard for a trader like Kim not to get excited about the prospect of making 420 percent on an 8 percent move in a stock. On the other hand, Kim has to put things in perspective. When the position is established, the call has a 0.185 delta. By the trader’s definition of delta, that means the call is estimated to have about an 18.5 percent chance of expiring in-the-money. More than four out of five times, this position will be trading below the strike at expiration. Although Kim is not likely to hold the position until expiration, this observation tells her something: she’s starting in the hole. She is more likely to lose than to win. She needs to be compensated well for her risk on the winners to make up for the more prevalent losers. Buying OTM calls can be considered more speculative than buying ITM or ATM calls. Unlike what the at-expiration diagrams would lead one to believe, OTM calls are not simply about direction. There’s a bit more to it. They are really about gamma, time, and the magnitude of the stock’s move (volatility). Long OTM calls require a big move in the right direction for gamma to do its job. Long ITM Call Kim also has the alternative to buy an ITM call. Instead of the 35 or 37.50 call, she can buy the 32.50. The 32.50 call shares some of the advantages the 37.50 call has over the 35 call, but its overall greek characteristics make it a very different trade from the two previous alternatives. Exhibit 4.10 shows a comparison of the greeks of the three different calls. EXHIBIT 4.10 Greeks for Disney 32.50, 35, and 37.50 calls. Like the 37.50 call, the 32.50 has a lower gamma, theta, and vega than the ATM 35-strike call. Because the call is ITM, it has a higher delta: 0.862. In this example, Kim can buy the 32.50 call for 3. That’s 0.40 over parity (3 − [35.10 − 32.50] = 0.40). There is not much time value, but more than the 37.50 call has. Thus, theta is of some concern. Ultimately, the ITMs have 0.40 of time value to lose compared with the 0.20 of the OTM calls. Vega is also of some concern, but not as much as in the other alternatives because the vega of the 32.50 is lower than the 35s or the 37.50s. Gamma doesn’t help much as the stock rallies—it will get smaller as the stock price rises. Gamma will, however, slow losses somewhat if the stock declines by decreasing delta at an increasing rate. In this case, the greek of greatest consequence is delta—it is a more purely directional play than the other alternatives discussed. Exhibit 4.11 shows the matrix of the delta of the 32.50 call. EXHIBIT 4.11 Disney 32.50 call price–time matrix–delta. Because the call starts in-the-money and has a relatively low gamma, the delta remains high even if Disney declines significantly. Gamma doesn’t really kick in until the stock retreats enough to bring the call closer to being at-the-money. At that point, the position will have suffered a big loss, and the higher gamma is of little comfort. Kim’s motivation for selecting the ITM call above the ATM and OTM calls would be increased delta exposure. The 0.86 delta makes direction the most important concern right out of the gate. Exhibit 4.12 shows the theoretical values of the 32.50 call. EXHIBIT 4.12 Disney 32.50 call price–time matrix–value. Small directional moves contribute to significant leveraged gains or losses. From share price $35 to $36, the call gains 0.90—from 2.91 to 3.81—about a 30 percent gain. However, from $35 to $34, the call loses 0.80, or 27 percent. With only 0.40 of time value, the nondirectional greeks (theta, gamma, and vega) are a secondary consideration. If this were a deeper ITM call, the delta would start out even higher, closer to 1.00, and the other relevant greeks would be closer to zero. The deeper ITM a call, the more it acts like the stock and the less its option characteristics (greeks) come into play. Long ATM Put The beauty of the free market is that two people can study all the available information on the same stock and come up with completely different outlooks. First of all, this provides for entertaining television on the business-news channels when the network juxtaposes an outspoken bullish analyst with an equally unreserved bearish analyst. But differing opinions also make for a robust marketplace. Differing opinions are the oil that greases the machine that is price discovery. From a market standpoint, it’s what makes the world go round. It is possible that there is another trader, Mick, in the market studying Disney, who arrives at the conclusion that the stock is overpriced. Mick believes the stock will decline in price over the next three weeks. He decides to buy one Disney March 35 put at 0.80. In this example, March has 44 days to expiration. Mick initiates this long put position to gain downside exposure, but along with his bearish position comes option-specific risk and opportunity. Mick is buying the same month and strike option as Kim did in the first example of this chapter: the March 35 strike. Despite the different directional bias, Mick’s position and Kim’s position share many similarities. Exhibit 4.13 offers a comparison of the greeks of the Disney March 35 call and the Disney March 35 put. EXHIBIT 4.13 Greeks for Disney 35 call and 35 put. Call Put Delta 0.57 −0.444 Gamma 0.166 0.174 Theta −0.013 −0.009 Vega 0.048 0.048 Rho 0.023 −0.015 The first comparison to note is the contrasting deltas. The put delta is negative, in contrast to the call delta. The absolute value of the put delta is close to 1.00 minus the call delta. The put is just slightly OTM, so its delta is just under 0.50, while that of the call is just over 0.50. The disparate, yet related deltas represent the main difference between these two trades. The difference between the gamma of the 35 put and that of the corresponding call is fairly negligible: 0.174 versus 0.166, respectively. The gamma of this ATM put will enter into the equation in much the same way as the gamma of the ATM call. The put’s negative delta will become more negative as the stock declines, drawing closer to −1.00. It will get less negative as the stock price rises, drawing closer to zero. Gamma is important here, because it helps the delta. Delta, however, still remains the most important greek. Exhibit 4.14 illustrates how the 35 put delta changes as time and price change. EXHIBIT 4.14 Disney 35 put price–time matrix–delta. Since this put is ATM, it starts out with a big enough delta to offer the directional exposure Mick desires. The delta can change, but gamma ensures that it always changes in Mick’s favor. Exhibit 4.15 shows how the value of the 35 put changes with the stock price. EXHIBIT 4.15 Disney 35 put price–time matrix–value. Over time, a decline of only 10 percent in the stock yields high percentage returns. This is due to the leveraged directional nature of this trade—delta. While the other greeks are not of primary concern, they must be monitored. At the onset, the 0.80 premium is all time value and, therefore subject to the influences of time decay and volatility. This is where trading greeks comes into play. Conventional trading wisdom says, “Cut your losses early, and let your profits run.” When trading a stock, that advice is intellectually easy to understand, although psychologically difficult to follow. Buyers of options, especially ATM options, must follow this advice from the standpoint of theta. Options are decaying assets. The time premium will be zero at expiration. ATMs decay at an increasing nonlinear rate. Exiting a long position before getting too close to expiration can cut losses caused by an increasing theta. When to cut those losses, however, will differ from trade to trade, situation to situation, and person to person. When buying options, accepting some loss of premium due to time decay should be part of the trader’s plan. It comes with the territory. In this example, Mick is willing to accept about three weeks of erosion. Mick needs to think about what his put will be worth, not just if the underlying rises or falls but also if it doesn’t move at all. At the time the position is established, the theta is 0.009, just under a penny. If Disney share price is unchanged when three weeks pass, his theta will be higher. Exhibit 4.16 shows how thetas and theoretical values change over time if DIS stock remains at $35.10. EXHIBIT 4.16 Disney 35 put—thetas and theoretical values. Mick needs to be concerned not only about what the theta is now but what it will be when he plans on exiting the position. His plan is to exit the trade in about three weeks, at which point the put theta will be −0.013. If he amortizes his theta over this three-week period, he theoretically loses an average of about 0.01 a day during this time if nothing else changes. The average daily theta is calculated here by subtracting the value of the put at 23 days to expiration from its value when the trade was established to find the loss of premium attributed to time decay, then dividing by the number of days until expiration. Since the theta doesn’t change much over the first three weeks, Mick can eyeball the theta rather easily. As expiration approaches and theta begins to grow more quickly, he’ll need to do the math. At nine days to expiration, the theoretical value of Mick’s put is about 0.35, assuming all other variables are held constant. By that time, he will have lost 0.45 (0.80 − 0.35) due to erosion over the 35-day period he held the position if the stock hasn’t moved. Mick’s average daily theta during that period is about 0.0129 (0.45 ÷ 35). The more time he holds the trade, the greater a concern is theta. Mick must weigh his assessment of the likelihood of the option’s gaining value from delta against the risk of erosion. If he holds the trade for 35 days, he must make 0.0129 on average per day from delta to offset theta losses. If the forecast is not realized within the expected time frame or if the forecast changes, Mick needs to act fast to curtail average daily theta losses. Finding the Right Risk Mick could lower the theta of his position by selecting a put with a greater number of days to expiration. This alternative has its own set of trade-offs: lower gamma and higher vega than the 44-day put. He could also select an ITM put or an OTM put. Like Kim’s call alternatives, the OTM put would have less exposure to time decay, lower vega, lower gamma, and a lower delta. It would have a lower premium, too. It would require a bigger price decline than the ATM put and would be more speculative. The ITM put would also have lower theta, vega, and gamma, but it would have a higher delta. It would take on more of the functionality of a short stock position in much the same way that Kim’s ITM call alternative did for a long stock position. In its very essence, however, an option trade, ITM or otherwise, is still fundamentally different than a stock trade. Stock has a 1.00 delta. The delta of a stock never changes, so it has zero gamma. Stock is not subject to time decay and has no volatility component to its pricing. Even though ITM options have deltas that approach 1.00 and other greeks that are relatively low, they have two important differences from an equity. The first is that the greeks of options are dynamic. The second is the built-in leverage feature of options. The relationship of an option’s strike price to the stock price can change constantly. Options that are ITM now may be OTM tomorrow and vice versa. Greeks that are not in play at the moment may be later. Even if there is no time value in the option now because it is so far away-from-the-money, there is the potential for time premium to become a component of the option’s price if the stock moves closer to the strike price. Gamma, theta, and vega always have the potential to come into play. Since options are leveraged by nature, small moves in the stock can provide big profits or big losses. Options can also curtail big losses if used for hedging. Long option positions can reap triple-digit percentage gains quickly with a favorable move in the underlying. Even though 100 percent of the premium can be lost just as easily, one option contract will have far less nominal exposure than a similar position in the stock. It’s All About Volatility What are Kim and Mick really trading? Volatility. The motivation for buying an option as opposed to buying or shorting the stock is volatility. To some degree, these options have exposure to both flavors of volatility—implied volatility and historical volatility (HV). The positions in each of the examples have positive vega. Their values are influenced, in part, by IV. Over time, IV begins to lose its significance if the option is no longer close to being at-the-money. The main objective of each of these trades is to profit from the volatility of the stock’s price movement, called future stock volatility or future realized volatility. The strategies discussed in this chapter are contingent on volatility being one directional. The bigger the move in the trader’s forecasted direction the better. Volatility in the form of an adverse directional move results in a decline in premium. The gamma in these long option positions makes volatility in the right direction more beneficial and volatility in the wrong direction less costly. This phenomenon is hardly unique to the long call and the long put. Although some basic strategies, such as the ones studied in this chapter, depend on a particular direction, many don’t. Except for interest rate strategies and perhaps some arbitrage strategies, all option trades are volatility trades in one way or another. In general, option strategies can be divided into two groups: volatility-buying strategies and volatility-selling strategies. The following is a breakdown of common option strategies into categories of volatility-buying strategies and volatility-selling strategies: Volatility-Selling Strategies Volatility-Buying Strategies Short Call, Short Put, Covered Call, Covered Put, Bull Call Spread, Bear Call Spread, Bull Put Spread, Bear Put Spread, Short Straddle, Short Strangle, Guts, Ratio Call Spread, Calendar, Butterfly, Iron Butterfly, Broken-Wing Butterfly, Condor, Iron Condor, Diagonals, Double Diagonals, Risk Reversals/Collars. Long Call, Long Put, Bull Call Spread, Bear Call Spread, Bull Put Spread, Bear Put Spread, Long Straddle, Long Strangle, Guts, Back Spread, Calendar, Butterfly, Iron Butterfly, Broken-Wing Butterfly, Condor, Iron Condor, Diagonals, Double Diagonals, Risk Reversals/Collars. Long option strategies appear in the volatility-buying group because they have positive gamma and positive vega. Short option strategies appear in the volatility-selling group because of negative gamma and vega. There are some strategies that appear in both groups—for example, the butterfly/condor family, which is typically associated with income generation. These particular volatility strategies are commonly instituted as volatility-selling strategies. However, depending on whether the position is bought or sold and where the stock price is in relation to the strike prices, the position could fall into either group. Some strategies, like the vertical spread family—bull and bear call and put spreads—and risk reversal/collar spreads naturally fall into either category, depending on where the stock is in relation to the strikes. The calendar spread family is unique in that it can have characteristics of each group at the same time. Direction Neutral, Direction Biased, and Direction Indifferent As typically traded, volatility-selling option strategies are direction neutral. This means that the position has the greatest results if the underlying price remains in a range—that is, neutral. Although some option-selling strategies—for example, a naked put—may have a positive or negative delta in the short term, profit potential is decidedly limited. This means that if traders are expecting a big move, they are typically better off with option-buying strategies. Option-buying strategies can be either direction biased or direction indifferent. Direction-biased strategies have been shown throughout this chapter. They are delta trades. Direction-indifferent strategies are those that benefit from increased volatility in the underlying but where the direction of the move is irrelevant to the profitability of the trade. Movement in either direction creates a winner. Are You a Buyer or a Seller? The question is: which is better, selling volatility or buying volatility? I have attended option seminars with instructors (many of whom I regard with great respect) teaching that volatility-selling strategies, or income-generating strategies, are superior to buying options. I also know option gurus that tout the superiority of buying options. The answer to the question of which is better is simple: it’s all a matter of personal preference. When I began trading on the floor of Chicago Board Options Exchange (CBOE) in the 1990s, I quickly became aware of a dichotomy among my market-making peers. Those making markets on the floor of the exchange at that time were divided into two groups: teenie buyers and teenie sellers. Teenie Buyers Before options traded in decimals (dollars and cents) like they do today, the lowest price increment in which an option could be traded was one sixteenth of a dollar—a teenie . Teenie buyers were market makers who would buy back OTM options at one sixteenth to eliminate short positions. They would sometimes even initiate long OTM option positions at a teenie, too. The focus of the teenie-buyer school of thought was the fact that long options have unlimited reward, while short options have unlimited risk. An option purchased so far OTM that it was offered at one sixteenth is unlikely to end up profitable, but it’s an inexpensive lottery ticket. At worst, the trader can only lose a teenie. Teenie buyers felt being short OTM options that could be closed by paying a sixteenth was an unreasonable risk. Teenie Sellers Teenie sellers, however, focused on the fact that options offered at one sixteenth were far enough OTM that they were very likely to expire worthless. This appears to be free money, unless the unexpected occurs, in which case potential losses can be unlimited. Teenie sellers would routinely save themselves $6.25 (one sixteenth of a dollar per contract representing 100 shares) by selling their long OTMs at a teenie to close the position. They sometimes would even initiate short OTM contracts at one sixteenth. These long-option or short-option biases hold for other types of strategies as well. Volatility-selling positions, such as the iron condor, can be constructed to have limited risk. The paradigm for these strategies is they tend to produce winners more often than not. But when the position loses, the trader loses more than he would stand to profit if the trade worked out favorably. Herein lies the issue of preference. Long-option traders would rather trade Babe Ruth–style. For years, Babe Ruth was the record holder for the most home runs. At the same time, he was also the record holder for the most strikeouts. The born fighters that are option buyers accept the fact that they will have more strikeouts, possibly many more strikeouts, than winning trades. But the strategy dictates that the profit on one winner more than makes up for the string of small losers. Short-option traders, conversely, like to have everything cool and copacetic. They like the warm and fuzzy feeling they get from the fact that month after month they tend to generate winners. The occasional loser that nullifies a few months of profits is all part of the game. Options and the Fair Game There may be a statistical advantage to buying stock as opposed to shorting stock, because the market has historically had a positive annualized return over the long run. A statistical advantage to being either an option buyer or an option seller, however, should not exist in the long run, because the option market prices IV. Assuming an overall efficient market for pricing volatility into options, there should be no statistical advantage to systematically buying or selling options. 1 Consider a game consisting of one six-sided die. Each time a one, two, or three is rolled, the house pays the player $1. Each time a four, five, or six is rolled, the house pays zero. What is the most a player would be willing to pay to play this game? If the player paid nothing, the house would be at a tremendous disadvantage, paying $1 50 percent of the time and nothing the other 50 percent of the time. This would not be a fair game from the house’s perspective, as it would collect no money. If the player paid $1, the player would get his dollar back when one, two, or three came up. Otherwise, he would lose his dollar. This is not a fair game from the player’s perspective. The chances of winning this game are 3 out of 6, or 50–50. If this game were played thousands of times, one would expect to receive $1 half the time and receive nothing the other half of the time. The average return per roll one would expect to receive would be $0.50, that’s ($1 × 50 percent + $0 × 50 percent). This becomes a fair game with an entrance fee of $0.50. Now imagine a similar game in which a six-sided die is rolled. This time if a one is rolled, the house pays $1. If any other number is rolled, the house pays nothing. What is a fair price to play this game? The same logic and the same math apply. There is a percent chance of a one coming up and the player receiving $1. And there is a percent chance of each of the other five numbers being rolled and the player receiving nothing. Mathematically, this translates to: percent percent). Fair value for a chance to play this game is about $0.1667 per roll. The fair game concept applies to option prices as well. The price of the game, or in this case the price of the option, is determined by the market in the form of IV. The odds are based on the market’s expectations of future volatility. If buying options offered a superior payout based on the odds of success, the market would put upward pressure on prices until this arbitrage opportunity ceased to exist. It’s the same for selling volatility. If selling were a fundamentally better strategy, the market would depress option prices until selling options no longer produced a way to beat the odds. The options market will always equalize imbalances. Note 1 . This is not to say that unique individual opportunities do not exist for overpriced or underpriced options, only that options are not overpriced or underpriced in general. Thus, neither an option-selling nor option-buying methodology should provide an advantage. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00014.html SCORE: 952.00 ================================================================================ CHAPTER 5 An Introduction to Volatility-Selling Strategies Along with death and taxes, there is one other fact of life we can all count on: the time value of all options ultimately going to zero. What an alluring concept! In a business where expected profits can be thwarted by an unexpected turn of events, this is one certainty traders can count on. Like all certainties in the financial world, there is a way to profit from this fact, but it’s not as easy as it sounds. Alas, the potential for profit only exists when there is risk of loss. In order to profit from eroding option premiums, traders must implement option-selling strategies, also known as volatility-selling strategies. These strategies have their own set of inherent risks. Selling volatility means having negative vega—the risk of implied volatility rising. It also means having negative gamma—the risk of the underlying being too volatile. This is the nature of selling volatility. The option-selling trader does not want the underlying stock to move—that is, the trader wants the stock to be less volatile. That is the risk. Profit Potential Profit for the volatility seller is realized in a roundabout sort of way. The reward for low volatility is achieved through time decay. These strategies have positive theta. Just as the volatility-buying strategies covered in Chapter 4 had time working against them, volatility-selling strategies have time working in their favor. The trader is effectively paid to assume the risk of movement. Gamma-Theta Relationship There exists a trade-off between gamma and theta. Long options have positive gamma and negative theta. Short options have negative gamma and positive theta. Positions with greater gamma, whether positive or negative, tend to have greater theta values, negative or positive. Likewise, lower absolute values for gamma tend to go hand in hand with lower absolute values for theta. The gamma-theta relationship is the most important consideration with many types of strategies. Gamma-theta is often the measurement with the greatest influence on the bottom line. Greeks and Income Generation With volatility-selling strategies (sometimes called income-generating strategies), greeks are often overlooked. Traders simply dismiss greeks as unimportant to this kind of trade. There is some logic behind this reasoning. Time decay provides the profit opportunity. In order to let all of time premium erode, the position must be held until expiration. Interim changes in implied volatility are irrelevant if the position is held to term. The gamma-theta loses some significance if the position is held until expiration, too. The position has either passed the break-even point on the at-expiration diagram, or it has not. Incremental daily time decay–related gains are not the ultimate goal. The trader is looking for all the time premium, not portions of it. So why do greeks matter to volatility sellers? Greeks allow traders to be flexible. Consider short-term-momentum stock traders. The traders buy a stock because they believe it will rise over the next month. After one week, if unexpected bearish news is announced causing the stock to break through its support lines, the traders have a decision to make. Short-term speculative traders very often choose to cut their losses and exit the position early rather than risk a larger loss hoping for a recovery. Volatility-selling option traders are often faced with the same dilemma. If the underlying stays in line with the traders’ forecast, there is little to worry about. But if the environment changes, the traders have to react. Knowing the greeks for a position can help traders make better decisions if they plan to close the position before expiration. Naked Call A naked call is when a trader shorts a call without having stock or other options to cover or protect it. Since the call is uncovered, it is one of the riskier trades a trader can make. Recall the at-expiration diagram for the naked call from Chapter 1, Exhibit 1.3 : Naked TGT Call. Theoretically, there is limited reward and unlimited risk. Yet there are times when experienced traders will justify making such a trade. When a stock has been trading in a range and is expected to continue doing so, traders may wait until it is near the top of the channel, where there is resistance, and then short a call. For example, a trader, Brendan, has been studying a chart of Johnson & Johnson (JNJ). Brendan notices that for a few months the stock has trading been in a channel between $60 and $65. As he observes Johnson & Johnson beginning to approach the resistance level of $65 again, he considers selling a call to speculate on the stock not rising above $65. Before selling the call, Brendan consults other technical analysis tools, like ADX/DMI, to confirm that there is no trend present. ADX/DMI is used by some traders as a filter to determine the strength of a trend and whether the stock is overbought or oversold. In this case, the indicator shows no strong trend present. Brendan then performs due diligence. He studies the news. He looks for anything specific that could cause the stock to rally. Is the stock a takeover target? Brendan finds nothing. He then does earnings research to find out when they will be announced, which is not for almost two more months. Next, Brendan pulls up an option chain on his computer. He finds that with the stock trading around $64 per share, the market for the November 65 call (expiring in four weeks) is 0.66 bid at 0.68 offer. Brendan considers when Johnson & Johnson’s earnings report falls. Although recent earnings have seldom been a major concern for Johnson & Johnson, he certainly wants to sell an option expiring before the next earnings report. The November fits the mold. Brendan sells ten of the November 65 calls at the bid price of 0.66. Brendan has a rather straightforward goal. He hopes to see Johnson & Johnson shares remain below $65 between now and expiration. If he is right, he stands to make $660. If he is wrong? Exhibit 5.1 shows how Brendan’s calls hold up if they are held until expiration. EXHIBIT 5.1 Naked Johnson & Johnson call at expiration. Considering the risk/reward of this trade, Brendan is rightfully concerned about a big upward move. If the stock begins to rally, he must be prepared to act fast. Brendan must have an idea in advance of what his pain threshold is. In other words, at what price will he buy back his calls and take a loss if Johnson & Johnson moves adversely? He decides he will buy all 10 of his calls back at 1.10 per contract if the trade goes against him. (1.10 is an arbitrary price used for illustrative purposes. The actual price will vary, based on the situation and the risk tolerance of the trader. More on when to take profits and losses is discussed in future chapters.) He may choose to enter a good-till-canceled (GTC) stop-loss order to buy back his calls. Or he may choose to monitor the stock and enter the order when he sees the calls offered at 1.10—a mental stop order. What Brendan needs to know is: How far can the stock price advance before the calls are at 1.10? Brendan needs to examine the greeks of this trade to help answer this question. Exhibit 5.2 shows the hypothetical greeks for the position in this example. EXHIBIT 5.2 Greeks for short Johnson & Johnson 65 call (per contract). Delta −0.34 Gamma −0.15 Theta 0.02 Vega −0.07 The short call has a negative delta. It also has negative gamma and vega, but it has positive time decay (theta). As Johnson & Johnson ticks higher, the delta increases the nominal value of the call. Although this is not a directional trade per se, delta is a crucial element. It will have a big impact on Brendan’s expectations as to how high the stock can rise before he must take his loss. First, Brendan considers how much the option price can move before he covers. The market now is 0.66 bid at 0.68 offer. To buy back his calls at 1.10, they must be offered at 1.10. The difference between the offer now and the offer price at which Brendan will cover is 0.42 (that’s 1.10 − 0.68). Brendan can use delta to convert the change in the ask prices into a stock price change. To do so, Brendan divides the change in the option price by the delta. The −0.34 delta indicates that if JNJ rises $1.24, the calls should be offered at 1.10. Brendan takes note that the bid-ask spreads are typically 0.01 to 0.03 wide in near-term Johnson & Johnson options trading under 1.00. This is not necessarily the case in other option classes. Less liquid names have wider spreads. If the spreads were wider, Brendan would have more slippage. Slippage is the difference between the assumed trade price and the actual price of the fill as a product of the bid-ask spread. It’s the difference between theory and reality. If the bid-ask spread had a typical width of, say, 0.70, the market would be something more like 0.40 bid at 1.10 offer. In this case, if the stock moved even a few cents higher, Brendan could not buy his calls back at his targeted exit price of 1.10. The tighter markets provide lower transaction costs in the form of lower slippage. Therefore, there is more leeway if the stock moves adversely when there are tighter bid-ask option spreads. But just looking at delta only tells a part of the story. In reality, the delta does not remain constant during the price rise in Johnson & Johnson but instead becomes more negative. Initially, the delta is −0.34 and the gamma is −0.15. After a rise in the stock price, the delta will be more negative by the amount of the gamma. To account for the entire effect of direction, Brendan needs to take both delta and gamma into account. He needs to estimate the average delta based on gamma during the stock price move. The formula for the change in stock price is Taking into account the effect of gamma as well as delta, Johnson & Johnson needs to rise only $1.01, in order for Brendan’s calls to be offered at his stop-loss price of 1.10. While having a predefined price point to cover in the event the underlying rises is important, sometimes traders need to think on their feet. If material news is announced that changes the fundamental outlook for the stock, Brendan will have to adjust his plan. If the news leads Brendan to become bullish on the stock, he should exit the trade at once, taking a small loss now instead of the bigger loss he would expect later. If the trader is uncertain as to whether to hold or close the position, the Would I Do It Now? rule is a useful rule of thumb. Would I Do It Now? Rule To follow this rule, ask yourself, “If I did not already have this position, would I do it now? Would I establish the position at the current market prices, given the current market scenario?” If the answer is no, then the solution is simple: Exit the trade. For example, if after one week material news is released and Johnson & Johnson is trading higher, at $64.50 per share, and the November 65 call is trading at 0.75, Brendan must ask himself, based on the price of the stock and all known information, “If I were not already short the calls, would I short them now at the current price of 0.75, with the stock trading at $64.50?” Brendan’s opinion of the stock is paramount in this decision. If, for example, based on the news that was announced he is now bullish, he would likely not want to sell the calls at 0.75—he only gets $0.09 more in option premium and the stock is 0.50 closer to the strike. If, however, he is not bullish, there is more to consider. Theta can be of great use in decision making in this situation. As the number of days until expiration decreases and the stock approaches $65 (making the option more at-the-money), Brendan’s theta grows more positive. Exhibit 5.3 shows the theta of this trade as the underlying rises over time. EXHIBIT 5.3 Theta of Johnson & Johnson. When the position is first established, positive theta comforts Brendan by showing that with each passing day he gets a little closer to his goal—to have the 65 calls expire out-of-the-money (OTM) and reap a profit of the entire 66-cent premium. Theta becomes truly useful if the position begins to move against him. As Johnson & Johnson rises, the trade gets more precarious. His negative delta increases. His negative gamma increases. His goal becomes more out of reach. In conjunction with delta and gamma, theta helps Brendan decide whether the risk is worth the reward. In the new scenario, with the stock at $64.50, Brendan would collect $18 a day (1.80 × 10 contracts). Is the risk of loss in the short run worth earning $18 a day? With Johnson & Johnson at $64.50, would Brendan now short 10 calls at 0.75 to collect $18 a day, knowing that each day may bring a continued move higher in the stock? The answer to this question depends on Brendan’s assessment of the risk of the underlying continuing its ascent. As time passes, if the stock remains closer to the strike, the daily theta rises, providing more reward. Brendan must consider that as theta—the reward—rises, so does gamma: a risk factor. A small but noteworthy risk is that implied volatility could rise. The negative vega of this position would, then, adversely affect the profitability of this trade. It will make Brendan’s 1.10 cover-point approach faster because it makes the option more expensive. Vega is likely to be of less consequence because it would ultimately take the stock’s rising though the strike price for the trade to be a loser at expiration. Short Naked Puts Another trader, Stacie, has also been studying Johnson & Johnson. Stacie believes Johnson & Johnson is on its way to test the $65 resistance level yet again. She believes it may even break through $65 this time, based on strong fundamentals. Stacie decides to sell naked puts. A naked put is a short put that is not sold in conjunction with stock or another option. With the stock around $64, the market for the November 65 put is 1.75 bid at 1.80. Stacie likes the fact that the 65 puts are slightly in-the-money (ITM) and thus have a higher delta. If her price rise comes sooner than expected, the high delta may allow her to take a profit early. Stacie sells 10 puts at 1.75. In the best-case scenario, Stacie retains the entire 1.75. For that to happen, she will need to hold this position until expiration and the stock will have to rise to be trading above the 65 strike. Logically, Stacie will want to do an at-expiration analysis. Exhibit 5.4 shows Stacie’s naked put trade if she holds it until expiration. EXHIBIT 5.4 Naked Johnson & Johnson put at expiration. While harvesting the entire premium as a profit sounds attractive, if Stacie can take the bulk of her profit early, she’ll be happy to close the position and eliminate her risk—nobody ever went broke taking a profit. Furthermore, she realizes that her outlook may be wrong: Johnson & Johnson may decline. She may have to close the position early—maybe for a profit, maybe for a loss. Stacie also needs to study her greeks. Exhibit 5.5 shows the greeks for this trade. EXHIBIT 5.5 Greeks for short Johnson & Johnson 65 put (per contract). Delta 0.65 Gamma −0.15 Theta 0.02 Vega −0.07 The first item to note is the delta. This position has a directional bias. This bias can work for or against her. With a positive 0.65 delta per contract, this position has a directional sensitivity equivalent to being long around 650 shares of the stock. That’s the delta × 100 shares × 10 contracts. Stacie’s trade is not just a bullish version of Brendan’s. Partly because of the size of the delta, it’s different—specific directional bias aside. First, she will handle her trade differently if it is profitable. For example, if over the next week or so Johnson & Johnson rises $1, positive delta and negative gamma will have a net favorable effect on Stacie’s profitability. Theta is small in comparison and won’t have too much of an effect. Delta/gamma will account for a decrease in the put’s theoretical value of about $0.73. That’s the estimated average delta times the stock move, or [0.65 + (–0.15/2)] × 1.00. Stacie’s actual profit would likely be less than 0.73 because of the bid-ask spread. Stacie must account for the fact that the bid-ask is 0.05 wide (1.75–1.80). Because Stacie would buy to close this position, she should consider the 0.73 price change relative to the 1.80 offer, not the 1.75 trade price—that is, she factors in a nickel of slippage. Thus, she calculates, that the puts will be offered at 1.07 (that’s 1.80 − 0.73) when the stock is at $65. That is a gain of $0.68. In this scenario, Stacie should consider the Would I Do It Now? rule to guide her decision as to whether to take her profit early or hold the position until expiration. Is she happy being short ten 65 puts at 1.07 with Johnson & Johnson at $65? The premium is lower now. The anticipated move has already occurred, and she still has 28 days left in the option that could allow for the move to reverse itself. If she didn’t have the trade on now, would she sell ten 65 puts at 1.07 with Johnson & Johnson at $65? Based on her original intention, unless she believes strongly now that a breakout through $65 with follow-through momentum is about to take place, she will likely take the money and run. Stacie also must handle this trade differently from Brendan in the event that the trade is a loser. Her trade has a higher delta. An adverse move in the underlying would affect Stacie’s trade more than it would Brendan’s. If Johnson & Johnson declines, she must be conscious in advance of where she will cover. Stacie considers both how much she is willing to lose and what potential stock-price action will cause her to change her forecast. She consults a stock chart of Johnson & Johnson. In this example, we’ll assume there is some resistance developing around $64 in the short term. If this resistance level holds, the trade becomes less attractive. The at-expiration breakeven is $63.25, so the trade can still be a winner if Johnson & Johnson retreats. But Stacie is looking for the stock to approach $65. She will no longer like the risk/reward of this trade if it looks like that price rise won’t occur. She makes the decision that if Johnson & Johnson bounces off the $64 level over the next couple weeks, she will exit the position for fear that her outlook is wrong. If Johnson & Johnson drifts above $64, however, she will ride the trade out. In this example, Stacie is willing to lose 1.00 per contract. Without taking into account theta or vega, that 1.00 loss in the option should occur at a stock price of about $63.28. Theta is somewhat relevant here. It helps Stacie’s potential for profit as time passes. As time passes and as the stock rises, so will theta, helping her even more. If the stock moves lower (against her) theta helps ease the pain somewhat, but the further in-the-money the put, the lower the theta. Vega can be important here for two reasons: first, because of how implied volatility tends to change with market direction, and second, because it can be read as an indication of the market’s expectations. The Double Whammy With the stock around $64, there is a negative vega of about seven cents. As the stock moves lower, away from the strike, the vega gets a bit smaller. However, the market conditions that would lead to a decline in the price of Johnson & Johnson would likely cause implied volatility (IV) to rise. If the stock drops, Stacie would have two things working against her—delta and vega—a double whammy. Stacie needs to watch her vega. Exhibit 5.6 shows the vega of Stacie’s put as it changes with time and direction. EXHIBIT 5.6 Johnson & Johnson 65 put vega. If after one week passes Johnson & Johnson gaps lower to, say, $63.00 a share, the vega will be 0.043 per contract. If IV subsequently rises 5 points as a result of the stock falling, vega will make Stacie’s puts theoretically worth 21.5 cents more per contract. She will lose $215 on vega (that’s 0.043 vega × 5 volatility points × 10 contracts) plus the adverse delta/gamma move. A gap opening will cause her to miss the opportunity to stop herself out at her target price entirely. Even if the stock drifts lower, her targeted stop-loss price will likely come sooner than expected, as the option price will likely increase both by delta/gamma and vega resulting from rising volatility. This can cause her to have to cover sooner, which leaves less room for error. With this trade, increases in IV due to market direction can make it feel as if the delta is greater than it actually is as the market declines. Conversely, IV softening makes it feel as if the delta is smaller than it is as the market rises. The second reason IV has importance for this trade (as for most other strategies) is that it can give some indication of how much the market thinks the stock can move. If IV is higher than normal, the market perceives there to be more risk than usual of future volatility. The question remains: Is the higher premium worth the risk? The answer to this question is subjective. Part of the answer is based on Stacie’s assessment of future volatility. Is the market right? The other part is based on Stacie’s risk tolerance. Is she willing to endure the greater price swings associated with the potentially higher volatility? This can mean getting whipsawed, which is exiting a position after reaching a stop-loss point only to see the market reverse itself. The would-be profitable trade is closed for a loss. Higher volatility can also mean a higher likelihood of getting assigned and acquiring an unwanted long stock position. Cash-Secured Puts There are some situations where higher implied volatility may be a beneficial trade-off. What if Stacie’s motivation for shorting puts was different? What if she would like to own the stock, just not at the current market price? Stacie can sell ten 65 puts at 1.75 and deposit $63,250 in her trading account to secure the purchase of 1,000 shares of Johnson & Johnson if she gets assigned. The $63,250 is the $65 per share she will pay for the stock if she gets assigned, minus the 1.75 premium she received for the put × $100 × 10 contracts. Because the cash required to potentially purchase the stock is secured by cash sitting ready in the account, this is called a cash-secured put. Her effective purchase price if assigned is $63.25—the same as her breakeven at expiration. The idea with this trade is that if Johnson & Johnson is anywhere under $65 per share at expiration, she will buy the stock effectively at $63.25. If assigned, the time premium of the put allows her to buy the stock at a discount compared with where it is priced when the trade is established, $64. The higher the time premium—or the higher the implied volatility—the bigger the discount. This discount, however, is contingent on the stock not moving too much. If it is above $65 at expiration she won’t get assigned and therefore can only profit a maximum of 1.75 per contract. If the stock is below $63.25 at expiration, the time premium no longer represents a discount, in fact, the trade becomes a loser. In a way, Stacie is still selling volatility. Covered Call The problem with selling a naked call is that it has unlimited exposure to upside risk. Because of this, many traders simply avoid trading naked calls. A more common, and some would argue safer, method of selling calls is to sell them covered. A covered call is when calls are sold and stock is purchased on a share-for-share basis to cover the unlimited upside risk of the call. For each call that is sold, 100 shares of the underlying security are bought. Because of the addition of stock to this strategy, covered calls are traded with a different motivation than naked calls. There are clearly many similarities between these two strategies. The main goal for both is to harvest the premium of the call. The theta for the call is the same with or without the stock component. The gamma and vega for the two strategies are the same as well. The only difference is the stock. When stock is added to an option position, the net delta of the position is the only thing affected. Stock has a delta of one, and all its other greeks are zero. The pivotal point for both positions is the strike price. That’s the point the trader wants the stock to be above or below at expiration. With the naked call, the maximum payout is reaped if the stock is below the strike at expiration, and there is unlimited risk above the strike. With the covered call, the maximum payout is reaped if the stock is above the strike at expiration. If the stock is below the strike at expiration, the risk is substantial—the stock can potentially go to zero. Putting It on There are a few important considerations with the covered call, both when putting on, or entering, the position and when taking off, or exiting, the trade. The risk/reward implications of implied volatility are important in the trade-planning process. Do I want to get paid more to assume more potential risk? More speculative traders like the higher premiums. More conservative (investment-oriented) covered-call sellers like the low implied risk of low-IV calls. Ultimately, a main focus of a covered call is the option premium. How fast can it go to zero without the movement hurting me? To determine this, the trader must study both theta and delta. The first step in the process is determining which month and strike call to sell. In this example, Harley-Davidson Motor Company (HOG) is trading at about $69 per share. A trader, Bill, is neutral to slightly bullish on Harley-Davidson over the next three months. Exhibit 5.7 shows a selection of available call options for Harley-Davidson with corresponding deltas and thetas. EXHIBIT 5.7 Harley-Davidson calls. In this example, the May 70 calls have 85 days until expiration and are 2.80 bid. If Harley-Davidson remained at $69 until May expiration, the 2.80 premium would represent a 4 percent profit over this 85-day period (2.80 ÷ 69). That’s an annualized return of about 17 percent ([0.04 / 85)] × 365). Bill considers his alternatives. He can sell the April (57-day) 70 calls at 2.20 or the March (22-day) 70 calls at 0.85. Since there is a different number of days until expiration, Bill needs to compare the trades on an apples-to-apples basis. For this, he will look at theta and implied volatility. Presumably, the March call has a theta advantage over the longer-term choices. The March 70 has a theta of 0.032, while the April 70’s theta is 0.026 and the May 70’s is 0.022. Based on his assessment of theta, Bill would have the inclination to sell the March. If he wants exposure for 90 days, when the March 70 call expires, he can roll into the April 70 call and then the May 70 call (more on this in subsequent chapters). This way Bill can continue to capitalize on the nonlinear rate of decay through May. Next, Bill studies the IV term structure for the Harley-Davidson ATMs and finds the March has about a 19.2 percent IV, the April has a 23.3 percent IV, and the May has a 23 percent IV. March is the cheapest option by IV standards. This is not necessarily a favorable quality for a short candidate. Bill must weigh his assessment of all relevant information and then decide which trade is best. With this type of a strategy, the benefits of the higher theta can outweigh the disadvantages of selling the lower IV. In this case, Bill may actually like selling the lower IV. He may infer that the market believes Harley-Davidson will be less volatile during this period. So far, Bill has been focusing his efforts on the 70 strike calls. If he trades the March 70 covered call, he will have a net delta of 0.588 per contract. That’s the negative 0.412 delta from shorting the call plus the 1.00 delta of the stock. His indifference point if the trade is held until expiration is $70.85. The indifference point is the point at which Bill would be indifferent as to whether he held only the stock or the covered call. This is figured by adding the strike price of $70 to the 0.85 premium. This is the effective sale price of the stock if the call is assigned. If Bill wants more potential for upside profit, he could sell a higher strike. He would have to sell the April or May 75, since the March 75s are a zero bid. This would give him a higher indifference point, and the upside profits would materialize quickly if HOG moved higher, since the covered-call deltas would be higher with the 75 calls. The April 75 covered-call net delta is 0.796 per contract (the stock delta of 1.00 minus the 0.204 delta of the call). The May 75 covered-call delta is 0.751. But Bill is neutral to only slightly bullish. In this case, he’d rather have the higher premium—high theta is more desirable than high delta in this situation. Bill buys 1,000 shares of Harley-Davidson at $69 and sells 10 Harley-Davidson March 70 calls at 0.85. Bill also needs to plan his exit. To exit, he must study two things: an at-expiration diagram and his greeks. Exhibit 5.8 shows the P&(L) at expiration of the Harley-Davidson March 70 covered call. Exhibit 5.9 shows the greeks. EXHIBIT 5.8 Harley-Davidson covered call. EXHIBIT 5.9 Greeks for Harley-Davidson covered call (per contract). Delta 0.591 Gamma −0.121 Theta 0.032 Vega −0.066 Taking It Off If the trade works out perfectly for Bill, 22 days from now Harley-Davidson will be trading right at $70. He’d profit on both delta and theta. If the trade isn’t exactly perfect, but still good, Harley-Davidson will be anywhere above $68.15 in 22 days. It’s the prospect that the trade may not be so good at March expiration that occupies Bill’s thoughts, but a trader has to hope for the best and plan for the worst. If it starts to trend, Bill needs to react. The consequences to the stock’s trending to the upside are not quite so dire, although he might be somewhat frustrated with any lost opportunity above the indifference point. It’s the downside risk that Bill will more vehemently guard against. First, the same IV/vega considerations exist as they did in the previous examples. In the event the trade is closed early, IV/vega may help or hinder profitability. A rise in implied volatility will likely accompany a decline in the stock price. This can bring Bill to his stop-loss sooner. Delta versus theta however, is the major consideration. He will plan his exit price in advance and cover when the planned exit price is reached. There are more moving parts with the covered call than a naked option. If Bill wants to close the position early, he can leg out, meaning close only one leg of the trade (the call or the stock) at a time. If he legs out of the trade, he’s likely to close the call first. The motivation for exiting a trade early is to reduce risk. A naked call is hardly less risky than a covered call. Another tactic Bill can use, and in this case will plan to use, is rolling the call. When the March 70s expire, if Harley-Davidson is still in the same range and his outlook is still the same, he will sell April calls to continue the position. After the April options expire, he’ll plan to sell the Mays. With this in mind, Bill may consider rolling into the Aprils before March expiration. If it is close to expiration and Harley-Davidson is trading lower, theta and delta will both have devalued the calls. At the point when options are close to expiration and far enough OTM to be offered close to zero, say 0.05, the greeks and the pricing model become irrelevant. Bill must consider in absolute terms if it is worth waiting until expiration to make 0.05. If there is a lot of time until expiration, the answer is likely to be no. This is when Bill will be apt to roll into the Aprils. He’ll buy the March 70s for a nickel, a dime, or maybe 0.15 and at the same time sell the Aprils at the bid. This assumes he wants to continue to carry the position. If the roll is entered as a single order, it is called a calendar spread or a time spread. Covered Put The last position in the family of basic volatility-selling strategies is the covered put, sometimes referred to as selling puts and stock. In a covered put, a trader sells both puts and stock on a one-to-one basis. The term covered put is a bit of a misnomer, as the strategy changes from limited risk to unlimited risk when short stock is added to the short put. A naked put can produce only losses until the stock goes to zero—still a substantial loss. Adding short stock means that above the strike gains on the put are limited, while losses on the stock are unlimited. The covered put functions very much like a naked call. In fact, they are synthetically equal. This concept will be addressed further in the next chapter. Let’s looks at another trader, Libby. Libby is an active trader who trades several positions at once. Libby believes the overall market is in a range and will continue as such over the next few weeks. She currently holds a short stock position of 1,000 shares in Harley-Davidson. She is becoming more neutral on the stock and would consider buying in her short if the market dipped. She may consider entering into a covered-put position. There is one caveat: Libby is leaving for a cruise in two weeks and does not want to carry any positions while she is away. She decides she will sell the covered put and actively manage the trade until her vacation. Libby will sell 10 Harley-Davidson March (22-day) 70 puts at 1.85 against her short 1,000 shares of Harley-Davidson, which is trading at $69 per share. She knows that her maximum profit if the stock declines and assignment occurs will be $850. That’s 0.85 × $100 × 10 contracts. Win or lose, she will close the position in two weeks when there are only eight days until expiration. To trade this covered put she needs to watch her greeks. Exhibit 5.10 shows the greeks for the Harley-Davidson 70-strike covered put. EXHIBIT 5.10 Greeks for Harley-Davidson covered put (per contract). Delta −0.419 Gamma −0.106 Theta 0.031 Vega −0.066 Libby is really focusing on theta. It is currently about $0.03 per day but will increase if the put stays close-to-the-money. In two weeks, the time premium will have decayed significantly. A move downward will help, too, as the −0.419 delta indicates. Exhibit 5.11 displays an array of theoretical values of the put at eight days until expiration as the stock price changes. EXHIBIT 5.11 HOG 70 put values at 8 days to expiry. As long as Harley-Davidson stays below the strike price, Libby can look at her put from a premium-over-parity standpoint. Below the strike, the intrinsic value of the put doesn’t matter too much, because losses on intrinsic value are offset by gains on the stock. For Libby, all that really matters is the time value. She sold the puts at 0.85 over parity. If Harley-Davidson is trading at $68 with eight days to go, she can buy her puts back for 0.12 over parity. That’s a 73-cent profit, or $730 on her 10 contracts. This doesn’t account for any changes in the time value that may occur as a result of vega, but vega will be small with Harley-Davidson at $68 and eight days to go. At this point, she would likely close down the whole position—buying the puts and buying the stock—to take a profit on a position that worked out just about exactly as planned. Her risk, though, is to the upside. A big rally in the stock can cause big losses. From a theoretical standpoint, losses are potentially unlimited with this type of trade. If the stock is above the strike, she needs to have a mental stop order in mind and execute the closing order with discipline. Curious Similarities These basic volatility-selling strategies are fairly simple in nature. If the trader believes a stock will not rise above a certain price, the most straightforward way to trade the forecast is to sell a call. Likewise, if the trader believes the stock will not go below a certain price he can sell a put. The covered call and covered put are also ways to generate income on long or short stock positions that have these same price thresholds. In fact, the covered call and covered put have some curious similarities to the naked put and naked call. The similarities between the two pairs of positions are no coincidence. The following chapter sheds light on these similarities. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00015.html SCORE: 975.00 ================================================================================ CHAPTER 6 Put-Call Parity and Synthetics In order to understand more complex spread strategies involving two or more options, it is essential to understand the arbitrage relationship of the put-call pair. Puts and calls of the same month and strike on the same underlying have prices that are defined in a mathematical relationship. They also have distinctly related vegas, gammas, thetas, and deltas. This chapter will show how the metrics of these options are interrelated. It will also explore synthetics and the idea that by adding stock to a position, a trader may trade with indifference either a call or a put to the same effect. Put-Call Parity Essentials Before the creation of the Black-Scholes model, option pricing was hardly an exact science. Traders had only a few mathematical tools available to compare the relative prices of options. One such tool, put-call parity, stems from the fact that puts and calls on the same class sharing the same month and strike can have the same functionality when stock is introduced. For example, traders wanting to own a stock with limited risk can buy a married put: long stock and a long put on a share-for-share basis. The traders have infinite profit potential, and the risk of the position is limited below the strike price of the option. Conceptually, long calls have the same risk/reward profile—unlimited profit potential and limited risk below the strike. Exhibit 6.1 is an overview of the at-expiration diagrams of a married put and a long call. EXHIBIT 6.1 Long call vs. long stock + long put (married put). Married puts and long calls sharing the same month and strike on the same security have at-expiration diagrams with the same shape. They have the same volatility value and should trade around the same implied volatility (IV). Strategically, these two positions provide the same service to a trader, but depending on margin requirements, the married put may require more capital to establish, because the trader must buy not just the option but also the stock. The stock component of the married put could be purchased on margin. Buying stock on margin is borrowing capital to finance a stock purchase. This means the trader has to pay interest on these borrowed funds. Even if the stock is purchased without borrowing, there is opportunity cost associated with the cash used to pay for the stock. The capital is tied up. If the trader wants to use funds to buy another asset, he will have to borrow money, which will incur an interest obligation. Furthermore, if the trader doesn’t invest capital in the stock, the capital will rest in an interest-bearing account. The trader forgoes that interest when he buys a stock. However the trader finances the purchase, there is an interest cost associated with the transaction. Both of these positions, the long call and the married put, give a trader exposure to stock price advances above the strike price. The important difference between the two trades is the value of the stock below the strike price—the part of the trade that is not at risk in either the long call or the married put. On this portion of the invested capital, the trader pays interest with the married put (whether actually or in the form of opportunity cost). This interest component is a pricing consideration that adds cost to the married put and not the long call. So if the married put is a more expensive endeavor than the long call because of the interest paid on the investment portion that is below the strike, why would anyone buy a married put? Wouldn’t traders instead buy the less expensive—less capital intensive—long call? Given the additional interest expense, they would rather buy the call. This relates to the concept of arbitrage. Given two effectively identical choices, rational traders will choose to buy the less expensive alternative. The market as a whole would buy the calls, creating demand which would cause upward price pressure on the call. The price of the call would rise until its interest advantage over the married put was gone. In a robust market with many savvy traders, arbitrage opportunities don’t exist for very long. It is possible to mathematically state the equilibrium point toward which the market forces the prices of call and put options by use of the put-call parity. As shown in Chapter 2, the put-call parity states where c is the call premium, PV(x) is the present value of the strike price, p is the put premium and s is the stock price. Another, less academic and more trader-friendly way of stating this equation is where Interest is calculated as Interest = Strike × Interest Rate ×(Days to Expiration/365) 1 The two versions of the put-call parity stated here hold true for European options on non-dividend-paying stocks. Dividends Another difference between call and married-put values is dividends. A call option does not extend to its owner the right to receive a dividend payment. Traders, however, who are long a put and long stock are entitled to a dividend if it is the corporation’s policy to distribute dividends to its shareholders. An adjustment must be made to the put-call parity to account for the possibility of a dividend payment. The equation must be adjusted to account for the absence of dividends paid to call holders. For a dividend-paying stock, the put-call parity states The interest advantage and dividend disadvantage of owning a call is removed from the market by arbitrageurs. Ultimately, that is what is expressed in the put-call parity. It’s a way to measure the point at which the arbitrage opportunity ceases to exist. When interest and dividends are factored in, a long call is an equal position to a long put paired with long stock. In options nomenclature, a long put with long stock is a synthetic long call. Algebraically rearranging the above equation: The interest and dividend variables in this equation are often referred to as the basis. From this equation, other synthetic relationships can be algebraically derived, like the synthetic long put. A synthetic long put is created by buying a call and selling (short) stock. The at-expiration diagrams in Exhibit 6.2 show identical payouts for these two trades. EXHIBIT 6.2 Long put vs. long call + short stock. The concept of synthetics can become more approachable when studied from the perspective of delta as well. Take the 50-strike put and call listed on a $50 stock. A general rule of thumb in the put-call pair is that the call delta plus the put delta equals 1.00 when the signs are ignored. If the 50 put in this example has a −0.45 delta, the 50 call will have a 0.55 delta. By combining the long call (0.55 delta) with short stock (–1.00 delta), we get a synthetic long put with a −0.45 delta, just like the actual put. The directional risk is the same for the synthetic put and the actual put. A synthetic short put can be created by selling a call of the same month and strike and buying stock on a share-for-share basis (i.e., a covered call). This is indicated mathematically by multiplying both sides of the put-call parity equation by −1: The at-expiration diagrams, shown in Exhibit 6.3 , are again conceptually the same. EXHIBIT 6.3 Short put vs. short call + long stock. A short (negative) put is equal to a short (negative) call plus long stock, after the basis adjustment. Consider that if the put is sold instead of buying stock and selling a call, the interest that would otherwise be paid on the cost of the stock up to the strike price is a savings to the put seller. To balance the equation, the interest benefit of the short put must be added to the call side (or subtracted from the put side). It is the same with dividends. The dividend benefit of owning the stock must be subtracted from the call side to make it equal to the short put side (or added to the put side to make it equal the call side). The same delta concept applies here. The short 50-strike put in our example would have a 0.45 delta. The short call would have a −0.55 delta. Buying one hundred shares along with selling the call gives the synthetic short put a net delta of 0.45 (–0.55 + 1.00). Similarly, a synthetic short call can be created by selling a put and selling (short) one hundred shares of stock. Exhibit 6.4 shows a conceptual overview of these two positions at expiration. EXHIBIT 6.4 Short call vs. short put + short stock. Put-call parity can be manipulated as shown here to illustrate the composition of the synthetic short call. Most professional traders earn a short stock rebate on the proceeds they receive when they short stock—an advantage to the short-put–short-stock side of the equation. Additionally, short-stock sellers must pay dividends on the shares they are short—a liability to the married-put seller. To make all things equal, one subtracts interest and adds dividends to the put side of the equation. Comparing Synthetic Calls and Puts The common thread among the synthetic positions explained above is that, for a put-call pair, long options have synthetic equivalents involving long options, and short options have synthetic equivalents involving short options. After accounting for the basis, the four basic synthetic option positions are: Because a call or put position is interchangeable with its synthetic position, an efficient market will ensure that the implied volatility is closely related for both. For example, if a long call has an IV of 25 percent, the corresponding put should have an IV of about 25 percent, because the long put can easily be converted to a synthetic long call and vice versa. The greeks will be similar for synthetically identical positions, too. The long options and their synthetic equivalents will have positive gamma and vega with negative theta. The short options and their synthetics will have negative gamma and vega with positive theta. American-Exercise Options Put-call parity was designed for European-style options. The early exercise possibility of American-style options gums up the works a bit. Because a call (put) and a synthetic call (put) are functionally the same, it is logical to assume that the implied volatility and the greeks for both will be exactly the same. This is not necessarily true with American-style options. However, put-call parity may still be useful with American options when the limitations of the equation are understood. With at-the-money American-exercise options, the differences in the greeks for a put-call pair are subtle. Exhibit 6.5 is a comparison of the greeks for the 50-strike call and the 50-strike put with the underlying at $50 and 66 days until expiration. EXHIBIT 6.5 Greeks for a 50-strike put-call pair on a $50 stock. Call Put Delta 0.554 0.457 Gamma 0.075 0.078 Theta 0.020 0.013 Vega 0.084 0.084 The examples used earlier in this chapter in describing the deltas of synthetics were predicated on the rule of thumb that the absolute values of call and put deltas add up to 1.00. To be a bit more realistic, consider that because of American exercise, the absolute delta values of put-call pairs don’t always add up to 1.00. In fact, Exhibit 6.5 shows that the call has closer to a 0.554 delta. The put struck at the same price then has a 0.457 delta. By selling 100 shares against the long call, we can create a combined-position delta (call delta plus stock delta) that is very close to the put’s delta. The delta of this synthetic put is −0.446 (0.554 − 1.00). The delta of a put will always be similar to the delta of its corresponding synthetic put. This is also true with call–synthetic-call deltas. This relationship mathematically is This holds true whether the options are in-, at-, or out-of-the-money. For example, with a stock at $54, the 50-put would have a −0.205 delta and the call would have a 0.799 delta. Selling 100 shares against the call to create the synthetic put yields a net delta of −0.201. If long or short stock is added to a call or put to create a synthetic, delta will be the only greek affected. With that in mind, note the other greeks displayed in Exhibit 6.5 —especially theta. Proportionally, the biggest difference in the table is in theta. The disparity is due in part to interest. When the effects of the interest component outweigh the effects of the dividend, the time value of the call can be higher than the time value of the put. Because the call must lose more premium than the put by expiration, the theta of the call must be higher than the theta of the put. American exercise can also cause the option prices in put-call parity to not add up. Deep in-the-money (ITM) puts can trade at parity while the corresponding call still has time value. The put-call equation can be unbalanced. The same applies to calls on dividend-paying stocks as the dividend date approaches. When the date is imminent, calls can trade close to parity while the puts still have time value. The role of dividends will be discussed further in Chapter 8. Synthetic Stock Not only can synthetic calls and puts be derived by manipulation of put-call parity, but synthetic positions for the other security in the equation—stock—can be derived, as well. By isolating stock on one side of the equation, the formula becomes After accounting for interest and dividends, buying a call and selling a put of the same strike and time to expiration creates the equivalent of a long stock position. This is called a synthetic stock position, or a combo. After accounting for the basis, the equation looks conceptually like this: This is easy to appreciate when put-call parity is written out as it is here. It begins to make even more sense when considering at-expiration diagrams and the greeks. Exhibit 6.6 illustrates a long stock position compared with a long call combined with a short put position. EXHIBIT 6.6 Long stock vs. long call + short put. A quick glance at these two strategies demonstrates that they are the same, but think about why. Consider the synthetic stock position if both options are held until expiration. The long call gives the trader the right to buy the stock at the strike price. The short put gives the trader the obligation to buy the stock at the same strike price. It doesn’t matter what the strike price is. As long as the strike is the same for the call and the put, the trader will have a long position in the underlying at the shared strike at expiration when exercise or assignment occurs. The options in this example are 50-strike options. At expiration, the trader can exercise the call to buy the underlying at $50 if the stock is above the strike. If the underlying is below the strike at expiration, he’ll get assigned on the put and buy the stock at $50. If the stock is bought, whether by exercise or assignment, the effective price of the potential stock purchase, however, is not necessarily $50. For example, if the trader bought one 50-strike call at 3.50 and sold one 50-strike put at 1.50, he will effectively purchase the underlying at $52 upon exercise or assignment. Why? The trader paid a net of $2 to get a long position in the stock synthetically (3.50 of call premium debited minus 1.50 of put premium credited). Whether the call or the put is ITM, the effective purchase price of the stock will always be the strike price plus or minus the cost of establishing the synthetic, in this case, $52. The question that begs to be asked is: would the trader rather buy the stock or pay $2 to have the same market exposure as long stock? Arbitrageurs in the market (with the help of the put-call parity) ensure that neither position—long stock or synthetic long stock—is better than the other. For example, assume a stock is trading at $51.54. With 71 days until expiration, 26.35 IV, a 5 percent interest rate, and no dividends, the 50-strike call is theoretically worth 3.50, and the 50-strike put is theoretically worth 1.50. Exhibit 6.7 charts the synthetic stock versus the actual stock when there are 71 days until expiration. EXHIBIT 6.7 Long stock and synthetic long stock with 71 days to expiration. Looking at this exhibit, it appears that being long the actual stock outperforms being long the stock synthetically. If the stock is purchased at $51.54, it need only rise a penny higher to profit (in the theoretical world where traders do not pay commissions on transactions). If the synthetic is purchased for $2, the stock needs to rise $0.46 to break even—an apparent disadvantage. This figure, however, does not include interest. The synthetic stock offers the same risk/reward as actually being long the stock. There is a benefit, from the perspective of interest, to paying only $2 for this exposure rather than $51.54. The interest benefit here is about $0.486. We can find this number by calculating the interest as we did earlier in the chapter. Interest, again, is computed as the strike price times the interest rate times the number of days to expiration divided by the number of days in a year. The formula is as follows: Inputting the numbers from this example: The $0.486 of interest is about equal to the $0.46 disparity between the diagrams of the stock and the synthetic stock with 71 days until expiration. The difference is due mainly to rounding and the early-exercise potential of the American put. In mathematical terms The synthetic long stock is approximately equal to the long stock position when considering the effect of interest. The two lines in Exhibit 6.7 —representing stock and synthetic stock—would converge with each passing day as the calculated interest decreases. This equation works as well for a synthetic short stock position; reversing the signs reveals the synthetic for short stock. Or, in this case, Shorting stock at $51.54 is about equal to selling the 50 call and buying the 50 put for a $2 credit based on the interest of 0.486 computed on the 50 strike. Again, the $0.016 disparity between the calculated interest and the actual difference between the synthetic value and the stock price is a function of rounding and early exercise. More on this in the “Conversions and Reversals” section. Synthetic Stock Strategies Ultimately, when we roll up our sleeves and get down to the nitty-gritty, options trading is less about having another alternative for trading the direction of the underlying than it is about trading the greeks. Different strategies allow traders to exploit different facets of option pricing. Some strategies allow traders to trade volatility. Some focus mainly on theta. Many of the strategies discussed in this section present ways for a trader to distill risk down mostly to interest rate exposure. Conversions and Reversals When calls and puts are combined to create synthetic stock, the main differences are the interest rate and dividends. This is important because the risks associated with interest and dividends can be isolated, and ultimately traded, when synthetic stock is combined with the underlying. There are two ways to combine synthetic stock with its underlying security: a conversion and a reversal. Conversion A conversion is a three-legged position in which a trader is long stock, short a call, and long a put. The options share the same month and strike price. By most metrics, this is a very flat position. A trader with a conversion is long the stock and, at the same time, synthetically short the same stock. Consider this from the perspective of delta. In a conversion, the trader is long 1.00 deltas (the long stock) and short very close to 1.00 deltas (the synthetic short stock). Conversions have net flat deltas. The following is a simple example of a typical conversion and the corresponding deltas of each component. Short one 35-strike call: −0.63 delta Long one 35-strike put: −0.37 delta Long 100 shares: 1.00 delta 0.00 delta The short call contributes a negative delta to the position, in this case, −0.63. The long put also contributes a negative delta, −0.37. The combined delta of the synthetic stock is −1.00 in this example, which is like being short 100 shares of stock. When the third leg of the spread is added, the long 100 shares, it counterbalances the synthetic. The total delta for the conversion is zero. Most of the conversion’s other greeks are pretty flat as well. Gamma, theta, and vega are similar for the call and the put in the conversion, because they have the same expiration month and strike price. Because the trader is selling one option and buying another—a call and a put, respectively—with the same month and strike, the greeks come very close to offsetting each other. For all intents and purposes, the trader is out of the primary risks of the position as measured by greeks when a position is converted. Let’s look at a more detailed example. A trader executes the following trade (for the purposes of this example, we assume the stock pays no dividend and the trade is executed at fair value): Sell one 71-day 50 call at 3.50 Buy one 71-day 50 put at 1.50 Buy 100 shares at $51.54 The trader buys the stock at $51.54 and synthetically sells the stock at $52. The synthetic price is computed as −3.50 + 1.50 − 50. Therefore, the stock is sold synthetically at $0.46 over the actual stock price. Exhibit 6.8 shows the analytics for the conversion. EXHIBIT 6.8 Conversion greeks. This position has very subtle sensitivity to the greeks. The net delta for the spread has a very slightly negative bias. The bias is so small it is negligible to most traders, except professionals trading very large positions. Why does this negative delta bias exist? Mathematically, the synthetic’s delta can be higher with American options than with their European counterparts because of the possibility of early exercise of the put. This anomaly becomes more tangible when we consider the unique directional risk associated with this trade. In this example, the stock is synthetically sold at $0.46 over the price at which the stock is bought. If the stock declines significantly in value before expiration, the put will, at some point, trade at parity while the call loses all its time value. In this scenario, the value of the synthetic stock will be short at effectively the same price as the actual stock price. For example, if the stock declines to $35 per share then the numbers are as follows: or With American options, a put this far in-the-money with less than 71 days until expiry will be all intrinsic value. Interest, in this case, will not factor into the put’s value, because the put can be exercised. By exercising the put, both the long stock leg and the long put leg can be closed for even money, leaving only the theoretically worthless call. The stock-synthetic spread is sold at 0.46 and essentially bought at zero when the put is exercised. If the put is exercised before expiration, the profit potential is 0.46 minus the interest calculated between the trade date and the day the put is exercised. If, however, the conversion is held until expiration, the $0.46 is negated by the $0.486 of interest incurred from holding long stock over the entire 71-day period, hence the trader’s desire to see the stock decline before expiration, and thus the negative bias toward delta. This is, incidentally, why the synthetic price (0.46 over the stock price) does not exactly equal the calculated value of the interest (0.486). The trader can exercise the put early if the stock declines and capitalize on the disparity between the interest calculated when the conversion was traded and the actual interest calculation given the shorter time frame. The model values the synthetic at a little less than the interest value would indicate—in this case $0.46 instead of $0.486. The gamma of this trade is fairly negligible. The theta is slightly positive. Rho is the figure that deserves the most attention. Rho is the change in an option’s price given a change in the interest rate. The −0.090 rho of the conversion indicates that if the interest rate rises one percentage point, the position as a whole loses $0.09. Why? The financing of the position gets more expensive as the interest rate rises. The trader would have to pay more in interest to carry the long stock. In this example, if interest rises by one percentage point, the synthetic stock, which had an effective short price of $0.46 over the price of the long stock before the interest rate increase, will be $0.55 over the price of the long stock afterward. If, however, the interest rate declines by one percentage point, the trader profits $0.09, as the synthetic is repriced by the market to $0.37 over the stock price. The lower the interest rate, the less expensive it is to finance the long stock. This is proven mathematically by put-call parity. Negative rho indicates a bearish position on the interest rate; the trader wants it to go lower. Positive rho is a bullish interest rate position. But a one-percentage-point change in the interest rate in one day is a big and uncommon change. The question is: is rho relevant? That depends on the type of position and the type of trader. A 0.090 rho would lead to a 0.0225 profit-and-loss (P&(L)) change per one lot conversion on a 25-basis-point, or quarter percent, change. That’s just $2.25 per spread. This incremental profit or loss, however, can be relevant to professional traders like market makers. They trade very large positions with the aspiration of making small incremental profits on each trade. A market maker with a 5,000-lot conversion would stand to make or lose $11,250, given a quarter-percentage-point change in interest rate and a 0.090 rho. The Mind of a Market Maker Market makers are among the only traders who can trade conversions and reversals profitably, because of the size of their trades and the fact that they can buy the bid and sell the offer. Market makers often attempt to leg into and out of conversions (and reversals). Given the conversion in this example, a market maker may set out to sell calls and in turn buy stock to hedge the call’s delta risk (this will be covered in Chapters 12 and 17), then buy puts and the rest of the stock to create a balanced conversion: one call to one put to one hundred shares. The trader may try to put on the conversion in the previous example for a total of $0.50 over the price of the long stock instead of the $0.46 it’s worth. He would then try to leg out of the trade for less, say $0.45 over the stock, with the goal of locking in a $0.05 profit per spread on the whole trade. Reversal A reversal, or reverse conversion, is simply the opposite of the conversion: buy call, sell put, and sell (short) stock. A reversal can be executed to close a conversion, or it can be an opening transaction. Using the same stock and options as in the previous example, a trader could establish a reversal as follows: Buy one 71-day 50 call at 3.50 Sell one 71-day 50 put at 1.50 Sell 100 shares at 51.54 The trader establishes a short position in the stock at $51.54 and a long synthetic stock position effectively at $52.00. He buys the stock synthetically at $0.46 over the stock price, again assuming the trade can be executed at fair value. With the reversal, the trader has a bullish position on interest rates, which is indicated by a positive rho. In this example, the rho for this position is 0.090. If interest rates rise one percentage point, the synthetic stock (which the trader is long) gains nine cents in value relative to the stock. The short stock rebate on the short stock leg earns more interest at a higher interest rate. If rates fall one percentage point, the synthetic long stock loses $0.09. The trader earns less interest being short stock given a lower interest rate. With the reversal, the fact that the put can be exercised early is a risk. Since the trader is short the put and short stock, he hopes not to get assigned. If he does, he misses out on the interest he planned on collecting when he put on the reversal for $0.46 over. Pin Risk Conversions and reversals are relatively low-risk trades. Rho and early exercise are relevant to market makers and other arbitrageurs, but they are among the lowest-risk positions they are likely to trade. There is one indirect risk of conversions and reversals that can be of great concern to market makers around expiration: pin risk. Pin risk is the risk of not knowing for certain whether an option will be assigned. To understand this concept, let’s revisit the mind of a market maker. Recall that market makers have two primary functions: 1. Buy the bid or sell the offer. 2. Manage risk. When institutional or retail traders send option orders to an exchange (through a broker), market makers are usually the ones with whom they trade. Customers sell the bid; the market makers buy the bid. Customers buy the offer; the market makers sell the offer. The first and arguably easier function of market makers is accomplished whenever a marketable order is sent to the exchange. Managing risk can get a bit hairy. For example, once the market makers buy April 40 calls, their first instinct is to hedge by selling stock to become delta neutral. Market makers are almost always delta neutral, which mitigates the direction risk. The next step is to mitigate theta, gamma, and vega risk by selling options. The ideal options to sell are the same calls that were bought—that is, get out of the trade. The next best thing is to sell the April 40 puts and sell more stock. In this case, the market makers have established a reversal and thereby have very little risk. If they can lock in the reversal for a small profit, they have done their job. What happens if the market makers still have the reversal in inventory at expiration? If the stock is above the strike price—40, in this case—the puts expire, the market makers exercise the calls, and the short stock is consequently eliminated. The market makers are left with no position, which is good. They’re delta neutral. If the stock is below 40, the calls expire, the puts get assigned, and the short stock is consequently eliminated. Again, no position. But what if the stock is exactly at $40? Should the calls be exercised? Will the puts get assigned? If the puts are assigned, the traders are left with no short stock and should let the calls expire without exercising so as not to have a long delta position after expiration. If the puts are not assigned, they should exercise the calls to get delta flat. It’s also possible that only some of the puts will be assigned. Because they don’t know how many, if any, of the puts will be assigned, the market makers have pin risk. To avoid pin risk, market makers try to eliminate their position if they have conversions or reversals close to expiration. Boxes and Jelly Rolls There are two other uses of synthetic stock positions that form conventional strategies: boxes and rolls. Boxes When long synthetic stock is combined with short synthetic stock on the same underlying within the same expiration cycle but with a different strike price, the resulting position is known as a box. With a box, a trader is synthetically both long and short the stock. The two positions, for all intents and purposes, offset each other directionally. The risk of stock-price movement is almost entirely avoided. A study of the greeks shows that the delta is close to zero. Gamma, theta, vega, and rho are also negligible. Here’s an example of a 60–70 box for April options: Short 1 April 60 call Long 1 April 60 put Long 1 April 70 call Short 1 April 70 put In this example, the trader is synthetically short the 60-strike and, at the same time, synthetically long the 70-strike. Exhibit 6.9 shows the greeks. EXHIBIT 6.9 Box greeks. Aside from the risks associated with early exercise implications, this position is just about totally flat. The near-1.00 delta on the long synthetic stock struck at 60 is offset by the near-negative-1.00 delta of the short synthetic struck at 70. The tiny gammas and thetas of both combos are brought closer to zero when they are spread against each another. Vega is zero. And the bullish interest rate sensitivity of the long combo is nearly all offset by the bearish interest sensitivity of the short combo. The stock can move, time can pass, volatility and interest can change, and there will be very little effect on the trader’s P&(L). The question is: Why would someone trade a box? Market makers accumulate positions in the process of buying bids and selling offers. But they want to eliminate risk. Ideally, they try to be flat the strike —meaning have an equal number of calls and puts at each strike price, whether through a conversion or a reversal. Often, they have a conversion at one strike and a reversal at another. The stock positions for these cancel each other out and the trader is left with only the four option legs—that is, a box. They can eliminate pin risk on both strikes by trading the box as a single trade to close all four legs. Another reason for trading a box has to do with capital. Borrowing and Lending Money The first thing to consider is how this spread is priced. Let’s look at another example of a box, the October 50–60 box. Long 1 October 60 call Short 1 October 60 put Short 1 October 70 call Long 1 October 70 put A trader with this position is synthetically long the stock at $60 and short the stock at $70. That sounds like $10 in the bank. The question is: How much would a trader be willing to pay for the right to $10? And for how much would someone be willing to sell it? At face value, the obvious answer is that the equilibrium point is at $10, but there is one variable that must be factored in: time. In this example, assume that the October call has 90 days until expiration and the interest rate is 6 percent. A rational trader would not pay $10 today for the right to have $10 90 days from now. That would effectively be like loaning the $10 for 90 days and not receiving interest—A losing proposition! The trader on the other side of this box would be happy to enter into the spread for $10. He would have interest-free use of $10 for 90 days. That’s free money! Certainly, there is interest associated with the cost of carrying the $10. In this case, the interest would be $0.15. This $0.15 is discounted from the price of the $10 box. In fact, the combined net value of the options composing the box should be about 9.85—with differences due mainly to rounding and the early exercise possibility for American options. A trader buying this box—that is, buying the more ITM call and more ITM put—would expect to pay $0.15 below the difference between the strike prices. Fair value for this trade is $9.85. The seller of this box—the trader selling the meatier options and buying the cheaper ones—would concede up to $0.15 on the credit. Jelly Rolls A jelly roll, or simply a roll, is also a spread with four legs and a combination of two synthetic stock trades. In a box, the difference between the synthetics is the strike price; in a roll, it’s the contract month. Here’s an example: Long 1 April 50 call Short 1 April 50 put Short 1 May 50 call Long 1 May 50 put The options in this spread all share the same strike price, but they involve two different months—April and May. In this example, the trader is long synthetic stock in April and short synthetic stock in May. Like the conversion, reversal, and box, this is a mostly flat position. Delta, gamma, theta, vega, and even rho have only small effects on a jelly roll, but like the others, this spread serves a purpose. A trader with a conversion or reversal can roll the option legs of the position into a month with a later expiration. For example, a trader with an April 50 conversion in his inventory (short the 50 call, long the 50 put, long stock) can avoid pin risk as April expiration approaches by trading the roll from the above example. The long April 50 call and short April 50 put cancel out the current option portion of the conversion leaving only the stock. Selling the May 50 calls and buying the May 50 puts reestablishes the conversion a month farther out. Another reason for trading a roll has to do with interest. The roll in this example has positive exposure to rho in April and negative exposure to rho in May. Based on a trader’s expectations of future changes in interest rates, a position can be constructed to exploit opportunities in interest. Theoretical Value and the Interest Rate The main focus of the positions discussed in this chapter is fluctuations in the interest rate. But which interest rate? That of 30-year bonds? That of 10- or 5-year notes? Overnight rates? The federal funds rate? In the theoretical world, the answer to this question is not really that important. Professors simply point to the riskless rate and continue with their lessons. But when putting strategies like these into practice, choosing the right rate makes a big difference. To answer the question of which interest rate, we must consider exactly what the rates represent from the standpoint of an economist. Therefore, we must understand how an economist makes arguments—by making assumptions. Take the story of the priest, the physicist, and the economist stranded on a desert island with nothing to eat except a can of beans. The problem is, the can is sealed. In order to survive, they must figure out how to open the can. The priest decides he will pray for the can to be opened by means of a miracle. He prays for hours, but, alas, the can remains sealed tight. The physicist devises a complex system of wheels and pulleys to pop the top off the can. This crude machine unfortunately fails as well. After watching the lack of success of his fellow strandees, the economist announces that he has the solution: “Assume we have a can opener.” In the spirit of economists’ logic, let’s imagine for a moment a theoretical economic microcosm in which a trader has two trading accounts at the same firm. The assumptions here are that a trader can borrow 100 percent of a stock’s value to finance the purchase of the security and that there are no legal, moral, or other limitations on trading. In one account the trader is long 100 shares, fully leveraged. In the other, the trader is short 100 shares of the same stock, in which case the trader earns a short-stock rebate. In the long run, what is the net result of this trade? Most likely, this trade is a losing proposition for the trader, because the interest rate at which the trader borrows capital is likely to be higher than the interest rate earned on the short-stock proceeds. In this example, interest is the main consideration. But interest matters in the real world, too. Professional traders earn interest on proceeds from short stock and pay interest on funds borrowed. Interest rates may vary slightly from firm to firm and trader to trader. Interest rates are personal. The interest rate a trader should use when pricing options is specific to his or her situation. A trader with no position in a particular stock who is interested in trading a conversion should consider that he will be buying the stock. This implies borrowing funds to open the long stock position. The trader should price his options according to the rate he will pay to borrow funds. Conversely, a trader trading a reversal should consider the fact that he is shorting the stock and will receive interest at the rate of the short-stock rebate. This trader should price his options at the short-stock rate. A Call Is a Put The idea that “a put is a call, a call is a put” is an important one, indeed. It lays the foundation for more advanced spreading strategies. The concepts in this chapter in one way or another enter into every spread strategy that will be discussed in this book from here on out. Note 1 . Note, for simplicity, simple interest is used in the computation. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00016.html SCORE: 420.00 ================================================================================ CHAPTER 7 Rho Interest is one of the six inputs of an option-pricing model for American options. Although interest rates can remain constant for long periods, when interest rates do change, call and put values can be positively or negatively affected. Some options are more sensitive to changes in the interest rate than others. To the unaware trader, interest-rate changes can lead to unexpected profits or losses. But interest rates don’t have to be a wild-card risk. They’re one that experienced traders watch closely to avoid unnecessary risk and increase profitability. To monitor the effect of changes in the interest rate, it is important to understand the quiet greek—rho. Rho and Interest Rates Rho is a measurement of the sensitivity of an option’s value to a change in the interest rate. To understand how and why the interest rate is important to the value of an option, recall the formula for put-call parity stated in Chapter 6. Call + Strike − Interest = Put + Stock 1 From this formula, it’s clear that as the interest rate rises, put prices must fall and call prices must rise to keep put-call parity balanced. With a little algebra, the equation can be restated to better illustrate this concept: and If interest rates fall, and Rho helps quantify this relationship. Calls have positive rho, and puts have negative rho. For example, a call with a rho of +0.08 will gain $0.08 with each one-percentage-point rise in interest rates and fall $0.08 with each one-percentage-point fall in interest rates. A put with a rho of −0.08 will lose $0.08 with each one-point rise and gain $0.08 in value with a one-point fall. The effect of changes in the interest variable of put-call parity on call and put values is contingent on three factors: the strike price, the interest rate, and the number of days until expiration. Interest = Strike×Interest Rate×(Days to Expiration/365) 2 Interest, for our purposes, is a function of the strike price. The higher the strike price, the greater the interest and, consequently the more changes in the interest rate will affect the option. The higher the interest rate is, the higher the interest variable will be. Likewise, the more time to expiration, the greater the effect of interest. Rho measures an option’s sensitivity to the end results of these three influences. To understand how changes in interest affect option prices, consider a typical at-the-money (ATM) conversion on a non-dividend-paying stock. Short 1 May 50 call at 1.92 Long 1 May 50 put at 1.63 Long 100 shares at $50 With 43 days until expiration at a 5 percent interest rate, the interest on the 50 strike will be about $0.29. Put-call parity ensures that this $0.29 shows up in option prices. After rearranging the equation, we get In this example, both options are exactly ATM. There is no intrinsic value. Therefore, the difference between the extrinsic values of the call and the put must equal interest. If one option were in-the-money (ITM), the intrinsic value on the left side of the equation would be offset by the Stock − Strike on the right side. Still, it would be the difference in the time value of the call and put that equals the interest variable. This is shown by the fact that the synthetic stock portion of the conversion is short at $50.29 (call − put + strike). This is $0.29 above the stock price. The synthetic stock equals the Stock + Interest, or Certainly, if the interest rate were higher, the interest on the synthetic stock would be a higher number. At a 6 percent interest rate, the effective short price of the synthetic stock would be about $50.35. The call would be valued at about 1.95, and the put would be 1.60—a net of $0.35. A one-percentage-point rise in the interest rate causes the synthetic stock position to be revalued by $0.06—a $0.03 gain in the call value and a $0.03 decline in the put. Therefore, by definition, the call has a +0.03 rho and the put has a −0.03 rho. Rho and Time The time component of interest has a big impact on the magnitude of an option’s rho, because the greater the number of days until expiration, the greater the interest. Long-term options will be more sensitive to changes in the interest rate and, therefore, have a higher rho. Take a stock trading at about $120 per share. The July, October, and January ATM calls have the following rhos with the interest rate at 5.5 percent. Option Rho July (38-day) 120 calls +0.068 October (130-day) 120 calls +0.226 January (221-day) 120 calls +0.385 If interest rates rise 25 basis points, or a quarter of a percentage point, the July calls with only 38 days until expiration will gain very little: only $0.017 (0.068 × 0.25). The October 120 calls with 130 days until expiration gain more: $0.057 (0.226 × 0.25). The January calls that have 221 days until they expire make $0.096 theoretically (0.385 × 0.25). If all else is held constant, the more time to expiration, the higher the option’s rho, and therefore, the more interest will affect the option’s value. Considering Rho When Planning Trades Just having an opinion on a stock is only half the battle in options trading. Choosing the best way to trade a forecast can make all the difference to the success of a trade. Options give traders choices. And one of the choices a trader has is the month in which to trade. When trading LEAPS—Long-Term Equity AnticiPation Securities—delta, gamma, theta, and vega are important, as always, but rho is also a valuable part of the strategy. LEAPS Options buyers have time working against them. With each passing day, theta erodes the value of their assets. Buying a long-term option, or a LEAPS, helps combat erosion because long-term options can decay at a slower rate. In environments where there is interest rate uncertainty, however, LEAPS traders have to think about more than the rate of decay. Consider two traders: Jason and Susanne. Both are bullish on XYZ Corp. (XYZ), which is trading at $59.95 per share. Jason decides to buy a May 60 call at 1.60, and Susanne buys a LEAPS 60 call at 7.60. In this example, May options have 44 days until expiration, and the LEAPS have 639 days. Both of these trades are bullish, but the traders most likely had slightly different ideas about time, volatility, and interest rates when they decided which option to buy. Exhibit 7.1 compares XYZ short-term at-the-money calls with XYZ LEAPS ATM calls. EXHIBIT 7.1 XYZ short-term call vs. LEAPS call. To begin with, it appears that Susanne was allowing quite a bit of time for her forecast to be realized—almost two years. Jason, however, was looking for short-term price appreciation. Concerns about time decay may have been a motivation for Susanne to choose a long-term option—her theta of 0.01 is half Jason’s, which is 0.02. With only 44 days until expiration, the theta of Jason’s May call will begin to rise sharply as expiration draws near. But the trade-off of lower time decay is lower gamma. At the current stock price, Susanne has a higher delta. If the XYZ stock price rises $2, the gamma of the May call will cause Jason’s delta to creep higher than Susanne’s. At $62, the delta for the May 60s would be about 0.78, whereas the LEAPS 60 call delta is about 0.77. This disparity continues as XYZ moves higher. Perhaps Susanne had implied volatility (IV) on her mind as well as time decay. These long-term ATM LEAPS options have vegas more than three times the corresponding May’s. If IV for both the May and the LEAPS is at a yearly low, LEAPS might be a better buy. A one- or two-point rise in volatility if IV reverts to its normal level will benefit the LEAPS call much more than the May. Theta, delta, gamma, and vega are typical considerations with most trades. Because this option is long term, in addition to these typical considerations, Susanne needs to take a good hard look at rho. The LEAPS rho is significantly higher than that of its short-term counterpart. A one-percentage-point change in the interest rate will change Susanne’s P&(L) by $0.64—that’s about 8.5 percent of the value of her option—and she has nearly two years of exposure to interest rate fluctuations. Certainly, when the Federal Reserve Board has great concerns about growth or inflation, rates can rise or fall by more than one percentage point in one year’s time. It is important to understand that, like the other greeks, rho is a snapshot at a particular price, volatility level, interest rate, and moment in time. If interest rates were to fall by one percentage point today, it would cause Susanne’s call to decline in value by $0.64. If that rate drop occurred over the life of the option, it would have a much smaller effect. Why? Rate changes closer to expiration have less of an effect on option values. Assume that on the trade date, when the LEAPS has 639 days until expiration, interest rates fall by 25 basis points. The effect will be a decline in the value of the call of 0.16—one-fourth of the 0.638 rho. If the next rate cut occurs six months later, the rho of the LEAPS will be smaller, because it will have less time until expiration. In this case, after six months, the rho will be only 0.46. Another 25-basis-point drop will hurt the call by $0.115. After another six months, the option will have a 0.26 rho. Another quarter-point cut costs Susanne only $0.065. Any subsequent rate cuts in ensuing months will have almost no effect on the now short-term option value. Pricing in Interest Rate Moves In the same way that volatility can get priced in to an option’s value, so can the interest rate. When interest rates are expected to rise or fall, those expectations can be reflected in the prices of options. Say current interest rates are at 8 percent, but the Fed has announced that the economy is growing at too fast of a pace and that it may raise interest rates at the next Federal Open Market Committee meeting. Analysts expect more rate hikes to follow. The options with expiration dates falling after the date of the expected rate hikes will have higher interest rates priced in. In this situation, the higher interest rates in the longer-dated options will be evident when entering parameters into the model. Take options on Already Been Chewed Bubblegum Corp. (ABC). A trader, Kyle, enters parameters into the model for ABC options and notices that the prices don’t line up. To get the theoretical values of the ATM calls for all the expiration months to sit in the middle of the actual market values, Kyle may have to tinker with the interest rate inputs. Assume the following markets for the ATM 70-strike calls in ABC options: Calls Puts Aug 70 calls 1.75–1.85 1.30–1.40 Sep 70 calls 2.65–2.75 1.75–1.85 Dec 70 calls 4.70–4.90 2.35–2.45 Mar 70 calls 6.50–6.70 2.65–2.75 ABC is at $70 a share, has a 20 percent IV in all months, and pays no dividend. August expiration is one month away. Entering the known inputs for strike price, stock price, time to expiration, volatility, and dividend and using an 8 percent interest rate yields the following theoretical values for ABC options: The theoretical values, in bold type, are those that don’t line up in the middle of the call and put markets. These values are wrong. The call theoretical values are too low, and the put theoretical values are too high. They are the product of an interest rate that is too low being applied to the model. To generate values that are indicative of market prices, Kyle must change the interest input to the pricing model to reflect the market’s expectations of future interest rate changes. Using new values for the interest rate yields the following new values: After recalculating, the theoretical values line up in the middle of the call and put markets. Using higher interest rates for the longer expirations raises the call values and lowers the put values for these months. These interest rates were inferred from, or backed out of, the option-market prices by use of the option-pricing model. In practice, it may take some trial and error to find the correct interest values to use. In times of interest rate uncertainty, rho can be an important factor in determining which strategy to select. When rates are generally expected to continue to rise or fall over time, they are normally priced in to the options, as shown in the previous example. When there is no consensus among analysts and traders, the rates that are priced in may change as economic data are made available. This can cause a revision of option values. In long-term options that have higher rhos, this is a bona fide risk. Short-term options are a safer play in this environment. But as all traders know, risk also implies opportunity. Trading Rho While it’s possible to trade rho, most traders forgo this niche for more dynamic strategies with greater profitability. The effects of rho are often overshadowed by the more profound effects of the other greeks. The opportunity to profit from rho is outweighed by other risks. For most traders, rho is hardly ever even looked at. Because LEAPS have higher rho values than corresponding short-term options, it makes sense that these instruments would be appropriate for interest-rate plays. But even with LEAPS, rho exposure usually pales in comparison with that of delta, theta, and vega. It is not uncommon for the rho of a long-term option to be 5 to 8 percent of the option’s value. For example, Exhibit 7.2 shows a two-year LEAPS on a $70 stock with the following pricing-model inputs and outputs: EXHIBIT 7.2 Long 70-strike LEAPS call. The rho is +0.793, or about 5.8 percent of the call value. That means a 25-basis-point rise in rates contributes to only a 20-cent profit on the call. That’s only about 1.5 percent of the call’s value. On one hand, 1.5 percent is not a very big profit on a trade. On the other hand, if there are more rate rises at following Fed meetings, the trader can expect further gains on rho. Even if the trader is compelled to wait until the next Fed meeting to make another $0.20—or less, as rho will get smaller as time passes—from a second 25-basis-point rate increase, other influences will diminish rho’s significance. If over the six-week period between Fed meetings, the underlying declines by just $0.60, the $0.40 that the trader hoped to make on rho is wiped out by delta loss. With the share price $0.60 lower, the 0.760 delta costs the trade about $0.46. Furthermore, the passing of six weeks (42 days) will lead to a loss of about $0.55 from time decay because of the −0.013 theta. There is also the risk from the fat vegas associated with LEAPS. A 1.5 percent drop in implied volatility completely negates any hopes of rho profits. Aside from the possibility that delta, theta, and vega may get in the way of profits, the bid-ask spread with these long-term options tends to be wider than with their short-term counterparts. If the bid-ask spread is more than $0.40 wide, which is often the case with LEAPS, rho profits are canceled out by this cost of doing business. Buying the offer and selling the bid negative scalps away potential profits. With LEAPS, rho is always a concern. It will contribute to prosperity or peril and needs to be part of the trade plan from forecast to implementation. Buying or selling a LEAPS call or put, however, is not a practical way to speculate on interest rates. To take a position on interest rates in the options market, risk needs to be distilled down to rho. The other greeks need to be spread off. This is accomplished only through the conversions, reversals, and jelly rolls described in Chapter 6. However, the bid-ask can still be a hurdle to trading these strategies for non–market makers. Generally, rho is a greek that for most traders is important to understand but not practical to trade. Notes 1 . Please note, for simplification, dividends are not included. 2 . Note, for simplicity, simple interest is used in the calculation. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00017.html SCORE: 297.00 ================================================================================ CHAPTER 8 Dividends and Option Pricing Much of this book studies how to break down and trade certain components of option prices. This chapter examines the role of dividends in the pricing structure. There is no greek symbol that measures an option’s sensitivity to changes in the dividend. And in most cases, dividends are not “traded” by means of options in the same way that volatility, interest, and other option price influences are. Dividends do, though, affect option prices, and therefore a trader’s P&(L), so they deserve attention. There are some instances where dividends provide ample opportunity to the option trader, and there some instances where a change in dividend policy can have desirable, or undesirable, effects on the bottom line. Despite the fact that dividends do not technically involve greeks, they need to be monitored in much the same way as do delta, gamma, theta, vega, and rho. Dividend Basics Let’s start at the beginning. When a company decides to pay a dividend, there are four important dates the trader must be aware of: 1. Declaration date 2. Ex-dividend date 3. Record date 4. Payable date The first date chronologically is the declaration date. This date is when the company formally declares the dividend. It’s when the company lets its shareholders know when and in what amount it will pay the dividend. Active traders, however, may buy and sell the same stock over and over again. How does the corporation know exactly who collects the dividend when it is opening up its coffers? Dividends are paid to shareholders of record who are on the company’s books as owning the stock at the opening of business on another important date: the record date. Anyone long the stock at this moment is entitled to the dividend. Anyone with a short stock position on the opening bell on the record date is required to make payment in the amount of the dividend. Because the process of stock settlement takes time, the important date is actually not the record date. For all intents and purposes, the key date is two days before the record date. This is called the ex-dividend date, or the ex-date. Traders who have earned a dividend by holding a stock in their account on the morning of the ex-date have one more important date they need to know—the date they get paid. The date that the dividend is actually paid is called the payable date. The payable date can be a few weeks after the ex-date. Let’s walk through an example. ABC Corporation announces on March 21 (the declaration date) that it will pay a 25-cent dividend to shareholders of record on April 3 (the record date), payable on April 23 (the payable date). This means market participants wishing to receive the dividend must own the stock on the open on April 1 (the ex-date). In practice, they must buy the stock before the closing bell rings on March 31 in order to have it for the open the next day. This presents a potential quandary. If a trader only needs to have the stock on the open on the ex-date, why not buy the stock just before the close on the day before the ex-date, in this case March 31, and sell it the next morning after the open? Could this be an opportunity for riskless profit? Unfortunately, no. There are a couple of problems with that strategy. First, as far as the riskless part is concerned, stock prices can and often do change overnight. Yesterday’s close and today’s open can sometimes be significantly different. When they are, it is referred to as a gap open. Whenever a stock is held (long or short), there is risk. The second problem with this strategy to earn riskless profit is with the profit part. On the ex-date, the opening stock price reflects the dividend. Say ABC is trading at $50 at the close on March 31. If the market for the stock opens unchanged the next morning—that is, a zero net change on the day on—ABC will be trading at $49.75 ($50 minus the $0.25 dividend). Alas, the quest for riskless profit continues. Dividends and Option Pricing The preceding discussion demonstrated how dividends affect stock traders. There’s one problem: we’re option traders! Option holders or writers do not receive or pay dividends, but that doesn’t mean dividends aren’t relevant to the pricing of these securities. Observe the behavior of a conversion or a reversal before and after an ex-dividend date. Assuming the stock opens unchanged on the ex-date, the relationship of the price of the synthetic stock to the actual stock price will change. Let’s look at an example to explore why. At the close on the day before the ex-date of a stock paying a $0.25 dividend, a trader has an at-the-money (ATM) conversion. The stock is trading right at $50 per share. The 50 puts are worth 2.34, and the 50 calls are worth 2.48. Before the ex-date, the trader is Long 100 shares at $50 Long one 50 put at 2.34 Short one 50 call at 2.48 Here, the trader is long the stock at $50 and short stock synthetically at $50.14—50 + (2.48 − 2.34). The trader is synthetically short $0.14 over the price at which he is long the stock. Assume that the next morning the stock opens unchanged. Since this is the ex-date, that means the stock opens at $49.75—$0.25 lower than the previous day’s close. The theoretical values of the options will change very little. The options will be something like 2.32 for the put and 2.46 for the call. After the ex-date, the trader is Long 100 shares at $49.75 Long one 50 put at 2.32 Short one 50 call at 2.46 Each option is two cents lower. Why? The change in the option prices is due to theta. In this case, it’s $0.02 for each option. The synthetic stock is still short from an effective price of $50.14. With the stock at $49.75, the synthetic short price is now $0.39 over the stock. Incidentally, $0.39 is $0.25 more than the $0.14 difference before the ex-date. Did the trader who held the conversion overnight from before the ex-date to after it make or lose money? Neither. Before the ex-date, he had an asset worth $50 per share (the stock) and he shorted the asset synthetically at $50.14. After the ex-date, he still has assets totaling $50 per share—the stock at $49.75 plus the 0.25 dividend—and he is still synthetically short the stock at $50.14. Before the ex-date, the $0.14 difference between the synthetic and the stock is interest minus the dividend. After the ex-date, the $0.39 difference is all interest. Dividends and Early Exercise As the ex-date approaches, in-the-money (ITM) calls on equity options can often be found trading at parity, regardless of the dividend amount and regardless of how far off expiration is. This seems counterintuitive. What about interest? What about dividends? Normally, these come into play in option valuation. But option models designed for American options take the possibility of early exercise into account. It is possible to exercise American-style calls and exchange them for the underlying stock. This would give traders, now stockholders, the right to the dividend—a right for which they would not be eligible as call holders. Because of the impending dividend, the call becomes an exercise just before the ex-date. For this reason, the call can trade for parity before the ex-date. Let’s look at an example of a reversal on a $70 stock that pays a $0.40 dividend. The options in this reversal have 24 days until expiration, which makes the interest on the 60 strike roughly $0.20, given a 5 percent interest rate. The day before the ex-date, a trader has the following position at the stated prices: Short 100 shares at $70 Long one 60 call at 10.00 Short one 60 put at 0.05 To understand how American calls work just before the ex-date, it is helpful first to consider what happens if the trader holds the position until the ex-date. Making the assumption that the stock is unchanged on the ex-dividend date, it will open at $69.60, lower by the amount of the dividend—in this case, $0.40. The put, being so far out-of-the-money (OTM) as to have a negligible delta, will remain unchanged. But what about the call? With no dividend left in the stock, the put call-parity states In this case, Before the ex-date, the model valued the call at parity. Now it values the same call at $0.25 over parity (9.85 − [69.60 − 60]). Another way to look at this is that the time value of the call is now made up of the interest plus the put premium. Either way, that’s a gain of $0.25 on the call. That sounds good, but because the trader is short stock, if he hasn’t exercised, he will owe the $0.40 dividend—a net loss of $0.15. The new position will be Short 100 shares at $69.60 Owe $0.40 dividend Long one 60 call at 9.85 Short one 60 put at 0.05 At the end of the trading day before the ex-date, this trader must exercise the call to capture the dividend. By doing so, he closes two legs of the trade—the call and the stock. The $10 call premium is forfeited, the stock that is short at $70 is bought at $60 (from the call exercise) for a $10 profit. The transaction leads to neither a profit nor a loss. The purpose of exercising is to avoid the $0.15 loss ($0.25 gain in call time value minus the $0.40 loss in dividends owed). The other way the trader could achieve the same ends is to sell the long call and buy in the short stock. This is tactically undesirable because the trader may have to sell the bid in the call and buy the offer in the stock. Furthermore, when legging a trade in this manner, there is the risk of slippage. If the call is sold first, the stock can move before the trader has a chance to buy it at the necessary price. It is generally better and less risky to exercise the call rather than leg out of the trade. In this transaction, the trader begins with a fairly flat position (short stock/long synthetic stock) and ends with a short put that is significantly out-of-the-money. For all intents and purposes, exercising the call in this trade is like synthetically selling the put. But at what price? In this case, it’s $0.15. This again is the cost benefit of saving $0.40 by avoiding the dividend obligation versus the $0.25 gain in call time value. Exercising the call is effectively like selling the put at 0.15 in this example. If the dividend is lower or the interest is higher, it may not be worth it to the trader to exercise the call to capture the dividend. How do traders know if their calls should be exercised? The traders must do the math before each ex-dividend date in option classes they trade. The traders have to determine if the benefit from exercising—or the price at which the synthetic put is essentially being sold—is more or less than the price at which they can sell the put. The math used here is adopted from put-call parity: This shows the case where the traders can effectively synthetically sell the put (by exercising) for more than the current put value. Tactically, it’s appropriate to use the bid price for the put in this calculation since that is the price at which the put can be sold. In this case, the traders would be inclined to not exercise. It would be theoretically more beneficial to sell the put if the trader is so inclined. Here, the traders, from a valuation perspective, are indifferent as to whether or not to exercise. The question then is simply: do they want to sell the put at this price? Professionals and big retail traders who are long (ITM) calls—whether as part of a reversal, part of another type of spread, or because they are long the calls outright—must do this math the day before each ex-dividend date to maximize profits and minimize losses. Not exercising, or forgetting to exercise, can be a costly mistake. Traders who are short ITM dividend-paying calls, however, can reap the benefits of those sleeping on the job. It works both ways. Traders who are long stock and short calls at parity before the ex-date may stand to benefit if some of the calls do not get assigned. Any shares of long stock remaining on the ex-date will result in the traders receiving dividends. If the dividends that will be received are greater in value than the interest that will subsequently be paid on the long stock, the traders may stand reap an arbitrage profit because of long call holders’ forgetting to exercise. Dividend Plays The day before an ex-dividend date in a stock, option volume can be unusually high. Tens of thousands of contracts sometimes trade in names that usually have average daily volumes of only a couple thousand. This spike in volume often has nothing to do with the market’s opinion on direction after the dividend. The heavy trading has to do with the revaluation of the relationship of exercisable options to the underlying expected to occur on the ex-dividend date. Traders that are long ITM calls and short ITM calls at another strike just before an ex-dividend date have a potential liability and a potential benefit. The potential liability is that they can forget to exercise. This is a liability over which the traders have complete control. The potential benefit is that some of the short calls may not get assigned. If traders on the other side of the short calls (the longs) forget to exercise, the traders that are short the call make out by not having to pay the dividend on short stock. Professionals and big retail traders who have very low transaction costs will sometimes trade ITM call spreads during the afternoon before an ex-dividend date. This consists of buying one call and selling another call with a different strike price. Both calls in the dividend-play strategy are ITM and have corresponding puts with little or no value (to be sure, the put value is less than the dividend minus the interest). The traders trade the spreads, fairly indifferent as to whether they buy or sell the spreads, in hope of skating—or not getting assigned—on some of their short calls. The more they don’t get assigned the better. This usually occurs in options that have high open interest, meaning there are a lot of outstanding contracts already. The more contracts in existence, the better the possibility of someone forgetting to exercise. The greatest volume also tends to occur in the front month. Strange Deltas Because American calls become an exercise possibility when the ex-date is imminent, the deltas can sometimes look odd. When the calls are trading at parity, they have a 1.00 delta. They are a substitute for the stock. They, in fact, will be stock if and when they are exercised just before the ex-date. But if the puts still have some residual time value, they may also have a small delta, of 0.05 or perhaps more. In this unique scenario, the delta of the synthetic can be greater than +1.00 or less than −1.00. It is not uncommon to see the absolute values of the call and put deltas add up to 1.07 or 1.08. When the dividend comes out of the options model on the ex-date, synthetics go back to normal. The delta of the synthetic again approaches 1.00. Because of the out-of-whack deltas, delta-neutral traders need to take extra caution in their analytics when ex-dates are near. A little common sense should override what the computer spits out. Inputting Dividend Data into the Pricing Model Often dividend payments are regular and predictable. With many companies, the dividend remains constant quarter after quarter. Some corporations have a track record of incrementally increasing their dividends every year. Some companies pay dividends in a very irregular fashion, by paying special dividends that are often announced as a surprise to investors. In a truly capitalist society, there are no restrictions and no rules on when, whether, or how corporations pay dividends to their shareholders. Unpredictability of dividends, though, can create problems in options valuation. When a company has a constant, reasonably predictable dividend, there is not a lot of guesswork. Take Exelon Corp. (EXC). From November 2008 to the time of this writing, Exelon has paid a regular quarterly dividend of $0.525. During that period, a trader has needed simply to enter 0.525 into the pricing calculator for all expected future dividends to generate the theoretical value. Based on recent past performance, the trader could feel confident that the computed analytics were reasonably accurate. If the trader believed the company would continue its current dividend policy, there would be little options-related dividend risk—unless things changed. When there is uncertainty about when future dividends will be paid in what amounts, the level of dividend-related risk begins to increase. The more uncertainty, the more risk. Let’s examine an interesting case study: General Electric (GE). For a long time, GE was a company that has had a history of increasing its dividends at fairly regular intervals. In fact, there was more than a 30-year stretch in which GE increased its dividend every year. During most of the first decade of the 2000s, increases in GE’s dividend payments were around one to six cents and tended to occur toward the end of December, after December expiration. The dividends were paid four times per year but not exactly quarterly. For several years, the ex-dates were in February, June, September, and December. Option traders trading GE options had a pretty easy time estimating their future dividend streams, and consequently evaded valuation problems that could result from using wrong dividend data. Traders would simply adjust the dividend data in the model to match their expectations for predictably increasing future dividends in order to achieve an accurate theoretical value. Let’s look back at GE to see how a trader might have done this. The following shows dividend-history data for GE. Ex-Date Dividend * 12/27/02 $0.19 02/26/03 $0.19 06/26/03 $0.19 09/25/03 $0.19 12/29/03 $0.20 02/26/04 $0.20 06/24/04 $0.20 09/23/04 $0.20 12/22/04 $0.22 02/24/05 $0.22 06/23/05 $0.22 09/22/05 $0.22 12/22/05 $0.25 02/23/06 $0.25 06/22/06 $0.25 09/21/06 $0.25 12/21/06 $0.28 02/22/07 $0.28 06/21/07 $0.28 * These data are taken from the following Web page on GE’s web site: www.ge.com/investors/stock_info/dividend_history.html . At the end of 2006, GE raised its dividend from $0.25 to $0.28. A trader trading GE options at the beginning of 2007 would have logically anticipated the next increase to occur again in the following December unless there was reason to believe otherwise. Options expiring before this anticipated next dividend increase would have the $0.28 dividend priced into their values. Options expiring after December 2007 would have a higher dividend priced into them—possibly an additional three cents to 0.31 (which indeed it was). Calls would be adversely affected by this increase, and puts would be favorably affected. A typical trader would have anticipated those changes. The dividend data a trader pricing GE options would have entered into the model in January 2007 would have looked something like this. Ex-Date Dividend * 02/22/07 $0.28 06/21/07 $0.28 09/20/07 $0.28 12/20/07 $0.31 02/21/08 $0.31 06/19/08 $0.31 09/18/08 $0.31 * These data are taken from the following Web page on GE’s web site: www.ge.com/investors/stock_info/dividend_history.html . The trader would have entered the anticipated future dividend amount in conjunction with the anticipated ex-dividend date. This trader projection goes out to February 2008, which would aid in valuing options expiring in 2007 as well as the 2008 LEAPS. Because the declaration dates had yet to occur, one could not know with certainty when the dividends would be announced or in what amount. Certainly, there would be some estimation involved for both the dates and the amount. But traders would probably get it pretty close—close enough. Then, something particularly interesting happened. Instead of raising the dividend going into December 2008 as would be a normal pattern, GE kept it the same. As shown, the 12/24/08 ex-dated dividend remained $0.31. Ex-Date Dividend * 02/22/07 $0.28 06/21/07 $0.28 09/20/07 $0.28 12/20/07 $0.31 02/21/08 $0.31 06/19/08 $0.31 09/18/08 $0.31 12/24/08 $0.31 * These data are taken from the following Web page on GE’s web site: www.ge.com/investors/stock_info/dividend_history.html . The dividend stayed at $0.31 until the June 2009 dividend, which held another jolt for traders pricing options. Around this time, GE’s stock price had taken a beating. It fell from around $42 a share in the fall of 2007 ultimately to about $6 in March 2009. GE had its first dividend cut in more than three decades. The dividend with the ex-date of 06/18/09 was $0.10. 12/24/08 $0.31 02/19/09 $0.31 06/18/09 $0.10 09/17/09 $0.10 12/23/09 $0.10 02/25/10 $0.10 06/17/10 $0.10 09/16/10 $0.12 12/22/10 $0.14 02/24/11 $0.14 06/16/11 $0.15 09/15/11 $0.15 Though the company gave warnings in advance, the drastic dividend change had a significant impact on option prices. Call prices were helped by the dividend cut (or anticipated dividend cut) and put prices were hurt. The break in the pattern didn’t stop there. The dividend policy remained $0.10 for five quarters until it rose to $0.12 in September 2010, then to $0.14 in December 2010, then to $0.15 in June 2011. These irregular changes in the historically predictable dividend policy made it tougher for traders to attain accurate valuations. If the incremental changes were bigger, the problem would have been even greater. Good and Bad Dates with Models Using an incorrect date for the ex-date in option pricing can lead to unfavorable results. If the ex-dividend date is not known because it has yet to be declared, it must be estimated and adjusted as need be after it is formally announced. Traders note past dividend history and estimate the expected dividend stream accordingly. Once the dividend is declared, the ex-date is known and can be entered properly into the pricing model. Not executing due diligence to find correct known ex-dates can lead to trouble. Using a bad date in the model can yield dubious theoretical values that can be misleading or worse—especially around the expiration. Say a call is trading at 2.30 the day before the ex-date of a $0.25 dividend, which happens to be thirty days before expiration. The next day, of course, the stock may have moved higher or lower. Assume for illustrative purposes, to compare apples to apples as it were, that the stock is trading at the same price—in this case, $76. If the trader is using the correct date in the model, the option value will adjust to take into account the effect of the dividend expiring, or reaching its ex-date, when the number of days to expiration left changes from 30 to 29. The call trading postdividend will be worth more relative to the same stock price. If the dividend date the trader is using in the model is wrong, say one day later than it should be, the dividend will still be an input of the theoretical value. The calculated value will be too low. It will be wrong. Exhibit 8.1 compares the values of a 30-day call on the ex-date given the right and the wrong dividend. EXHIBIT 8.1 Comparison of 30-day call values At the same stock price of $76 per share, the call is worth $0.13 more after the dividend is taken out of the valuation. Barring any changes in implied volatility (IV) or the interest rate, the market prices of the options should reflect this change. A trader using an ex-date in the model that is farther in the future than the actual ex-date will still have the dividend as part of the generated theoretical value. With the ex-date just one day later, the call would be worth 2.27. The difference in option value is due to the effect of theta—in this case, $0.03. With a bad date, the value of 2.27 would likely be significantly below market price, causing the market value of the option to look more expensive than it actually is. If the trader did not know the date was wrong, he would need to raise IV to make the theoretical value match the market. This option has a vega of 0.08, which translates into a difference of about two IV points for the theoretical values 2.43 and 2.27. The trader would perceive the call to be trading at an IV two points higher than the market indicates. Dividend Size It’s not just the date but also the size of the dividend that matters. When companies change the amount of the dividend, options prices follow in step. In 2004, when Microsoft (MSFT) paid a special dividend of $3 per share, there were unexpected winners and losers in the Microsoft options. Traders who were long calls or short puts were adversely affected by this change in dividend policy. Traders with short calls or long puts benefited. With long-term options, even less anomalous changes in the size of the dividend can have dramatic effects on options values. Let’s study an example of how an unexpected rise in the quarterly dividend of a stock affects a long call position. Extremely Yellow Zebra Corp. (XYZ) has been paying a quarterly dividend of $0.10. After a steady rise in stock price to $61 per share, XYZ declares a dividend payment of $0.50. It is expected that the company will continue to pay $0.50 per quarter. A trader, James, owns the 528-day 60-strike calls, which were trading at 9.80 before the dividend increase was announced. Exhibit 8.2 compares the values of the long-term call using a $0.10 quarterly dividend and using a $0.50 quarterly dividend. EXHIBIT 8.2 Effect of change in quarterly dividend on call value. This $0.40 dividend increase will have a big effect on James’s calls. With 528 days until expiration, there will be six dividends involved. Because James is long the calls, he loses 1.52 per option. If, however, he were short the calls, 1.52 would be his profit on each option. Put traders are affected as well. Another trader, Marty, is long the 60-strike XYZ puts. Before the dividend announcement, Marty was running his values with a $0.10 dividend, giving his puts a value of 5.42. Exhibit 8.3 compares the values of the puts with a $0.10 quarterly dividend and with a $0.50 quarterly dividend. EXHIBIT 8.3 Effect of change in quarterly dividend on put value. When the dividend increase is announced, Marty will benefit. His puts will rise because of the higher dividend by $0.66 (all other parameters held constant). His long-term puts with six quarters of future expected dividends will benefit more than short-term XYZ puts of the same strike would. Of course, if he were short the puts, he would lose this amount. The dividend inputs to a pricing model are best guesses until the dates and amounts are announced by the company. How does one find dividend information? Regularly monitoring the news and press releases on the companies one trades is a good way to stay up to date on dividend information, as well as other company news. Dividend announcements are widely disseminated by the major news services. Most companies also have an investor-relations phone number and section on their web sites where dividend information can be found. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00019.html SCORE: 1565.00 ================================================================================ CHAPTER 9 Vertical Spreads Risk—it is the focal point around which all trading revolves. It may seem as if profit should be occupying this seat, as most important to trading options, but without risk, there would be no profit! As traders, we must always look for ways to mitigate, eliminate, preempt, and simply avoid as much risk as possible in our pursuit of success without diluting opportunity. Risk must be controlled. Trading vertical spreads takes us one step further in this quest. The basic strategies discussed in Chapters 4 and 5 have strengths when compared with pure linear trading in the equity markets. But they have weaknesses, too. Consider the covered call, one of the most popular option strategies. A covered call is best used as an augmentation to an investment plan. It can be used to generate income on an investment holding, as an entrance strategy into a stock, or as an exit strategy out of a stock. But from a trading perspective, one can often find better ways to trade such a forecast. If the forecast on a stock is neutral to moderately bullish, accepting the risk of stock ownership is often unwise. There is always the chance that the stock could collapse. In many cases, this is an unreasonable risk to assume. To some extent, we can make the same case for the long call, short put, naked call, and the like. In certain scenarios, each of these basic strategies is accompanied with unwanted risks that serve no beneficial purpose to the trader but can potentially cause harm. In many situations, a vertical spread is a better alternative to these basic spreads. Vertical spreads allow a trader to limit potential directional risk, limit theta and vega risk, free up margin, and generally manage capital more efficiently. Vertical Spreads Vertical spreads involve buying one option and selling another. Both are on the same underlying and expire the same month, and both are either calls or puts. The difference is in the strike prices of the two options. One is higher than the other, hence the name vertical spread . There are four vertical spreads: bull call spread, bear call spread, bear put spread, and bull put spread. These four spreads can be sliced and diced into categories a number of ways: call spreads and put spreads, bull spreads and bear spreads, debit spreads and credit spreads. There is overlap among the four verticals in how and when they are used. The end of this chapter will discuss how the spreads are interrelated. Bull Call Spread A bull call spread is a long call combined with a short call that has a higher strike price. Both calls are on the same underlying and share the same expiration month. Because the purchased call has a lower strike price, it costs more than the call being sold. Establishing the trade results in a debit to the trader’s account. Because of this debit, it’s called a debit spread. Below is an example of a bull call spread on Apple Inc. (AAPL): In this example, Apple is trading around $391. With 40 days until February expiration, the trader buys the 395–405 call spread for a net debit of $4.40, or $440 in actual cash. Or one could simply say the trader paid $4.40 for the 395–405 call. Consider the possible outcomes if the spread is held until expiration. Exhibit 9.1 shows an at-expiration diagram of the bull call spread. EXHIBIT 9.1 AAPL bull call spread. Before discussing the greeks, consider the bull call spread from an at-expiration perspective. Unlike the long call, which has two possible outcomes at expiration—above or below the strike—this spread has three possibilities: below both strikes, between the strikes, or above both strikes. In this example, if Apple is below $395 at expiration, both calls expire worthless. The rights and obligations of the options are gone, as is the cash spent on the trade. In this case, the entire debit of $4.40 is lost. If Apple is between the strikes at expiration, the 405-strike call expires worthless. The trader is long stock at an effective price of $399.40. This is the $395-strike price at which the stock would be purchased if the call is exercised, plus the $4.40 premium spent on the spread. The break-even price of the trade is $399.40. If Apple is above $399.40 at expiration, the trade is profitable; below $399.40, it is a loser. The aptly named bull call spread requires the stock to rise to reach its profit potential. But unlike an outright long call, profits are capped with the spread. If Apple is above $405 at expiration, both calls are in-the-money (ITM). If the 395-strike calls are exercised, the trader buys 100 shares of Apple at $395 and these shares, in turn, would be sold at $405 when the 405-strike calls are assigned, for a $10 gain per share. Subtract from that $10 the $4.40 debit spent on the trade and the net profit is $5.60 per share. There are some other differences between the 395–405 call spread and the outright purchase of the 395 call. The absolute risk is lower. To buy the 395-strike call costs 14.60, versus 4.40 for the spread—a big difference. Because the debit is lower, the margin for the spread is lower at most option-friendly brokers, as well. If we dig a little deeper, we find some other differences between the bull call spread and the outright call. Long options are haunted by the specter of time. Because the spread involves both a long and a short option, the time-decay risk is lower than that associated with owning an option outright. Implied volatility (IV) risk is lower, too. Exhibit 9.2 compares the greeks of the long 395 call with those of the 395–405 call spread. EXHIBIT 9.2 Apple call versus bull call spread (Apple @ $391). 395 Call 395–405 Call Delta 0.484 0.100 Gamma 0.0097 0.0001 Theta −0.208 −0.014 Vega 0.513 0.020 The positive deltas indicate that both positions are bullish, but the outright call has a higher delta. Some of the 395 call’s directional sensitivity is lost when the 405 call is sold to make a spread. The negative delta of the 405 call somewhat offsets the positive delta of the 395 call. The spread delta is only about 20 percent of the outright call’s delta. But for a trader wanting to focus on trading direction, the smaller delta can be a small sacrifice for the benefit of significantly reduced theta and vega. Theta spread’s risk is about 7 percent that of the outright. The spread’s vega risk is also less than 4 percent that of the outright 395 call. With the bull call spread, a trader can spread off much of the exposure to the unwanted risks and maintain a disproportionately higher greeks in the wanted exposure (delta). These relationships change as the underlying moves higher. Remember, at-the-money (ATM) options have the greatest sensitivity to theta and vega. With Apple sitting at around the long strike, gamma and vega have their greatest positive value, and theta has its most negative value. Exhibit 9.3 shows the spread greeks given other underlying prices. EXHIBIT 9.3 AAPL 395–405 bull call spread. As the stock moves higher toward the 405 strike, the 395 call begins to move away from being at-the-money, and the 405 call moves toward being at-the-money. The at-the-money is the dominant strike when it comes to the characteristics of the spread greeks. Note the greeks position when the underlying is directly between the two strike prices: The long call has ceased to be the dominant influence on these metrics. Both calls influence the analytics pretty evenly. The time-decay risk has been entirely spread off. The volatility risk is mostly spread off. Gamma remains a minimal concern. When the greeks of the two calls balance each other, the result is a directional play. As AAPL continues to move closer to the 405-strike, it becomes the at-the-money option, with the dominant greeks. The gamma, theta, and vega of the 405 call outweigh those of the ITM 395 call. Vega is more negative. Positive theta now benefits the trade. The net gamma of the spread has turned negative. Because of the negative gamma, the delta has become smaller than it was when the stock was at $400. This means that the benefit of subsequent upward moves in the stock begins to wane. Recall that there is a maximum profit threshold with a vertical spread. As the stock rises beyond $405, negative gamma makes the delta smaller and time decay becomes less beneficial. But at this point, the delta has done its work for the trader who bought this spread when the stock was trading around $395. The average delta on a move in the stock from $395 to $405 is about 0.10 in this case. When the stock is at the 405 strike, the characteristics of the trade are much different than they are when the stock is at the 395 strike. Instead of needing movement upward in the direction of the delta to combat the time decay of the long calls, the position can now sit tight at the short strike and reap the benefits of option decay. The key with this spread, and with all vertical spreads, is that the stock needs to move in the direction of the delta to the short strike. Strengths and Limitations There are many instances when a bull call spread is superior to other bullish strategies, such as a long call, and there are times when it isn’t. Traders must consider both price and time. A bull call spread will always be cheaper than the outright call purchase. That’s because the cost of the long-call portion of the spread is partially offset by the premium of the higher-strike short call. Spending less for the same exposure is always a better choice, but the exposure of the vertical is not exactly the same as that of the long call. The most obvious trade-off is the fact that profit is limited. For smaller moves—up to the price of the short strike—vertical spreads tend to be better trades than outright call purchases. Beyond the strike? Not so much. But time is a trade-off, too. There have been countless times that I have talked with new traders who bought a call because they thought the stock was going up. They were right and still lost money. As the adage goes, timing is everything. The more time that passes, the more advantageous the lower-theta vertical spread becomes. When held until expiration, a vertical spread can be a better trade than an outright call in terms of percentage profit. In the previous example, when Apple is at $391 with 40 days until expiration, the 395 call is worth 14.60 and the spread is worth 4.40. If Apple were to rise to be trading at $405 at expiration, the call rises to be worth 10, for a loss of 4.60 on the 14.60 debit paid. The spread also is worth 10. It yields a gain of about 127 percent on the initial $4.40 per share debit. But look at this same trade if the move occurs before expiration. If Apple rallies to $405 after only a couple weeks, the outcome is much different. With four weeks still left until expiration, the 395 call is worth 19.85 with the underlying at $405. That’s a 36 percent gain on the 14.60. The spread is worth 5.70. That’s a 30 percent gain. The vertical spread must be held until expiration to reap the full benefits, which it accomplishes through erosion of the short option. The long-call-only play (with a significantly larger negative theta) is punished severely by time passing. The long call benefits more from a quick move in the underlying. And of course, if the stock were to rise to a price greater than $405, in a short amount of time—the best of both worlds for the outright call—the outright long 395 call would be emphatically superior to the spread. Bear Call Spread The next type of vertical spread is called a bear call spread . A bear call spread is a short call combined with a long call that has a higher strike price. Both calls are on the same underlying and share the same expiration month. In this case, the call being sold is the option of higher value. This call spread results in a net credit when the trade is put on and, therefore, is called a credit spread. The bull call spread and the bear call spread are two sides of the same coin. The difference is that with the bull call spread, one is buying the call spread, and with the bear call spread, one is selling the call spread. An example of a bear call spread can be shown using the same trade used earlier. Here we are selling one AAPL February (40-day) 395 call at 14.60 and buying the 405 call at 10.20. We are selling the 395–405 call at $4.40 per share, or $440. Exhibit 9.4 is an at-expiration diagram of the trade. EXHIBIT 9.4 Apple bear call spread. The same three at-expiration outcomes are possible here as with the bull call spread: the stock can be above both strikes, between both strikes, or below both strikes. If the stock is below both strikes at expiration, both calls will expire worthless. The rights and obligations cease to exist. In this case, the entire credit of $440 is profit. If AAPL is between the two strike prices at expiration, the 395-strike call will be in-the-money. The short call will get assigned and result in a short stock position at expiration. The break-even price falls at $399.40—the short strike plus the $4.40 net premium. This is the price at which the stock will effectively be sold if assignment occurs. If Apple is above both strikes at expiration, it means both calls are in-the-money. Stock is sold at $395 because of assignment and bought back at $405 through exercise. This leads to a loss of $10 per share on the negative scalp. Factoring in the $4.40-per-share credit makes the net loss only $5.60 per share with AAPL above $405 at February expiration. Just as the at-expiration diagram is the same but reversed, the greeks for this call spread will be similar to those in the bull call spread example except for the positive and negative signs. See Exhibit 9.5 . EXHIBIT 9.5 Apple 395–405 bear call spread. A credit spread is commonly traded as an income-generating strategy. The idea is simple: sell the option closer-to-the-money and buy the more out-of-the-money (OTM) option—that is, sell volatility—and profit from nonmovement (above a certain point). In this example, with Apple at $391, a neutral to slightly bearish trader would think about selling this spread at 4.40 in hopes that the stock will remain below $395 until expiration. The best-case scenario is that the stock is below $395 at expiration and both options expire, resulting in a $4.40-per-share profit. The strategy profits as long as Apple is under its break-even price, $399.40, at expiration. But this is not so much a bearish strategy as it is a nonbullish strategy. The maximum gain with a credit spread is the premium received, in this case $4.40 per share. Traders who thought AAPL was going to decline sharply would short it or buy a put. If they thought it would rise sharply, they’d use another strategy. From a greek perspective, when the trade is executed it’s very close to its highest theta price point—the 395 short strike price. This position theoretically collects $0.90 a day with Apple at around $395. As time passes, that theta rises. The key is that the stock remains at around $395 until the short option is just about worthless. The name of the game is sit and wait. Although the delta is negative, traders trading this spread to generate income want the spread to expire worthless so they can pocket the $4.40 per share. If Apple declines, profits will be made on delta, and theta profits will be foregone later. All that matters is the break-even point. Essentially, the idea is to sell a naked call with a maximum potential loss. Sell the 395s and buy the 405s for protection. If the underlying decreases enough in the short term and significant profits from delta materialize, it is logical to consider closing the spread early. But it often makes more sense to close part of the spread. Consider that the 405-strike call is farther out-of-the-money and will lose its value before the 395 call. Say that after two weeks a big downward move occurs. Apple is trading at $325 a share; the 405s are 0.05 bid at 0.10, and the 395s are 0.50 bid at 0.55. At this point, the lion’s share of the profits can be taken early. A trader can do so by closing only the 395 calls. Closing the 395s to eliminate the risk of negative delta and gamma makes sense. But does it make sense to close the 405s for 0.05? Usually not. Recouping this residual value accomplishes little. It makes more sense to leave them in your position in case the stock rebounds. If the stock proves it can move down $70; it can certainly move up $70. Because the majority of the profits were taken on the 395 calls, holding on to the 405s is like getting paid to own calls. In scenarios where a big move occurs and most of the profits can be taken early, it’s often best to hold the long calls, just in case. It’s a win-win situation. Credit and Debit Spread Similarities The credit call spread and the debit call spread appear to be exactly opposite in every respect. Many novice traders perceive credit spreads to be fundamentally different from debit spreads. That is not necessarily so. Closer study reveals that these two are not so different after all. What if Apple’s stock price was higher when the trade was put on? What if the stock was at $405? First, the spread would have had more value. The 395 and 405 calls would both be worth more. A trader could have sold the spread for a $5.65-per-share credit. The at-expiration diagram would look almost the same. See Exhibit 9.6 . EXHIBIT 9.6 Apple bear call spread initiated with Apple at $405. Because the net premium is much higher in this example, the maximum gain is more—it is $5.65 per share. The breakeven is $400.65. The price points on the at-expiration diagram, however, have nothing to do with the greeks. The analytics from Exhibit 9.5 are the same either way. The motivation for a trader selling this call spread, which has both options in-the-money, is different from that for the typical income generator. When the spread is sold in this context, the trader is buying volatility. Long gamma, long vega, negative theta. The trader here has a trade more like the one in the bull call spread example—except that instead of needing a rally, the trader needs a rout. The only difference is that the bull call spread has a bullish delta, and the bear call spread has a bearish delta. Bear Put Spread There is another way to take a bearish stance with vertical spreads: the bear put spread. A bear put spread is a long put plus a short put that has a lower strike price. Both puts are on the same underlying and share the same expiration month. This spread, however, is a debit spread because the more expensive option is being purchased. Imagine that a stock has had a good run-up in price. The chart shows a steady march higher over the past couple of months. A study of technical analysis, though, shows that the run-up may be pausing for breath. An oscillator, such as slow stochastics, in combination with the relative strength index (RSI), indicates that the stock is overbought. At the same time, the average directional movement index (ADX) confirms that the uptrend is slowing. For traders looking for a small pullback, a bear put spread can be an excellent strategy. The goal is to see the stock drift down to the short strike. So, like the other members of the vertical spread family, strike selection is important. Let’s look at an example of ExxonMobil (XOM). After the stock has rallied over a two-month period to $80.55, a trader believes there will be a short-term temporary pullback to $75. Instead of buying the June 80 puts for 1.75, the trader can buy the 75–80 put spread of the same month for 1.30 because the 75 put can be sold for 0.45. 1 In this example, the June put has 40 days until expiration. Exhibit 9.7 illustrates the payout at expiration. EXHIBIT 9.7 ExxonMobil bear put spread. If the trader is wrong and ExxonMobil is still above 80 at expiry, both puts expire and the 1.30 premium is lost. If ExxonMobil is between the two strikes, the 80 puts are ITM, resulting in an exercise, and the 75 puts are OTM and expire. The net effect is short stock at an effective price of $78.70. The effective sale price is found by taking the price at which the short stock is established when the puts are exercised—$80—minus the net 1.30 paid for the spread. This is the spread’s breakeven at expiration. If the trader is right and ExxonMobil is below both strikes at expiration, both puts are ITM, and the result is a 3.70 profit and no position. Why a 3.70 profit? The 80 puts are exercised, making the trader short at $80, and the 75 puts are assigned, so the short is bought back at $75 for a positive stock scalp of $5. Including the 1.30 debit for the spread in the profit and loss (P&(L)), the net profit is $3.70 per share when the stock is below both strikes at expiration. This is a bearish trade. But is the bear put spread necessarily a better trade than buying an outright ATM put? No. The at-expiration diagram makes this clear. Profits are limited to $3.70 per share. This is an important difference. But because in this particular example, the trader expects the stock to retrace only to around $75, the benefits of lower cost and lower theta and vega risk can be well worth the trade-off of limited profit. The trader’s objectives are met more efficiently by buying the spread. The goal is to profit from the delta move down from $80 to $75. Exhibit 9.8 shows the differences between the greeks of the outright put and the spread when the trade is put on with ExxonMobil at $80.55. EXHIBIT 9.8 ExxonMobil put vs. bear put spread (ExxonMobil @ $80.55). 80 Put 75–80 Put Delta −0.445 −0.300 Gamma +0.080 +0.041 Theta −0.018 −0.006 Vega +0.110 +0.046 As in the call-spread examples discussed previously, the spread delta is smaller than the outright put’s. It appears ironic that the spread with the smaller delta is a better trade in this situation, considering that the intent is to profit from direction. But it is the relative differences in the greeks besides delta that make the spread worthwhile given the trader’s goal. Gamma, theta, and vega are proportionately much smaller than the delta in the spread than in the outright put. While the spread’s delta is two thirds that of the put, its gamma is half, its theta one third, and its vega around 42 percent of the put’s. Retracements such as the one called for by the trader in this example can happen fast, sometimes over the course of a week or two. It’s not necessarily bad if this move occurs quickly. If ExxonMobil drops by $5 right away, the short delta will make the position profitable. Exhibit 9.9 shows how the spread position changes as the stock declines from $80 to $75. EXHIBIT 9.9 75–80 bear put spread as ExxonMobil declines. The delta of this trade remains negative throughout the stock’s descent to $75. Assuming the $5 drop occurs in one day, a delta averaging around −0.36 means about a 1.80 profit, or $180 per spread, for the $5 move (0.36 times $5 times 100). This is still a far cry from the spread’s $3.70 potential profit. Although the stock is at $75, the maximum profit potential has yet to be reached, and it won’t be until expiration. How does the rest of the profit materialize? Time decay. The price the trader wants the stock to reach is $75, but the assumption here is that the move happens very fast. The trade went from being a long-volatility play—long gamma and vega—to a short-vol play: short gamma and vega. The trader wanted movement when the stock was at $80 and wants no movement when the stock is at $75. When the trade changes characteristics by moving from one strike to another, the trader has to reconsider the stock’s outlook. The question is: if I didn’t have this position on, would I want it now? The trader has a choice to make: take the $180 profit—which represents a 138 percent profit on the 1.30 debit—or wait for theta to do its thing. The trader looking for a retracement would likely be inclined to take a profit on the trade. Nobody ever went broke taking a profit. But if the trader thinks the stock will sit tight for the remaining time until expiration, he will be happy with this income-generating position. Although the trade in the last, overly simplistic example did not reap its full at-expiration potential, it was by no means a bad trade. Holding the spread until expiration is not likely to be part of a trader’s plan. Buying the 80 put outright may be a better play if the trader is expecting a fast move. It would have a bigger delta than the spread. Debit and credit spreads can be used as either income generators or as delta plays. When they’re used as delta plays, however, time must be factored in. Bull Put Spread The last of the four vertical spreads is a bull put spread. A bull put spread is a short put with one strike and a long put with a lower strike. Both puts are on the same underlying and in the same expiration cycle. A bull put spread is a credit spread because the more expensive option is being sold, resulting in a net credit when the position is established. Using the same options as in the bear put example: With ExxonMobil at $80.55, the June 80 puts are sold for 1.75 and the June 75 puts are bought at 0.45. The trade is done for a credit of 1.30. Exhibit 9.10 shows the payout of this spread if it is held until expiration. EXHIBIT 9.10 ExxonMobil bull put spread. The sale of this spread generates a 1.30 net credit, which is represented by the maximum profit to the right of the 80 strike. With ExxonMobil above $80 per share at expiration, both options expire OTM and the premium is all profit. Between the two strike prices, the 80 put expires in the money. If the ITM put is still held at expiration, it will be assigned. Upon assignment, the put becomes long stock, profiting with each tick higher up to $80, or losing with each tick lower to $75. If the 80 put is assigned, the effective price of the long stock will be $78.70. The assignment will “hit your sheets” as a buy at $80, but the 1.30 credit lowers the effective net cost to $78.70. If the stock is below $75 at option expiration, both puts will be ITM. This is the worst case scenario, because the higher-struck put was sold. At expiration, the 80 puts would be assigned, the 75 puts exercised. That’s a negative scalp of $5 on the resulting stock. The initial credit lessens the pain by 1.30. The maximum possible loss with ExxonMobil below both strikes at expiration is $3.70 per spread. The spread in this example is the flip side of the bear put spread of the previous example. Instead of buying the spread, as with the bear put, the spread in this case is sold. Exhibit 9.11 shows the analytics for the bull put spread. EXHIBIT 9.11 Greeks for ExxonMobil 75–80 bull put spread. Instead of having a short delta, as with the bear spread, the bull spread is long delta. There is negative theta with positive gamma and vega as XOM approaches the long strike—the 75s, in this case. There is also positive theta with negative gamma and vega around the short strike—the 80s. Exhibit 9.11 shows the characteristics that define the vertical spread. If one didn’t know which particular options were being traded here, this could almost be a table of greeks for either a 75–80 bull put spread or a 75–80 bull call spread. Like the other three verticals, this spread can be a delta play or a theta play. A bullish trader may sell the spread if both puts are in-the-money. Imagine that XOM is trading at around $75. The spread will have a positive 0.364 delta, positive gamma, and negative theta. The spread as a whole is a decaying asset. It needs the underlying to rally to combat time decay. A bullish trader may also sell this spread if XOM is between the two strikes. In this case, with XOM at, say, $77, the delta is +0.388, and all other greeks are negligible. At this particular price point in the underlying, the trader has almost pure leveraged delta exposure. But this trade would be positioned for only a small move, not much above $80. A speculator wanting to trade direction for a small move while eliminating theta and vega risks achieves her objectives very well with a vertical spread. A bullish-to-neutral trader would be inclined to sell this spread if ExxonMobil were around $80 or higher. Day by day, the 1.30 premium would start to come in. With 40 days until expiration, theta would be small, only 0.004. But if the stock remained at $80, this ATM put would begin decaying faster and faster. The objective of trading this spread for a neutral trader is selling future realized volatility—selling gamma to earn theta. A trader can also trade a vertical spread to profit from IV. Verticals and Volatility The IV component of a vertical spread, although small compared with that of an outright call or put, is still important—especially for large traders with low margin and low commissions who can capitalize on small price changes efficiently. Whether it’s a call spread or a put spread, a credit spread or a debit spread, if the underlying is at the short option’s strike, the spread will have a net negative vega. If the underlying is at the long option’s strike, the spread will have positive vega. Because of this characteristic, there are three possible volatility plays with vertical spreads: speculating on IV changes when the underlying remains constant, profiting from IV changes resulting from movement of the underlying, and special volatility situations. Vertical spreads offer a limited-risk way to speculate on volatility changes when the underlying remains fairly constant. But when the intent of a vertical spread is to benefit from vega, one must always consider the delta—it’s the bigger risk. Chapter 13 discusses ways to manage this risk by hedging with stock, a strategy called delta-neutral trading. Non-delta-neutral traders may speculate on vol with vertical spreads by assuming some delta risk. Traders whose forecast is vega bearish will sell the option with the strike closest to where the underlying is trading—that is, the ATM option—and buy an OTM strike. Traders would lean with their directional bias by choosing either a call spread or a put spread. As risk managers, the traders balance the volatility stance being taken against the additional risk of delta. Again, in this scenario, delta can hurt much more than help. In the ExxonMobil bull put spread example, the trader would sell the 80-strike put if ExxonMobil were around $80 a share. In this case, if the stock didn’t move as time passed, theta would benefit from historical volatility being’s low—that is, from little stock movement. At first, the benefit would be only 0.004 per day, speeding up as expiration nears. And if implied volatility decreased, the trader would profit 0.04 for every 1 percent decline in IV. Small directional moves upward help a little. But in the long run, those profits are leveled off by the fact that theta gets smaller as the stock moves higher above $80—more profit on direction, less on time. For the delta player, bull call spreads and bull put spreads have a potential added benefit that stems from the fact that IV tends to decrease as stocks rise and increase when stocks fall. This offers additional opportunity to the bull spread player. With the bull call spread or the bull put spread, the trader gains on positive delta with a rally. Once the underlying comes close to the short option’s strike, vega is negative. If IV declines, as might be anticipated, there is a further benefit of vega profits on top of delta profits. If the underlying declines, the trader loses on delta. But the pain can potentially be slightly lessened by vega profits. Vega will get positive as the underlying approaches the long strike, which will benefit from the firming of IV that often occurs when the stock drops. But this dual benefit is paid for in the volatility skew. In most stocks or indexes, the lower strikes—the ones being bought in a bull spread—have higher IVs than the higher strikes, which are being sold. Then there are special market situations in which vertical spreads that benefit from volatility changes can be traded. Traders can trade vertical spreads to strategically position themselves for an expected volatility change. One example of such a situation is when a stock is rumored to be a takeover target. A natural instinct is to consider buying calls as an inexpensive speculation on a jump in price if the takeover is announced. Unfortunately, the IV of the call is often already bid up by others with the same idea who were quicker on the draw. Buying a call spread consisting of a long ITM call and a short OTM call can eliminate immediate vega risk and still provide wanted directional exposure. Certainly, with this type of trade, the trader risks being wrong in terms of direction, time, and volatility. If and when a takeover bid is announced, it will likely be for a specific price. In this event, the stock price is unlikely to rise above the announced takeover price until either the deal is consummated or a second suitor steps in and offers a higher price to buy the company. If the takeover is a “cash deal,” meaning the acquiring company is tendering cash to buy the shares, the stock will usually sit in a very tight range below the takeover price for a long time. In this event, implied volatility will often drop to very low levels. Being short an ATM call when the stock rallies will let the trader profit from collapsing IV through negative vega. Say XYZ stock, trading at $52 a share, is a rumored takeover target at $60. When the rumors are first announced, the stock will likely rise, to say $55, with IV rising as well. Buying the 50–60 call spread will give a trader a positive delta and a negligible vega. If the rumors are realized and a cash takeover deal is announced at $60, the trade gains on delta, and the spread will now have negative vega. The negative vega at the 60 strike gains on implied volatility declining, and the stock will sit close to $60, producing the benefits of positive theta. Win, win, win. The Interrelations of Credit Spreads and Debit Spreads Many traders I know specialize in certain niches. Sometimes this is because they find something they know well and are really good at. Sometimes it’s because they have become comfortable and don’t have the desire to try anything new. I’ve seen this strategy specialization sometimes with traders trading credit spreads and debit spreads. I’ve had serial credit spread traders tell me credit spreads are the best trades in the world, much better than debit spreads. Habitual debit spread traders have likewise said their chosen spread is the best. But credit spreads and debit spreads are not so different. In fact, one could argue that they are really the same thing. Conventionally, credit-spread traders have the goal of generating income. The short option is usually ATM or OTM. The long option is more OTM. The traders profit from nonmovement via time decay. Debit-spread traders conventionally are delta-bet traders. They buy the ATM or just out-of-the-money option and look for movement away from or through the long strike to the short strike. The common themes between the two are that the underlying needs to end up around the short strike price and that time has to pass to get the most out of either spread. With either spread, movement in the underlying may be required, depending on the relationship of the underlying price to the strike prices of the options. And certainly, with a credit spread or debit spread, if the underlying is at the short strike, that option will have the most premium. For the trade to reach the maximum profit, it will need to decay. For many retail traders, debit spreads and credit spreads begin to look even more similar when margin is considered. Margin requirements can vary from firm to firm, but verticals in retail accounts at option-friendly brokerage firms are usually margined in such a way that the maximum loss is required to be deposited to hold the position (this assumes Regulation T margining). For all intents and purposes, this can turn the trader’s cash position from a credit into a debit. From a cash perspective, all vertical spreads are spreads that require a debit under these margin requirements. Professional traders and retail traders who are subject to portfolio margining are subject to more liberal margin rules. Although margin is an important concern, what we really care about as traders is risk versus reward. A credit call spread and a debit put spread on the same underlying, with the same expiration month, sharing the same strike prices will also share the same theoretical risk profile. This is because call and put prices are bound together by put-call parity. Building a Box Two traders, Sam and Isabel, share a joint account. They have each been studying Johnson & Johnson (JNJ), which is trading at around $63.35 per share. Sam and Isabel, however, cannot agree on direction. Sam thinks Johnson & Johnson will rise over the next five weeks, and Isabel believes it will decline during that period. Sam decides to buy the January 62.50 −65 call spread (January has 38 days until expiration in this example). Sam can buy this spread for 1.28. His maximum risk is 1.28. This loss occurs if Johnson & Johnson is below $62.50 at expiration, leaving both calls OTM. His maximum gain is 1.22, realized if Johnson & Johnson is above $65 (65–62.50–1.28). With Johnson & Johnson at $63.35, Sam’s delta is long 0.29 and his other greeks are about flat. Isabel decides to buy the January 62.50–65 put spread for a debit of 1.22. Isabel’s biggest potential loss is 1.22, incurred if Johnson & Johnson is above $65 a share at expiration, leaving both puts OTM. Her maximum possible profit is 1.28, realized if the stock is below $62.50 at option expiration. With Johnson & Johnson at $63.35, Isabel has a delta that is short around 0.27 and is nearly flat gamma, theta, and vega. Collectively, if both Sam and Isabel hold their trades until expiration, it’s a zero-sum game. With Johnson & Johnson below $62.50, Sam loses his investment of 1.28, but Isabel profits. She cancels out Sam’s loss by making 1.28. Above $65, Sam makes 1.22 while Isabel loses the same amount, canceling out Sam’s gains. Between the two strikes, Sam has gains on his 62.50 call and Isabel has gains on her 65 put. The gains on the two options will total 2.50, the combined total spent on the spreads—another draw. EXHIBIT 9.12 Sam’s long call spread in Johnson & Johnson. 62.50–65 Call Spread Delta +0.290 Gamma +0.001 Theta −0.004 Vega +0.006 EXHIBIT 9.13 Isabel’s long put spread in Johnson & Johnson. 62.50–65 Put Spread Delta −0.273 Gamma −0.001 Theta +0.005 Vega −0.006 These two spreads were bought for a combined total of 2.50. The collective position, composed of the four legs of these two spreads, forms a new strategy altogether. The two traders together have created a box. This box, which is empty of both profit and loss, is represented by greeks that almost entirely offset each other. Sam’s positive delta of 0.29 is mostly offset by Isabel’s −0.273 delta. Gamma, theta, and vega will mostly offset each other, too. Chapter 6 described a box as long synthetic stock combined with short synthetic stock having a different strike price but the same expiration month. It can also be defined, however, as two vertical spreads: a bull (bear) call spread plus a bear (bull) put spread with the same strike prices and expiration month. The value of a box equals the present value of the distance between the two strike prices (American-option models will also account for early exercise potential in the box’s value). This 2.50 box, with 38 days until expiration at a 1 percent interest rate, has less than a penny of interest affecting its value. Boxes with more time until expiration will have a higher interest rate component. If there was one year until expiration, the combined value of the two verticals would equal 2.475. This is simply the distance between the strikes minus interest (2.50–[2.50 × 0.01]). Credit spreads are often made up of OTM options. Traders betting against a stock rising through a certain price tend to sell OTM call spreads. For a stock at $50 per share, they might sell the 55 calls and buy the 60 calls. But because of the synthetic relationship that verticals have with one another, the traders could buy an ITM put spread for the same exposure, after accounting for interest. The traders could buy the 60 puts and sell the 55 puts. An ITM call (put) spread is synthetically equal to an OTM put (call) spread. Verticals and Beyond Traders who want to take full advantage of all that options have to offer can do so strategically by trading spreads. Vertical spreads truncate directional risk compared with strategies like the covered call or single-legged option trades. They also reduce option-specific risk, as indicated by their lower gamma, theta, and vega. But lowering risk both in absolute terms and in the greeks has a trade-off compared with buying options: limited profit potential. This trade-off can be beneficial, depending on the trader’s forecast. Debit spreads and credit spreads can be traded interchangeably to achieve the same goals. When a long (short) call spread is combined with a long (short) put spread, the product is a box. Chapter 10 describes other ways vertical spreads can be combined to form positions that achieve different trading objectives. Note 1 . Note that it is customary when discussing the purchase or sale of spreads to state the lower strike first, regardless of which is being bought or sold. In this case, the trader is buying the 75–80 put spread. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00020.html SCORE: 1052.50 ================================================================================ CHAPTER 10 Wing Spreads Condors and Butterflies The “wing spread” family is a set of option strategies that is very popular, particularly among experienced traders. These strategies make it possible for speculators to accomplish something they could not possibly do by just trading stocks: They provide a means to profit from a truly neutral market in a security. Stocks that don’t move one iota can earn profits month after month for income-generating traders who trade these strategies. These types of spreads have a lot of moving parts and can be intimidating to newcomers. At their heart, though, they are rather straightforward break-even analysis trades that require little complex math to maintain. A simple at-expiration diagram reveals in black and white the range in which the underlying stock must remain in order to have a profitable position. However, applying the greeks and some of the mathematics discussed in previous chapters can help a trader understand these strategies on a deeper level and maximize the chance of success. This chapter will discuss condors and butterflies and how to put them into action most effectively. Taking Flight There are four primary wing spreads: the condor, the iron condor, the butterfly, and the iron butterfly. Each of these spreads involves trading multiple options with three or four strikes prices. We can take these spreads at face value, we can consider each option as an individual component of the spread, or we can view the spreads as being made up of two vertical spreads. Condor A condor is a four-legged option strategy that enables a trader to capitalize on volatility—increased or decreased. Traders can trade long or short iron condors. Long Condor Long one call (put) with strike A; short one call (put) with a higher strike, B; short one call (put) at strike C, which is higher than B; and long one call (put) at strike D, which is higher than C. The distance between strike price A and B is equal to the distance between strike C and strike D. The options are all on the same security, in the same expiration cycle, and either all calls or all puts. Long Condor Example Buy 1 XYZ November 70 call (A) Sell 1 XYZ November 75 call (B) Sell 1 XYZ November 90 call (C) Buy 1 XYZ November 95 call (D) Short Condor Short one call (put) with strike A; long one call (put) with a higher strike, B; long one call (put) with a strike, C, that is higher than B; and short one call (put) with a strike, D, that is higher than C. The options must be on the same security, in the same expiration cycle, and either all calls or all puts. The differences in strike price between the vertical spread of strike prices A and B and the strike prices of the vertical spread of strikes C and D are equal. Short Condor Example Sell 1 XYZ November 70 call (A) Buy 1 XYZ November 75 call (B) Buy 1 XYZ November 90 call (C) Sell 1 XYZ November 95 call (D) Iron Condor An iron condor is similar to a condor, but with a mix of both calls and puts. Essentially, the condor and iron condor are synthetically the same. Short Iron Condor Long one put with strike A; short one put with a higher strike, B; short one call with an even higher strike, C; and long one call with a still higher strike, D. The options are on the same security and in the same expiration cycle. The put credit spread has the same distance between the strike prices as the call credit spread. Short Iron Condor Example Buy 1 XYZ November 70 put (A) Sell 1 XYZ November 75 put (B) Sell 1 XYZ November 90 call (C) Buy 1 XYZ November 95 call (D) Long Iron Condor Short one put with strike A; long one put with a higher strike, B; long one call with an even higher strike, C; and short one call with a still higher strike, D. The options are on the same security and in the same expiration cycle. The put debit spread (strikes A and B) has the same distance between the strike prices as the call debit spread (strikes C and D). Long Iron Condor Example Sell 1 XYZ November 70 put (A) Buy 1 XYZ November 75 put (B) Buy 1 XYZ November 90 call (C) Sell 1 XYZ November 95 call (D) Butterflies Butterflies are wing spreads similar to condors, but there are only three strikes involved in the trade—not four. Long Butterfly Long one call (put) with strike A; short two calls (puts) with a higher strike, B; and long one call (put) with an even higher strike, C. The options are on the same security, in the same expiration cycle, and are either all calls or all puts. The difference in price between strikes A and B equals that between strikes B and C. Long Butterfly Example Buy 1 XYZ December 50 call (A) Sell 2 XYZ December 60 call (B) Buy 1 XYZ December 70 call (C) Short Butterfly Short one call (put) with strike A; long two calls (puts) with a higher strike, B; and short one call (put) with an even higher strike, C. The options are on the same security, in the same expiration cycle, and are either all calls or all puts. The vertical spread made up of the options with strike A and strike B has the same distance between the strike prices of the vertical spread made up of the options with strike B and strike C. Short Butterfly Example Sell 1 XYZ December 50 call Buy 2 XYZ December 60 call Sell 1 XYZ December 70 call Iron Butterflies Much like the relationship of the condor to the iron condor, a butterfly has its synthetic equal as well: the iron butterfly. Short Iron Butterfly Long one put with strike A; short one put with a higher strike, B; short one call with strike B; long one call with a strike higher than B, C. The options are on the same security and in the same expiration cycle. The distances between the strikes of the put spread and between the strikes of the call spread are equal. Short Iron Butterfly Example Buy 1 XYZ December 50 put (A) Sell 1 XYZ December 60 put (B) Sell 1 XYZ December 60 call (B) Buy 1 XYZ December 70 call (C) Long Iron Butterfly Short one put with strike A; long one put with a higher strike, B; long one call with strike B; short one call with a strike higher than B, C. The options are on the same security and in the same expiration cycle. The distances between the strikes of the put spread and between the strikes of the call spread are equal. The put debit spread has the same distance between the strike prices as the call debit spread. Long Iron Butterfly Example Sell 1 XYZ December 50 put Buy 1 XYZ December 60 put Buy 1 XYZ December 60 call Sell 1 XYZ December 70 call These spreads were defined in terms of both long and short for each strategy. Whether the spread is classified as long or short depends on whether it was established at a credit or a debit. Debit condors or butterflies are considered long spreads. And credit condors or butterflies are considered short spreads. The words long and short mean little, though in terms of the spread as a whole. The important thing is which strikes have long options and which have short options. A call debit spread is synthetically equal to a put credit spread on the same security, with the same expiration month and strike prices. That means a long condor is synthetically equal to a short iron condor, and a long butterfly is synthetically equal to a short iron butterfly, when the same strikes are used. Whichever position is constructed, the best-case scenario is to have debit spreads expire with both options in-the-money (ITM) and credit spreads expire with both options out-of-the-money (OTM). Many retail traders prefer trading these spreads for the purpose of generating income. In this case, a trader would sell the guts, or middle strikes, and buy the wings, or outer strikes. When a trader is short the guts, low realized volatility is usually the objective. For long butterflies and short iron butterflies, the stock needs to be right at the middle strike for the maximum payout. For long condors and short iron condors, the stock needs to be between the short strikes at expiration for maximum payout. In both instances, the wings are bought to limit potential losses of the otherwise naked options. Long Butterfly Example A trader, Kathleen, has been studying United Parcel Service (UPS), which is trading at around $70.65. She believes UPS will trade sideways until July expiration. Kathleen buys the July 65–70–75 butterfly for 2.00. She executes the following legs: Kathleen looks at her trade as two vertical spreads, the 65–70 bull (debit) call spread and the 70–75 bear (credit) call spread. Intuitively, she would want UPS to be at or above $70 at expiration for her bull call spread to have maximum value. But she has the seemingly conflicting goal of also wanting UPS to be at or below $70 to get the most from her 70–75 bear call spread. The ideal price for the stock to be trading at expiration in this example is right at $70 per share—the best of both worlds. The at-expiration diagram, Exhibit 10.1 , shows the profit or loss of all possible outcomes at expiration. EXHIBIT 10.1 UPS 65–70–75 butterfly. If the price of UPS shares declines below $65 at expiration, all these calls will expire. The entire 2.00 spent on the trade will be lost. If UPS is above $65 at expiration, the 65 call will be ITM and will be exercised. The call will profit like a long position in 100 shares of the underlying. The maximum profit is reached if UPS is at $70 at expiration. Kathleen makes a 5.00 profit from $65 to $70 on her 65 calls. But because she paid 2.00 initially for the spread, her net profit at $70 is just 3.00. If UPS is above $70 a share at expiration in this example, the two 70 calls will be assigned. The assignment of one call will offset the long stock acquired by the 65 calls being exercised. Assignment of the other call will create a short position in the underlying. That short position loses as UPS moves higher up to $75 a share, eating away at the 3.00 profit. If UPS is above $75 at expiration, the 75 call can be exercised to buy back the short stock position that resulted from the 70’s being assigned. The loss on the short stock between $70 and $75 will cost Kathleen 5.00, stripping her of her 3.00 profit and giving her a net loss of 2.00 to boot. End result? Above $75 at expiration, she has no position in the underlying and loses 2.00. A butterfly is a break-even analysis trade . This name refers to the idea that the most important considerations in this strategy are the breakeven points. The at-expiration diagram, Exhibit 10.2 , shows the break-even prices for this trade. EXHIBIT 10.2 UPS 65–70–75 butterfly breakevens. If the position is held until expiration and UPS is between $65 and $70 at that time, the 65 calls are exercised, resulting in long stock. The effective purchase price of that stock is $67. That’s the strike price plus the cost of the spread; that’s the lower break-even price. The other break-even is at $73. The net short position of 100 shares resulting from assignment of the 70 call loses more as the stock rises between $70 and $75. The entire 3.00 profit realized at the $70 share price is eroded when the stock reaches $73. Above $73, the trade produces a loss. Kathleen’s trading objective is to profit from UPS trading between $67 and $73 at expiration. The best-case scenario is that it declines only slightly from its price of $70.65 when the trade is established, to $70 per share. Alternatives Kathleen had other alternative positions she could have traded to meet her goals. An iron butterfly with the same strike prices would have shown about the same risk/reward picture, because the two positions are synthetically equivalent. But there may, in some cases, be a slight advantage to trading the iron butterfly over the long butterfly. The iron butterfly uses OTM put options instead of ITM calls, meaning the bid-ask spreads may be tighter. This means giving up less edge to the liquidity providers. She could have also bought a condor or sold an iron condor. With condor-family spreads, there is a lower maximum profit potential but a wider range in which that maximum payout takes place. For example, Kathleen could have executed the following legs to establish an iron condor: Essentially, Kathleen would be selling two credit spreads: the July 60–65 put spread for 0.30 and the July 75–80 call spread for 0.35. Exhibit 10.3 shows the payout at expiration of the UPS July 60–65–75–80 iron condor. EXHIBIT 10.3 UPS 60–65–75–80 iron condor. Although the forecast and trading objectives may be similar to those for the butterfly, the payout diagram reveals some important differences. First, the maximum loss is significantly higher with a condor or iron condor. In this case, the maximum loss is 4.35. This unfortunate situation would occur if UPS were to drop to below $60 or rise above $80 by expiration. Below $60, the call spread expires, netting 0.35. But the put spread is ITM. Kathleen would lose a net of 4.70 on the put spread. The gain on the call spread combined with the loss on the put spread makes the trade a loser of 4.35 if the stock is below $60 at expiration. Above $80, the put spread is worthless, earning 0.30, but the call spread is a loser by 4.65. The gain on the put spread plus the loss on the call spread is a net loser of 4.35. Between $65 and $75, all options expire and the 0.65 credit is all profit. So far, this looks like a pretty lousy alternative to the butterfly. You can lose 4.35 but only make 0.65! Could there be any good reason for making this trade? Maybe. The difference is wiggle room. The breakevens are 2.65 wider in each direction with the iron condor. Exhibit 10.4 shows these prices on the graph. EXHIBIT 10.4 UPS 60–65–75–80 iron condor breakevens. The lower threshold for profit occurs at $64.35 and the upper at $75.65. With condor/iron condors, there can be a greater chance of producing a winning trade because the range is wider than that of the butterfly. This benefit, however, has a trade-off of lower potential profit. There is always a parallel relationship of risk and reward. When risk increases so does reward, and vice versa. This way of thinking should now be ingrained in your DNA. The risk of failure is less, so the payout is less. Because the odds of winning are higher, a trader will accept lower payouts on the trade. Keys to Success No matter which trade is more suitable to Kathleen’s risk tolerance, the overall concept is the same: profit from little directional movement. Before Kathleen found a stock on which to trade her spread, she will have sifted through myriad stocks to find those that she expects to trade in a range. She has a few tools in her trading toolbox to help her find good butterfly and condor candidates. First, Kathleen can use technical analysis as a guide. This is a rather straightforward litmus test: does the stock chart show a trending, volatile stock or a flat, nonvolatile stock? For the condor, a quick glance at the past few months will reveal whether the stock traded between $65 and $75. If it did, it might be a good iron condor candidate. Although this very simplistic approach is often enough for many traders, those who like lots of graphs and numbers can use their favorite analyses to confirm that the stock is trading in a range. Drawing trendlines can help traders to visualize the channel in which a stock has been trading. Knowing support and resistance is also beneficial. The average directional movement index (ADX) or moving average converging/diverging (MACD) indicator can help to show if there is a trend present. If there is, the stock may not be a good candidate. Second, Kathleen can use fundamentals. Kathleen wants stocks with nothing on their agendas. She wants to avoid stocks that have pending events that could cause their share price to move too much. Events to avoid are earnings releases and other major announcements that could have an impact on the stock price. For example, a drug stock that has been trading in a range because it is awaiting Food and Drug Administration (FDA) approval, which is expected to occur over the next month, is not a good candidate for this sort of trade. The last thing to consider is whether the numbers make sense. Kathleen’s iron condor risks 4.35 to make 0.65. Whether this sounds like a good trade depends on Kathleen’s risk tolerance and the general environment of UPS, the industry, and the market as a whole. In some environments, the 0.65/4.35 payout-to-risk ratio makes a lot of sense. For other people, other stocks, and other environments, it doesn’t. Greeks and Wing Spreads Much of this chapter has been spent on how wing spreads perform if held until expiration, and little has been said of option greeks and their role in wing spreads. Greeks do come into play with butterflies and condors but not necessarily the same way they do with other types of option trades. The vegas on these types of spreads are smaller than they are on many other types of strategies. For a typical nonprofessional trader, it’s hard to trade implied volatility with condors or butterflies. The collective commissions on the four legs, as well as margin and capital considerations, put these out of reach for active trading. Professional traders and retail traders subject to portfolio margining are better equipped for volatility trading with these spreads. The true strength of wing spreads, however, is in looking at them as break-even analysis trades much like vertical spreads. The trade is a winner if it is on the correct side of the break-even price. Wing spreads, however, are a combination of two vertical spreads, so there are two break-even prices. One of the verticals is guaranteed to be a winner. The stock can be either higher or lower at expiration—not both. In some cases, both verticals can be winners. Consider an iron condor. Instead of reaping one premium from selling one OTM call credit spread, iron condor sellers double dip by additionally selling an OTM put credit spread. They collect a double credit, but only one of the credit spreads can be a loser at expiration. The trader, however, does have to worry about both directions independently. There are two ways for greeks and volatility analysis to help traders trade wing spreads. One of them involves using delta and theta as tools to trade a directional spread. The other uses implied volatility in strike selection decisions. Directional Butterflies Trading a butterfly can be an excellent way to establish a low-cost, relatively low-risk directional trade when a trader has a specific price target in mind. For example, a trader, Ross, has been studying Walgreen Co. (WAG) and believes it will rise from its current level of $33.50 to $36 per share over the next month. Ross buys a butterfly consisting of all OTM January calls with 31 days until expiration. He executes the following legs: As a directional trade alternative, Ross could have bought just the January 35 call for 1.15. As a cheaper alternative, he could have also bought the 35–36 bull call spread for 0.35. In fact, Ross actually does buy the 35–36 spread, but he also sells the January 36–37 call spread at 0.25 to reduce the cost of the bull call spread, investing only a dime. The benefit of lower cost, however, comes with trade-offs. Exhibit 10.5 compares the bull call spread with a bullish butterfly. EXHIBIT 10.5 Bull call spread vs. bull butterfly (Walgreen Co. at $33.50). The butterfly has lower nominal risk—only 0.10 compared with 0.35 for the call spread. The maximum reward is higher in nominal terms, too—0.90 versus 0.65. The trade-off is what is given up. With both strategies, the goal is to have Walgreen Co. at $36 around expiration. But the bull call spread has more room for error to the upside. If the stock trades a lot higher than expected, the butterfly can end up being a losing trade. Given Ross’s expectations in this example, this might be a risk he is willing to take. He doesn’t expect Walgreen Co. to close right at $36 on the expiration date. It could happen, but it’s unlikely. However, he’d have to be wildly wrong to have the trade be a loser on the upside. It would be a much larger move than expected for the stock to rise significantly above $36. If Ross strongly believes Walgreen Co. can be around $36 at expiration, the cost benefit of 0.10 vs. 0.35 may offset the upside risk above $37. As a general rule, directional butterflies work well in trending, low-volatility stocks. When Ross monitors his butterfly, he will want to see the greeks for this position as well. Exhibit 10.6 shows the trade’s analytics with Walgreen Co. at $33.50. EXHIBIT 10.6 Walgreen Co. 35–36–37 butterfly greeks (stock at $33.50, 31 days to expiration). Delta +0.008 Gamma −0.004 Theta +0.001 Vega −0.001 When the trade is first put on, the delta is small—only +0.008. Gamma is slightly negative and theta is very slightly positive. This is important information if Walgreen Co.’s ascent happens sooner than Ross planned. The trade will show just a small profit if the stock jumps to $36 per share right away. Ross’s theoretical gain will be almost unnoticeable. At $36 per share, the position will have its highest theta, which will increase as expiration approaches. Ross will have to wait for time to pass to see the trade reach its full potential. This example shows the interrelation between delta and theta. We know from an at-expiration analysis that if Walgreen Co. moves from $33.50 to $36, the butterfly’s profit will be 0.90 (the spread of $1 minus the 0.10 initial debit). If we distribute the 0.90 profit over the 2.50 move from $33.50 to $36, the butterfly gains about 0.36 per dollar move in Walgreen Co. (0.90/(36 − 33.50). This implies a delta of about 0.36. But the delta, with 31 days until expiration and Walgreen Co. at $33.50, is only 0.008, and because of negative gamma this delta will get even smaller as Walgreen Co. rises. Butterflies, like the vertical spreads of which they are composed, can profit from direction but are never purely directional trades. Time is always a factor. It is theta, working in tandem with delta, that contributes to profit or peril. A bearish butterfly can be constructed as well. One would execute the trade with all OTM puts or all ITM calls. The concept is the same: sell the guts at the strike at which the stock is expected to be trading at expiration, and buy the wings for protection. Constructing Trades to Maximize Profit Many traders who focus on trading iron condors trade exchange-traded funds (ETFs) or indexes. Why? Diversification. Because indexes are made up of many stocks, they usually don’t have big gaps caused by surprise earnings announcements, takeovers, or other company-specific events. But it’s not just selecting the right underlying to trade that is the challenge. A trader also needs to pick the right strike prices. Finding the right strike prices to trade can be something of an art, although science can help, as well. Three Looks at the Condor Strike selection is essential for a successful condor. If strikes are too close together or two far apart, the trade can become much less attractive. Strikes Too Close The QQQs are options on the ETFs that track the Nasdaq 100 (QQQ). They have strikes in $1 increments, giving traders a lot to choose from. With QQQ trading at around $55.95, consider the 54–55–57–58 iron condor. In this example, with 31 days until expiration, the following legs can be executed: In this trade, the maximum profit is 0.63. The maximum risk is 0.37. This isn’t a bad profit-to-loss ratio. The break-even price on the downside is $54.37 and on the upside is $57.63. That’s a $3.26 range—a tight space for a mover like the QQQ to occupy in a month. The ETF can drop about only 2.8 percent or rise 3 percent before the trade becomes a loser. No one needs any fancy math to show that this is likely a losing proposition in the long run. While choosing closer strikes can lead to higher premiums, the range can be so constricting that it asphyxiates the possibility of profit. Strikes Too Far Strikes too far apart can make for impractical trades as well. Exhibit 10.7 shows an options chain for the Dow Jones Industrial Average Index (DJX). These prices are from around 2007 when implied volatility (IV) was historically low, making the OTM options fairly low priced. In this example, DJX is around $135.20 and there are 51 days until expiration. EXHIBIT 10.7 Options chain for DJIA. If the goal is to choose strikes that are far enough apart to be unlikely to come into play, a trader might be tempted to trade the 120–123–142–145 iron condor. With this wingspan, there is certainly a good chance of staying between those strikes—you could drive a proverbial truck through that range. This would be a great trade if it weren’t for the prices one would have to accept to put it on. First, the 120 puts are offered at 0.25 and the 123 puts are 0.25 bid. This means that the put spread would be sold at zero! The maximum risk is 3.00, and the maximum gain is zero. Not a really good risk/reward. The 142–145 call spread isn’t much better: it can be sold for a dime. At the time, again a low-volatility period, many traders probably felt it was unlikely that the DJX will rise 5 percent in a 51-day period. Some traders may have considered trading a similarly priced iron condor (though of course they’d have to require some small credit for the risk). A little over a year later the DJX was trading around 50 percent lower. Traders must always be vigilant of the possibility of volatility, even unexpected volatility and structure their risk/reward accordingly. Most traders would say the risk/reward of this trade isn’t worth it. Strikes too far apart have a greater chance of success, but the payoff just isn’t there. Strikes with High Probabilities of Success So how does a trader find the happy medium of strikes close enough together to provide rich premiums but far enough apart to have a good chance of success? Certainly, there is something to be said for looking at the prices at which a trade can be done and having a subjective feel for whether the underlying is likely to move outside the range of the break-even prices. A little math, however, can help quantify this likelihood and aid in the decision-making process. Recall that IV is read by many traders to be the market’s consensus estimate of future realized volatility in terms of annualized standard deviation. While that is a mouthful to say—or in this case, rather, an eyeful to read—when broken down it is not quite as intimidating as it sounds. Consider a simplified example in which an underlying security is trading at $100 a share and the implied volatility of the at-the-money (ATM) options is 10 percent. That means, from a statistical perspective, that if the expected return for the stock is unchanged, the one-year standard deviations are at $90 and $110. 1 In this case, there is about a 68 percent chance of the stock trading between $90 and $110 one year from now. IV then is useful information to a trader who wants to quantify the chances of an iron condor’s expiring profitable, but there are a few adjustments that need to be made. First, because with an iron condor the idea is to profit from net short option premium, it usually makes more sense to sell shorter-term options to profit from higher rates of time decay. This entails trading condors composed of one- or two-month options. The IV needs to be deannualized and converted to represent the standard deviation of the underlying at expiration. The first step is to compute the one-day standard deviation. This is found by dividing the implied volatility by the square root of the number of trading days in a year, then multiplying by the square root of the number of trading days until expiration. The result is the standard deviation (σ) at the time of expiration stated as a percent. Next, multiply that percentage by the price of the underlying to get the standard deviation in absolute terms. The formula 2 for calculating the shorter-term standard deviation is as follows: This value will be added to or subtracted from the price of the underlying to get the price points at which the approximate standard deviations fall. Consider an example using options on the Standard & Poor’s 500 Index (SPX). With 50 days until expiration, the SPX is at 1241 and the implied volatility is 23.2 percent. To find strike prices that are one standard deviation away from the current index price, we need to enter the values into the equation. We first need to know how many actual trading days are in the 50-day period. There are 35 business days during this particular 50-day period (there is one holiday and seven weekend days). We now have all the data we need to calculate which strikes to sell. The lower standard deviation is 1134.55 (1241 − 106.45) and the upper is 1347.45 (1241 + 106.45). This means there would be about a 68 percent chance of SPX ending up between 1134.55 and 1347.45 at expiration. In this example, to have about a two-thirds chance of success, one would sell the 1135 puts and the 1350 calls as part of the iron condor. Being Selective There is about a two-thirds chance of the underlying staying between the upper and lower standard deviation points and about a one-third chance it won’t. Reasonably good odds. But the maximum loss of an iron condor will be more than the maximum profit potential. In fact, the max-profit-to-max-loss ratio is usually less than 1 to 3. For every $1 that can be made, often $4 or $5 will be at risk. The pricing model determines fair value of an option based on the implied volatility set by the market. Again, many traders consider IV to be the market’s consensus estimate of future realized volatility. Assuming the market is generally right and options are efficiently priced, in the long run, future stock volatility should be about the same as the implied volatility from options prices. That means that if all of your options trades are executed at fair value, you are likely to break even in the long run. The caveat is that whether the options market is efficient or not, retail or institutional traders cannot generally execute trades at fair value. They have to sell the bid (sell below theoretical value) and buy the offer (buy above theoretical value). This gives the trade a statistical disadvantage, called giving up the edge, from an expected return perspective. Even though you are more likely to win than to lose with each individual trade when strikes are sold at the one-standard-deviation point, the edge given up to the market in conjunction with the higher price tag on losers makes the trade a statistical loser in the long run. While this means for certain that the non-market-making trader is at a constant disadvantage, trading condors and butterflies is no different from any other strategy. Giving up the edge is the plight of retail and institutional traders. To profit in the long run, a trader needs to beat the market, which requires careful planning, selectivity, and risk management. Savvy traders trade iron condors with strikes one standard deviation away from the current stock price only when they think there is more than a two-thirds chance of market neutrality. In other words, if you think the market will be less volatile than the prices in the options market imply, sell the iron condor or trade another such premium-selling strategy. As discussed above, this opinion should reflect sound judgment based on some combination of technical analysis, fundamental analysis, volatility analysis, feel, and subjectivity. A Safe Landing for an Iron Condor Although traders can’t control what the market does, they can control how they react to the market. Assume a trader has done due diligence in studying a stock and feels it is a qualified candidate for a neutral strategy. With the stock at $90, a 16.5 percent implied volatility, and 41 days until expiration, the standard deviation is about 5. The trader sells the following iron condor: With the stock at $90, directly between the two short strikes, the trade is direction neutral. The maximum profit is equal to the total premium taken in, which in this case is $800. The maximum loss is $4,200. There is about a two-thirds chance of retaining the $800 at expiration. After one week, the overall market begins trending higher on unexpected bullish economic news. This stock follows suit and is now trading at $93, and concern is mounting that the rally will continue. The value of the spread now is about 1.10 per contract (we ignore slippage from trading on the bid-ask spreads of the four legs of the spread). This means the trade has lost $300 because it would cost $1,100 to buy back what the trader sold for a total of $800. One strategy for managing this trade looking forward is inaction. The philosophy is that sometimes these trades just don’t work out and you take your lumps. The philosophy is that the winners should outweigh the losers over the long term. For some of the more talented and successful traders with a proven track record, this may be a viable strategy, but there are more active options as well. A trader can either close the spread or adjust it. The two sets of data that must be considered in this decision are the prices of the individual options and the greeks for the trade. Exhibit 10.8 shows the new data with the stock at $93. EXHIBIT 10.8 Greeks for iron condor with stock at $93. The trade is no longer neutral, as it was when the underlying was at $90. It now has a delta of −2.54, which is like being short 254 shares of the underlying. Although the more time that passes the better—as indicated by the +0.230 theta—delta is of the utmost concern. The trader has now found himself short a market that he thinks may rally. Closing the entire position is one alternative. To be sure, if you don’t have an opinion on the underlying, you shouldn’t have a position. It’s like making a bet on a sporting event when you don’t really know who you think will win. The spread can also be dismantled piecemeal. First, the 85 puts are valued at $0.07 each. Buying these back is a no-brainer. In the event the stock does retrace, why have the positive delta of that leg working against you when you can eliminate the risk inexpensively now? The 80 puts are worthless, offered at 0.05, presumably. There is no point in trying to sell these. If the market does turn around, they may benefit, resulting in an unexpected profit. The 80 and 85 puts are the least of his worries, though. The concern is a continuing rally. Clearly, the greater risk is in the 95–100 call spread. Closing the call spread for a loss eliminates the possibility of future losses and may be a wise choice, especially if there is great uncertainty. Taking a small loss now of only around $300 is a better trade than risking a total loss of $4,200 when you think there is a strong chance of that total loss occurring. But if the trader is not merely concerned that the stock will rally but truly believes that there is a good chance it will, the most logical action is to position himself for that expected move. Although there are many ways to accomplish this, the simplest way is to buy to close the 95 calls to eliminate the position at that strike. This eliminates the short delta from the 95 calls, leading to a now-positive delta for the position as a whole. The new position after adjusting by buying the 85 puts and the 95 calls is shown in Exhibit 10.9 . EXHIBIT 10.9 Iron condor adjusted to strangle. The result is a long strangle: a long call and a long put of the same month with two different strikes. Strangles will be discussed in subsequent chapters. The 80 puts are far enough out-of-the-money to be fairly irrelevant. Effectively, the position is long ten 100-strike calls. This serves the purpose of changing the negative 2.54 delta into a positive 0.96 delta. The trader now has a bullish position in the stock that he thinks will rally—a much smarter position, given that forecast. The Retail Trader versus the Pro Iron condors are very popular trades among retail traders. These days one can hardly go to a cocktail party and mention the word options without hearing someone tell a story about an iron condor on which he’s made a bundle of money trading. Strangely, no one ever tells stories about trades in which he has lost a bundle of money. Two of the strengths of this strategy that attract retail traders are its limited risk and high probability of success. Another draw of this type of strategy is that the iron condor and the other wing spreads offer something truly unique to the retail trader: a way to profit from stocks that don’t move. In the stock-trading world, the only thing that can be traded is direction—that is, delta. The iron condor is an approachable way for a nonprofessional to dabble in nonlinear trading. The iron condor does a good job in eliminating delta—unless, of course, the stock moves and gamma kicks in. It is efficient in helping income-generating retail traders accomplish their goals. And when a loss occurs, although it can be bigger than the potential profits, it is finite. But professional option traders, who have access to lots of capital and have very low commissions and margin requirements, tend to focus their efforts in other directions: they tend to trade volatility. Although iron condors are well equipped for profiting from theta when the stock cooperates, it is also possible to trade implied volatility with this strategy. The examples of iron condors, condors, iron butterflies, and butterflies presented in this chapter so far have for the most part been from the perspective of the neutral trader: selling the guts and buying the wings. A trader focusing on vega in any of these strategies may do just the opposite—buy the guts and sell the wings—depending on whether the trader is bullish or bearish on volatility. Say a trader, Joe, had a bullish outlook on volatility in Salesforce.com (CRM). Joe could sell the following condor 100 times. In this example, February is 59 days from expiration. Exhibit 10.10 shows the analytics for this trade with CRM at $104.32. EXHIBIT 10.10 Salesforce.com condor ( Salesforce.com at $104.32). As expected with the underlying centered between the two middle strikes, delta and gamma are about flat. As Salesforce.com moves higher or lower, though, gamma and, consequently, delta will change. As the stock moves closer to either of the long strikes, gamma will become more positive, causing the delta to change favorably for Joe. Theta, however, is working against him with Salesforce.com at $104.32, costing $150 a day. In this instance, movement is good. Joe benefits from increased realized volatility. The best-case scenario would be if Salesforce.com moves through either of the long strikes to, or through, either of the short strikes. The prime objective in this example, though, is to profit from a rise in IV. The position has a positive vega. The position makes or loses $400 with every point change in implied volatility. Because of the proportion of theta risk to vega risk, this should be a short-term play. If Joe were looking for a small rise in IV, say five points, the move would have to happen within 13 calendar days, given the vega and theta figures. The vega gain on a rise of five vol points would be $2,000, and the theta loss over 13 calendar days would be $1,950. If there were stock movement associated with the IV increase, that delta/gamma gain would offset some of the havoc that theta wreaked on the option premiums. However, if Joe traded a strategy like a condor as a vol play, he would likely expect a bigger volatility move than the five points discussed here as well as expecting increased realized volatility. A condor bullish vol play works when you expect something to change a stock’s price action in the short term. Examples would be rumors of a new product’s being unveiled, a product recall, a management change, or some other shake-up that leads to greater uncertainty about the company’s future—good or bad. The goal is to profit from a rise in IV, so the trade needs to be put on before the announcement occurs. The motto in option-volatility trading is “Buy the rumor; sell the news.” Usually, by the time the news is out, the increase in IV is already priced into option premiums. As uncertainty decreases, IV decreases as well. Notes 1 . It is important to note that in the real world, interest and expectations for future stock-price movement come into play. For simplicity’s sake, they’ve been excluded here. 2 . This is an approximate formula for estimating standard deviation. Although it is mathematically only an approximation, it is the convention used by many option traders. It is a traders’ short cut. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00021.html SCORE: 1385.00 ================================================================================ CHAPTER 11 Calendar and Diagonal Spreads Option selling is a niche that attracts many retail and professional traders because it’s possible to profit from the passage of time. Calendar and diagonal spreads are practical strategies to limit risk while profiting from time. But these spreads are unique in many ways. In order to be successful with them, it is important to understand their subtle qualities. Calendar Spreads Definition : A calendar spread, sometimes called a time spread or a horizontal spread , is an option strategy that involves buying one option and selling another option with the same strike price but with a different expiration date. At-expiration diagrams do a calendar-spread trader little good. Why? At the expiration of the short-dated option, the trader is left with another option that may have time value. To estimate what the position will be worth when the short-term option expires, the value of the long-term option must be analyzed using the greeks. This is true of the variants of the calendar—double calendars, diagonals, and double diagonals—as well. This chapter will show how to analyze strategies that involve options with different expirations and discuss how and when to use them. Buying the Calendar The calendar spread and all its variations are commonly associated with income-generating spreads. Using calendar spreads as income generators is popular among retail and professional traders alike. The process involves buying a longer-term at-the-money option and selling a shorter-term at-the-money (ATM) option. The options must be either both calls or both puts. Because this transaction results in a net debit—the longer-term option being purchased has a higher premium than the shorter-term option being sold—this is referred to as buying the calendar. The main intent of buying a calendar spread for income is to profit from the positive net theta of the position. Because the shorter-term ATM option decays at a faster rate than the longer-term ATM option, the net theta is positive. As for most income spreads, the ideal outcome occurs when the underlying is at the short strike (in this case, shared strike) when the shorter-term option expires. At this strike price, the long option has its highest value, while the short option expires without the trader’s getting assigned. As long as the underlying remains close to the strike price, the value of the spread rises as time passes, because the short option decreases in value faster than the long option. For example, a trader, Richard, watches Bed Bath & Beyond Inc. (BBBY) on a regular basis. Richard believes that Bed Bath & Beyond will trade in a range around $57.50 a share (where it is trading now) over the next month. Richard buys the January–February 57.50 call calendar for 0.80. Assuming January has 25 days until expiration and February has 53 days, Richard will execute the following trade: Richard’s best-case scenario occurs when the January calls expire at expiration and the February calls retain much of their value. If Richard created an at-expiration P&(L) diagram for his position, he’d have trouble because of the staggered expiration months. A general representation would look something like Exhibit 11.1 . EXHIBIT 11.1 Bed Bath & Beyond January–February 57.50 calendar. The only point on the diagram that is drawn with definitive accuracy is the maximum loss to the downside at expiration of the January call. The maximum loss if Bed Bath & Beyond falls low enough is 0.80—the debit paid for the spread. If Bed Bath & Beyond is below $57.50 at January expiration, the January 57.50 call expires worthless, and the February 57.50 call may or may not have residual value. If Bed Bath & Beyond declines enough, the February 57.50 call can lose all of its value, even with residual time until expiration. If the stock falls enough, the entire 0.80 debit would be a loss. If Bed Bath & Beyond is above $57.50 at January expiration, the January 57.50 call will be trading at parity. It will be a negative-100-delta option, imitating short stock. If Bed Bath & Beyond is trading high enough, the February 57.50 call will become a positive-100-delta option trading at parity plus the interest calculated on the strike. The February deep-in-the-money option would imitate long stock. At a 2 percent interest rate, interest on the 57.50 strike is about 0.17. Therefore, Richard would essentially have a short stock position from $57.50 from the January 57.50 call and would be essentially long stock from $57.50 plus 0.28 from the February call. The maximum loss to the upside is about 0.63 (0.80 − 0.17). The maximum loss if Bed Bath & Beyond is trading over $57.50 at expiration is only an estimate that assumes there is no time value and that interest and dividends remain constant. Ultimately, the maximum loss will be 0.80, the premium paid, if there is no time value or carry considerations. The maximum profit is gained if Bed Bath & Beyond is at $57.50 at expiration. At this price, the February 57.50 call is worth the most it can be worth without having the January 57.50 call assigned and creating negative deltas to the upside. But how much precisely is the maximum profit? Richard would have to know what the February 57.50 call would be worth with Bed Bath & Beyond stock trading at $57.50 at February expiration before he can know the maximum profit potential. Although Richard can’t know for sure at what price the calls will be trading, he can use a pricing model to estimate the call’s value. Exhibit 11.2 shows analytics at January expiration. EXHIBIT 11.2 Bed Bath & Beyond January–February 57.50 call calendar greeks at January expiration. With an unchanged implied volatility of 23 percent, an interest rate of two percent, and no dividend payable before February expiration, the February 57.50 calls would be valued at 1.53 at January expiration. In this best-case scenario, therefore, the spread would go from 0.80, where Richard purchased it, to 1.53, for a gain of 91 percent. At January expiration, with Bed Bath & Beyond at $57.50, the January call would expire; thus, the spread is composed of just the February 57.50 call. Let’s now go back in time and see how Richard figured this trade. Exhibit 11.3 shows the position when the trade is established. EXHIBIT 11.3 Bed Bath & Beyond January–February 57.50 call calendar. A small and steady rise in the stock price with enough time to collect theta is the recipe for success in this trade. As time passes, delta will flatten out if Bed Bath & Beyond is still right at-the-money. The delta of the January call that Richard is short will move closer to exactly −0.50. The February call delta moves toward exactly +0.50. Gamma and theta will both rise if Bed Bath & Beyond stays around the strike. As expiration approaches, there is greater risk if there is movement and greater reward if there is not. Vega is positive because the long-term option with the higher vega is the long leg of the spread. When trading calendars for income, implied volatility (IV) must be considered as a possible threat. Because it is Richard’s objective to profit from Bed Bath & Beyond being at $57.50 at expiration, he will try to avoid vega risk by checking that the implied volatility of the February call is in the lower third of the 12-month range. He will also determine if there are any impending events that could cause IV to change. The less likely IV is to drop, the better. If there is an increase in IV, that may benefit the profitability of the trade. But a rise in IV is not really a desired outcome for two reasons. First, a rise in IV is often more pronounced in the front month than in the months farther out. If this happens, Richard can lose more on the short call than he makes on the long call. Second, a rise in IV can indicate anxiety and therefore a greater possibility for movement in the underlying stock. Richard doesn’t want IV to rock the boat. “Buy low, stay low” is his credo. Rho is positive also. A rise in interest rates benefits the position because the long-term call is helped by the rise more than the short call is hurt. With only a one-month difference between the two options, rho is very small. Overall, rho is inconsequential to this trade. There is something curious to note about this trade: the gamma and the vega. Calendar spreads are the one type of trade where gamma can be negative while vega is positive, and vice versa. While it appears—at least on the surface—that Richard wants higher IV, he certainly wants low realized volatility. Bed Bath & Beyond January–February 57.50 Put Calendar Richard’s position would be similar if he traded the January–February 57.50 put calendar rather than the call calendar. Exhibit 11.4 shows the put calendar. EXHIBIT 11.4 Bed Bath & Beyond January–February 57.50 put calendar. The premium paid for the put spread is 0.75. A huge move in either direction means a loss. It is about the same gamma/theta trade as the 57.50 call calendar. At expiration, with Bed Bath & Beyond at $57.50 and IV unchanged, the value of the February put would be 1.45—a 93 percent gain. The position is almost exactly the same as the call calendar. The biggest difference is that the rho is negative, but that is immaterial to the trade. As with the call spread, being short the front-month option means negative gamma and positive theta; being long the back month means positive vega. Managing an Income-Generating Calendar Let’s say that instead of trading a one-lot calendar, Richard trades it 20 times. His trade in this case is His total cash outlay is $1,600 ($80 times 20). The greeks for this trade, listed in Exhibit 11.5 , are also 20 times the size of those in Exhibit 11.3 . EXHIBIT 11.5 20-Lot Bed Bath & Beyond January–February 57.50 call calendar. Note that Richard has a +0.18 delta. This means he’s long the equivalent of about 18 shares of stock—still pretty flat. A gamma of −0.72 means that if Bed Bath & Beyond moves $1 higher, his delta will be starting to get short; and if it moves $1 lower he will be longer, long 90 deltas. Richard can use the greeks to get a feel for how much the stock can move before negative gamma causes a loss. If Bed Bath & Beyond starts trending in either direction, Richard may need to react. His plan is to cover his deltas to continue the position. Say that after one week Bed Bath & Beyond has dropped $1 to $56.50. Richard will have collected seven days of theta, which will have increased slightly from $18 per day to $20 per day. His average theta during that time is about $19, so Richard’s profit attributed to theta is about $133. With a big-enough move in either direction, Richard’s delta will start working against him. Since he started with a delta of +0.18 on this 20-lot spread and a gamma of −0.72, one might think that his delta would increase to 0.90 with Bed Bath & Beyond a dollar lower (18 − [−0.072 × 1.00]). But because a week has passed, his delta would actually get somewhat more positive. The shorter-term call’s delta will get smaller (closer to zero) at a faster rate compared to the longer-term call because it has less time to expiration. Thus, the positive delta of the long-term option begins to outweigh the negative delta of the short-term option as time passes. In this scenario, Richard would have almost broken even because what would be lost on stock price movement, is made up for by theta gains. Richard can sell about 100 shares of Bed Bath & Beyond to eliminate his immediate directional risk and stem further delta losses. The good news is that if Bed Bath & Beyond declines more after this hedge, the profit from the short stock offsets losses from the long delta. The bad news is that if BBBY rebounds, losses from the short stock offset gains from the long delta. After Richard’s hedge trade is executed, his delta would be zero. His other greeks remain unchanged. The idea is that if Bed Bath & Beyond stays at its new price level of $56.50, he reaps the benefits of theta increasing with time from $18 per day. Richard is accepting the new price level and any profits or losses that have occurred so far. He simply adjusts his directional exposure to a zero delta. Rolling and Earning a “Free” Call Many traders who trade income-generating strategies are conservative. They are happy to sell low IV for the benefits afforded by low realized volatility. This is the problem-avoidance philosophy of trading. Due to risk aversion, it’s common to trade calendar spreads by buying the two-month option and selling the one-month option. This can allow traders to avoid buying the calendar in earnings months, and it also means a shorter time horizon, signifying less time for something unwanted to happen. But there’s another school of thought among time-spread traders. There are some traders who prefer to buy a longer-term option—six months to a year—while selling a one-month option. Why? Because month after month, the trader can roll the short option to the next month. This is a simple tactic that is used by market makers and other professional traders as well as savvy retail traders. Here’s how it works. XYZ stock is trading at $60 per share. A trader has a neutral outlook over the next six months and decides to buy a calendar. Assuming that July has 29 days until expiration and December has 180, the trader will take the following position: The initial debit here is 2.55. The goal is basically the same as for any time spread: collect theta without negative gamma spoiling the party. There is another goal in these trades as well: to roll the spread. At the end of month one, if the best-case scenario occurs and XYZ is sitting at $60 at July expiration, the July 60 call expires. The December 60 call will then be worth 3.60, assuming all else is held constant. The positive theta of the short July call gives full benefits as the option goes from 1.45 to zero. The lower negative theta of the December call doesn’t bite into profits quite as much as the theta of a short-term call would. The profit after month one is 1.05. Profit is derived from the December call, worth 3.60 at July expiry, minus the 2.55 initial spread debit. This works out to about a 41 percent return. The profit is hardly as good as it would have been if a short-term, less expensive August 60 call were the long leg of this spread. Rolling the Spread The July–December spread is different from short-term spreads, however. When the Julys expire, the August options will have 29 days until expiration. If volatility is still the same, XYZ is still at $60, and the trader’s forecast is still neutral, the 29-day August 60 calls can be sold for 1.45. The trader can either wait until the Monday after July expiration and then sell the August 60s, or when the Julys are offered at 0.05 or 0.10, he can buy the Julys and sell the Augusts as a spread. In either case, it is called rolling the spread. When the August expires, he can sell the Septembers, and so on. The goal is to get a credit month after month. At some point, the aggregate credit from the call sales each month is greater than the price initially paid for the long leg of the spread, thus eliminating the original net debit. Exhibit 11.6 shows how the monthly credits from selling the one-month calls aggregate over time. EXHIBIT 11.6 A “free” call. After July has expired, 1.45 of premium is earned. After August expiration, the aggregate increases to 2.90. When the September calls, which have 36 days until expiration, are sold, another 1.60 is added to the total premium collected. Over three months—assuming the stock price, volatility, and the other inputs don’t change—this trader collects a total of 4.50. That’s 0.50 more than the price originally paid for the December 60 call leg of the spread. At this point, he effectively owns the December call for free. Of course, this call isn’t really free; it’s earned. It’s paid for with risk and maybe a few sleepless nights. At this point, even if the stock and, consequently, the December call go to zero, the position is still a profitable trade because of the continued month-to-month rolling. This is now a no-lose situation. When the long call of the spread has been paid for by rolling, there are three choices moving forward: sell it, hold it, or continue writing calls against it. If the trader’s opinion calls for the stock to decline, it’s logical to sell the December call and take the residual value as profit. In this case, over three months the trade will have produced 4.50 in premium from the sale of three consecutive one-month calls, which is more than the initial purchase price of the December call. At September expiration, the premium that will be received for selling the December call is all profit, plus 0.50, which is the aggregate premium minus the initial cost of the December call. If the outlook is for the underlying to rise, it makes sense to hold the call. Any appreciation in the value of the call resulting from delta gains as the underlying moves higher is good—$0.50 plus whatever the call can be sold for. If the forecast is for XYZ to remain neutral, it’s logical to continue selling the one-month call. Because the December call has been financed by the aggregate short call premiums already, additional premiums earned by writing calls are profit with “free” protection. As long as the short is closed at its expiration, the risk of loss is eliminated. This is the general nature of rolling calls in a calendar spread. It’s a beautiful plan when it works! The problem is that it is incredibly unlikely that the stock will stay right at $60 per share for five months. It’s almost inevitable that it will move at some point. It’s like a game of Russian roulette. At some point it’s going to be a losing proposition—you just don’t know when. The benefit of rolling is that if the trade works out for a few months in a row, the long call is paid for and the risk of loss is covered by aggregate profits. If we step outside this best-case theoretical world and consider what is really happening on a day-to-day basis, we can gain insight on how to manage this type of trade when things go wrong. Effectively, a long calendar is a typical gamma/theta trade. Negative gamma hurts. Positive theta helps. If we knew which way the stock was going, we would simply buy or sell stock to adjust to get long or short deltas. But, unfortunately, we don’t. Our only tool is to hedge by buying or selling stock as mentioned above to flatten out when gamma causes the position delta to get more positive or negative. 1 The bottom line is that if the effect of gamma creates unwanted long deltas but the theta/gamma is still a desirable position, selling stock flattens out the delta. If the effect of gamma creates unwanted short deltas, buying stock flattens out the delta. Trading Volatility Term Structure There are other reasons for trading calendar spreads besides generating income from theta. If there is skew in the term structure of volatility, which was discussed in Chapter 3, a calendar spread is a way to trade volatility. The tactic is to buy the “cheap” month and sell the “expensive” month. Selling the Front, Buying the Back If for a particular stock, the February ATM calls are trading at 50 volatility and the May ATM calls are trading at 35 volatility, a vol-calendar trader would buy the Mays and sell the Februarys. Sounds simple, right? The devil is in the details. We’ll look at an example and then discuss some common pitfalls with vol-trading calendars. George has been studying the implied volatility of a $164.15 stock. George notices that front-month volatility has been higher than that of the other months for a couple of weeks. There is nothing in the news to indicate immediate risk of extraordinary movement occurring in this example. George sees that he can sell the 22-day July 165 calls at a 45 percent IV and buy the 85-day September 165 calls at a 38 percent IV. George would like to buy the calendar spread, because he believes the July ATM volatility will drop down to around 38, where the September is trading. If he puts on this trade, he will establish the following position: What are George’s risks? Because he would be selling the short-term ATM option, negative gamma could be a problem. The greeks for this trade, shown in Exhibit 11.7 , confirm this. The negative gamma means each dollar of stock price movement causes an adverse change of about 0.09 to delta. The spread’s delta becomes shorter when the stock rises and longer when the stock falls. Because the position’s delta is long 0.369 from the start, some price appreciation may be welcomed in the short term. The stock advance will yield profits but at a diminishing rate, as negative gamma reduces the delta. EXHIBIT 11.7 10-lot July–September 165 call calendar. But just looking at the net position greeks doesn’t tell the whole story. It is important to appreciate the fact that long calendar spreads such as this have long vegas. In this case, the vega is +1.522. But what does this number really mean? This vega figure means that if IV rises or falls in both the July and the September calls by the same amount, the spread makes or loses $152 per vol point. George’s plan, however, is to see the July’s volatility decline to converge with the September’s. He hopes the volatilities of the two months will move independently of each other. To better gauge his risk, he needs to look at the vega of each option. With the stock at $164.15 the vegas are as follows: If George is right and July volatility declines 8 points, from 46 to 38, he will make $1,283 ($1.604 × 100 × 8). There are a couple of things that can go awry. First, instead of the volatilities converging, they can diverge further. Implied volatility is a slave to the whims of the market. If the July IV continues to rise while the September IV stays the same, George loses $160 per vol point. The second thing that can go wrong is the September IV declining along with the July IV. This can lead George into trouble, too. It depends the extent to which the September volatility declines. In this example, the vega of the September leg is about twice that of the July leg. That means that if the July volatility loses eight points while the September volatility declines four points, profits from the July calls will be negated by losses from the September calls. If the September volatility falls even more, the trade is a loser. IV is a common cause of time-spread failure for market makers. When i in the front month rises, the volatility of the back-months sometimes does as well. When this happens, it’s often because market makers who sold front-month options to retail or institutional buyers buy the back-month options to hedge their short-gamma risk. If the market maker buys enough back-month options, he or she will accumulate positive vega. But when the market sells the front-month volatility back to the market makers, the back months drop, too, because market makers no longer need the back months for a hedge. Traders should study historical implied volatility to avoid this pitfall. As is always the case with long vega strategies, there is a risk of a decline in IV. Buying long-term options with implied volatility in the lower third of the 12-month IV range helps improve the chances of success, since the volatility being bought is historically cheap. This can be tricky, however. If a trader looks back on a chart of IV for an option class and sees that over the past six months it has ranged between 20 and 30 but nine months ago it spiked up to, say, 55, there must be a reason. This solitary spike could be just an anomaly. To eliminate the noise from volatility charts, it helps to filter the data. News stories from that time period and historical stock charts will usually tell the story of why volatility spiked. Often, it is a one-time event that led to the spike. Is it reasonable to include this unique situation when trying to get a feel for the typical range of implied volatility? Usually not. This is a judgment call that needs to be made on a case-by-case basis. The ultimate objective of this exercise is to determine: “Is volatility cheap or expensive?” Buying the Front, Selling the Back All trading is based on the principle of “buy low, sell high”—even volatility trading. With time spreads, we can do both at once, but we are not limited to selling the front and buying the back. When short-term options are trading at a lower IV than long-term ones, there may be an opportunity to sell the calendar. If the IV of the front month is 17 and the back-month IV is 25, for example, it could be a wise trade to buy the front and sell the back. But selling time spreads in this manner comes with its own unique set of risks. First, a short calendar’s greeks are the opposite of those of a long calendar. This trade has negative theta with positive gamma. A sideways market hurts this position as negative theta does its damage. Each day of carrying the position is paid for with time decay. The short calendar is also a short-vega trade. At face value, this implies that a drop in IV leads to profit and that the higher the IV sold in the back month, the better. As with buying a calendar, there are some caveats to this logic. If there is an across-the-board decline in IV, the net short vega will lead to a profit. But an across-the-board drop in volatility, in this case, is probably not a realistic expectation. The front month tends to be more sensitive to volatility. It is a common occurrence for the front month to be “cheap” while the back month is “expensive.” The volatilities of the different months can move independently, as they can when one buys a time spread. There are a couple of scenarios that might lead to the back-month volatility’s being higher than the front month. One is high complacency in the short term. When the market collectively sells options in expectation of lackluster trading, it generally prefers to sell the short-term options. Why? Higher theta. Because the trade has less time until expiration, the trade has a shorter period of risk. Because of this, selling pressure can push down IV in the front-month options more than in the back. Again, the front month is more sensitive to changes in implied volatility. Because volatility has peaks and troughs, this can be a smart time to sell a calendar. The focus here is in seeing the “cheap” front month rise back up to normal levels, not so much in seeing the “expensive” back month fall. This trade is certainly not without risk. If the market doesn’t move, the negative theta of the short calendar leads to a slow, painful death for calendar sellers. Another scenario in which the back-month volatility can trade higher than the front is when the market expects higher movement after the expiration of the short-term option but before the expiration of the long-term option. Situations such as the expectation of the resolution of a lawsuit, a product announcement, or some other one-time event down the road are opportunities for the market to expect such movement. This strategy focuses on the back-month vol coming back down to normal levels, not on the front-month vol rising. This can be a more speculative situation for a volatility trade, and more can go wrong. The biggest volatility risk in selling a time spread is that what goes up can continue to go up. The volatility disparity here is created by hedgers and speculators favoring long-term options, hence pushing up the volatility, in anticipation of a big future stock move. As the likely date of the anticipated event draws near, more buyers can be attracted to the market, driving up IV even further. Realized volatility can remain low as investors and traders lie in wait. This scenario is doubly dangerous when volatility rises and the stock doesn’t move. A trader can lose on negative theta and lose on negative vega. A Directional Approach Calendar spreads are often purchased when the outlook for the underlying is neutral. Sell the short-term ATM option; buy the long-term ATM option; collect theta. But with negative gamma, these trades are never really neutral. The delta is constantly changing, becoming more positive or negative. It’s like a rubber band: at times being stretched in either direction but always demanding a pull back to the strike. When the strike price being traded is not ATM, calendar spreads can be strategically traded as directional plays. Buying a calendar, whether using calls or puts, where the strike price is above the current stock price is a bullish strategy. With calls, the positive delta of the long-term out-of-the-money (OTM) call will be greater than the negative delta of the short-term OTM call. For puts, the positive delta of the short-term in-the-money (ITM) put will be greater than the negative delta of the long-term ITM put. Just the opposite applies if the strike price is below the current stock price. The negative delta of the short-term ITM call is greater than the positive delta of the long-term ITM call. The negative delta of the long-term OTM put is greater than the positive delta of the short-term OTM put. When the position starts out with either a positive or negative delta, movement in the direction of the delta is necessary for the trade to be profitable. Negative gamma is also an important strategic consideration. Stock-price movement is needed, but not too much. Buying calendar spreads is like playing outfield in a baseball game. To catch a fly ball, an outfielder must focus on both distance and timing. He must gauge how far the ball will be hit and how long it will take to get there. With calendars, the distance is the strike price—that’s where the stock needs to be—and the time is the expiration day of the short month’s option: that’s when it needs to be at the target price. For example, with Wal-Mart (WMT) at $48.50, a trader, Pete, is looking for a rise to about $50 over the next five or six weeks. Pete buys the August–September call calendar. In this example, August has 39 days until expiration and September has 74 days. Exactly what does 50 cents buy Pete? The stock price sitting below the strike price means a net positive delta. This long time spread also has positive theta and vega. Gamma is negative. Exhibit 11.8 shows the specifics. EXHIBIT 11.8 10-lot Wal-Mart August–September 50 call calendar. The delta of this trade, while positive, is relatively small with 39 days left until August expiration. It’s not rational to expect a quick profit if the stock advances faster than expected. But ultimately, a rise in stock price is the goal. In this example, Wal-Mart needs to rise to $50, and timing is everything. It needs to be at that price in 39 days. In the interim, a move too big and too fast in either direction hurts the trade because of negative gamma. Starting with Wal-Mart at $48.50, delta/gamma problems are worse to the downside. Exhibit 11.9 shows the effects of stock price on delta, gamma, and theta. EXHIBIT 11.9 Stock price movement and greeks. If Wal-Mart moves lower, the delta gets more positive, racking up losses at a higher rate. To add to Pete’s woes, theta becomes less of a benefit as the stock drifts lower. At $47 a share, theta is about flat. With Wal-Mart trading even lower than $47, the positive theta of the August call is overshadowed by the negative theta of the September. Theta can become negative, causing the position to lose value as time passes. A big move to the upside doesn’t help either. If Wal-Mart rises just a bit, the −0.323 gamma only lessens the benefit of the 0.563 delta. But above $50, negative gamma begins to cause the delta to become increasingly negative. Theta begins to wither away at higher stock prices as well. The place to be is right at $50. The delta is flat and theta is highest. As long as Wal-Mart finds its way up to this price by the third Friday of August, life is good for Pete. The In-or-Out Crowd Pete could just as well have traded the Aug–Sep 50 put calendar in this situation. If he’d been bearish, he could have traded either the Aug–Sep 45 call spread or the Aug–Sep 45 put spread. Whether bullish or bearish, as mentioned earlier, the call calendar and the put calendar both function about the same. When deciding which to use, the important consideration is that one of them will be in-the-money and the other will be OTM. Whether you have an ITM spread or an OTM spread has potential implications for the success of the trade. The bid-ask spreads tend to be wider for higher-delta, ITM options. Because of this, it can be more expensive to enter into an ITM calendar. Why? Trading options with wider markets requires conceding more edge. Take the following options series: By buying the May 50 calls at 3.20, a trader gives up 0.10 of theoretical edge (3.20 is 0.10 higher than the theoretical value). Buying the put at 1.00 means buying only 0.05 over theoretical. Because a calendar is a two-legged spread, the double edge given up by trading the wider markets of two in-the-money options can make the out-of-the-money spread a more attractive trade. The issue of wider markets is compounded when rolling the spread. Giving up a nickel or a dime each month can add up, especially on nominally low-priced spreads. It can cut into a high percentage of profits. Early assignment can complicate ITM calendars made up of American options, as dividends and interest can come into play. The short leg of the spread could get assigned before the expiration date as traders exercise calls to capture the dividend. Short ITM puts may get assigned early because of interest. Although assignment is an undesirable outcome for most calendar spread traders, getting assigned on the short leg of the calendar spread may not necessarily create a significantly different trade. If a long put calendar, for example, has a short front-month put that is so deep in-the-money that it is likely to get assigned, it is trading close to a 100 delta. It is effectively a long stock position already. After assignment, when a long stock position is created, the resulting position is long stock with a deep ITM long put—a fairly delta-flat position. Double Calendars Definition : A double calendar spread is the execution of two calendar spreads that have the same months in common but have two different strike prices. Example Sell 1 XYZ February 70 call Buy 1 XYZ March 70 call Sell 1 XYZ February 75 call Buy 1 XYZ March 75 call Double calendars can be traded for many reasons. They can be vega plays. If there is a volatility-time skew, a double calendar is a way to take a position without concentrating delta or gamma/theta risk at a single strike. This spread can also be a gamma/theta play. In that case, there are two strikes, so there are two potential focal points to gravitate to (in the case of a long double calendar) or avoid (in the case of a short double calendar). Selling the two back-month strikes and buying the front-month strikes leads to negative theta and positive gamma. The positive gamma creates favorable deltas when the underlying moves. Positive or negative deltas can be covered by trading the underlying stock. With positive gamma, profits can be racked up by buying the underlying to cover short deltas and subsequently selling the underlying to cover long deltas. Buying the two back-month strikes and selling the front-month strikes creates negative gamma and positive theta, just as in a conventional calendar. But the underlying stock has two target price points to shoot for at expiration to achieve the maximum payout. Often double calendars are traded as IV plays. Many times when they are traded as IV plays, traders trade the lower-strike spread as a put calendar and the higher-strike spread a call calendar. In that case, the spread is sometimes referred to as a strangle swap . Strangles are discussed in Chapter 15. Two Courses of Action Although there may be many motivations for trading a double calendar, there are only two courses of action: buy it or sell it. While, for example, the trader’s goal may be to capture theta, buying a double calendar comes with the baggage of the other greeks. Fully understanding the interrelationship of the greeks is essential to success. Option traders must take a holistic view of their positions. Let’s look at an example of buying a double calendar. In this example, Minnesota Mining & Manufacturing (MMM) has been trading in a range between about $85 and $97 per share. The current price of Minnesota Mining & Manufacturing is $87.90. Economic data indicate no specific reasons to anticipate that Minnesota Mining & Manufacturing will deviate from its recent range over the next month—that is, there is nothing in the news, no earnings anticipated, and the overall market is stable. August IV is higher than October IV by one volatility point, and October implied volatility is in line with 30-day historical volatility. There are 38 days until August expiration, and 101 days until October expiration. The Aug–Oct 85–90 double calendar can be traded at the following prices: Much like a traditional calendar spread, the price points cannot be definitively plotted on a P&(L) diagram. What is known for certain is that at August expiration, the maximum loss is $3,200. While it’s comforting to know that there is limited loss, losing the entire premium that was paid for the spread is an outcome most traders would like to avoid. We also know the maximum gains occur at the strike prices; but not exactly what the maximum profit can be. Exhibit 11.10 provides an alternative picture of the position that is useful in managing the trade on a day-to-day basis. EXHIBIT 11.10 10-lot Minnesota Mining & Manufacturing Aug–Oct 85–90 double call calendar. These numbers are a good representation of the position’s risk. Knowing that long calendars and long double calendars have maximum losses at the expiration of the short-term option equal to the net premiums paid, the max loss in this example is 3.20. Break-even prices are not relevant to this position because they cannot be determined with any certainty. What is important is to get a feel for how much movement can hurt the position. To make $19 a day in theta, a −0.468 gamma must be accepted. In the long run, $1 of movement is irrelevant. In fact, some movement is favorable because the ideal point for MMM to be at, at August expiration is either $85 or $90. So while small moves are acceptable, big moves are of concern. The negative gamma is an illustration of this warning. The other risk besides direction is vega. A positive 1.471 vega means the calendar makes or loses about $147 with each one-point across-the-board change in implied volatility. Implied volatility is a risk in all calendar trades. Volatility was one of the criteria studied when considering this trade. Recall that the August IV was one point higher than the October and that the October IV was in line with the 30-day historical volatility at inception of the trade. Considering the volatility data is part of the due diligence when considering a calendar or a double calendar. First, the (slightly) more expensive options (August) are being sold, and the cheaper ones are being bought (October). A study of the company reveals no news to lead one to believe that Minnesota Mining & Manufacturing should move at a higher realized volatility than it currently is in this example. Therefore, the front month’s higher IV is not a red flag. Because the volatility of the October option (the month being purchased) is in line with the historical volatility, the trader could feel that he is paying a reasonable price for this volatility. In the end, the trade is evaluated on the underlying stock, realized volatility, and IV. The trade should be executed only after weighing all the available data. Trading is both cerebral and statistical in nature. It’s about gaining a statistically better chance of success by making rational decisions. Diagonals Definition : A diagonal spread is an option strategy that involves buying one option and selling another option with a different strike price and with a different expiration date. Diagonals are another strategy in the time spread family. Diagonals enable a trader to exploit opportunities similar to those exploited by a calendar spread, but because the options in a diagonal spread have two different strike prices, the trade is more focused on delta. The name diagonal comes from the fact that the spread is a combination of a horizontal spread (two different months) and a vertical spread (two different strikes). Say it’s 22 days until January expiration and 50 days until February expiration. Apple Inc. (AAPL) is trading at $405.10. Apple has been in an uptrend heading toward the peak of its six-month range, which is around $420. A trader, John, believes that it will continue to rise and hit $420 again by February expiration. Historical volatility is 28 percent. The February 400 calls are offered at a 32 implied volatility and the January 420 calls are bid on a 29 implied volatility. John executes the following diagonal: Exhibit 11.11 shows the analytics for this trade. EXHIBIT 11.11 Apple January–February 400–420 call diagonal. From the presented data, is this a good trade? The answer to this question is contingent on whether the position John is taking is congruent with his view of direction and volatility and what the market tells him about these elements. John is bullish up to August expiration, and the stock in this example is in an uptrend. Any rationale for bullishness may come from technical or fundamental analysis, but techniques for picking direction, for the most part, are beyond the scope of this book. Buying the lower strike in the February option gives this trade a more positive delta than a straight calendar spread would have. The trader’s delta is 0.255, or the equivalent of about 25.5 shares of Apple. This reflects the trader’s directional view. The volatility is not as easy to decipher. A specific volatility forecast was not stated above, but there are a few relevant bits of information that should be considered, whether or not the trader has a specific view on future volatility. First, the historical volatility is 28 percent. That’s lower than either the January or the February calls. That’s not ideal. In a perfect world, it’s better to buy below historical and sell above. To that point, the February option that John is buying has a higher volatility than the January he is selling. Not so good either. Are these volatility observations deal breakers? A Good Ex-Skews It’s important to take skew into consideration. Because the January calls have a higher strike price than the February calls, it’s logical for them to trade at a lower implied volatility. Is this enough to justify the possibility of selling the lower volatility? Consider first that there is some margin for error. The bid-ask spreads of each of the options has a volatility disparity. In this case, both the January and February calls are 10 cents wide. That means with a January vega of 0.34 the bid-ask is about 0.29 vol points wide. The Februarys have a 0.57 vega. They are about 0.18 vol points wide. That accounts for some of the disparity. Natural vertical skew accounts for the rest of the difference, which is acceptable as long as the skew is not abnormally pronounced. As for other volatility considerations, this diagonal has the rather unorthodox juxtaposition of positive vega and negative gamma seen with other time spreads. The trader is looking for a move upward, but not a big one. As the stock rises and Apple moves closer to the 420 strike, the positive delta will shrink and the negative gamma will increase. In order to continue to enjoy profits as the stock rises, John may have to buy shares of Apple to keep his positive delta. The risk here is that if he buys stock and Apple retraces, he may end up negative scalping stock. In other words, he may sell it back at a lower price than he bought it. Using stock to adjust the delta in a negative-gamma play can be risky business. Gamma scalping is addressed further in Chapter 13. Making the Most of Your Options The trader from the previous example had a time-spread alternative to the diagonal: John could have simply bought a traditional time spread at the 420 strike. Recall that calendars reap the maximum reward when they are at the shared strike price at expiration of the short-term option. Why would he choose one over the other? The diagonal in that example uses a lower-strike call in the February than a straight 420 calendar spread and therefore has a higher delta, but it costs more. Gamma, theta, and vega may be slightly lower with the in-the-money call, depending on how far from the strike price the ITM call is and how much time until expiration it has. These, however, are less relevant differences. The delta of the February 400 call is about 0.57. The February 420 call, however, has only a 0.39 delta. The 0.18 delta difference between the calls means the position delta of the time spread will be only about 0.07 instead of about 0.25 of the diagonal—a big difference. But the trade-off for lower delta is that the February 420 call can be bought for 12.15. That means a lower debit paid—that means less at risk. Conversely, though there is greater risk with the diagonal, the bigger delta provides a bigger payoff if the trader is right. Double Diagonals A double diagonal spread is the simultaneous trading of two diagonal spreads: one call spread and one put spread. The distance between the strikes is the same in both diagonals, and both have the same two expiration months. Usually, the two long-term options are more out-of-the-money than the two shorter-term options. For example Buy 1 XYZ May 70 put Sell 1 XYZ March 75 put Sell 1 XYZ March 85 call Buy 1 XYZ May 90 call Like many option strategies, the double diagonal can be looked at from a number of angles. Certainly, this is a trade composed of two diagonal spreads—the March–May 70–75 put and the March–May 85–90 call. It is also two strangles—buying the May 70–90 strangle and selling the March 75–85 strangle. One insightful way to look at this spread is as an iron condor in which the guts are March options and the wings are May options. Trading a double diagonal like this one, rather than a typically positioned iron condor, can offer a few advantages. The first advantage, of course, is theta. Selling short-term options and buying long-term options helps the trader reap higher rates of decay. Theta is the raison d’être of the iron condor. A second advantage is rolling. If the underlying asset stays in a range for a long period of time, the short strangle can be rolled month after month. There may, in some cases, also be volatility-term-structure discrepancies on which to capitalize. A trader, Paul, is studying JPMorgan (JPM). The current stock price is $49.85. In this example, JPMorgan has been trading in a pretty tight range over the past few months. Paul believes it will continue to do so over the next month. Paul considers the following trade: Paul considers volatility. In this example, the JPMorgan ATM call, the August 50 (which is not shown here), is trading at 22.9 percent implied volatility. This is in line with the 20-day historical volatility, which is 23 percent. The August IV appears to be reasonably in line with the September volatility, after accounting for vertical skew. The IV of the August 52.50 calls is 1.5 points above that of the September 55 calls and the August 47.50 put IV is 1.6 points below the September 45 put IV. It appears that neither month’s volatility is cheap or expensive. Exhibit 11.12 shows the trade’s greeks. EXHIBIT 11.12 10-lot JPMorgan August–September 45–47.50–52.50–55 double diagonal. The analytics of this trade are similar to those of an iron condor. Immediate directional risk is almost nonexistent, as indicated by the delta. But gamma and theta are high, even higher than they would be if this were a straight September iron condor, although not as high as if this were an August iron condor. Vega is positive. Surely, if this were an August or a September iron condor, vega would be negative. In this example, Paul is indifferent as to whether vega is positive or negative because IV is fairly priced in terms of historical volatility and term structure. In fact, to play it close to the vest, Paul probably wants the smallest vega possible, in case of an IV move. Why take on the risk? The motivation for Paul’s double diagonal was purely theta. The volatilities were all in line. And this one-month spread can’t be rolled. If Paul were interested in rolling, he could have purchased longer-term options. But if he is anticipating a sideways market for only the next month and feels that volatility could pick up after that, the one-month play is the way to go. After August expiration, Paul will have three choices: sell his Septembers, hold them, or turn them into a traditional iron condor by selling the September 47.50s and 52.50s. This depends on whether he is indifferent, expects high volatility, or expects low volatility. The Strength of the Calendar Spreads in the calendar-spread family allow traders to take their trading to a higher level of sophistication. More basic strategies, like vertical spreads and wing spreads, provide a practical means for taking positions in direction, realized volatility, and to some extent implied volatility. But because calendar-family spreads involve two expiration months, traders can take positions in the same market variables as with these more basic strategies and also in the volatility spread between different expiration months. Calendar-family spreads are veritable volatility spreads. This is a powerful tool for option traders to have at their disposal. Note 1 . Advanced hedging techniques are discussed in subsequent chapters. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00023.html SCORE: 607.00 ================================================================================ CHAPTER 12 Delta-Neutral Trading Trading Implied Volatility Many of the strategies covered so far have been option-selling strategies. Some had a directional bias; some did not. Most of the strategies did have a primary focus on realized volatility—especially selling it. These short volatility strategies require time. The reward of low stock volatility is theta. In general, most of the strategies previously covered were theta trades in which negative gamma was an unpleasant inconvenience to be dealt with. Moving forward, much of the remainder of this book will involve more in-depth discussions of trading both realized and implied volatility (IV), with a focus on the harmonious, and sometimes disharmonious, relationship between the two types. Much attention will be given to how IV trades in the option market, describing situations in which volatility moves are likely to occur and how to trade them. Direction Neutral versus Direction Indifferent In the world of nonlinear trading, there are two possible nondirectional views of the underlying asset: direction neutral and direction indifferent. Direction neutral means the trader believes the stock will not trend either higher or lower. The trader is neutral in his or her assessment of the future direction of the asset. Short iron condors, long time spreads, and out-of-the-money (OTM) credit spreads are examples of direction-neutral strategies. These strategies generally have deltas close to zero. Because of negative gamma, movement is the bane of the direction-neutral trade. Direction indifferent means the trader may desire movement in the underlying but is indifferent as to whether that movement is up or down. Some direction-indifferent trades are almost completely insulated from directional movement, with a focus on interest or dividends instead. Examples of these types of trades are conversions, reversals, and boxes, which are described in Chapter 6, as well as dividend plays, which are described in Chapter 8. Other direction-indifferent strategies are long option strategies that have positive gamma. In these trades, the focus is on movement, but the direction of that movement is irrelevant. These are plays that are bullish on realized volatility. Yet other direction-indifferent strategies are volatility plays from the perspective of IV. These are trades in which the trader’s intent is to take a bullish or bearish position in IV. Delta Neutral To be truly direction neutral or direction indifferent means to have a delta equal to zero. In other words, there are no immediate gains if the underlying moves incrementally higher or lower. This zero-delta method of trading is called delta-neutral trading . A delta-neutral position can be created from any option position simply by trading stock to flatten out the delta. A very basic example of a delta-neutral trade is a long at-the-money (ATM) call with short stock. Consider a trade in which we buy 20 ATM calls that have a 50 delta and sell stock on a delta-neutral ratio. Buy 20 50-delta calls (long 1,000 deltas) Short 1,000 shares (short 1,000 deltas) In this position, we are long 1,000 deltas from the calls (20 × 50) and short 1,000 deltas from the short sale of stock. The net delta of the position is zero. Therefore, the immediate directional exposure has been eliminated from the trade. But intuitively, there are other opportunities for profit or loss with this trade. The addition of short stock to the calls will affect only the delta, not the other greeks. The long calls have positive gamma, negative theta, and positive vega. Exhibit 12.1 is a simplified representation of the greeks for this trade. EXHIBIT 12.1 20-lot delta-neutral long call. With delta not an immediate concern, the focus here is on gamma, theta, and vega. The +1.15 vega indicates that each one-point change in IV makes or loses $115 for this trade. Yet there is more to the volatility story. Each day that passes costs the trader $50 in time decay. Holding the position for an extended period of time can produce a loser even if IV rises. Gamma is potentially connected to the success of this trade, too. If the underlying moves in either direction, profit from deltas created by positive gamma may offset the losses from theta. In fact, a big enough move in either direction can produce a profitable trade, regardless of what happens to IV. Imagine, for a moment, that this trade is held until expiration. If the stock is below the strike price at this point, the calls expire. The resulting position is short 1,000 shares of stock. If the stock is above the strike price at expiration, the calls can be exercised, creating 2,000 shares of long stock. Because the trade is already short 1,000 shares, the resulting net position is long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock moves in either direction the greater the profit potential. The underlying has to move far enough above or below the strike price to allow the beneficial gains from buying or selling stock to cover the option premium lost from time decay. If the trade is held until expiration, the underlying needs to move far enough to cover the entire premium spent on the calls. The solid lines forming a V in Exhibit 12.2 conceptually illustrate the profit or loss for this delta-neutral long call at expiration. EXHIBIT 12.2 Profit-and-loss diagram for delta-neutral long-call trade. Because of gamma, some deltas will be created by movement of the underlying before expiration. Gamma may lead to this being a profitable trade in the short term, depending on time and what happens with IV. The dotted line illustrates the profit or loss of this trade at the point in time when the trade is established. Because the options may still have time value at this point—depending on how far from the strike price the stock is trading—the value of the position, as a whole, is higher than it will be if the calls are trading at parity at expiration. Regardless, the plan is for the stock to make a move in either direction. The bigger the move and the faster it happens, the better. Why Trade Delta Neutral? A few years ago, I was teaching a class on option trading. Before the seminar began, I was talking with one of the students in attendance. I asked him what he hoped to learn in the class. He said that he was really interested in learning how to trade delta neutral. When I asked him why he was interested in that specific area of trading, he replied, “I hear that’s where all the big money is made!” This observation, right or wrong, probably stems from the fact that in the past most of the trading in this esoteric discipline has been executed by professional traders. There are two primary reasons why the pros have dominated this strategy: high commissions and high margin requirements for retail traders. Recently, these two reasons have all but evaporated. First, the ultracompetitive world of online brokers has driven commissions for retail traders down to, in some cases, what some market makers pay. Second, the oppressive margin requirements that retail option traders were subjected to until 2007 have given way to portfolio margining. Portfolio Margining Customer portfolio margining is a method of calculating customer margin in which the margin requirement is based on the “up and down risk” of the portfolio. Before the advent of portfolio margining, retail traders were subject to strategy-based margining, also called Reg. T margining, which in many cases required a significantly higher amount of capital to carry a position than portfolio margining does. With portfolio margining, highly correlated securities can be offset against each other for purposes of calculating margin. For example, SPX options and SPY options—both option classes based on the Standard & Poor’s 500 Index—can be considered together in the margin calculation. A bearish position in one and a bullish position in the other may partially offset the overall risk of the portfolio and therefore can help to reduce the overall margin requirement. With portfolio margining, many strategies are margined in such a way that, from the point of view of this author, they are subject to a much more logical means of risk assessment. Strategy-based margining required traders of some strategies, like a protective put, to deposit significantly more capital than one could possibly lose by holding the position. The old rules require a minimum margin of 50 percent of the stock’s value and up to 100 percent of the put premium. A portfolio-margined protective put may require only a fraction of what it would with strategy-based margining. Even though Reg. T margining is antiquated and sometimes unreasonable, many traders must still abide by these constraints. Not all traders meet the eligibility requirements to qualify for portfolio-based margining. There is a minimum account balance for retail traders to be eligible for this treatment. A broker may also require other criteria to be met for the trader to benefit from this special margining. Ultimately, portfolio margining allows retail traders to be margined similarly to professional traders. There are some traders, both professional and otherwise, who indeed have made “big money,” as the student in my class said, trading delta neutral. But, to be sure, there are successful and unsuccessful traders in many areas of trading. The real motivation for trading delta neutral is to take a position in volatility, both implied and realized. Trading Implied Volatility With a typical option, the sensitivity of delta overshadows that of vega. To try and profit from a rise or fall in IV, one has to trade delta neutral to eliminate immediate directional sensitivity. There are many strategies that can be traded as delta-neutral IV strategies simply by adding stock. Throughout this chapter, I will continue using a single option leg with stock, since it provides a simple yet practical example. It’s important to note that delta-neutral trading does not refer to a specific strategy; it refers to the fact that the trader is indifferent to direction. Direction isn’t being traded, volatility is. Volatility trading is fundamentally different from other types of trading. While stocks can rise to infinity or decline to zero, volatility can’t. Implied volatility, in some situations, can rise to lofty levels of 100, 200, or even higher. But in the long-run, these high levels are not sustainable for most stocks. Furthermore, an IV of zero means that the options have no extrinsic value at all. Now that we have established that the thresholds of volatility are not as high as infinity and not as low as zero, where exactly are they? The limits to how high or low IV can go are not lines in the sand. They are more like tides that ebb and flow, but normally come up only so far onto the beach. The volatility of an individual stock tends to trade within a range that can be unique to that particular stock. This can be observed by studying a chart of recent volatility. When IV deviates from the range, it is typical for it to return to the range. This is called reversion to the mean , which was discussed in Chapter 3. IV can get stretched in either direction like a rubber band but then tends to snap back to its original shape. There are many examples of situations where reversion to the mean enters into trading. In some, volatility temporarily dips below the typical range, and in some, it rises beyond the recent range. One of the most common examples is the rush and the crush. The Rush and the Crush In this situation, volatility rises before and falls after a widely anticipated news announcement, of earnings, for instance, or of a Food and Drug Administration (FDA) approval. In this situation, option buyers rush in and bid up IV. The more uncertainty—the more demand for insurance—the higher vol rises. When the event finally occurs and the move takes place or doesn’t, volatility gets crushed. The crush occurs when volatility falls very sharply—sometimes 10 points, 20 points, or more—in minutes. Traders with large vega positions appreciate the appropriateness of the term crush all too well. Volatility traders also affectionately refer to this sudden drop in IV by saying that volatility has gotten “whacked.” In order to have a feel for whether implied volatility is high or low for a particular stock, you need to know where it’s been. It’s helpful to have an idea of where realized volatility is and has been, too. To be sure, one analysis cannot be entirely separate from the other. Studying both implied and realized volatility and how they relate is essential to seeing the big picture. The Inertia of Volatility Sir Isaac Newton said that an object in motion tends to stay in motion unless acted upon by another force. Volatility acts much the same way. Most stocks tend to trade with a certain measurable amount of daily price fluctuations. This can be observed by looking at the stock’s realized volatility. If there is no outside force—some pivotal event that fundamentally changes how the stock is likely to behave—one would expect the stock to continue trading with the same level of daily price movement. This means IV (the market’s expectation of future stock volatility) should be the same as realized volatility (the calculated past stock volatility). But just as in physics, it seems there is always some friction affecting the course of what is in motion. Corporate earnings, Federal Reserve Board reports, apathy, lulls in the market, armed conflicts, holidays, rumors, and takeovers, among other market happenings all provide a catalyst for volatility changes. Divergences of realized and implied volatility, then, are commonplace. These divergences can create tradable conditions, some of which are more easily exploited than others. To find these opportunities, a trader must conduct a study of volatility. Volatility charts can help a trader visualize the big picture. This historical information offers a comparison of what is happening now in volatility with what has happened in the past. The following examples use a volatility chart to show how two different traders might have traded the rush and crush of an earnings report. Volatility Selling Susie Seller, a volatility trader, studies semiconductor stocks. Exhibit 12.3 shows the volatilities of a $50 chip stock. The circled area shows what happened before and after second-quarter earnings were reported in July. The black line is the IV, and the gray is the 30-day historical. EXHIBIT 12.3 Chip stock volatility before and after earnings reports. Source : Chart courtesy of iVolatility.com In mid-July, Susie did some digging to learn that earnings were to be announced on July 24, after the close. She was careful to observe the classic rush and crush that occurred to varying degrees around the last three earnings announcements, in October, January, and April. In each case, IV firmed up before earnings only to get crushed after the report. In mid-to-late July, she watched as IV climbed to the mid-30s (the rush) just before earnings. As the stock lay in wait for the report, trading came to a proverbial screeching halt, sending realized volatility lower, to about 13 percent. Susie waited for the end of the day just before the report to make her move. Before the closing bell, the stock was at $50. Susie sold 20 one-month 50-strike calls at 2.10 (a 35 volatility) and bought 1,100 shares of the underlying stock at $50 to become delta neutral. Exhibit 12.4 shows Susie’s position. EXHIBIT 12.4 Delta-neutral short ATM call, long stock position. Her delta was just about flat. The delta for the 50 calls was 0.54 per contract. Selling a 20-lot creates 10.80 short deltas for her overall position. After buying 1,100 shares, she was left long 0.20 deltas, about the equivalence of being long 20 shares. Where did her risk lie? Her biggest concern was negative gamma. Without even seeing a chart of the stock’s price, we can see from the volatility chart that this stock can have big moves on earnings. In October, earnings caused a more than 10-point jump in realized volatility, to its highest level during the year shown. Whether the stock rose or fell is irrelevant. Either event means risk for a premium seller. The positive theta looks good on the surface, but in fact, theta provided Susie with no significant benefit. Her plan was “in and out and nobody gets hurt.” She got into the trade right before the earnings announcement and out as soon as implied volatility dropped off. Ideally, she’d like to hold these types of trades for less than a day. The true prize is vega. Susie was looking for about a 10-point drop in IV, which this option class had following the October and January earnings reports. April had a big drop in IV, as well, of about eight or nine points. Ultimately, what Susie is looking for is reversion to the mean. She gauges the normal level of volatility by observing where it is before and after the surges caused by earnings. From early November to mid- to late- December, the stock’s IV bounced around the 25 percent level. In the month of February, the IV was around 25. After the drop-off following April earnings and through much of May, the IV was closer to 20 percent. In June, IV was just above 25. Susie surmised from this chart that when no earnings event is pending, this stock’s options typically trade at about a 25 percent IV. Therefore, anticipating a 10-point decline from 35 was reasonable, given the information available. If Susie gets it right, she stands to make $1,150 from vega (10 points × 1.15 vegas × 100). As we can see from the right side of the volatility chart in Exhibit 12.3 , Susie did get it right. IV collapsed the next morning by just more than ten points. But she didn’t make $1,150; she made less. Why? Realized volatility (gamma). The jump in realized volatility shown on the graph is a function of the fact that the stock rallied $2 the day after earnings. Negative gamma contributed to negative deltas in the face of a rallying market. This negative delta affected some of Susie’s potential vega profits. So what was Susie’s profit? On this trade she made $800. The next morning at the open, she bought back the 50-strike calls at 2.80 (25 IV) and sold the stock at $52. To compute her actual profit, she compared the prices of the spread when entering the trade with the prices of the spread when exiting. Exhibit 12.5 shows the breakdown of the trade. EXHIBIT 12.5 Profit breakdown of delta-neutral trade. After closing the trade, Susie knew for sure what she made or lost. But there are many times when a trader will hold a delta-neutral position for an extended period of time. If Susie hadn’t closed her trade, she would have looked at her marks to see her P&(L) at that point in time. Marks are the prices at which the securities are trading in the actual market, either in real time or at end of day. With most online brokers’ trading platforms or options-trading software, real-time prices are updated dynamically and always at their fingertips. The profit or loss is, then, calculated automatically by comparing the actual prices of the opening transaction with the current marks. What Susie will want to know is why she made $800. Why not more? Why not less, for that matter? When trading delta neutral, especially with more complex trades involving multiple legs, a manual computation of each leg of the spread can be tedious. And to be sure, just looking at the profit or loss on each leg doesn’t provide an explanation. Susie can see where her profits or losses came from by considering the profit or loss for each influence contributing to the option’s value. Exhibit 12.6 shows the breakdown. EXHIBIT 12.6 Profit breakdown by greek. Delta Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40 profit attributable to that initial delta. Gamma As the stock rose, the negative delta of the position increased as a result of negative gamma. The delta of the stock remained the same, but the negative delta of the 50 call grew by the amount of the gamma. Deriving an exact P&(L) attributable to gamma is difficult because gamma is a dynamic metric: as the stock price changes, so can the gamma. This calculation assumes that gamma remains constant. Therefore, the gamma calculation here provides only an estimate. The initial position gamma of −1.6 means the delta decreases by 3.2 with a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then, would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But she wasn’t short 3.2 deltas for the whole $2. She started out with zero deltas attributable to gamma and ended up being 3.2 shorter from gamma over that $2 move. Therefore, if she assumes her negative delta from gamma grew steadily from 0 to −3.2, she can estimate her average delta loss over that move by dividing by 2. Theta Susie held this trade one day. Her total theta contributed 0.75 or $75 to her position. Vega Vega is where Susie made her money on this trade. She was able to buy her call back 10 IV points lower. The initial position vega was −1.15. Multiplying −1.15 by the negative 10-point crush of volatility yields a vega profit of $1,150. Conclusions Studying her position’s P&(L) by observing what happened in her greeks provides Susie with an alternate—and in some ways, better—method to evaluate her trade. The focus of this delta-neutral trade is less on the price at which Susie can buy the calls back to close the position than on the volatility level at which she can buy them back, weighed against the P&(L) from her other risks. Analyzing her position this way gives her much more information than just comparing opening and closing prices. Not only does she get a good estimate of how much she made or lost, but she can understand why as well. The Imprecision of Estimation It is important to notice that the P&(L) found by adding up the P&(L)’s from the greeks is slightly different from the actual P&(L). There are a couple of reasons for this. First, the change in delta resulting from gamma is only an estimate, because gamma changes as the stock price changes. For small moves in the underlying, the gamma change is less significant, but for larger moves, the rate of change of the gamma can be bigger, and it can be nonlinear. For example, as an option moves from being at-the-money (ATM) to being out-of-the-money (OTM), its gamma decreases. But as the option becomes more OTM, its gamma decreases at a slower rate. Another reason that the P&(L) from the greeks is different from the actual P&(L) is that the greeks are derived from the option-pricing model and are therefore theoretical values and do not include slippage. Furthermore, the volatility input in this example is rounded a bit for simplicity. For example, a volatility of 25 actually yielded a theoretical value of 2.796, while the call was bought at 2.80. Because some options trade at minimum price increments of a nickel, and none trade in fractions of a penny, IV is often rounded. Caveat Venditor Reversion to the mean holds the promise of profit in this trade, but Susie also knows that this strategy does not come without risks of loss. The mean to which volatility is expected to revert is not a constant. This benchmark can and does change. In this example, if the company had an unexpectedly terrible quarter, the stock could plunge sharply. In some cases, this would cause IV to find a new, higher level at which to reside. If that had happened here, the trade could have been a big loser. Gamma and vega could both have wreaked havoc. In trading, there is no sure thing, no matter what the chart looks like. Remember, every ship on the bottom of the ocean has a chart! Volatility Buying This same earnings event could have been played entirely differently. A different trader, Bobby Buyer, studied the same volatility chart as Susie. It is shown again here as Exhibit 12.7 . Bobby also thought there would be a rush and crush of IV, but he decided to take a different approach. EXHIBIT 12.7 Chip stock volatility before and after earnings reports. Source : Chart courtesy of iVolatility.com About an hour before the close of business on July 21, just three days before earnings announcements, Bobby saw that he could buy volatility at 30 percent. In Bobby’s opinion, volatility seemed cheap with earnings so close. He believed that IV could rise at least five points over the next three days. Note that we have the benefit of 20/20 hindsight in the example. Near the end of the trading day, the stock was at $49.70. Bobby bought 20 33-day 50-strike calls at 1.75 (30 volatility) and sold short 1,000 shares of the underlying stock at $49.70 to become delta neutral. Exhibit 12.8 shows Bobby’s position. EXHIBIT 12.8 Delta-neutral long call, short stock position. With the stock at $49.70, the calls had +0.51 delta per contract, or +10.2 for the 20-lot. The short sale of 1,000 shares got Bobby as close to delta-neutral as possible without trading an odd lot in the stock. The net position delta was +0.20, or about the equivalent of being long 20 shares of stock. Bobby’s objective in this case is to profit from an increase in implied volatility leading up to earnings. While Susie was looking for reversion to the mean, Bobby hoped for a further divergence. For Bobby, positive gamma looked like a good thing on the surface. However, his plan was to close the position just before earnings were released—before the vol crush and before the potential stock-price move. With realized volatility already starting to drop off at the time the trade was put on, gamma offered little promise of gain. As fate would have it, IV did indeed increase. At the end of the day before the July earnings report, IV was trading at 35 percent. Bobby closed his trade by selling his 20-lot of the 50 calls at 2.10 and buying his 1,000 shares of stock back at $50. Exhibit 12.9 shows the P&(L) for each leg of the spread. EXHIBIT 12.9 Profit breakdown. The calls earned Bobby a total of $700, while the stock lost $300. Of course, with this type of trade, it is not relevant which leg was a winner and which a loser. All that matters is the bottom line. The net P&(L) on the trade was a gain of $400. The gain in this case was mostly a product of IV’s rising. Exhibit 12.10 shows the P&(L) per greek. EXHIBIT 12.10 Profit breakdown by greek. Delta The position began long 0.20 deltas. The 0.30-point rise earned Bobby a 0.06 point gain in delta per contract. Gamma Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P&(L) in this example, assuming gamma remained constant. A 0.30 rise in the stock price multiplied by the 1.8 gamma means that with the stock at $50, Bobby was long an additional 0.54 deltas. We can estimate that over the course of the 0.30 rise in the stock price, Bobby was long an average of 0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is a gain of about 0.08 (0.27 × 0.30). Theta Bobby held this trade for three days. His total theta cost him 1.92 or $192. Vega The biggest contribution to Bobby’s profit on this trade was made by the spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position vega earned him 6.00, or $600. Conclusions The $422 profit is not exact, but the greeks provide a good estimate of the hows and the whys behind it. Whether they are used for forecasting profits or for doing a postmortem evaluation of a trade, consulting the greeks offers information unavailable by just looking at the transaction prices. By thinking about all these individual pricing components, a trader can make better decisions. For example, about two weeks earlier, Bobby could have bought an IV level closer to 26 percent. Being conscious of his theta, however, he decided to wait. The $64-a-day theta would have cost him $896 over 14 days. That’s much more that the $480 he could have made by buying volatility four points lower with his 1.20 vega. Risks of the Trade Like Susie’s trade, Bobby’s play was not without risk. Certainly theta was a concern, but in addition to that was the possibility that IV might not have played out as he planned. First, IV might not have risen enough to cover three days’ worth of theta. It needed to rise, in this case, about 1.6 volatility points for the 1.20 vega to cover the 1.92 theta loss. It might even have dropped. An earlier-than-expected announcement that the earnings numbers were right on target could have spoiled Bobby’s trade. Or the market simply might not have reacted as expected; volatility might not have risen at all, or might have fallen. Remember, IV is a function of the market. It does not always react as one thinks it should. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00024.html SCORE: 612.00 ================================================================================ CHAPTER 13 Delta-Neutral Trading Trading Realized Volatility So far, we’ve discussed many option strategies in which realized volatility is an important component of the trade. And while the management of these positions has been the focus of much of the discussion, the ultimate gain or loss for many of these strategies has been from movement in a single direction. For example, with a long call, the higher the stock rallies the better. But increases or decreases in realized volatility do not necessarily have an exclusive relationship with direction. Recall that realized volatility is the annualized standard deviation of daily price movements. Take two similarly priced stocks that have had a net price change of zero over a one-month period. Stock A had small daily price changes during that period, rising $0.10 one day and falling $0.10 the next. Stock B went up or down by $5 each day for a month. In this rather extreme example, Stock B was much more volatile than Stock A, regardless of the fact that the net price change for the period for both stocks was zero. A stock’s volatility—either high or low volatility—can be capitalized on by trading options delta neutral. Simply put, traders buy options delta neutral when they believe a stock will have more movement and sell options delta neutral when they believe a stock will move less. Delta-neutral option sellers profit from low volatility through theta. Every day that passes in which the loss from delta/gamma movement is less than the gain from theta is a winning day. Traders can adjust their deltas by hedging. Delta-neutral option buyers exploit volatility opportunities through a trading technique called gamma scalping. Gamma Scalping Intraday trading is seldom entirely in one direction. A stock may close higher or lower, even sharply higher or lower, on the day, but during the day there is usually not a steady incremental rise or fall in the stock price. A typical intraday stock chart has peaks and troughs all day long. Delta-neutral traders who have gamma don’t remain delta neutral as the underlying price changes, which inevitably it will. Delta-neutral trading is kind of a misnomer. In fact, it is gamma trading in which delta-neutral traders engage. For long-gamma traders, the position delta gets more positive as the underlying moves higher and more negative as the underlying moves lower. An upward move in the underlying increases positive deltas, resulting in exponentially increasing profits. But if the underlying price begins to retrace downward, the gain from deltas can be erased as quickly as it was racked up. To lock in delta gains, a trader can adjust the position to delta neutral again by selling short stock to cover long deltas. If the stock price declines after this adjustment, losses are curtailed thanks to the short stock. In fact, the delta will become negative as the underlying price falls, leading to growing profits. To lock in profits again, the trader buys stock to cover short deltas to once again become delta neutral. The net effect is a stock scalp. Positive gamma causes the delta-neutral trader to sell stock when the price rises and buy when the stock falls. This adds up to a true, realized profit. So positive gamma is a money-making machine, right? Not so fast. As in any business, the profits must be great enough to cover expenses. Theta is the daily cost of running this gamma-scalping business. For example, a trader, Harry, notices that the intraday price swings in a particular stock have been increasing. He takes a bullish position in realized volatility by buying 20 off the 40-strike calls, which have a 50 delta, and selling stock on a delta-neutral ratio. Buy 20 40-strike calls (50 delta) (long 1,000 deltas) Short 1,000 shares at $40 (short 1,000 deltas) The immediate delta of this trade is flat, but as the stock moves up or down, that will change, presenting gamma-scalping opportunities. Gamma scalping is the objective here. The position greeks in Exhibit 13.1 show the relationship of the two forces involved in this trade: gamma and theta. EXHIBIT 13.1 Greeks for 20-lot delta-neutral long call. The relationship of gamma to theta in this sort of trade is paramount to its success. Gamma-scalping plays are not buy-and-hold strategies. This is active trading. These spreads need to be monitored intraday to take advantage of small moves in the underlying security. Harry will sell stock when the underlying rises and buy it when the underlying falls, taking a profit with each stock trade. The goal for each day that passes is to profit enough from positive gamma to cover the day’s theta. But that’s not always as easy as it sounds. Let’s study what happens the first seven days after this hypothetical trade is executed. For the purposes of this example, we assume that gamma remains constant and that the trader is content trading odd lots of stock. Day One The first day proves to be fairly volatile. The stock rallies from $40 to $42 early in the day. This creates a positive position delta of 5.60, or the equivalent of being long about 560 shares. At $42, Harry covers the position delta by selling 560 shares of the underlying stock to become delta neutral again. Later in the day, the market reverses, and the stock drops back down to $40 a share. At this point, the position is short 5.60 deltas. Harry again adjusts the position, buying 560 shares to get flat. The stock then closes right at $40. The net result of these two stock transactions is a gain of $1,070. How? The gamma scalp minus the theta, as shown below. The volatility of day one led to it being a profitable day. Harry scalped 560 shares for a $2 profit, resulting from volatility in the stock. If the stock hadn’t moved as much, the delta would have been smaller, and the dollar amount scalped would have been smaller, leading to an exponentially smaller profit. If there had been more volatility, profits would have been exponentially larger. It would have led to a bigger bite being taken out of the market. Day Two The next day, the market is a bit quieter. There is a $0.40 drop in the price of the stock, at which point the position delta is short 1.12. Harry buys 112 shares at $39.60 to get delta neutral. Following Harry’s purchase, the stock slowly drifts back up and is trading at $40 near the close. Harry decides to cover his deltas and sell 112 shares at $40. It is common to cover all deltas at the end of the day to get back to being delta neutral. Remember, the goal of gamma scalping is to trade volatility, not direction. Starting the next trading day with a delta, either positive or negative, means an often unwanted directional bias and unwanted directional risk. Tidying up deltas at the end of the day to get neutral is called going home flat. Today was not a banner day. Harry did not quite have the opportunity to cover the decay. Day Three On this day, the market trends. First, the stock rises $0.50, at which point Harry sells 140 shares of stock at $40.50 to lock in gains from his delta and to get flat. However, the market continues to rally. At $41 a share, Harry is long another 1.40 deltas and so sells another 140 shares. The rally continues, and at $41.50 he sells another 140 shares to cover the delta. Finally, at the end of the day, the stock closes at $42 a share. Harry sells a final 140 shares to get flat. There was not any literal scalping of stock today. It was all selling. Nonetheless, gamma trading led to a profitable day. As the stock rose from $40 to $40.50, 140 deltas were created from positive gamma. Because the delta was zero at $40 and 140 at $40.50, the estimated average delta is found by dividing 140 in half. This estimated average delta multiplied by the $0.50 gain on the stock equals a $35 profit. The delta was zero after the adjustment made at $40.50, when 140 shares were sold. When the stock reached $41, another $35 was reaped from the average delta of 70 over the $0.50 move. This process was repeated every time the stock rose $0.50 and the delta was covered. Day Four Day four offers a pleasant surprise for Harry. That morning, the stock opens $4 lower. He promptly covers his short delta of 11.2 by buying 1,120 shares of the stock at $38 a share. The stock barely moves the rest of the day and closes at $38. An exponentially larger profit was made because there was $4 worth of gains on the growing delta when the stock gapped open. The whole position delta was covered $4 lower, so both the delta and the dollar amount gained on that delta had a chance to grow. Again, Harry can estimate the average delta over the $4 move to be half of 11.20. Multiplying that by the $4 stock advance gives him his gamma profit of $2,240. After accounting for theta, the net profit is $2,190. Days Five and Six Days five and six are the weekend; the market is closed. Day Seven This is a quiet day after the volatility of the past week. Today, the stock slowly drifts up $0.25 by the end of the day. Harry sells 70 shares of stock at $38.25 to cover long deltas. This day was a loser for Harry, as profits from gamma were not enough to cover his theta. Art and Science Although this was a very simplified example, it was typical of how a profitable week of gamma scalping plays out. This stock had a pretty volatile week, and overall the week was a winner: there were four losing days and three winners. The number of losing days includes the weekends. Weekends and holidays are big hurdles for long-gamma traders because of the theta loss. The biggest contribution to this being a winning week was made by the gap open on day four. Part of the reason was the sheer magnitude of the move, and part was the fact that the deltas weren’t covered too soon, as they had been on day three. In a perfect world, a long-gamma trader will always buy the low of the day and sell the high of the day when covering deltas. This, unfortunately, seldom happens. Long-gamma traders are very often wrong when trading stock to cover deltas. Being wrong can be okay on occasion. In fact, it can even be rewarding. Day three was profitable despite the fact that 140 shares were sold at $40.50, $41, and $41.50. The stock closed at $42; the first three stock trades were losers. Harry sold stock at a lower price than the close. But the position still made money because of his positive gamma. To be sure, Harry would like to have sold all 560 shares at $42 at the end of the day. The day’s profits would have been significantly higher. The problem is that no one knows where the stock will move next. On day three, if the stock had topped out at $40.50 and Harry did not sell stock because he thought it would continue higher, he would have missed an opportunity. Gamma scalping is not an exact science. The art is to pick spots that capture the biggest moves possible without missing opportunities. There are many methods traders have used to decide where to cover deltas when gamma scalping: the daily standard deviation, a fixed percentage of the stock price, a fixed nominal value, covering at a certain time of day, “market feel.” No system appears to be absolutely better than another. This is where it gets personal. Finding what works for you, and what works for the individual stocks you trade, is the art of this science. Gamma, Theta, and Volatility Clearly, more volatile stocks are more profitable for gamma scalping, right? Well . . . maybe. Recall that the higher the implied volatility, the lower the gamma and the higher the theta of at-the-money (ATM) options. In many cases, the more volatile a stock, the higher the implied volatility (IV). That means that a volatile stock might have to move more for a trader to scalp enough stock to cover the higher theta. Let’s look at the gamma-theta relationship from another perspective. In this example, for 0.50 of theta, Harry could buy 2.80 gamma. This relationship is based on an assumed 25 percent implied volatility. If IV were 50 percent, theta for this 20 lot would be higher, and the gamma would be lower. At a volatility of 50, Harry could buy 1.40 gammas for 0.90 of theta. The gamma is more expensive from a theta perspective, but if the stock’s statistical volatility is significantly higher, it may be worth it. Gamma Hedging Knowing that the gamma and theta figures of Exhibit 13.1 are derived from a 25 percent volatility assumption offers a benchmark with which to gauge the potential profitability of gamma trading the options. If the stock’s standard deviation is below 25 percent, it will be difficult to make money being long gamma. If it is above 25 percent, the play becomes easier to trade. There is more scalping opportunity, there are more opportunities for big moves, and there are more likely to be gaps in either direction. The 25 percent volatility input not only determines the option’s theoretical value but also helps determine the ratio of gamma to theta. A 25 percent or higher realized volatility in this case does not guarantee the trade’s success or failure, however. Much of the success of the trade has to do with how well the trader scalps stock. Covering deltas too soon leads to reduced profitability. Covering too late can lead to missed opportunities. Trading stock well is also important to gamma sellers with the opposite trade: sell calls and buy stock delta neutral. In this example, a trader will sell 20 ATM calls and buy stock on a delta-neutral ratio. This is a bearish position in realized volatility. It is the opposite of the trade in the last example. Consider again that 25 percent IV is the benchmark by which to gauge potential profitability. Here, if the stock’s volatility is below 25, the chances of having a profitable trade are increased. Above 25 is a bit more challenging. In this simplified example, a different trader, Mary, plays the role of gamma seller. Over the same seven-day period as before, instead of buying calls, Mary sold a 20 lot. Exhibit 13.2 shows the analytics for the trade. For the purposes of this example, we assume that gamma remains constant and the trader is content trading odd lots of stock. EXHIBIT 13.2 Greeks for 20-lot delta-neutral short call. Day One This was one of the volatile days. The stock rallied from $40 to $42 early in the day and had fallen back down to $40 by the end of the day. Big moves like this are hard to trade as a short-gamma trader. As the stock rose to $42, the negative delta would have been increasing. That means losses were adding up at an increasing rate. The only way to have stopped the hemorrhaging of money as the stock continued to rise would have been to buy stock. Of course, if Mary buys stock and the stock then declines, she has a loser. Let’s assume the best-case scenario. When the stock reached $42 and she had a −560 delta, Mary correctly felt the market was overbought and would retrace. Sometimes, the best trades are the ones you don’t make. On this day, Mary traded no stock. When the stock reached $40 a share at the end of the day, she was back to being delta neutral. Theta makes her a winner today. Because of the way Mary handled her trade, the volatility of day one was not necessarily an impediment to it being profitable. Again, the assumption is that Mary made the right call not to negative scalp the stock. Mary could have decided to hedge her negative gamma when the stock reach $42 and the position delta was at −$560 by buying stock and then selling it at $40. There are a number of techniques for hedging deltas resulting from negative gamma. The objective of hedging deltas is to avoid losses from the stock trending in one direction and creating increasingly adverse deltas but not to overtrade stock and negative scalp. Day Two Recall that this day had a small dip and then recovered to close again at $40. It is more reasonable to assume that on this day there was no negative scalping. A $0.40 decline is a more typical move in a stock and nothing to be afraid of. The 112 delta created by negative gamma when the stock fell wouldn’t be perceived as a major concern by most traders in most situations. It is reasonable to assume Mary would take no action. Today, again, was a winner thanks to theta. Day Three Day three saw the stock price trending. It slowly drifted up $2. There would have been some judgment calls throughout this day. Again, delta-neutral trades are for active traders. Prepare to watch the market much of the day if implementing this kind of strategy. When the stock was at $41 a share, Mary decided to guard against further advances in stock price and hedged her delta. At that point, the position would have had a −2.80 delta. She bought 280 shares at $41. As the day progressed, the market proved Mary to be right. The stock rose to $42 giving the position a delta of −2.80 again. She covered her deltas at the end of the day by buying another 280 shares. Covering the negative deltas to get flat at $41 proved to be a smart move today. It curtailed an exponentially growing delta and let Mary take a smaller loss at $41 and get a fresh start. While the day was a loser, it would have been $280 worse if she had not purchased stock at $41 before the run-up to $42. This is evidenced by the fact that she made a $280 profit on the 280 shares of stock bought at $41, since the stock closed at $42. Day Four Day four offered a rather unpleasant surprise. This was the day that the stock gapped open $4 lower. This is the kind of day short-gamma traders dread. There is, of course, no right way to react to this situation. The stock can recover, heading higher; it can continue lower; or it can have a dead-cat bounce, remaining where it is after the fall. Staring at a quite contrary delta of 11.20, Mary was forced to take action by selling stock. But how much stock was the responsible amount to sell for a pure short-gamma trader not interested in trading direction? Selling 1,120 shares would bring the position back to being delta neutral, but the only way the trade would stay delta neutral would be if the stock stayed right where it was. Hedging is always a difficult call for short-gamma traders. Long-gamma traders are taking a profit on deltas with every stock trade that covers their deltas. Short-gamma traders are always taking a loss on delta. In this case, Mary decided to cover half her deltas by selling 560 shares. The other 560 deltas represent a loss, too; it’s just not locked in. Here, Mary made the conscious decision not to go home flat. On the one hand, she was accepting the risk of the stock continuing its decline. On the other hand, if she had covered the whole delta, she would have been accepting the risk of the stock moving in either direction. Mary felt the stock would regain some of its losses. She decided to lead the stock a little, going into the weekend with a positive delta bias. Days Five and Six Days five and six are the weekend. Day Seven This was the quiet day of the week, and a welcome respite. On this day, the stock rose just $0.25. The rise in price helped a bit. Mary was still long 560 deltas from Friday. Negative gamma took only a small bite out of her profit. The P&(L) can be broken down into the profit attributable to the starting delta of the trade, the estimated loss from gamma, and the gain from theta. Mary ends these seven days of trading worse off than she started. What went wrong? The bottom line is that she sold volatility on an asset that proved to be volatile. A $4 drop in price of a $42 dollar stock was a big move. This stock certainly moved at more than 25 percent volatility. Day four alone made this trade a losing proposition. Could Mary have done anything better? Yes. In a perfect world, she would not have covered her negative deltas on day 3 by buying 280 shares at $41 and another 280 at $42. Had she not, this wouldn’t have been such a bad week. With the stock ending at $38.25, she lost $1,050 on the 280 shares she bought at $42 ($3.75 times 280) and lost $770 on the 280 shares bought at $41 ($2.75 times 280). Then again, if the stock had continued higher, rising beyond $42, those would have been good buys. Mary can’t beat herself up too much for protecting herself in a way that made sense at the time. The stock’s $2 rally is more to blame than the fact that she hedged her deltas. That’s the risk of selling volatility: the stock may prove to be volatile. If the stock had not made such a move, she wouldn’t have faced the dilemma of whether or not to hedge. Conclusions The same stock during the same week was used in both examples. These two traders started out with equal and opposite positions. They might as well have made the trade with each other. And although in this case the vol buyer (Harry) had a pretty good week and the vol seller (Mary) had a not-so-good week, it’s important to notice that the dollar value of the vol buyer’s profit was not the same as the dollar value of the vol seller’s loss. Why? Because each trader hedged his or her position differently. Option trading is not a zero-sum game. Option-selling delta-neutral strategies work well in low-volatility environments. Small moves are acceptable. It’s the big moves that can blow you out of the water. Like long-gamma traders, short-gamma traders have many techniques for covering deltas when the stock moves. It is common to cover partial deltas, as Mary did on day four of the last example. Conversely, if a stock is expected to continue along its trajectory up or down, traders will sometimes overhedge by buying more deltas (stock) than they are short or selling more than they are long, in anticipation of continued price rises. Daily standard deviation derived from implied volatility is a common measure used by short-gamma players to calculate price points at which to enter hedges. Market feel and other indicators are also used by experienced traders when deciding when and how to hedge. Each trader must find what works best for him or her. Smileys and Frowns The trade examples in this chapter have all involved just two components: calls and stock. We will explore delta-neutral strategies in other chapters that involve more moving parts. Regardless of the specific makeup of the position, the P&(L) of each individual leg is not of concern. It is the profitability of the position as a whole that matters. For example, after a volatile move in a stock occurs, a positive-gamma trader like Harry doesn’t care whether the calls or the stock made the profit on the move. The trader would monitor the net delta that was produced—positive or negative—and cover accordingly. The process is the same for a negative-gamma trader. In either case, it is gamma and delta that need to be monitored closely. Gamma can make or break a trade. P&(L) diagrams are helpful tools that offer a visual representation of the effect of gamma on a position. Many option-trading software applications offer P&(L) graphing applications to study the payoff of a position with the days to expiration as an adjustable variable to study the same trade over time. P&(L) diagrams for these delta-neutral positions before the options’ expiration generally take one of two shapes: a smiley or a frown. The shape of the graph depends on whether the position gamma is positive or negative. Exhibit 13.3 shows a typical positive-gamma trade. EXHIBIT 13.3 P&(L) diagram for a positive-gamma delta-neutral position/l. This diagram is representative of the P&L of a delta-neutral positive-gamma trade calculated using the prices at which the trade was executed. With this type of trade, it is intuitive that when the stock price rises or falls, profits increase because of favorably changing deltas. This is represented by the graph’s smiley-face shape. The corners of the graph rise higher as the underlying moves away from the center of the graph. The graph is a two-dimensional snapshot showing that the higher or lower the underlying moves, the greater the profit. But there are other dimensions that are not shown here, such as time and IV. Exhibit 13.4 shows the effects of time on a typical long-gamma trade. EXHIBIT 13.4 The effect of time on P&(L). As time passes, the reduction in profit is reflected by the center point of the graph dipping farther into negative territory. That is the effect of time decay. The long options will have lost value at that future date with the stock still at the same price (all other factors held constant). Still, a move in either direction can lead to a profitable position. Ultimately, at expiration, the payoff takes on a rigid kinked shape. In the delta-neutral long call examples used in this chapter the position becomes net long stock if the calls are in-the-money at expiration or net short stock if they are out-of-the-money and only the short stock remains. Volatility, as well, would move the payoff line vertically. As IV increases, the options become worth more at each stock price, and as IV falls, they are worth less, assuming all other factors are held constant. A delta-neutral short-gamma play would have a P&(L) diagram quite the opposite of the smiley-faced long-gamma graph. Exhibit 13.5 shows what is called the short-gamma frown. EXHIBIT 13.5 Short-gamma frown. At first glance, this doesn’t look like a very good proposition. The highest point on the graph coincides with a profit of zero, and it only gets worse as the price of the underlying rises or falls. This is enough to make any trader frown. But again, this snapshot does not show time or volatility. Exhibit 13.6 shows the payout diagram as time passes. EXHIBIT 13.6 The effect of time on the short-gamma frown. A decrease in value of the options from time decay causes an increase in profitability. This profit potential pinnacles at the center (strike) price at expiration. Rising IV will cause a decline in profitability at each stock price point. Declining IV will raise the payout on the Y axis as profitability increases at each price point. Smileys and frowns are a mere graphical representation of the technique discussed in this chapter: buying and selling realized volatility. These P&(L) diagrams are limited, because they show the payout only of stock-price movement. The profitability of direction-indifferent and direction-neutral trading is also influenced by time and implied volatility. These actively traded strategies are best evaluated on a gamma-theta basis. Long-gamma traders strive each day to scalp enough to cover the day’s theta, while short-gamma traders hope to keep the loss due to adverse movement in the underlying lower than the daily profit from theta. The strategies in this chapter are the same ones traded in Chapter 12. The only difference is the philosophy. Ultimately, both types of volatility are being traded using these and other option strategies. Implied and realized volatility go hand in hand. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00025.html SCORE: 387.50 ================================================================================ CHAPTER 14 Studying Volatility Charts Implied and realized volatility are both important to option traders. But equally important is to understand how the two interact. This relationship is best studied by means of a volatility chart. Volatility charts are invaluable tools for volatility traders (and all option traders for that matter) in many ways. First, volatility charts show where implied volatility (IV) is now compared with where it’s been in the past. This helps a trader gauge whether IV is relatively high or relatively low. Vol charts do the same for realized volatility. The realized volatility line on the chart answers three questions: Have the past 30 days been more or less volatile for the stock than usual? What is a typical range for the stock’s volatility? How much volatility did the underlying historically experience in the past around specific recurring events? When IV lines and realized volatility lines are plotted on the same chart, the divergences and convergences of the two spell out the whole volatility story for those who know how to read it. Nine Volatility Chart Patterns Each individual stock and the options listed on it have their own unique realized and implied volatility characteristics. If we studied the vol charts of 1,000 stocks, we’d likely see around 1,000 different volatility patterns. The number of permutations of the relationship of realized to implied volatility is nearly infinite, but for the sake of discussion, we will categorize volatility charts into nine general patterns. 1 1. Realized Volatility Rises, Implied Volatility Rises The first volatility chart pattern is that in which both IV and realized volatility rise. In general, this kind of volatility chart can line up three ways: implied can rise more than realized volatility; realized can rise more than implied; or they can both rise by about the same amount. The chart below shows implied volatility rising at a faster rate than realized vol. The general theme in this case is that the stock’s price movement has been getting more volatile, and the option prices imply even higher volatility in the future. This specific type of volatility chart pattern is commonly seen in active stocks with a lot of news. Stocks du jour, like some Internet stocks during the tech bubble of the late 1990s, story stocks like Apple (AAPL) around the release of the iPhone in 2007, have rising volatilities, with the IV outpacing the realized volatility. Sometimes individual stocks and even broad market indexes and exchange-traded funds (ETFs) see this pattern, when the market is declining rapidly, like in the summer of 2011. A delta-neutral long-volatility position bought at the beginning of May, according to Exhibit 14.1 , would likely have produced a winner. IV took off, and there were sure to be plenty of opportunities to profit from gamma with realized volatility gaining strength through June and July. EXHIBIT 14.1 Realized volatility rises, implied volatility rises. Source : Chart courtesy of iVolatility.com Looking at the right side of the chart, in late July, with IV at around 50 percent and realized vol at around 35 percent, and without the benefit of knowing what the future will bring, it’s harder to make a call on how to trade the volatility. The IV signals that the market is pricing a higher future level of stock volatility into the options. If the market is right, gamma will be good to have. But is the price right? If realized volatility does indeed catch up to implied volatility—that is, if the lines converge at 50 or realized volatility rises above IV—a trader will have a good shot at covering theta. If it doesn’t, gamma will be very expensive in terms of theta, meaning it will be hard to cover the daily theta by scalping gamma intraday. The question is: why is IV so much higher than realized? If important news is expected to be released in the near future, it may be perfectly reasonable for the IV to be higher, even significantly higher, than the stock’s realized volatility. One big move in the stock can produce a nice profit, as long as theta doesn’t have time to work its mischief. But if there is no news in the pipeline, there may be some irrational exuberance—in the words of ex-Fed chairman Alan Greenspan—of option buyers rushing to acquire gamma that is overvalued in terms of theta. In fact, a lack of expectation of news could indicate a potential bearish volatility play: sell volatility with the intent of profiting from daily theta and a decline in IV. This type of play, however, is not for the fainthearted. No one can predict the future. But one thing you can be sure of with this trade: you’re in for a wild ride. The lines on this chart scream volatility. This means that negative-gamma traders had better be good and had better be right! In this situation, hedgers and speculators in the market are buying option volatility of 50 percent, while the stock is moving at 35 percent volatility. Traders putting on a delta-neutral volatility-selling strategy are taking the stance that this stock will not continue increasing in volatility as indicated by option prices; specifically, it will move at less than 50 percent volatility—hopefully a lot less. They are taking the stance that the market’s expectations are wrong. Instead of realized and implied volatility both trending higher, sometimes there is a sharp jump in one or the other. When this happens, it could be an indication of a specific event that has occurred (realized volatility) or news suddenly released of an expected event yet to come (implied volatility). A sharp temporary increase in IV is called a spike, because of its pointy shape on the chart. A one-day surge in realized volatility, on the other hand, is not so much a volatility spike as it is a realized volatility mesa. Realized volatility mesas are shown in Exhibit 14.2 . EXHIBIT 14.2 Volatility mesas. Source : Chart courtesy of iVolatility.com The patterns formed by the gray line in the circled areas of the chart shown below are the result of typical one-day surges in realized volatility. Here, the 30-day realized volatility rose by nearly 20 percentage points, from about 20 percent to about 40 percent, in one day. It remained around the 40 percent level for 30 days and then declined 20 points just as fast as it rose. Was this entire 30-day period unusually volatile? Not necessarily. Realized volatility is calculated by looking at price movements within a certain time frame, in this case, thirty business days. That means that a really big move on one day will remain in the calculation for the entire time. Thirty days after the unusually big move, the calculation for realized volatility will no longer contain that one-day price jump. Realized volatility can then drop significantly. 2. Realized Volatility Rises, Implied Volatility Remains Constant This chart pattern can develop from a few different market conditions. One scenario is a one-time unanticipated move in the underlying that is not expected to affect future volatility. Once the news is priced into the stock, there is no point in hedgers’ buying options for protection or speculators’ buying options for a leveraged bet. What has happened has happened. There are other conditions that can cause this type of pattern to materialize. In Exhibit 14.3 , the IV was trading around 25 for several months, while the realized volatility was lagging. With hindsight, it makes perfect sense that something had to give—either IV needed to fall to meet realized, or realized would rise to meet market expectations. Here, indeed, the latter materialized as realized volatility had a steady rise to and through the 25 level in May. Implied, however remained constant. EXHIBIT 14.3 Realized volatility rises, implied volatility remains constant. Source : Chart courtesy of iVolatility.com Traders who were long volatility going into the May realized-vol rise probably reaped some gamma benefits. But those who got in “too early,” buying in January or February, would have suffered too great of theta losses before gaining any significant profits from gamma. Time decay (theta) can inflict a slow, painful death on an option buyer. By studying this chart in hindsight, it is clear that options were priced too high for a gamma scalper to have a fighting chance of covering the daily theta before the rise in May. This wasn’t necessarily an easy vol-selling trade before the May realized-vol rise, either, depending on the trader’s timing. In early February, realized did in fact rise above implied, making the short volatility trade much less attractive. Traders who sold volatility just before the increase in realized volatility in May likely ended up losing on gamma and not enough theta profits to make up for it. There was no volatility crush like what is often seen following a one-day move leading to sharply higher realized volatility. IV simply remained pretty steady throughout the month of May and well into June. 3. Realized Volatility Rises, Implied Volatility Falls This chart pattern can manifest itself in different ways. In this scenario, the stock is becoming more volatile, and options are becoming cheaper. This may seem an unusual occurrence, but as we can see in Exhibit 14.4 , volatility sometimes plays out this way. This chart shows two different examples of realized vol rising while IV falls. EXHIBIT 14.4 Realized volatility rises, implied volatility falls. Source : Chart courtesy of iVolatility.com The first example, toward the left-hand side of the chart, shows realized volatility trending higher while IV is trending lower. Although fundamentals can often provide logical reasons for these volatility changes, sometimes they just can’t. Both implied and realized volatility are ultimately a function of the market. There is a normal oscillation to both of these figures. When there is no reason to be found for a volatility change, it might be an opportunity. The potential inefficiency of volatility pricing in the options market sometimes creates divergences such as this one that vol traders scour the market in search of. In this first example, after at least three months of IV’s trading marginally higher than realized volatility, the two lines converge and then cross. The point at which these lines meet is an indication that IV may be beginning to get cheap. First, it’s a potentially beneficial opportunity to buy a lower volatility than that at which the stock is actually moving. The gamma/theta ratio would be favorable to gamma scalpers in this case, because the lower cost of options compared with stock fluctuations could lead to gamma profits. Second, with IV at 35 at the first crossover on this chart, IV is dipping down into the lower part of its four-month range. One can make the case that it is getting cheaper from a historical IV standpoint. There is arguably an edge from the perspective of IV to realized volatility and IV to historical IV. This is an example of buying value in the context of volatility. Furthermore, if the actual stock volatility is rising, it’s reasonable to believe that IV may rise, too. In hindsight we see that this did indeed occur in Exhibit 14.4 , despite the fact that realized volatility declined. The example circled on the right-hand side of the chart shows IV declining sharply while realized volatility rises sharply. This is an example of the typical volatility crush as a result of an earnings report. This would probably have been a good trade for long volatility traders—even those buying at the top. A trader buying options delta neutral the day before earnings are announced in this example would likely lose about 10 points of vega but would have a good chance to more than make up for that loss on positive gamma. Realized volatility nearly doubled, from around 28 percent to about 53 percent, in a single day. 4. Realized Volatility Remains Constant, Implied Volatility Rises Exhibit 14.5 shows that the stock is moving at about the same volatility from the beginning of June to the end of July. But during that time, option premiums are rising to higher levels. This is an atypical chart pattern. If this was a period leading up to an anticipated event, like earnings, one would anticipate realized volatility falling as the market entered a wait-and-see mode. But, instead, statistical volatility stays the same. This chart pattern may indicate a potential volatility-selling opportunity. If there is no news or reason for IV to have risen, it may simply be high tide in the normal ebb and flow of volatility. EXHIBIT 14.5 Realized volatility remains constant, implied volatility rises. Source : Chart courtesy of iVolatility.com In this example, the historical volatility oscillates between 20 and 24 for nearly two months (the beginning of June through the end of July) as IV rises from 24 to over 30. The stock price is less volatile than option prices indicate. If there is no news to be dug up on the stock to lead one to believe there is a valid reason for the IV’s trading at such a level, this could be an opportunity to sell IV 5 to 10 points higher than the stock volatility. The goal here is to profit from theta or falling vega or both while not losing much on negative gamma. As time passes, if the stock continues to move at 20 to 23 vol, one would expect IV to fall and converge with realized volatility. 5. Realized Volatility Remains Constant, Implied Volatility Remains Constant This volatility chart pattern shown in Exhibit 14.6 is typical of a boring, run-of-the-mill stock with nothing happening in the news. But in this case, no news might be good news. EXHIBIT 14.6 Realized volatility remains constant, implied volatility remains constant. Source : Chart courtesy of iVolatility.com Again, the gray is realized volatility and the black line is IV. It’s common for IV to trade slightly above or below realized volatility for extended periods of time in certain assets. In this example, the IV has traded in the high teens from late January to late July. During that same time, realized volatility has been in the low teens. This is a prime environment for option sellers. From a gamma/theta standpoint, the odds favor short-volatility traders. The gamma/theta ratio provides an edge, setting the stage for theta profits to outweigh negative-gamma scalping. Selling calls and buying stock delta neutral would be a trade to look at in this situation. But even more basic strategies, such as time spreads and iron condors, are appropriate to consider. This vol-chart pattern, however, is no guarantee of success. When the stock oscillates, delta-neutral traders can negative scalp stock if they are not careful by buying high to cover short deltas and then selling low to cover long deltas. Time-spread and iron condor trades can fail if volatility increases and the increase results from the stock trending in one direction. The advantage of buying IV lower than realized, or selling it above, is statistical in nature. Traders should use a chart of the stock price in conjunction with the volatility chart to get a more complete picture of the stock’s price action. This also helps traders make more informed decisions about when to hedge. 6. Realized Volatility Remains Constant, Implied Volatility Falls Exhibit 14.7 shows two classic implied-realized convergences. From mid-September to early November, realized volatility stayed between 22 and 25. In mid-October the implied was around 33. Within the span of a few days, the implied vol collapsed to converge with the realized at about 22. EXHIBIT 14.7 Realized volatility remains constant, implied volatility falls. Source : Chart courtesy of iVolatility.com There can be many catalysts for such a drop in IV, but there is truly only one reason: arbitrage. Although it is common for a small difference between implied and realized volatility—1 to 3 points—to exist even for extended periods, bigger disparities, like the 7- to 10-point difference here cannot exist for that long without good reason. If, for example, IV always trades significantly above the realized volatility of a particular underlying, all rational market participants will sell options because they have a gamma/theta edge. This, in turn, forces options prices lower until volatility prices come into line and the arbitrage opportunity no longer exists. In Exhibit 14.7 , from mid-March to mid-May a similar convergence took place but over a longer period of time. These situations are often the result of a slow capitulation of market makers who are long volatility. The traders give up on the idea that they will be able to scalp enough gamma to cover theta and consequently lower their offers to advertise their lower prices. 7. Realized Volatility Falls, Implied Volatility Rises This setup shown in Exhibit 14.8 should now be etched into the souls of anyone who has been reading up to this point. It is, of course, the picture of the classic IV rush that is often seen in stocks around earnings time. The more uncertain the earnings, the more pronounced this divergence can be. EXHIBIT 14.8 Realized volatility falls, implied volatility rises. Source : Chart courtesy of iVolatility.com Another classic vol divergence in which IV rises and realized vol falls occurs in a drug or biotech company when a Food and Drug Administration (FDA) decision on one of the company’s new drugs is imminent. This is especially true of smaller firms without big portfolios of drugs. These divergences can produce a huge implied–realized disparity of, in some cases, literally hundreds of volatility points leading up to the announcement. Although rising IV accompanied by falling realized volatility can be one of the most predictable patterns in trading, it is ironically one of the most difficult to trade. When the anticipated news breaks, the stock can and often will make a big directional move, and in that case, IV can and likely will get crushed. Vega and gamma work against each other in these situations, as IV and realized volatility converge. Vol traders will likely gain on one vol and lose on the other, but it’s very difficult to predict which will have a more profound effect. Many traders simply avoid trading earnings events altogether in favor of less erratic opportunities. For most traders, there are easier ways to make money. 8. Realized Volatility Falls, Implied Volatility Remains Constant This volatility shift can be marked by a volatility convergence, divergence, or crossover. Exhibit 14.9 shows the realized volatility falling from around 30 percent to about 23 percent while IV hovers around 25. The crossover here occurs around the middle of February. EXHIBIT 14.9 Realized volatility falls, implied volatility remains constant. Source : Chart courtesy of iVolatility.com The relative size of this volatility change makes the interpretation of the chart difficult. The last half of September saw around a 15 percent decline in realized volatility. The middle of October saw a one-day jump in realized of about 15 points. Historical volatility has had several dynamic moves that were larger and more abrupt than the seven-point decline over this six-week period. This smaller move in realized volatility is not necessarily an indication of a volatility event. It could reflect some complacency in the market. It could indicate a slow period with less trading, or it could simply be a natural contraction in the ebb and flow of volatility causing the calculation of recent stock-price fluctuations to wane. What is important in this interpretation is how the options market is reacting to the change in the volatility of the stock—where the rubber hits the road. The market’s apparent assessment of future volatility is unchanged during this period. When IV rises or falls, vol traders must look to the underlying stock for a reason. The options market reacts to stock volatility, not the other way around. Finding fundamental or technical reasons for surges in volatility is easier than finding specific reasons for a decline in volatility. When volatility falls, it is usually the result of a lack of news, leading to less price action. In this example, probably nothing happened in the market. Consequently, the stock volatility drifted lower. But it fell below the lowest IV level seen for the six-month period leading up to the crossover. It was probably hard to take a confident stance in volatility immediately following the crossover. It is difficult to justify selling volatility when the implied is so cheap compared with its historic levels. And it can be hard to justify buying volatility when the options are priced above the stock volatility. The two-week period before the realized line moved beneath the implied line deserves closer study. With the IV four or five points lower than the realized volatility in late January, traders may have been tempted to buy volatility. In hindsight, this trade might have been profitable, but there was surely no guarantee of this. Success would have been greatly contingent on how the traders managed their deltas, and how well they adapted as realized volatility fell. During the first half of this period, the stock volatility remained above implied. For an experienced delta-neutral trader, scalping gamma was likely easy money. With the oscillations in stock price, the biggest gamma-scalping risk would have been to cover too soon and miss out on opportunities to take bigger profits. Using the one-day standard deviation based on IV (described in Chapter 3) might have produced early covering for long-gamma traders. Why? Because in late January, the standard deviation derived from IV was lower than the actual standard deviation of the stock being traded. In the latter half of the period being studied, the end of February on this chart, using the one-day standard deviation based on IV would have produced scalping that was too late. This would have led to many missed opportunities. Traders entering hedges at regular nominal intervals—every $0.50, for example—would probably have needed to decrease the interval as volatility ebbed. For instance, if in late January they were entering orders every $0.50, by late February they might have had to trade every $0.40. 9. Realized Volatility Falls, Implied Volatility Falls This final volatility-chart permutation incorporates a fall of both realized and IV. The chart in Exhibit 14.10 clearly represents the slow culmination of a highly volatile period. This setup often coincides with news of some scary event’s being resolved—a law suit settled, unpopular upper management leaving, rumors found to be false, a happy ending to political issues domestically or abroad, for example. After a sharp sell-off in IV, from 75 to 55, in late October, marking the end of a period of great uncertainty, the stock volatility began a steady decline, from the low 50s to below 25. IV fell as well, although it remained a bit higher for several months. EXHIBIT 14.10 Realized volatility falls, implied volatility falls. Source : Chart courtesy of iVolatility.com In some situations where an extended period of extreme volatility appears to be coming to an end, there can be some predictability in how IV will react. To be sure, no one knows what the future holds, but when volatility starts to wane because a specific issue that was causing gyrations in the stock price is resolved, it is common, and intuitive, for IV to fall with the stock volatility. This is another type of example of reversion to the mean. There is a potential problem if the high-volatility period lasted for an extended period of time. Sometimes, it’s hard to get a feel for what the mean volatility should be. Or sometimes, because of the event, the stock is fundamentally different—in the case of a spin-off, merger, or other corporate action, for example. When it is difficult or impossible to look back at a stock’s performance over the previous 6 to 12 months and appraise what the normal volatility should be, one can look to the volatility of other stocks in the same industry for some guidance. Stocks that are substitutable for one another typically trade at similar volatilities. From a realized volatility perspective, this is rather intuitive. When one stock within an industry rises or falls, others within the same industry tend to follow. They trade similarly and therefore experience similar volatility patterns. If the stock volatility among names within one industry tends to be similar, it follows that the IV should be, too. Regardless which of the nine patterns discussed here show up, or how the volatilities line up, there is one overriding observation that’s representative of all volatility charts: vol charts are simply graphical representations of realized and implied volatility that help traders better understand the two volatilities’ interaction. But the divergences and convergences in the examples in this chapter have profound meaning to the volatility trader. Combined with a comparison of current and past volatility (both realized and implied), they give traders insight into how cheap or expensive options are. Note 1 . The following examples use charts supplied by iVolatility.com . The gray line is the 30-day realized volatility, and the black line is the implied volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00027.html SCORE: 1471.50 ================================================================================ CHAPTER 15 Straddles and Strangles Straddles and strangles are the quintessential volatility strategies. They are the purest ways to buy and sell realized and implied volatility. This chapter discusses straddles and strangles, how they work, when to use them, what to look out for, and the differences between the two. Long Straddle Definition : Buying one call and one put in the same option class, in the same expiration cycle, and with the same strike price. Linearly, the long straddle is the best of both worlds—long a call and a put. If the stock rises, the call enjoys the unlimited potential for profit while the put’s losses are decidedly limited. If the stock falls, the put’s profit potential is bound only by the stock’s falling to zero, while the call’s potential loss is finite. Directionally, this can be a win-win situation—as long as the stock moves enough for one option’s profit to cover the loss on the other. The risk, however, is that this may not happen. Holding two long options means a big penalty can be paid for stagnant stocks. The Basic Long Straddle The long straddle is an option strategy to use when a trader is looking for a big move in a stock but is uncertain which direction it will move. Technically, the Commodity Channel Index (CCI), Bollinger bands, or pennants are some examples of indicators which might signal the possibility of a breakout. Or fundamental data might call for a revaluation of the stock based on an impending catalyst. In either case, a long straddle, is a way for traders to position themselves for the expected move, without regard to direction. In this example, we’ll study a hypothetical $70 stock poised for a breakout. We’ll buy the one-month 70 straddle for 4.25. Exhibit 15.1 shows the payout of the straddle at expiration. EXHIBIT 15.1 At-expiration diagram for a long straddle. At expiration, with the stock at $70, neither the call nor the put is in-the-money. The straddle expires worthless, leaving a loss of 4.25 in its wake from erosion. If, however, the stock is above or below $70, either the call or the put will have at least some value. The farther the stock price moves from the strike price in either direction, the higher the net value of the options. Above $70, the call has value. If the underlying is at $74.25 at expiration, the put will expire worthless, but the call will be worth 4.25—the price initially paid for the straddle. Above this break-even price, the trade is a winner, and the higher, the better. Below $70, the put has value. If the underlying is at $65.75 at expiration, the call expires, and the put is worth 4.25. Below this breakeven, the straddle is a winner, and the lower, the better. Why It Works In this basic example, if the underlying is beyond either of the break-even points at expiration, the trade is a winner. The key to understanding this is the fact that at expiration, the loss on one option is limited—it can only fall to zero—but the profit potential on the other can be unlimited. In practice, most active traders will not hold a straddle until expiration. Even if the trade is not held to term, however, movement is still beneficial—in fact, it is more beneficial, because time decay will not have depleted all the extrinsic value of the options. Movement benefits the long straddle because of positive gamma. But movement is a race against the clock—a race against theta. Theta is the cost of trading the long straddle. Only pay it for as long as necessary. When the stock’s volatility appears poised to ebb, exit the trade. Exhibit 15.2 shows the P&(L) of the straddle both at expiration and at the time the trade was made. EXHIBIT 15.2 Long straddle P&(L) at initiation and expiration. Because this is a short-term at-the-money (ATM) straddle, we will assume for simplicity that it has a delta of zero. 1 When the trade is consummated, movement can only help, as indicated by the dotted line on the exhibit. This is the classic graphic representation of positive gamma—the smiley face. When the stock moves higher, the call gains value at an increasing rate while the put loses value at a decreasing rate. When the stock moves lower, the put gains at an increasing rate while the call loses at a decreasing rate. This is positive gamma. This still may not be an entirely fair representation of how profits are earned. The underlying is not required to move continuously in one direction for traders to reap gamma profits. As described in Chapter 13, traders can scalp gamma by buying and selling stock to offset long or short deltas created by movement in the underlying. When traders scalp gamma, they lock in profits as the stock price oscillates. The potential for gamma scalping is an important motivation for straddle buyers. Gamma scalping a straddle gives traders the chance to profit from a stock that has dynamic price swings. It should be second nature to volatility traders to understand that theta is the trade-off of gamma scalping. The Big V Gamma and theta are not alone in the straddle buyer’s thoughts. Vega is a major consideration for a straddle buyer, as well. In a straddle, there are two long options of the same strike, which means double the vega risk of a single-leg trade at that strike. With no short options in this spread, the implied-volatility exposure is concentrated. For example, if the call has a vega of 0.05, the put’s vega at that same strike will also be about 0.05. This means that buying one straddle gives the trader exposure of around 10 cents per implied volatility (IV) point. If IV rises by one point, the trader makes $10 per one-lot straddle, $20 for two points, and so on. If IV falls one point, the trader loses $10 per straddle, $20 for two points, and so on. Traders who want maximum positive exposure to volatility find it in long straddles. This strategy is a prime example of the marriage of implied and realized volatility. Traders who buy straddles because they are bullish on realized volatility will also have bullish positions in implied volatility—like it or not. With this in mind, traders must take care to buy gamma via a straddle that it is not too expensive in terms of the implied volatility. A winning gamma trade can quickly become a loser because of implied volatility. Likewise, traders buying straddles to speculate on an increase in implied volatility must take the theta risk of the trade very seriously. Time can eat away all a trade’s vega profits and more. Realized and implied exposure go hand in hand. The relationship between gamma and vega depends on, among other things, the time to expiration. Traders have some control over the amount of gamma relative to the amount of vega by choosing which expiration month to trade. The shorter the time until expiration, the higher the gammas and the lower the vegas of ATM options. Gamma traders may be better served by buying short-term contracts that coincide with the period of perceived high stock volatility. If the intent of the straddle is to profit from vega, the choice of the month to trade depends on which month’s volatility is perceived to be too high or too low. If, for example, the front-month IV looks low compared with historical IV, current and historical realized volatility, and the expected future volatility, but the back months’ IVs are higher and more in line with these other metrics, there would be no point in buying the back-month options. In this case, traders would need to buy the month that they think is cheap. Trading the Long Straddle Option trading is all about optimizing the statistical chances of success. A long-straddle trade makes the most sense if traders think they can make money on both implied volatility and gamma. Many traders make the mistake of buying a straddle just before earnings are announced because they anticipate a big move in the stock. Of course, stock-price action is only half the story. The option premium can be extraordinarily expensive just before earnings, because the stock move is priced into the options. This is buying after the rush and before the crush. Although some traders are successful specializing in trading earnings, this is a hard way to make money. Ideally, the best time to buy volatility is before the move is priced in—that is, before everyone else does. This is conceptually the same as buying a stock in anticipation of bullish news. Once news comes out, the stock rallies, and it is often too late to participate in profits. The goal is to get in at the beginning of the trend, not the end—the same goal as in trading volatility. As in analyzing a stock, fundamental and technical tools exist for analyzing volatility—namely, news and volatility charts. For fundamentals, buy the rumor, sell the news applies to the rush and crush of implied volatility. Previous chapters discussed fundamental events that affect volatility; be prepared to act fast when volatility-changing situations present themselves. With charts, the elementary concept of buy low, sell high is obvious, yet profound. Review Chapter 14 for guidance on reading volatility charts. With all trading, getting in is easy. It’s managing the position, deciding when to hedge and when to get out that is the tricky part. This is especially true with the long straddle. Straddles are intended to be actively managed. Instead of waiting for a big linear move to evolve over time, traders can take profits intermittently through gamma scalping. Furthermore, they hold the trade only as long as gamma scalping appears to be a promising opportunity. Legging Out There are many ways to exiting a straddle. In the right circumstances, legging out is the preferred method. Instead of buying and selling stock to lock in profits and maintain delta neutrality, traders can reduce their positions by selling off some of the calls or puts that are part of the straddle. In this technique, when the underlying rises, traders sell as many calls as needed to reduce the delta to zero. As the underlying falls, they sell enough puts to reduce their position to zero delta. As the stock oscillates, they whittle away at the position with each hedging transaction. This serves the dual purpose of taking profits and reducing risk. A trader, Susan, has been studying Acme Brokerage Co. (ABC). Susan has noticed that brokerage stocks have been fairly volatile in recent past. Exhibit 15.3 shows an analysis of Acme’s volatility over the past 30 days. EXHIBIT 15.3 Acme Brokerage Co. volatility. Stock Price Realized Volatility Front-Month Implied Volatility 30-day high $78.66 30-day high 47% 30-day high 55% 30-day low $66.94 30-day low 36% 30-day low 34% Current px $74.80 Current vol 36% Current vol 36% During this period, Acme stock ranged more than $11 in price. In this example, Acme’s volatility is a function of interest rate concerns and other macroeconomic issues affecting the brokerage industry as a whole. As the stock price begins to level off in the latter half of the 30-day period, realized volatility begins to ebb. The front month’s IV recedes toward recent lows as well. At this point, both realized and implied volatility converge at 36 percent. Although volatility is at its low for the past month, it is still relatively high for a brokerage stock under normal market conditions. Susan does not believe that the volatility plaguing this stock is over. She believes that an upcoming scheduled Federal Reserve Board announcement will lead to more volatility. She perceives this to be a volatility-buying opportunity. Effectively, she wants to buy volatility on the dip. Susan pays 5.75 for 20 July 75-strike straddles. Exhibit 15.4 shows the analytics of this trade with four weeks until expiration. EXHIBIT 15.4 Analytics for long 20 Acme Brokerage Co. 75-strike straddles. As with any trade, the risk is that the trader is wrong. The risk here is indicated by the −2.07 theta and the +3.35 vega. Susan has to scalp an average of at least $207 a day just to break even against the time decay. And if IV continues to ebb down to a lower, more historically normal, level, she needs to scalp even more to make up for vega losses. Effectively, Susan wants both realized and implied volatility to rise. She paid 36 volatility for the straddle. She wants to be able to sell the options at a higher vol than 36. In the interim, she needs to cover her decay just to break even. But in this case, she thinks the stock will be volatile enough to cover decay and then some. If Acme moves at a volatility greater than 36, her chances of scalping profitably are more favorable than if it moves at less than 36 vol. The following is one possible scenario of what might have happened over two weeks after the trade was made. Week One During the first week, the stock’s volatility tapered off a bit more, but implied volatility stayed firm. After some oscillation, the realized volatility ended the week at 34 percent while IV remained at 36 percent. Susan was able to scalp stock reasonably well, although she still didn’t cover her seven days of theta. Her stock buys and sells netted a gain of $1,100. By the end of week one, the straddle was 5.10 bid. If she had sold the straddle at the market, she would have ended up losing $200. Susan decided to hold her position. Toward the end of week two, there would be the Federal Open Market Committee (FOMC) meeting. Week Two The beginning of the week saw IV rise as the event drew near. By the close on Tuesday, implied volatility for the straddle was 40 percent. But realized volatility continued its decline, which meant Susan was not able to scalp to cover the theta of Saturday, Sunday, Monday, and Tuesday. But, the straddle was now 5.20 bid, 0.10 higher than it had been on previous Friday. The rising IV made up for most of the theta loss. At this point, Susan could have sold her straddle to scratch her trade. She would have lost $1,100 on the straddle [(5.20 − 5.75) × 20] but made $1,100 by scalping gamma in the first week. Susan decided to wait and see what the Fed chairman had to say. By week’s end, the trade had proved to be profitable. After the FOMC meeting, the stock shot up more than $4 and just as quickly fell. It continued to bounce around a bit for the rest of the week. Susan was able to lock in $5,200 from stock scalps. After much gyration over this two-week period, the price of Acme stock incidentally returned to around the same price it had been at when Susan bought her straddle: $74.50. As might have been expected after the announcement, implied volatility softened. By Friday, IV had fallen to 30. Realized volatility was sharply higher as a result of the big moves during the week that were factored into the 30-day calculation. With seven more days of decay and a lower implied volatility, the straddle was 3.50 bid at midafternoon on Friday. Susan sold her 20-lot to close the position. Her profit for week two was $2,000. What went into Susan’s decision to close her position? Susan had two objectives: to profit from a rise in implied volatility and to profit from a rise in realized volatility. The rise in IV did indeed occur, but not immediately. By Tuesday of the second week, vega profits were overshadowed by theta losses. Gamma was the saving grace with this trade. The bulk of the gain occurred in week two when the Fed announcement was made. Once that event passed, the prospects for covering theta looked less attractive. They were further dimmed by the sharp drop in implied volatility from 40 to 30. In this hypothetical scenario, the trade ended up profitable. This is not always the case. Here the profit was chiefly produced by one or two high-volatility days. Had the stock not been unusually volatile during this time, the trade would have been a certain loser. Even though implied volatility had risen four points by Tuesday of the second week, the trade did not yield a profit. The time decay of holding two options can make long straddles a tough strategy to trade. Short Straddle Definition : Selling one call and one put in the same option class, in the same expiration cycle, and with the same strike price. Just as buying a straddle is a pure way to buy volatility, selling a straddle is a way to short it. When a trader’s forecast calls for lower implied and realized volatility, a straddle generates the highest returns of all volatility-selling strategies. Of course, with high reward necessarily comes high risk. A short straddle is one of the riskiest positions to trade. Let’s look at a one-month 70-strike straddle sold at 4.25. The risk is easily represented graphically by means of a P&(L) diagram. Exhibit 15.5 shows the risk and reward of this short straddle. EXHIBIT 15.5 Short straddle P&(L) at initiation and expiration. If the straddle is held until expiration and the underlying is trading below the strike price, the short put is in-the-money (ITM). The lower the stock, the greater the loss on the +1.00 delta from the put. The trade as a whole will be a loser if the underlying is below the lower of the two break-even points—in this case $65.75. This point is found by subtracting the premium received from the strike. Before expiration, negative gamma adversely affects profits as the underlying falls. The lower the underlying is trading below the strike price, the greater the drain on P&(L) due to the positive delta of the short put. It is the same proposition if the underlying is above $70 at expiration. But in this case, it is the short call that would be in-the-money. The higher the underlying price, the more the −1.00 delta adversely impacts P&(L). If at expiration the underlying is above the higher breakeven, which in this case is $74.25 (the strike plus the premium), the trade is a loser. The higher the underlying, the worse off the trade. Before expiration, negative gamma creates negative deltas as the underlying climbs above the strike, eating away at the potential profit, which is the net premium received. The best-case scenario is that the underlying is right at $70 at the closing bell on expiration Friday. In this situation, neither option is ITM, meaning that the 4.25 premium is all profit. In reaping the maximum profit, both time and price play roles. If the position is closed before expiration, implied volatility enters into the picture as well. It’s important to note that just because neither option is ITM if the underlying is right at $70 at expiration, it doesn’t mean with certainty that neither option will be assigned. Sometimes options that are ATM or even out-of-the-money (OTM) get assigned. This can lead to a pleasant or unpleasant surprise the Monday morning following expiration. The risk of not knowing whether or not you will be assigned—that is, whether or not you have a position in the underlying security—is a risk to be avoided. It is the goal of every trader to remove unnecessary risk from the equation. Buying the call and the put for 0.05 or 0.10 to close the position is a small price to pay when one considers the possibility of waking up Monday morning to find a loss of hundreds of dollars per contract because a position you didn’t even know you owned had moved against you. Most traders avoid this risk, referred to as pin risk, by closing short options before expiration. The Risks with Short Straddles Looking at an at-expiration diagram or even analyzing the gamma/theta relationship of a short straddle may sometimes lead to a false sense of comfort. Sometimes it looks as if short straddles need a pretty big move to lose a lot of money. So why are they definitely among the riskiest strategies to trade? That is a matter of perspective. Option trading is about risk management. Dealing with a proverbial train wreck every once in a while is part of the game. But the big disasters can end one’s trading career in an instant. Because of its potential—albeit sometimes small potential—for a colossal blowup, the short straddle is, indeed, one of the riskiest positions one can trade. That said, it has a place in the arsenal of option strategies for speculative traders. Trading the Short Straddle A short straddle is a trade for highly speculative traders who think a security will trade within a defined range and that implied volatility is too high. While a long straddle needs to be actively traded, a short straddle needs to be actively monitored to guard against negative gamma. As adverse deltas get bigger because of stock price movement, traders have to be on alert, ready to neutralize directional risk by offsetting the delta with stock or by legging out of the options. To be sure, with a short straddle, every stock trade locks in a loss with the intent of stemming future losses. The ideal situation is that the straddle is held until expiration and expires with the underlying right at $70 with no negative-gamma scalping. Short-straddle traders must take a longer-term view of their positions than long-straddle traders. Often with short straddles, it is ultimately time that provides the payout. While long straddle traders would be inclined to watch gamma and theta very closely to see how much movement is required to cover each day’s erosion, short straddlers are more inclined to focus on the at-expiration diagram so as not to lose sight of the end game. There are some situations that are exceptions to this long-term focus. For example, when implied volatility gets to be extremely high for a particular option class relative to both the underlying stock’s volatility and the historical implied volatility, one may want to sell a straddle to profit from a fall in IV. This can lead to leveraged short-term profits if implied volatility does, indeed, decline. Because of the fact that there are two short options involved, these straddles administer a concentrated dose of negative vega. For those willing to bet big on a decline in implied volatility, a short straddle is an eager croupier. These trades are delta neutral and double the vega of a single-leg trade. But they’re double the gamma, too. As with the long straddle, realized and implied volatility levels are both important to watch. Short-Straddle Example For this example, a trader, John, has been watching Federal XYZ Corp. (XYZ) for a year. During the 12 months that John has followed XYZ, its front-month implied volatility has typically traded at around 20 percent, and its realized volatility has fluctuated between 15 and 20 percent. The past 30 days, however, have been a bit more volatile. Exhibit 15.6 shows XYZ’s recent volatility. EXHIBIT 15.6 XYZ volatility. Stock Price Realized Volatility Front-Month Implied Volatility 30-day high $111.71 30-day high 26% 30-day high 30% 30-day low $102.05 30-day low 21% 30-day low 24% Current px $104.75 Current vol 22% Current vol 26% The stock volatility has begun to ease, trading now at a 22 volatility compared with the 30-day high of 26, but still not down to the usual 15-to-20 range. The stock, in this scenario, has traded in a channel. It currently lies in the lower half of its recent range. Although the current front-month implied volatility is in the lower half of its 30-day range, it’s historically high compared with the 20 percent level that John has been used to seeing, and it’s still four points above the realized volatility. John believes that the conditions that led to the recent surge in volatility are no longer present. His forecast is for the stock volatility to continue to ease and for implied volatility to continue its downtrend as well and revert to its long-term mean over the next week or two. John sells 10 September 105 straddles at 5.40. Exhibit 15.7 shows the greeks for this trade. EXHIBIT 15.7 Greeks for short XYZ straddle. The goal here is for implied volatility to fall to around 20. If it does, John makes $1,254 (6 vol points × 2.09 vega). He also thinks theta gains will outpace gamma losses. The following is a two-week examination of one possible outcome for John’s trade. Week One The first week in this example was a profitable one, but it came with challenges. John paid for his winnings with a few sleepless nights. On the Monday following his entry into the trade, the stock rose to $106. While John collected a weekend’s worth of time decay, the $1.25 jump in stock price ate into some of those profits and naturally made him uneasy about the future. At this point, John was sitting on a profit, but his position delta began to grow negative, to around −1.22 [(–1.18 × 1.25) + 0.26]. For a $104.75 stock, a move of $1.25—or just over 1 percent—is not out of the ordinary, but it put John on his guard. He decided to wait and see what happened before hedging. The following day, the rally continued. The stock was at $107.30 by noon. His delta was around −3. In the face of an increasingly negative delta, John weighed his alternatives: He could buy back some of his calls to offset his delta, which would have the added benefit of reducing his gamma as well. He could buy stock to flatten out. Lastly, he could simply do nothing and wait. John felt the stock was overbought and might retrace. He also still believed volatility would fall. He decided to be patient and enter a stop order to buy all of his deltas at $107.50 in case the stock continued trending up. The XYZ shares closed at $107.45 that day. This time inaction proved to be the best action. The stock did retrace. Week one ended with Federal XYZ back down around $105.50. The IV of the straddle was at 23. The straddle finished up week one offered at $4.10. Week Two The future was looking bright at the start of week two until Wednesday. Wednesday morning saw XYZ gap open to $109. When you have a short straddle, a $3.50 gap move in the underlying tends to instantly give you a sinking feeling in the pit of your stomach. But the damage was truly not that bad. The offer in the straddle was 4.75, so the position was still a winner if John bought it back at this point. Gamma/delta hurt. Theta helped. A characteristic that enters into this trade is volatility’s changing as a result of movement in the stock price. Despite the fact that the stock gapped $3.50 higher, implied volatility fell by 1 percent, to 22. This volatility reaction to the underlying’s rise in price is very common in many equity and index options. John decided to close the trade. Nobody ever went broke taking a profit. The trade in this example was profitable. Of course, this will not always be the case. Sometimes short straddles will be losers—sometimes big ones. Big moves and rising implied volatility can be perilous to short straddles and their writers. If the XYZ stock in the previous example had gapped up to $115—which is not an unreasonable possibility—John’s trade would have been ugly. Synthetic Straddles Straddles are the pet strategy of certain professional traders who specialize in trading volatility. In fact, in the mind of many of these traders, a straddle is all there is. Any single-legged trade can be turned into a straddle synthetically simply by adding stock. Chapter 6 discussed put-call parity and showed that, for all intents and purposes, a put is a call and a call is a put. For the most part, the greeks of the options in the put-call pair are essentially the same. The delta is the only real difference. And, of course, that can be easily corrected. As a matter of perspective, one can make the case that buying two calls is essentially the same as buying a call and a put, once stock enters into the equation. Take a non-dividend-paying stock trading at $40 a share. With 60 days until expiration, a 25 volatility, and a 4 percent interest rate, the greeks of the 40-strike calls and puts of the straddle are as follows: Essentially, the same position can be created by buying one leg of the spread synthetically. For example, in addition to buying one 40 call, another 40 call can be purchased along with shorting 100 shares of stock to create a 40 put synthetically. Combined, the long call and the synthetic long put (long call plus short stock) creates a synthetic straddle. A long synthetic straddle could have similarly been constructed with a long put and a long synthetic call (long put plus long stock). Furthermore, a short synthetic straddle could be created by selling an option with its synthetic pair. Notice the similarities between the greeks of the two positions. The synthetic straddle functions about the same as a conventional straddle. Because the delta and gamma are nearly the same, the up-and-down risk is nearly the same. Time and volatility likewise affect the two trades about the same. The only real difference is that the synthetic straddle might require a bit more cash up front, because it requires buying or shorting the stock. In practice, straddles will typically be traded in accounts with retail portfolio margining or professional margin requirements (which can be similar to retail portfolio margining). So the cost of the long stock or margin for short stock is comparatively small. Long Strangle Definition : Buying one call and one put in the same option class, in the same expiration cycle, but with different strike prices. Typical long strangles involve an OTM call and an OTM put. A strangle in which an ITM call and an ITM put are purchased is called a long guts strangle. A long strangle is similar to a long straddle in many ways. They both require buying a call and a put on the same class in the same expiration month. They are both buying volatility. There are, however, some functional differences. These differences stem from the fact that the options have different strike prices. Because there is distance between the strike prices, from an at-expiration perspective, the underlying must move more for the trade to show a profit. Exhibit 15.8 illustrates the payout of options as part of a long strangle on a $70 stock. The graph is much like that of Exhibit 15.1 , which shows the payout of a long straddle. But the net cost here is only 1.00, compared with 4.25 for the straddle with the same time and volatility inputs. The cost is lower because this trade consists of OTM options instead of ATM options. The breakdown is as follows: EXHIBIT 15.8 Long strangle at-expiration diagram. The underlying has a bit farther to go by expiration for the trade to have value. If the underlying is above $75 at expiration, the call is ITM and has value. If the underlying is below $65 at expiration, the put is ITM and has value. If the underlying is between the two strike prices at expiration both options expire and the 1.00 premium is lost. An important difference between a straddle and a strangle is that if a strangle is held until expiration, its break-even points are farther apart than those of a comparable straddle. The 70-strike straddle in Exhibit 15.1 had a lower breakeven of $65.75 and an upper break-even of $74.25. The comparable strangle in this example has break-even prices of $64 and $76. But what if the strangle is not held until expiration? Then the trade’s greeks must be analyzed. Intuitively, two OTM options (or ITM ones, for that matter) will have lower gamma, theta, and vega than two comparable ATM options. This has a two-handed implication when comparing straddles and strangles. On the one hand, from a realized volatility perspective, lower gamma means the underlying must move more than it would have to for a straddle to produce the same dollar gain per spread, even intraday. But on the other hand, lower theta means the underlying doesn’t have to move as much to cover decay. A lower nominal profit but a higher percentage profit is generally reaped by strangles as compared with straddles. A long strangle composed of two OTM options will also give positive exposure to implied volatility but, again, not as much as an ATM straddle would. Positive vega really kicks in when the underlying is close to one of the strike prices. This is important when anticipating changes in the stock price and in IV. Say a trader expects implied volatility to rise as a result of higher stock volatility. As the stock rises or falls, the strangle will move toward the price point that offers the highest vega (the strike). With a straddle, the stock will be moving away from the point with the highest vega. If the stock doesn’t move as anticipated, the lower theta and vega of the strangle compared with the ATM straddle have a less adverse effect on P&L. Long-Strangle Example Let’s return to Susan, who earlier in this chapter bought a straddle on Acme Brokerage Co. (ABC). Acme currently trades at $74.80 a share with current realized volatility at 36 percent. The stock’s volatility range for the past month was between 36 and 47. The implied volatility of the four-week options is 36 percent. The range over the past month for the IV of the front month has been between 34 and 55. As in the long-straddle example earlier in this chapter, there is a great deal of uncertainty in brokerage stocks revolving around interest rates, credit-default problems, and other economic issues. An FOMC meeting is expected in about one week’s time about whose possible actions analysts’ estimates vary greatly, from a cut of 50 basis points to no cut at all. Add a pending earnings release to the docket, and Susan thinks Acme may move quite a bit. In this case, however, instead of buying the 75-strike straddle, Susan pays 2.35 for 20 one-month 70–80 strangles. Exhibit 15.9 compares the greeks of the long ATM straddle with those of the long strangle. EXHIBIT 15.9 Long straddle versus long strangle. The cost of the strangle, at 2.35, is about 40 percent of the cost of the straddle. Of course, with two long options in each trade, both have positive gamma and vega and negative theta, but the exposure to each metric is less with the strangle. Assuming the same stock-price action, a strangle would enjoy profits from movement and losses from lack of movement that were similar to those of a straddle—just nominally less extreme. For example, if Acme stock rallies $5, from $74.80 to $79.80, the gamma of the 75 straddle will grow the delta favorably, generating a gain of 1.50, or about 25 percent. The 70–80 strangle will make 1.15 from the curvature of the delta–almost a 50 percent gain. With the straddle and especially the strangle, there is one more detail to factor in when considering potential P&L: IV changes due to stock price movement. IV is likely to fall as the stock rallies and rise as the stock declines. The profits of both the long straddle and the long strangle would likely be adversely affected by IV changes as the stock rose toward $79.80. And because the stock would be moving away from the straddle strike and toward one of the strangle strikes, the vegas would tend to become more similar for the two trades. The straddle in this example would have a vega of 2.66, while the strangle’s vega would be 2.67 with the underlying at $79.80 per share. Short Strangle Definition : Selling one call and one put in the same option class, in the same expiration cycle, but with different strike prices. Typically, an OTM call and an OTM put are sold. A strangle in which an ITM call and an ITM put are sold is called a short guts strangle. A short strangle is a volatility-selling strategy, like the short straddle. But with the short strangle, the strikes are farther apart, leaving more room for error. With these types of strategies, movement is the enemy. Wiggle room is the important difference between the short-strangle and short-straddle strategies. Of course, the trade-off for a higher chance of success is lower option premium. Exhibit 15.10 shows the at-expiration diagram of a short strangle sold at 1.00, using the same options as in the diagram for the long strangle. EXHIBIT 15.10 Short strangle at-expiration diagram. Note that if the underlying is between the two strike prices, the maximum gain of 1.00 is harvested. With the stock below $65 at expiration, the short put is ITM, with a +1.00 delta. If the stock price is below the lower breakeven of $64 (the put strike minus the premium), the trade is a loser. The lower the stock, the bigger the loss. If the underlying is above $75, the short call is ITM, with a −1.00 delta. If the stock is above the upper breakeven of $76 (the call strike plus the premium), the trade is a loser. The higher the stock, the bigger the loss. Intuitively, the signs of the greeks of this strangle should be similar to those of a short straddle—negative gamma and vega, positive theta. That means that increased realized volatility hurts. Rising IV hurts. And time heals all wounds—unless, of course, the wounds caused by gamma are greater than the net premium received. This brings us to an important philosophical perspective that emphasizes the differences between long straddles and strangles and their short counterparts. Losses from rising vega are temporary; the time value of all options will be zero at expiration. But gamma losses can be permanent and profound. These short strategies have limited profit potential and unlimited loss potential. Although short-term profits (or losses) can result from IV changes, the real goal here is to capture theta. Short-Strangle Example Let’s revisit John, a Federal XYZ (XYZ) trader. XYZ is at $104.75 in this example, with an implied volatility of 26 percent and a stock volatility of 22. Both implied and realized volatility are higher than has been typical during the past twelve months. John wants to sell volatility. In this example, he believes the stock price will remain in a fairly tight range, causing realized volatility to revert to its normal level, in this case between 15 and 20 percent. He does everything possible to ensure success. This includes scanning the news headlines on XYZ and its financials for a reason not to sell volatility. Playing devil’s advocate with oneself can uncover unforeseen yet valid reasons to avoid making bad trades. John also notes the recent price range, which has been between $111.71 and $102.05 over the past month. Once John commits to an outlook on the stock, he wants to set himself up for maximum gain if he’s right and, for that matter, to maximize his chances of being right. In this case, he decides to sell a strangle to give himself as much margin for error as possible. He sells 10 three-week 100–110 strangles at 1.80. Exhibit 15.11 compares the greeks of this strangle with those of the 105 straddle. EXHIBIT 15.11 Short straddle vs. short strangle. As expected, the strangle’s greeks are comparable to the straddle’s but of less magnitude. If John’s intention were to capture a drop in IV, he’d be better off selling the bigger vega of the straddle. Here, though, he wants to see the premium at zero at expiration, so the strangle serves his purposes better. What he is most concerned about are the breakevens—in this case, 98.20 and 111.8. The straddle has closer break-even points, of $99.60 and $110.40. Despite the fact that in this case, John is not really trading the greeks or IV per se, they still play an important role in his trade. First, he can use theta to plan the best strangle to trade. In this case, he sells the three-week strangle because it has the highest theta of the available months. The second month strangle has a −0.71 theta, and the third month has a −0.58 theta. With strangles, because the options are OTM, this disparity in theta among the tradable months may not always be the case. But for this trade, if he is still bearish on realized volatility after expiration, John can sell the next month when these options expire. Certainly, he will monitor his risk by watching delta and gamma. These are his best measures of directional exposure. He will consider implied volatility in the decision-making process, too. An implied volatility significantly higher than the realized volatility can be a red flag that the market expects something to happen, but there’s a bigger payoff if there is no significant volatility. An IV significantly lower than the realized can indicate the risk of selling options too cheaply: the premium received is not high enough, based on how much the stock has been moving. Ideally, the IV should be above the realized volatility by between 2 and 20 percent, perhaps more for highly speculative traders. Limiting Risk The trouble with short straddles and strangles is that every once in a while the stock unexpectedly reacts violently, moving by three or more standard deviations. This occurs when there is a takeover, an extreme political event, a legal action, or some other extraordinary incident. These events can be guarded against by buying farther OTM options for protection. Essentially, instead of selling a straddle or a strangle, one sells an iron butterfly or iron condor. Then, when disaster strikes, it’s not a complete catastrophe. How Cheap Is Too Cheap? At some point, the absolute premium simply is not worth the risk of the trade. For example, it would be unwise to sell a two-month 45–55 strangle for 0.10 no matter what the realized volatility was. With the knowledge that there is always a chance for a big move, it’s hard to justify risking dollars to make a dime. Note 1 . This depends on interest, dividends, and time to expiration. The delta will likely not be exactly zero. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00028.html SCORE: 1001.00 ================================================================================ CHAPTER 16 Ratio Spreads and Complex Spreads The purpose of spreading is to reduce risk. Buying one contract and selling another can reduce some or all of a trade’s risks, as measured by the greeks, compared with simply holding an outright option. But creative traders have the ability to exercise great control over their greeks risk. They can practically eliminate risk in some greeks, while retaining risks in just the desired greeks. To do so, traders may have to use more complex, and less conventional spreads. These spreads often involve buying or selling options in quantities other than one-to-one ratios. Ratio Spreads The simplest versions of these strategies used by retail traders, institutional traders, proprietary traders, and others are referred to as ratio spreads . In ratio spreads, options are bought and sold in quantities based on a ratio. For example, a 1:3 spread is when one option is bought (or sold) and three are sold (or bought)—a ratio of one to three. This kind of ratio spread would be called a “one-by-three.” However, some option positions can get a lot more complicated. Market makers and other professional traders manage a complex inventory of long and short options. These types of strategies go way beyond simple at-expiration diagrams. This chapter will discuss the two most common types of ratio spreads—backspreads and ratio vertical spreads—and also the delta-neutral position management of market makers and other professional traders. Backspreads Definition : An option strategy consisting of more long options than short options having the same expiration month. Typically, the trader is long calls (or puts) in one series of options and short a fewer number of calls (or puts) in another series with the same expiration month in the same option class. Some traders, such as market makers, refer generically to any delta-neutral long-gamma position as a backspread. Shades of Gray In its simplest form, trading a backspread is trading a one-by-two call or put spread and holding it until expiration in hopes that the underlying stock’s price will make a big move, particularly in the more favorable direction. But holding a backspread to expiration as described has its challenges. Let’s look at a hypothetical example of a backspread held to term and its at-expiration diagram. With the stock at $71 and one month until March expiration: In this example, there is a credit of 3.20 from the sale of the 70 call and a debit of 1.10 for each of the two 75 calls. This yields a total net credit of 1.00 (3.20 − 1.10 − 1.10). Let’s consider how this trade performs if it is held until expiration. If the stock falls below $70 at expiration, all the calls expire and the 1.00 credit is all profit. If the stock is between $70 and $75 at expiration, the 70 call is in-the-money (ITM) and the −1.00 delta starts racking up losses above the breakeven of $71 (the strike plus the credit). At $75 a share this trade suffers its maximum potential loss of $4. If the stock is above $75 at expiration, the 75 calls are ITM. The net delta of +1.00, resulting from the +2.00 deltas of the 75 calls along with the −1.00 delta of the 70 call, makes money as the stock rises. To the upside, the trade is profitable once the stock is at a high enough price for the gain on the two 75 calls to make up for the loss on the 70 call. In this case, the breakeven is $79 (the $4 maximum potential loss plus the strike price of 75). While it’s good to understand this at-expiration view of this trade, this diagram is a bit misleading. What does the trader of this spread want to have happen? If the trader is bearish, he could find a better way to trade his view than this, which limits his gains to 1.00—he could buy a put. If the trader believes the stock will make a volatile move in either direction, the backspread offers a decidedly limited opportunity to the downside. A straddle or strangle might be a better choice. And if the trader is bullish, he would have to be very bullish for this trade to make sense. The underlying needs to rise above $79 just to break even. If instead he just bought 2 of the 75 calls for 1.10, the maximum risk would be 2.20 instead of 4, the breakeven would be $77.20 instead of $79, and profits at expiration would rack up twice as fast above the breakeven, since the trader is net long two calls instead of one. Why would a trader ever choose to trade a backspread? EXHIBIT 16.1 Backspread at expiration. The backspread is a complex spread that can be fully appreciated only when one has a thorough knowledge of options. Instead of waiting patiently until expiration, an experienced backspreader is more likely to gamma scalp intermittent opportunities. This requires trading a large enough position to make scalping worthwhile. It also requires appropriate margining (either professional-level margin requirements or retail portfolio margining). For example, this 1:2 contract backspread has a delta of −0.02 and a gamma of +0.05. Fewer than 10 deltas could be scalped if the stock moves up and down by one point. It becomes a more practical trade as the position size increases. Of course, more practical doesn’t necessarily guarantee it will be more profitable. The market must cooperate! Backspread Example Let’s say a 20:40 contract backspread is traded. ( Note : In trader lingo this is still called a one-by-two; it is just traded 20 times.) The spread price is still 1.00 credit per contract; in this case, that’s $2,000. But with this type of trade, the spread price is not the best measure of risk or reward, as it is with some other kinds of spreads. Risk and reward are best measured by delta, gamma, theta, and vega. Exhibit 16.2 shows this trade’s greeks. EXHIBIT 16.2 Greeks for 20:40 backspread with the underlying at $71. Backspreads are volatility plays. This spread has a +1.07 vega with the stock at $71. It is, therefore, a bullish implied volatility (IV) play. The IV of the long calls, the 75s, is 30 percent, and that of the 70s is 32 percent. Much as with any other volatility trade, traders would compare current implied volatility with realized volatility and the implied volatility of recent past and consider any catalysts that might affect stock volatility. The objective is to buy an IV that is lower than the expected future stock volatility, based on all available data. The focus of traders of this backspread is not the dollar credit earned. They are more interested in buying a 30 volatility—that’s the focus. But the 75 calls’ IV is not the only volatility figure to consider. The short options, the 70s, have implied volatility of 32 percent. Because of their lower strike, the IV is naturally higher for the 70 calls. This is vertical skew and is described in Chapter 3. The phenomenon of lower strikes in the same option class and with the same expiration month having higher IV is very common, although it is not always the case. Backspreads usually involve trading vertical skew. In this spread, traders are buying a 30 volatility and selling a 32 volatility. In trading the skew, the traders are capturing two volatility points of what some traders would call edge by buying the lower volatility and selling the higher. Based on the greeks in Exhibit 16.2 , the goal of this trade appears fairly straightforward: to profit from gamma scalping and rising IV. But, sadly, what appears to be straightforward is not. Exhibit 16.3 shows the greeks of this trade at various underlying stock prices. EXHIBIT 16.3 70–75 backspread greeks at various stock prices. Notice how the greeks change with the stock price. As the stock price moves lower through the short strike, the 70 strike calls become the more relevant options, outweighing the influence of the 75s. Gamma and vega become negative, and theta becomes positive. If the stock price falls low enough, this backspread becomes a very different position than it was with the stock price at $71. Instead of profiting from higher implied and realized volatility, the spread needs a lower level of both to profit. This has important implications. First, gamma traders must approach the backspread a little differently than they would most spreads. The backspread traders must keep in mind the dynamic greeks of the position. With a trade like a long straddle, in which there are no short options, traders scalping gamma simply buy to cover short deltas as the stock falls and sell to cover long deltas as the stock rises. The only risks are that the stock may not move enough to cover theta or that the traders may cover deltas too soon to maximize profits. With the backspread, the changing gamma adds one more element of risk. In this example, buying stock to flatten out delta as the stock falls can sometimes be a premature move. Traders who buy stock may end up with more long deltas than they bargained for if the stock falls into negative-gamma territory. Exhibit 16.3 shows that with the stock at $68, the delta for this trade is −2.50. If the traders buy 250 shares at $68, they will be delta neutral. If the stock subsequently falls to $62 a share, instead of being short 1.46 deltas, as the figure indicates, they will be long 1.04 because of the 250 shares they bought. These long deltas start to hurt as the stock continues lower. Backspreaders must therefore anticipate stock movements to avoid overhedging. The traders in this example may decide to lean short if the stock shows signs of weakness. Leaning short means that if the delta is −2.50 at $68 a share, the traders may decide to underhedge by buying just 100 or 200 shares. If the stock continues to fall and negative gamma kicks in, this gives the traders some cushion to the downside. The short delta of the position moves closer to being flat as the stock falls. Because there is a long strike and a short strike in this delta-neutral position, trading ratio spreads is like trading a long and a short volatility position at the same time. Trading backspreads is not an exact science. The stock has just as good a chance of rising as it does of falling, and if it does rise and the traders have underhedged at $68, they will not participate in all the gains they would have if they had fully hedged by buying 250 shares of stock. If trading were easy, everyone would do it! Backspreaders must also be conscious of the volatility of each leg of the spread. There is an inherent advantage in this example to buying the lower volatility of the 75 calls and selling the higher volatility of the 70 calls. But there is also implied risk. Equity prices and IV tend to have an inverse relationship. When stock prices fall—especially if the drop happens quickly—IV will often rise. When stock prices rise, IV often falls. In this backspread example, as the stock price falls to or through the short strike, vega becomes negative in the face of a potentially rising IV. As the stock price rises into positive vega turf, there is the risk of IV’s declining. A dynamic volatility forecast should be part of a backspread-trading plan. One of the volatility questions traders face in this example is whether the two-point volatility skew between the two strike prices is enough to compensate for the potential adverse vega move as the stock price changes. Put backspreads have the opposite skew/volatility issues. Buying two lower-strike puts against one higher-strike put means the skew is the other direction—buying the higher IV and selling the lower. The put backspread would have long gamma/vega to the downside and short gamma/vega to the upside. But if the vega firms up as the stock falls into positive-vega territory, it would be in the trader’s favor. As the stock rises, leading to negative vega, there is the potential for vega profits if IV indeed falls. There are a lot of things to consider when trading a backspread. A good trader needs to think about them all before putting on the trade. Ratio Vertical Spreads Definition : An option strategy consisting of more short options than long options having the same expiration month. Typically, the trader is short calls (or puts) in one series of options and long a fewer number of calls (or puts) in another series in the same expiration month on the same option class. A ratio vertical spread, like a backspread, involves options struck at two different prices—one long strike and one short. That means that it is a volatility strategy that may be long or short gamma or vega depending on where the underlying price is at the time. The ratio vertical spread is effectively the opposite of a backspread. Let’s study a ratio vertical using the same options as those used in the backspread example. With the stock at $71 and one month until March expiration: In this case, we are buying one ITM call and selling two OTM calls. The relationship of the stock price to the strike price is not relevant to whether this spread is considered a ratio vertical spread. Certainly, all these options could be ITM or OTM at the time the trade is initiated. It is also not important whether the trade is done for a debit or a credit. If the stock price, time to expiration, volatility, or number of contracts in the ratio were different, this could just as easily been a credit ratio vertical. Exhibit 16.4 illustrates the payout of this strategy if both legs of the 1:2 contract are still open at expiration. EXHIBIT 16.4 Short ratio spread at expiration. This strategy is a mirror image of the backspread discussed previously in this chapter. With limited risk to the downside, the maximum loss to the trade is the initial debit of 1 if the stock is below $70 at expiration and all the calls expire. There is a maximum profit potential of 4 if the stock is at the short strike at expiration. There is unlimited loss potential, since a short net delta is created on the upside, as one short 75 call is covered by the long 70 call, and one is naked. The breakevens are at $71 and $79. Low Volatility With the stock at $71, gamma and vega are both negative. Just as the backspread was a long volatility play at this underlying price, this ratio vertical is a short-vol play here. As in trading a short straddle, the name of the game is low volatility—meaning both implied and realized. This strategy may require some gamma hedging. But as with other short volatility delta-neutral trades, the fewer the negative scalps, the greater the potential profit. Delta covering should be implemented in situations where it looks as if the stock will trend deep into negative-gamma territory. Murphy’s Law of trading dictates that delta covering will likely be wrong at least as often as it is right. Ratio Vertical Example Let’s examine a trade of 20 contracts by 40 contracts. Exhibit 16.5 shows the greeks for this ratio vertical. EXHIBIT 16.5 Short ratio vertical spread greeks. Before we get down to the nitty-gritty of the mechanics and management of this trade—the how—let’s first look at the motivations for putting the trade on—the why. For the cost of 1.00 per spread, this trader gets a leveraged position if the stock rises moderately. The profits max out with the stock at the short-strike target price—$75—at expiration. Another possible profit engine is IV. Because of negative vega, there is the chance of taking a quick profit if IV falls in the interim. But short-term losses are possible, too. IV can rise, or negative gamma can hurt the trader. Ultimately, having naked calls makes this trade not very bullish. A big move north can really hurt. Basically, this is a delta-neutral-type short-volatility play that wins the most if the stock is at $75 at expiration. One would think about making this trade if the mechanics fit the forecast. If this trader were a more bullish than indicated by the profit and loss diagram, a more-balanced bull call spread would be a better strategy, eliminating the unlimited upside risk. If upside risk were acceptable, this trader could get more aggressive by trading the spread one-by-three. That would result in a credit of 0.05 per spread. There would then be no ultimate risk below $70 but rather a 0.05 gain. With double the naked calls, however, there would be double punishment if the stock rallied strongly beyond the upside breakeven. Ultimately, mastering options is not about mastering specific strategies. It’s about having a thorough enough understanding of the instrument to be flexible enough to tailor a position around a forecast. It’s about minimizing the unwanted risks and optimizing exposure to the intended risks. Still, there always exists a trade-off in that where there is the potential for profit, there is the possibility of loss—you can always be wrong. Recalling the at-expiration diagram and examining the greeks, the best-case scenario is intuitive: the stock at $75 at expiration. The biggest theta would be right at that strike. But that strike price is also the center of the biggest negative gamma. It is important to guard against upward movement into negative delta territory, as well as movement lower where the position has a slightly positive delta. Exhibit 16.6 shows what happens to the greeks of this trade as the stock price moves. EXHIBIT 16.6 Ratio vertical spread at various prices for the underlying. As the stock begins to rise from $71 a share, negative deltas grow fast in the short term. Careful trend monitoring is necessary to guard against a rally. The key, however, is not in knowing what will happen but in skillfully hedging against the unknown. The talented option trader is a disciplined risk manager, not a clairvoyant. One of the risks that the trader willingly accepted when placing this trade was short gamma. But when the stock moves and deltas are created, decisions have to be made. Did the catalyst(s)—if any—that contributed to the rise in stock price change the outlook for volatility? If not, the decision is simply whether or not to hedge by buying stock. However, if it appears that volatility is on the rise, it is not just a delta decision. A trader may consider buying some of the short options back to reduce volatility exposure. In this example, if the stock rises and it’s feared that volatility may increase, a good choice may be to buy back some of the short 75-strike calls. This has the advantage of reducing delta (buy enough deltas to flatten out) and reducing gamma and vega. Of course, the downside to this strategy is that in purchasing the calls, a loss is likely to be locked in. Unless a lot of time has passed or implied volatility has dropped sharply, the calls will probably be bought at a higher price than they were sold. If the stock makes a violent move upward, a loss will be incurred. Whether this loss is locked in by closing all or part of the position, the account will still be down in value. The decision to buy the calls back at a loss is based on looking forward. Nothing good can come of looking back. How Market Makers Manage Delta-Neutral Positions While market makers are not position traders per se, they are expert position managers. For the most part, market makers make their living by buying the bid and selling the offer. In general, they don’t act; they react. Most of their trades are initiated by taking the other side of what other people want to do and then managing the risk of the positions they accumulate. The business of a market maker is much like that of a casino. A casino takes the other side of people’s bets and, in the long run, has a statistical (theoretical) edge. For market makers, because theoretical value resides in the middle of the bid and the ask, these accommodating trades lead to a theoretical profit—that is, the market maker buys below theoretical value and sells above. Actual profit—cold, hard cash you can take to the bank—is, however, dependent on sound management of the positions that are accumulated. My career as a market maker was on the floor of the Chicago Board Options Exchange (CBOE) from 1998 to 2005. Because, over all, the trades I made had a theoretical edge, I hoped to trade as many contracts as possible on my markets without getting too long or too short in any option series or any of my greeks. As a result of reacting to order flow, market makers can accumulate a large number of open option series for each class they trade, resulting in a single position. For example, Exhibit 16.7 shows a position I had in Ford Motor Co. (F) options as a market maker. EXHIBIT 16.7 Market-maker position in Ford Motor Co. options. With all the open strikes, this position is seemingly complex. There is not a specific name for this type of “spread.” The position was accumulated over a long period of time by initiating trades via other traders selling options to me at prices I wanted to buy them—my bid—and buying options from me at prices I wanted to sell them—my offer. Upon making an option trade, I needed to hedge directional risk immediately. I usually did so by offsetting my option trades by taking the opposite delta position in the stock—especially on big-delta trades. Through this process of providing liquidity to the market, I built up option-centric risk. To manage this risk I needed to watch my other greeks. To be sure, trying to draw a P&L diagram of this position would be a fruitless endeavor. Exhibit 16.8 shows the risk of this trade in its most distilled form. EXHIBIT 16.8 Analytics for market-maker position in Ford Motor Co. (stock at $15.72). Delta +1,075 Gamma −10,191 Theta +1,708 Vega +7,171 Rho −33,137 The +1,075 delta shows comparatively small directional risk relative to the −10,191 gamma. Much of the daily task of position management would be to carefully guard against movement by delta hedging when necessary to earn the $1,708 per day theta. Much of the negative gamma/positive theta comes from the combined 1,006 short January 15 calls and puts. (Note that because this position is traded delta neutral, the net long or short options at each strike is what matters, not whether the options are calls or puts. Remember that in delta-neutral trading, a put is a call, and a call is a put.) The positive vega stems from the fact that the position is long 1,927 January 2003 20-strike options. Although this position has a lot going on, it can be broken down many ways. Having long LEAPS options and short front-month options gives this position the feel of a time spread. One way to think of where most of the gamma risk is coming from is to bear in mind that the 15 strike is synthetically short 503 straddles (1,006 options ÷ two). But this position overall is not like a straddle. There are more strikes involved—a lot more. There is more short gamma to the downside if the price of Ford falls toward $12.50. To the upside, the 17.50 strike is long a combined total of 439 options. Looking at just the 15 and 17.50 strikes, we can see something that looks more like a ratio spread: 1,006:439. If the stock were at $17.50, the gamma would be around +5,000. With the stock at $15.72, there is realized volatility risk of F rallying, but with gamma changing from negative to positive as the stock rallies, the risk of movement decreases quickly. The 20 strike is short 871 options which brings the position back to negative-gamma territory. Having alternating long and short strikes, sometimes called a butterflied position, is a handy way for market makers to reduce risk. A position is perfectly butterflied if it has alternating long and short strikes with the same number of contracts. Through Your Longs to Your Shorts With market-maker-type positions consisting of many strikes, the greatest profit is gained if the underlying security moves through the longs to the shorts. This provides kind of a win-win scenario for greeks traders. In this situation, traders get the benefit of long gamma as the stock moves higher or lower through the long strike. They also reap the benefits of theta when the stock sits at the short strike. Trading Flat Most market makers like to trade flat—that is, profit from the bid-ask spread and strive to lower exposure to direction, time, volatility, and interest as much as possible. But market makers are at the mercy of customer orders, or paper, as it’s known in the industry. If someone sells, say, the March 75 calls to a market maker at the bid, the best-case scenario is that moments later someone else buys the same number of the same calls—the March 75s, in this case—from that same market maker at the offer. This is locking in a profit. Unfortunately, this scenario seldom plays out this way. In my seven years as a market maker, I can count on one hand the number of times the option gods smiled upon me in such a way as to allow me to immediately scalp an option. Sometimes, the same option will not trade again for a week or longer. Very low-volume options trade “by appointment only.” A market maker trading illiquid options may hold the position until it expires, having no chance to get out at a reasonable price, often taking a loss on the trade. More typically, if a market maker buys an option, he must sell a different option to lessen the overall position risk. The skills these traders master are to lower bids and offers on options when they are long gamma and/or vega and to raise bids and offers on options when they are short gamma and/or vega. This raising and lowering of markets is done to manage risk. Effectively, this is your standard high school economics supply-and-demand curves in living color. When the market demands (buys) all the options that are supplied (offered) at a certain price, the price rises. When the market supplies (sells) all the options demanded (bid) at a price level, the price falls. The catalyst of supply and demand is the market maker and his risk tolerance. But instead of the supply and demand for individual options, it is supply and demand for gamma, theta, and vega. This is trading option greeks. Hedging the Risk Delta is the easiest risk for floor traders to eliminate quickly. It becomes second nature for veteran floor traders to immediately hedge nearly every trade with the underlying. Remember, these liquidity providers are in the business of buying option bids and selling option offers, not speculating on direction. The next hurdle is to trade out of the option-centric risk. This means that if the market maker is long gamma, he needs to sell options; if he’s short gamma, he needs to buy some. Same with theta and vega. Market makers move their bids and offers to avoid being saddled with too much gamma, theta, and vega risk. Experienced floor traders are good at managing option risk by not biting off more than they can chew. They strive to never buy or sell more options than they can spread off by selling or buying other options. This breed of trader specializes in trading the spread and managing risk, not in predicting the future. They’re market makers, not market takers. Trading Skew There are some trading strategies for which market makers have a natural propensity that stems from their daily activity of maintaining their positions. While money managers who manage equity funds get to know the fundamentals of the stocks they trade very well, options market makers know the volatility of the option classes they trade. When they adjust their markets in reacting to order flow, it’s, mechanically, implied volatility that they are raising or lowering to change theoretical values. They watch this figure very carefully and trade its subtle changes. A characteristic of options that many market makers and some other active professional traders observe and trade is the volatility skew. Savvy traders watch the implied volatility of the strikes above the at-the-money (ATM)—referred to as calls , for simplicity—compared with the strikes below the ATM, referred to as puts . In most stocks, there typically exists a “normal” volatility skew inherent to options on that stock. When this skew gets out of line, there may be an opportunity. Say for a particular option class, the call that is 10 percent OTM typically trades about four volatility points lower than the put that is 10 percent OTM. For example, for a $50 stock, the 55 calls are trading at a 21 IV and the 45 puts are trading at a 25 volatility. If the 45 puts become bid higher, say, nine points above where the calls are offered—for instance, the puts are bid at 32 volatility bid while the calls are offered at 23 vol—a trader can speculate on the skew reverting back to its normal relationship by selling the puts, buying the calls, and hedging the delta by selling the right amount of stock. This position—long a call, short a put with a different strike, and short stock on a delta-neutral ratio—is called a risk reversal. The motive for risk reversals is to capture vega as the skew realigns itself. But there are many risk factors that require careful attention. First, as in other positions consisting of both long and short strikes, the gamma, theta, and vega of the position will vary from positive to negative depending on the price of the underlying. Risk-reversal traders must be prepared to trade long gamma (and battle time decay) when the stock rallies closer to the long-call strike and trade short gamma (and assume the risk of possible increased realized volatility) when the stock moves closer to the short-put strike. As for vega, being short implied volatility on the downside and long on the upside is inherently a potentially bad position whichever way the stock moves. Why? As equities decline in price, the implied volatility of their options tends to rise. But the downside is where the risk reversal has its short vega. Furthermore, as equities rally, their IV tends to fall. That means the long vega of the upside hurts as well. When Delta Neutral Isn’t Direction Indifferent Many dynamic-volatility option positions, such as the risk reversal, have vega risk from potential IV changes resulting from the stock’s moving. This is indirectly a directional risk. While having a delta-neutral position hedges against the rather straightforward directional risk of the position delta, this hidden risk of stock movement is left unhedged. In some circumstances, a delta-lean can help abate some of the vega risk of stock-price movement. Say an option position has fairly flat greeks at the current stock price. Say that given the way this particular position is set up, if the stock rises, the position is still fairly flat, but if the stock falls, short lower-strike options will lead to negative gamma and vega. One way to partially hedge this position is to lean short deltas—that is, instead of maintaining a totally flat delta, have a slightly short delta. That way, if the stock falls, the trade profits some on the short stock to partially offset some of the anticipated vega losses. The trade-off of this hedge is that if the stock rises, the trade loses on the short delta. Delta leans are more of an art than a science and should be used as a hedge only by experienced vol traders. They should be one part of a well-orchestrated plan to trade the delta, gamma, theta, and vega of a position. And, to be sure, a delta lean should be entered into a model for simulation purposes before executing the trade to study the up-and-down risk of the position. If the lean reduces the overall risk of the position, it should be implemented. But if it creates a situation where there is an anticipated loss if the stock moves in either direction and there is little hope of profiting from the other greeks, the lean is not the answer—closing the position is. Managing Multiple-Class Risk Most traders hold option positions in more than one option class. As an aside, I recommend doing so, capital and experience permitting. In my experience, having positions in multiple classes psychologically allows for a certain level of detachment from each individual position. Most traders can make better decisions if they don’t have all their eggs in one basket. But holding a portfolio of option positions requires one more layer of risk management. The trader is concerned about the delta, gamma, theta, vega, and rho not only of each individual option class but also of the portfolio as a whole. The trader’s portfolio is actually one big position with a lot of moving parts. To keep it running like a well-oiled machine requires monitoring and maintaining each part to make sure they are working together. To have the individual trades work in harmony with one another, it is important to keep a well-balanced series of strategies. Option trading requires diversification, just like conventional linear stock trading or investing. Diversification of the option portfolio is easily measured by studying the portfolio greeks. By looking at the net greeks of the portfolio, the trader can get some idea of exposure to overall risk in terms of delta, gamma, theta, vega, and rho. ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00029.html SCORE: 396.00 ================================================================================ CHAPTER 17 Putting the Greeks into Action This book was intended to arm the reader with the knowledge of the greeks needed to make better trading decisions. As the preface stated, this book is not so much a how-to guide as a how-come tutorial. It is step one in a three-step learning process: Step One: Study . First, aspiring option traders must learn as much as possible from books such as this one and from other sources, such as articles, both in print and online, and from classes both in person and online. After completing this book, the reader should have a solid base of knowledge of the greeks. Step Two: Paper Trade . A truly deep understanding requires practice, practice, and more practice! Fortunately, much of this practice can be done without having real money on the line. Paper trading—or simulated trading—in which one trades real markets but with fake money is step two in the learning process. I highly recommend paper trading to kick the tires on various types of strategies and to see how they might work differently in reality than you thought they would in theory. Step Three: Showtime ! Even the most comprehensive academic study or windfall success with paper profits doesn’t give one a true feel for how options work in the real world. There are some lessons that must be learned from the black and the blue. When there’s real money on the line, you will trade differently—at least in the beginning. It’s human nature to be cautious with wealth. This is not a bad thing. But emotions should not override sound judgment. Start small—one or two lots per trade—until you can make rational decisions based on what you have learned, keeping emotions in check. This simple three-step process can take years of diligent work to get it right. But relax. Getting rich quick is truly a poor motivation for trading options. Option trading is a beautiful thing! It’s about winning. It’s about beating the market. It’s about being smart. Don’t get me wrong—wealth can be a nice by-product. I’ve seen many people who have made a lot of money trading options, but it takes hard work. For every successful option trader I’ve met, I’ve met many more who weren’t willing to put in the effort, who brashly thought this is easy, and failed miserably. Trading Option Greeks Traders must take into account all their collective knowledge and experience with each and every trade. Now that you’re armed with knowledge of the greeks, use it! The greeks come in handy in many ways. Choosing between Strategies A very important use of the greeks is found in selecting the best strategy for a given situation. Consider a simple bullish thesis on a stock. There are plenty of bullish option strategies. But given a bullish forecast, which option strategy should a trader choose? The answer is specific to each unique opportunity. Trading is situational. Example 1 Imagine a trader, Arlo, is studying the following chart of Agilent Technologies Inc. (A). See Exhibit 17.1 . EXHIBIT 17.1 Agilent Technologies Inc. daily candles. Source : Chart courtesy of Livevol ® Pro ( www.livevol.com ) The stock has been in an uptrend for six weeks or so. Close-to-close volatility hasn’t increased much. But intraday volatility has increased greatly as indicated by the larger candles over the past 10 or so trading sessions. Earnings is coming up in a week in this example, however implied volatility has not risen much. It is still “cheap” relative to historical volatility and past implied volatility. Arlo is bullish. But how does he play it? He needs to use what he knows about the greeks to guide his decision. Arlo doesn’t want to hold the trade through earnings, so it will be a short-term trade. Thus, theta is not much of a concern. The low-priced volatility guides his strategy selection in terms of vega. Arlo certainly wouldn’t want a short-vega trade. Not with the prospect of implied volatility potential rising going into earnings. In fact, he’d actually want a big positive vega position. That rules out a naked/cash-secured put, put credit spread and the likes. He can probably rule out vertical spreads all together. He doesn’t need to spread off theta. He doesn’t want to spread off vega. Positive gamma is attractive for this sort of trade. He wouldn’t want to spread that off either. Plus, the inherent time component of spreads won’t work well here. As discussed in Chapter 9, the bulk of vertical spreads profits (or losses) take time to come to fruition. The deltas of a call spread are smaller than an outright call. Profits would come from both delta and theta, if the stock rises to the short strike and positive theta kicks in. The best way for Arlo to play this opportunity is by buying a call. It gives him all the greeks attributes he wants (comparatively big positive delta, gamma and vega) and the detriment (negative theta) is not a major issue. He’d then select among in-the-money (ITM), at-the-money (ATM), and out-of-the-money (OTM) calls and the various available expiration cycles. In this case, because positive gamma is attractive and theta is not an issue, he’d lean toward a front month (in this case, three week) option. The front month also benefits him in terms of vega. Though the vegas are smaller for short-term options, if there is a rise in implied volatility leading up to earnings, the front month will likely rise much more than the rest. Thus, the trader has a possibility for profits from vega. Example 2 A trader, Luke, is studying the following chart for United States Steel Corp. (X). See Exhibit 17.2 . EXHIBIT 17.2 United States Steel Corp. daily candles. Source : Chart courtesy of Livevol ® Pro ( www.livevol.com ) This stock is in a steady uptrend, which Luke thinks will continue. Earnings are out and there are no other expected volatility events on the horizon. Luke thinks that over the next few weeks, United States Steel can go from its current price of around $31 a share to about $34. Volatility is midpriced in this example—not cheap, not expensive. This scenario is different than the previous one. Luke plans to potentially hold this trade for a few weeks. So, for Luke, theta is an important concern. He cares somewhat about volatility, too. He doesn’t necessarily want to be long it in case it falls; he doesn’t want to be short it in case it rises. He’d like to spread it off; the lower the vega, the better (positive or negative). Luke really just wants delta play that he can hold for a few weeks without all the other greeks getting in the way. For this trade, Luke would likely want to trade a debit call spread with the long call somewhat ITM and the short call at the $34 strike. This way, Luke can start off with nearly no theta or vega. He’ll retain some delta, which will enable the spread to profit if United States Steel rises and as it approaches the 34 strike, positive theta will kick in. This spread is superior to a pure long call because of its optimized greeks. It’s superior to an OTM bull put spread in its vega position and will likely produce a higher profit with the strikes structured as such too, as it would have a bigger delta. Integrating greeks into the process of selecting an option strategy must come natural to a trader. For any given scenario, there is one position that best exploits the opportunity. In any option position, traders need to find the optimal greeks position. Managing Trades Once the trade is on, the greeks come in handy for trade management. The most important rule of trading is Know Thy Risk . Knowing your risk means knowing the influences that expose your position to profit or peril in both absolute and incremental terms. At-expiration diagrams reveal, in no uncertain terms, what the bottom-line risk points are when the option expires. These tools are especially helpful with simple short-option strategies and some long-option strategies. Then traders need the greeks. After all, that’s what greeks are: measurements of option risk. The greeks give insight into a trade’s exposure to the other pricing factors. Traders must know the greeks of every trade they make. And they must always know the net-portfolio greeks at all times. These pricing factors ultimately determine the success or failure of each trade, each portfolio, and eventually each trader. Furthermore, always—and I do mean always—traders must know their up and down risk, that is, the directional risk of the market moving up or down certain benchmark intervals. By definition, moves of three standard deviations or more are very infrequent. But they happen. In this business anything can happen. Take the “flash crash of 2010 in which the Dow Jones Industrial Average plunged more than 1,000 points in “a flash.” In my trading career, I’ve seen some surprises. Traders have to plan for the worst. It’s not too hard to tell your significant other, “Sorry I’m late, but I hit unexpected traffic. I just couldn’t plan for it.” But to say, “Sorry, I lost our life savings, and the kids’ college fund, and our house because the market made an unexpected move. I couldn’t plan for it,” won’t go over so well. The fact is, you can plan for it. And as an option trader, you have to. The bottom line is, expect the unexpected because the unexpected will sometimes happen. Traders must use the greeks and up and down risk, instead of relying on other common indicators, such as the HAPI. The HAPI: The Hope and Pray Index So you bought a call spread. At the opening bell the next morning, you find that the market for the underlying has moved lower—a lot lower. You have a loss on your hands. What do you do? Keep a positive attitude? Wear your lucky shirt? Pray to the options gods? When traders finds themselves hoping and praying—I swear I’ll never do that again if I can just get out of this position!—it is probably time for them to take their losses and move on to the next trade. The Hope and Pray Index is a contraindicator. Typically, the higher it is, the worse the trade. There are two numbers a trader can control: the entry price and the exit price. All of the other flashing green and red numbers on the screen are out of the trader’s control. Savvy traders observe what the market does and make decisions on whether and when to enter a position and when to exit. Traders who think about their positions in terms of probability make better decisions at both of these critical moments. In entering a trade, traders must consider their forecast, their assessment of the statistical likelihood of success, the potential payout and loss, and their own tolerance for risk. Having considered these criteria helps the traders stay the course and avoid knee-jerk reactions when the market moves in the wrong direction. Trading is easy when positions make money. It is how traders deal with adverse positions that separates good traders from bad. Good traders are good at losing money. They take losses quickly and let profits run. Accepting, before entering the trade, the statistical nature of trading can help traders trade their positions with less emotion. It then becomes a matter of competent management of those positions based on their knowledge of the factors affecting option values: the greeks. Learning to think in terms of probability is among the most difficult challenges for a new options trader. Chapter 5 discussed my Would I Do It Now? Rule, in which a trader asks himself: if I didn’t currently have this position, would I put it on now at current market prices? This rule is a handy technique to help traders filter out the noise in their heads that clouds judgment and to help them to make rational decisions on whether to hold a position, close it out or adjust it. Adjusting Sometimes the position a trader starts off with is not the position he or she should have at present. Sometimes positions need to be changed, or adjusted, to reflect current market conditions. Adjusting is very important to option traders. To be good at adjusting, traders need to use the greeks. Imagine a trader makes the following trade in Halliburton Company (HAL) when the stock is trading $36.85. Sell 10 February 35–36–38–39 iron condors at 0.45 February has 10 days until expiration in this example. The greeks for this trade are as follows: Delta: −6.80 Gamma: −119.20 Theta: +21.90 Vega: −12.82 The trader has a neutral outlook, which can be inferred by the near-flat delta. But what if the underlying stock begins to rise? Gamma starts kicking in. The trader can end up with a short-biased delta that loses exponentially if the stock continues to climb. If Halliburton rises (or falls for that matter) the trader needs to recalibrate his outlook. Surely, if the trader becomes bullish based on recent market activity, he’d want to close the trade. If the trader is bearish, he’d probably let the negative delta go in hopes of making back what was lost from negative gamma. But what if the trader is still neutral? A neutral trader needs a position that has greeks which reflect that outlook. The trader would want to get delta back towards zero. Further, depending on how much the stock rises, theta could start to lose its benefit. If Halliburton approaches one of the long strikes, theta could move toward zero, negating the benefit of this sort of trade all together. If after the stock rises, the trader is still neutral at the new underlying price level, he’d likely adjust to get delta and theta back to desired territory. A common adjustment in this scenario is to roll the call-credit-spread legs of the iron condor up to higher strikes. The trader would buy ten 38 calls and sell ten 39 calls to close the credit spread. Then the trader would buy 10 of the 39 calls as sell 10 of the 40 calls to establish an adjusted position that is short a 10 lot of the February 35–36–39–40 iron condor. This, of course, is just one possible adjustment a trader can make. But the common theme among all adjustments is that the trader’s greeks must reflect the trader’s outlook. The position greeks best describe what the position is—that is, how it profits or loses. When the market changes it affects the dynamic greeks of a position. If the market changes enough to make a trader’s position greeks no longer represent his outlook, the trader must adjust the position (adjust the greeks) to put it back in line with expectations. In option trading there are an infinite number of uses for the greeks. From finding trades, to planning execution, to managing and adjusting them, to planning exits; the greeks are truly a trader’s best resource. They help traders see potential and actual position risk. They help traders project potential and actual trade profitability too. Without the greeks, a trader is at a disadvantage in every aspect of option trading. Use the greeks on each and every trade, and exploit trades to their greatest potential. I wish you good luck ! For me, trading option greeks has been a labor of love through the good trades and the bad. To succeed in the long run at greeks trading—or any endeavor, for that matter—requires enjoying the process. Trading option greeks can be both challenging and rewarding. And remember, although option trading is highly statistical and intellectual in nature, a little luck never hurt! That said, good luck trading! ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00030.html SCORE: 26.00 ================================================================================ About the Author Dan Passarelli is an author, trader, and former member of the Chicago Board Options Exchange (CBOE) and CME Group. Dan has written two books on options trading— Trading Option Greeks and The Market Taker’s Edge . He is also the founder and CEO of Market Taker Mentoring, a leading options education firm that provides personalized, one-on-one mentoring for option traders and online classes. The company web site is www.markettaker.com . Dan began his trading career on the floor of the CBOE as an equity options market maker. He also traded agricultural options and futures on the floor of the Chicago Board of Trade (now part of CME Group). In 2005, Dan joined CBOE’s Options Institute and began teaching both basic and advanced trading concepts to retail traders, brokers, institutional traders, financial planners and advisers, money managers, and market makers. In addition to his work with the CBOE, he has taught options strategies at the Options Industry Council (OIC), the International Securities Exchange (ISE), CME Group, the Philadelphia Stock Exchange, and many leading options-based brokerage firms. Dan has been seen on FOX Business News and other business television programs. Dan also contributes to financial publications such as TheStreet.com , SFO.com , and the CBOE blog. Dan can be reached at his web site, MarketTaker.com , or by e-mail: dan@markettaker.com . He can be followed on Twitter at twitter.com/Dan_Passarelli . ================================================================================ SOURCE: eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00031.html SCORE: 289.00 ================================================================================ Index American-exercise options Arbitrageurs At-the-money (ATM) Backspreads Bear call spread Bear put spread Bernanke, Ben Black, Fischer Black-Scholes option-pricing model Boxes building Bull call spread strengths and limitations Bull put spread Butterflies long alternatives example short iron long short Buy-to-close order Calendar spreads buying “free” call, rolling and earning rolling the spread income-generating, managing strength of trading volatility term structure buying the front, selling the back directional approach double calendars ITM or OTM selling the front, buying the back Calls buying covered entering exiting long ATM delta gamma rho theta tweaking greeks vega long ITM long OTM selling Cash settlement Chicago Board Options Exchange (CBOE) Volatility Index ® Condors iron long short long short strikes safe landing selectiveness too close too far with high probability of success Contractual rights and obligations open interest and volume opening and closing Options Clearing Corporation (OCC) standardized contracts exercise style expiration month option series, option class, and contract size option type premium quantity strike price Credit call spread Debit call spread Delta dynamic inputs effect of stock price on effect of time on effect of volatility on moneyness and Delta-neutral trading art and science direction neutral vs. direction indifferent gamma, theta, and volatility gamma scalping implied volatility, trading selling portfolio margining realized volatility, trading reasons for smileys and frowns Diagonal spreads double Dividends basics and early exercise dividend plays strange deltas and option pricing pricing model, inputting data into dates, good and bad dividend size Estimation, imprecision of European-exercise options Exchange-traded fund (ETF) options Exercise style Expected volatility CBOE Volatility Index® implied stock Expiration month Ford Motor Company Fundamental analysis Gamma dynamic scalping Greeks adjusting defined delta dynamic inputs effect of stock price on effect of time on effect of volatility on moneyness and gamma dynamic HAPI: Hope and Pray Index managing trades online, caveats with regard to price vs. value rho counterintuitive results effect of time on put-call parity strategies, choosing between theta effect of moneyness and stock price on effects of volatility and time on positive or negative taking the day out trading vega effect of implied volatility on effect of moneyness on effect of time on implied volatility (IV) and where to find Greenspan, Alan HOLDR options Implied volatility (IV) trading selling and vega In-the-money (ITM) Index options Interest, open Interest rate moves, pricing in Intrinsic value Jelly rolls Long-Term Equity AnticiPation Securities® (LEAPS®) Open interest Option, definition of Option class Option prices, measuring incremental changes in factors affecting Option series Options Clearing Corporation (OCC) Out-of-the-money (OTM) Parity, definition of Pin risk borrowing and lending money boxes jelly rolls Premium Price discovery Price vs. value Pricing model, inputting data into dates, good and bad dividend size “The Pricing of Options and Corporate Liabilities” (Black & Scholes) Put-call parity American exercise options essentials dividends synthetic calls and puts, comparing synthetic stock strategies theoretical value and interest rate Puts buying cash-secured long ATM married selling Ratio spreads and complex spreads delta-neutral positions, management by market makers through longs to shorts risk, hedging trading flat multiple-class risk ratio spreads backspreads vertical skew, trading Realized volatility trading Reversion to the mean Rho counterintuitive results effect of time on and interest rates in planning trades interest rate moves, pricing in LEAPS put-call parity and time trading Risk and opportunity, option-specific finding the right risk long ATM call delta gamma rho theta tweaking greeks vega long ATM put long ITM call long OTM call options and the fair game volatility buying and selling direction neutral, direction biased, and direction indifferent Scholes, Myron Sell-to-open transaction Skew term structure trading vertical Spreads calendar buying “free” call, rolling and earning income-generating, managing strength of trading volatility term structure diagonal double ratio and complex delta-neutral positions, management by market makers multiple-class risk ratio skew, trading vertical bear call bear put box, building bull call bull put credit and debit, interrelations of credit and debit, similarities in and volatility wing butterflies condors greeks and keys to success retail trader vs. pro trades, constructing to maximize profit Standard deviation and historical volatility Standard & Poor’s Depositary Receipts (SPDRs or Spiders) Straddles long basic trading short risks with trading synthetic Strangles long example short premium risk, limiting Strategies and At-Expiration Diagrams buy call buy put factors affecting option prices, measuring incremental changes in sell call sell put Strike price Supply and demand Synthetic stock strategies conversion market makers pin risk reversal Technical analysis Teenie buyers Teenie sellers Theta effect of moneyness and stock price on effects of volatility and time on positive or negative risk taking the day out Time value Trading strategies Value Vega effect of implied volatility on effect of moneyness on effect of time on implied volatility (IV) and Vertical spreads bear call bear put box, building bull call bull put credit and debit interrelations of similarities in and volatility Volatility buying and selling teenie buyers teenie sellers calculating data direction neutral, direction biased, and direction indifferent expected CBOE Volatility Index® implied stock historical (HV) standard deviation implied (IV) and direction HV-IV divergence inertia relationship of HV and IV selling supply and demand realized trading skew term structure vertical vertical spreads and Volatility charts, studying patterns implied and realized volatility rise realized volatility falls, implied volatility falls realized volatility falls, implied volatility remains constant realized volatility falls, implied volatility rises realized volatility remains constant, implied volatility falls realized volatility remains constant, implied volatility remains constant realized volatility remains constant, implied volatility rises realized volatility rises, implied volatility falls realized volatility rises, implied volatility remains constant Volatility-selling strategies profit potential covered call covered put gamma-theta relationship greeks and income generation naked call short naked puts similarities Would I Do It Now? Rule Volume Weeklys SM Wing spreads butterflies directional long short iron condors iron long short greeks and keys to success retail trader vs. pro trades, constructing to maximize profit Would I Do It Now? Rule ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:11 SCORE: 10.00 ================================================================================ NASDAQ-100 Index® is a registered trademark of The NASDAQ Stock Market, Inc. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com . Library of Congress Cataloging-in-Publication Data : Passarelli, Dan, 1971- Trading options Greeks : how time, volatility, and other pricing factors drive profits / Dan Passarelli. – 2nd ed. p. cm. – (Bloomberg financial series) Includes index. ISBN 978-1-118-13316-3 (cloth); ISBN 978-1-118-22512-7 (ebk); ISBN 978-1-118-26322-8 (ebk); ISBN 978-1-118-23861-5 (ebk) 1. Options (Finance) 2. Stock options. 3. Derivative securities. I. Title. HG6024.A3P36 2012 332.64′53—dc23 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:14 SCORE: 20.00 ================================================================================ Disclaimer This book is intended to be educational in nature, both theoretically and practically. It is meant to generally explore the factors that influence option prices so that the reader may gain an understanding of how options work in the real world. This book does not prescribe a specific trading system or method. This book makes no guarantees. Any strategies discussed, including examples using actual securities and price data, are strictly for illustrative and educational purposes only and are not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. Examples may or may not be based on factual or historical data. In order to simplify the computations, examples may not include commissions, fees, margin, interest, taxes, or other transaction costs. Commissions and other costs will impact the outcome of all stock and options transactions and must be considered prior to entering into any transactions. Investors should consult their tax adviser about potential tax consequences. Past performance is not a guarantee of future results. Options involve risks and are not suitable for everyone. While much of this book focuses on the risks involved in option trading, there are market situations and scenarios that involve unique risks that are not discussed. Prior to buying or selling an option, a person should read Characteristics and Risks of Standardized Options (ODD) . Copies of the ODD are available from your broker, by calling 1-888-OPTIONS, or from The Options Clearing Corporation, One North Wacker Drive, Chicago, Illinois 60606. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:15 SCORE: 24.00 ================================================================================ Foreword The past several years have brought about a resurgence in market volatility and options volume unlike anything that has been seen since the close of the twentieth century. As markets have become more interdependent, interrelated, and international, the U.S. listed option markets have solidified their place as the most liquid and transparent venue for risk management and hedging activities of the world’s largest economy. Technology, competition, innovation, and reliability have become the hallmarks of the industry, and our customer base has benefited tremendously from this ongoing evolution. However, these advances can be properly tapped only when the users of the product continue to expand their knowledge of the options product and its unique features. Education has always been the driver of growth in our business, and it will be the steward of the next generation of options traders. Dan Passarelli’s new and updated book Trading Option Greeks is a necessity for customers and traders alike to ensure that they possess the knowledge to succeed and attain their objectives in the high-speed, highly technical arena that the options market has become. The retail trader of the past has given way to a new retail trader of the present—one with an increased level of technology, support, capital treatment, and product selection. The impact of the staggering growth in such products as the CBOE Holdings’ VIX options and futures, and the literally dozens of other products tied to it, have made the volatility asset class a new, unique, and permanent pillar of today’s option markets. Dan’s updated book continues his mission of supporting, preparing, and reinforcing the trader’s understanding of pricing, volatility, market terminology, and strategy, in a way that few other books have been able. Using a perspective forged from years as an options market maker, professional trader, and customer, Dan has once again provided a resource for those who wish to know best how the option markets behave today, and how they are likely to continue to behave in the future. It is important to understand not only what happens in the options space, but also why it ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:17 SCORE: 12.00 ================================================================================ Preface I’ve always been fascinated by trading. When I was young, I’d see traders on television, in their brightly colored jackets, shouting on the seemingly chaotic trading floor, and I’d marvel at them. What a wonderful job that must be! These traders seemed to me to be very different from the rest of us. It’s all so very esoteric. It is easy to assume that professional traders have closely kept secrets to their ways of trading—something that secures success in trading for them, but is out of reach for everyone else. In fact, nothing could be further from the truth. If there are any “secrets” of professional traders, this book will expose them. True enough, in years past there have been some barriers to entry to trading success that did indeed make it difficult for nonprofessionals to succeed. For example, commissions, bid-ask spreads, margin requirements, and information flow all favored the professional trader. Now, these barriers are gone. Competition among brokers and exchanges—as well as the ubiquity of information as propagated on the Internet—has torn down those walls. The only barrier left between the Average Joe and the options pro is that of knowledge. Those who have it will succeed; those who do not will fail. To be sure, the knowledge held by successful traders is not that of what will happen in the future; it is the knowledge of how to manage the uncertainty. No matter what our instincts tell us, we do not know what will happen in the future with regard to the market. As Socrates put it, “The only true wisdom is in knowing you know nothing.” The masters of option trading are masters of managing the risk associated with what they don’t know—the risk of uncertainty. As an instructor, I’ve talked to many traders who were new to options who told me, “I made a trade based on what I thought was going to happen. I was right, but my position lost money!” Choosing the right strategy makes all the difference when it comes to mastery of risk management and ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:18 SCORE: 36.00 ================================================================================ ultimate trading success. Knowing which option strategy is the right strategy for a given situation comes with knowledge and experience. All option strategies are differentiated by their unique risk characteristics. Some are more sensitive to directional movement of the underlying asset than others; some are more affected by time passing than others. The exact exposure positions have to these market influences determines the success of individual trades and, indeed, the long-term success of the trader who knows how to exploit these risk characteristics. These option-value sensitivities can be controlled when a trader understands the option greeks. Option greeks are metrics used to measure an option’s sensitivity to influences on its price. This book will provide the reader with an understanding of these metrics, to help the reader truly master the risk of uncertainty associated with option trading. Successful traders strive to create option positions with risk-reward profiles that benefit them the most in a given situation. A trader’s objectives will dictate the right strategy for the right situation. Traders can tailor a position to fit a specific forecast with respect to the time horizon; the degree of bullishness, bearishness, neutrality, or volatility in the underlying stock; and the desired amount of leverage. Furthermore, they can exploit opportunities unique to options. They can trade option greeks. This opens the door to many new opportunities. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:20 SCORE: 18.00 ================================================================================ Trading Strategies Buying stock is a trading strategy that most people understand. In practical terms, traders who buy stock are generally not concerned with the literal ownership stake in a corporation, just the opportunity to profit if the stock rises. Although it’s important for traders to understand that the price of a stock is largely tied to the success or failure of the corporation, it’s essential to keep in mind exactly what the objective tends to be for trading a stock: to profit from changes in its price. A bullish position can also be taken in the options market. The most basic example is buying a call. A bearish position can be taken by trading stock or options, as well. If traders expect the value of a stock they own to fall, they will sell the stock. This eliminates the risk of losses from the stock’s falling. If the traders do not own the stock that they think will decline, they can take a more active stance and short it. The short-seller borrows the stock from a party that owns it and then sells the borrowed shares to another party. The goal of selling stock short is to later repurchase the shares at a lower price before returning the stock to its owner. It is simply reversing the order of “buy low/sell high.” The risk is that the stock rises and shares have to be bought at a higher price than that at which they were sold. Although shorting stock can lead to profits when the market cooperates, in the options market, there are alternative ways to profit from falling prices. The most basic example is buying a put. A trader can use options to take a bullish or bearish position, given a directional forecast. Sideways, nontrending stocks and their antithesis, volatile stocks, can be traded as well. In the later market conditions, profit or loss can be independent of whether the stock rises or falls. Opportunity in option trading is not necessarily black and white—not necessarily up and down. Option trading is nonlinear. Consequently, more opportunities can be exploited by trading options than by trading stock. Option traders must consider the time period in question, the volatility expected during this period, interest rates, and dividends. Along with the stock price, these factors make up the dynamic components of an option’s value. These individual factors can be isolated, measured, and exploited. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:22 SCORE: 44.00 ================================================================================ This Second Edition of Trading Option Greeks This book addresses the complex price behavior of options by discussing option greeks from both a theoretical and a practical standpoint. There is some tactical discussion throughout, although the objective of this book is to provide education to the reader. This book is meant to be less a how-to manual than a how-come tutorial. This informative guide will give the retail trader a look inside the mind of a professional trader. It will help the professional trader better understand the essential concepts of his craft. Even the novice trader will be able to apply these concepts to basic options strategies. Comprehensive knowledge of the greeks can help traders to avoid common pitfalls and increase profit potential. Much of this book is broken down into a discussion of individual strategies. Although the nuances of each specific strategy are not relevant, presenting the material this way allows for a discussion of very specific situations in which greeks come into play. Many of the concepts discussed in a section on one option strategy can be applied to other option strategies. As in the first edition of Trading Option Greeks , Chapter 1 discusses basic option concepts and definitions. It was written to be a review of the basics for the intermediate to advanced trader. For newcomers, it’s essential to understand these concepts before moving forward. A detailed explanation of option greeks begins in Chapter 2. Be sure to leave a bookmark in this chapter, as you will flip to it several times while reading the rest of the book and while studying the market thereafter. Chapter 3 introduces volatility. The same bookmark advice can be applied here, as well. Chapters 4 and 5 explore the minds of option traders. What are the risks they look out for? What are the opportunities they seek? These chapters also discuss direction-neutral and direction-indifferent trading. The remaining chapters take the reader from concept to application, discussing ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:24 SCORE: 16.00 ================================================================================ Acknowledgments A book like Trading Option Greeks is truly a collaboration of the efforts of many people. In my years as a trader, I had many teachers in the School of Hard Knocks. I have had the support of friends and family during the trials and tribulations throughout my trading career, as well as during the time spent writing this book, both the first edition and now this second edition. Surely, there are hundreds of people whose influences contributed to the creation of this book, but there are a few in particular to whom I’d like to give special thanks. I’d like to give a very special thanks to my mentor and friend from the CBOE’s Options Institute, Jim Bittman. Without his help this book would not have been written. Thanks to Marty Kearney and Joe Troccolo for looking over the manuscript. Their input was invaluable. Thanks to Debra Peters for her help during my career at the Options Institute. Thanks to Steve Fossett and Bob Kirkland for believing in me. Thanks to the staff at Bloomberg Press, especially Stephen Isaacs and Kevin Commins. Thanks to my friends at the Chicago Board Options Exchange, the Options Industry Council, and the CME group. Thanks to John Kmiecik for his diligent content editing. Thanks to those who contribute to sharing option ideas on my website, markettaker.com . Thanks to my wife, Kathleen, who has been more patient and supportive than anyone could reasonably ask for. And thanks, especially, to my students and those of you reading this book. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:27 SCORE: 64.00 ================================================================================ Contractual Rights and Obligations The option buyer is the party who owns the right inherent in the contract. The buyer is referred to as having a long position and may also be called the holder, or owner, of the option. The right doesn’t last forever. At some point the option will expire. At expiration, the owner may exercise the right or, if the option has no value to the holder, let it expire without exercising it. But he need not hold the option until expiration. Options are transferable—they can be traded intraday in much the same way as stock is traded. Because it’s uncertain what the underlying stock price of the option will be at expiration, much of the time this right has value before it expires. The uncertainty of stock prices, after all, is the raison d’être of the option market. A long position in an option contract, however, is fundamentally different from a long position in a stock. Owning corporate stock affords the shareholder ownership rights, which may include the right to vote in corporate affairs and the right to receive dividends. Owning an option represents strictly the right either to buy the stock or to sell it, depending on whether it’s a call or a put. Option holders do not receive dividends that would be paid to the shareholders of the underlying stock, nor do they have voting rights. The corporation has no knowledge of the parties to the option contract. The contract is created by the buyer and seller of the option and made available by being listed on an exchange. The party to the contract who is referred to as the option seller, also called the option writer, has a short position in the option. Instead of having a right to take a position in the underlying stock, as the buyer does, the seller incurs an obligation to potentially either buy or sell the stock. When a trader who is long an option exercises, a trader with a short position gets assigned . Assignment means the trader with the short option position is called on to fulfill the obligation that was established when the contract was sold. Shorting an option is fundamentally different from shorting a stock. Corporations have a quantifiable number of outstanding shares available for trading, which must be borrowed to create a short position, but establishing a short position in an option does not require borrowing; the contract is simply created. The strategy of shorting stock is implemented statistically ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:30 SCORE: 28.00 ================================================================================ Open Interest and Volume Traders use many types of market data to make trading decisions. Two items that are often studied but sometimes misunderstood are volume and open interest. Volume, as the name implies, is the total number of contracts traded during a time period. Often, volume is stated on a one-day basis, but could be stated per week, month, year, or otherwise. Once a new period (day) begins, volume begins again at zero. Open interest is the number of contracts that have been created and remain outstanding. Open interest is a running total. When an option is first listed, there are no open contracts. If Trader A opens a long position in a newly listed option by buying a one-lot, or one contract, from Trader B, who by selling is also opening a position, a contract is created. One contract traded, so the volume is one. Since both parties opened a position and one contract was created, the open interest in this particular option is one contract as well. If, later that day, Trader B closes his short position by buying one contract from Trader C, who had no position to start with, the volume is now two contracts for that day, but open interest is still one. Only one contract exists; it was traded twice. If the next day, Trader C buys her contract back from Trader A, that day’s volume is one and the open interest is now zero. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:31 SCORE: 26.00 ================================================================================ The Options Clearing Corporation Remember when Wimpy would tell Popeye, “I’ll gladly pay you Tuesday for a hamburger today.” Did Popeye ever get paid for those burgers? In a contract, it’s very important for each party to hold up his end of the bargain —especially when there is money at stake. How does a trader know the party on the other side of an option contract will in fact do that? That’s where the Options Clearing Corporation (OCC) comes into play. The OCC ultimately guarantees every options trade. In 2010, that was almost 3.9 billion listed-options contracts. The OCC accomplishes this through many clearing members. Here’s how it works: When Trader X buys an option through a broker, the broker submits the trade information to its clearing firm. The trader on the other side of this transaction, Trader Y, who is probably a market maker, submits the trade to his clearing firm. The two clearing firms (one representing Trader X’s buy, the other representing Trader Y’s sell) each submit the trade information to the OCC, which “matches up” the trade. If Trader Y buys back the option to close the position, how does that affect Trader X if he wants to exercise it? It doesn’t. The OCC, acting as an intermediary, assigns one of its clearing members with a customer that is short the option in question to deliver the stock to Trader X’s clearing firm, which in turn delivers the stock to Trader X. The clearing member then assigns one of its customers who is short the option. The clearing member will assign the trader either randomly or first in, first out. Effectively, the OCC is the ultimate counterparty to both the exercise and the assignment. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:32 SCORE: 51.00 ================================================================================ Standardized Contracts Exchange-listed options contracts are standardized, meaning the terms of the contract, or the contract specifications, conform to a customary structure. Standardization makes the terms of the contracts intuitive to the experienced user. To understand the contract specifications in a typical equity option, consider an example: Buy 1 IBM December 170 call at 5.00 Quantity In this example, one contract is being purchased. More could have been purchased, but not less—options cannot be traded in fractional units. Option Series, Option Class, and Contract Size All calls or puts of the same class, the same expiration month, and the same strike price are called an option series . For example, the IBM December 170 calls are a series. Options series are displayed in an option chain on an online broker’s user interface. An option chain is a full or partial list of the options that are listed on an underlying. Option class means a group of options that represent the same underlying. Here, the option class is denoted by the symbol IBM—the contract represents rights on International Business Machines Corp. (IBM) shares. Buying one contract usually gives the holder the right to buy or to sell 100 shares of the underlying stock. This number is referred to as contract size . Though this is usually the case, there are times when the contract size is something other than 100 shares of a stock. This situation may occur after certain types of stock splits, spin-offs, or stock dividends, for example. In the minority of cases in which the one contract represents rights on something besides 100 shares, there may be more than one class of options listed on a stock. A fairly unusual example was presented by the Ford Motor Company options in the summer of 2000. In June 2000, Ford spun off Visteon ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:33 SCORE: 48.00 ================================================================================ Corporation. Then, in August 2000, Ford offered shareholders a choice of converting their shares into (a) new shares of Ford plus $20 cash per share, (b) new Ford stock plus fractional shares with an aggregate value of $20, or (c) new Ford stock plus a combination of more new Ford stock and cash. There were three classes of options listed on Ford after both of these changes: F represented 100 shares of the new Ford stock; XFO represented 100 shares of Ford plus $20 per share ($2,000) plus cash in lieu of $1.24; and FOD represented 100 shares of new Ford, 13 shares of Visteon, and $2,001.24. Sometimes these changes can get complicated. If there is ever a question as to what the underlying is for an option class, the authority is the OCC. A lot of time, money, and stress can be saved by calling the OCC at 888- OPTIONS and clarifying the matter. Expiration Month Options expire on the Saturday following the third Friday of the stated month, which in this case is December. The final trading day for an option is commonly the day before expiration—here, the third Friday of December. There are usually at least four months listed for trading on an option class. There may be a total of six months if Long-Term Equity AnticiPation Securities® or LEAPS® are listed on the class. LEAPS can have one year to about two-and-a-half years until expiration. Some underlyings have one-week options called WeeklysSM listed on them. Strike Price The price at which the option holder owns the right to buy or to sell the underlying is called the strike price, or exercise price. In this example, the holder owns the right to buy the stock at $170 per share. There is method to the madness regarding how strike prices are listed. Strike prices are generally listed in $1, $2.50, $5, or $10 increments, depending on the value of the strikes and the liquidity of the options. The relationship of the strike price to the stock price is important in pricing options. For calls, if the stock price is above the strike price, the call is in-the-money (ITM). If the stock and the strike prices are close, the call is ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:34 SCORE: 92.00 ================================================================================ at-the-money (ATM). If the stock price is below the strike price the call is out-of-the-money (OTM). This relationship is just the opposite for puts. If the stock price is below the strike price, the put is in-the-money. If the stock price and the strike price are about the same, the put is at-the-money. And, if the stock price is above the put strike, it is out-of-the-money. Option Type There are two types of options: calls and puts. Calls give the holder the right to buy the underlying and the writer the obligation to sell the underlying. Puts give the holder the right to sell the underlying and the writer the obligation to buy the underlying. Premium The price of an option is called its premium. The premium of this option is $5. Like stock prices, option premiums are stated in dollars and cents per share. Since the option represents 100 shares of IBM, the buyer of this option will pay $500 when the transaction occurs. Certain types of spreads may be quoted in fractions of a penny. An option’s premium is made up of two parts: intrinsic value and time value. Intrinsic value is the amount by which the option is in-the-money. For example, if IBM stock were trading at 171.30, this 170-strike call would be in-the-money by 1.30. It has 1.30 of intrinsic value. The remaining 3.70 of its $5 premium would be time value. Options that are out-of-the-money have no intrinsic value. Their values consist only of time premium. Sometimes options have no time value left. Options that consist of only intrinsic value are trading at what traders call parity . Time value is sometimes called premium over parity . Exercise Style One contract specification that is not specifically shown here is the exercise style. There are two main exercise styles: American and European. American-exercise options can be exercised, and therefore assigned, anytime after the contract is entered into until either the trader closes the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:37 SCORE: 28.00 ================================================================================ ETF Options Exchange-traded funds are vehicles that represent ownership in a fund or investment trust. This fund is made up of a basket of an underlying index’s securities—usually equities. The contract specifications of ETF options are similar to those of equity options. Let’s look at an example. One actively traded optionable ETF is the Standard & Poor’s Depositary Receipts (SPDRs or Spiders). Spider shares and options trade under the symbol SPY. Exercising one SPY call gives the exerciser a long position of 100 shares of Spiders at the strike price of the option. Expiration for ETF options typically falls on the same day as for equity options—the Saturday following the third Friday of the month. The last trading day is the Friday before. ETF options are American exercise. Traders of ETFs should be aware of the relationship between the price of the ETF shares and the value of the underlying index. For example, the stated value of the Spiders is about one tenth the stated value of the S&P 500. The PowerShares QQQ ETF, representing the Nasdaq 100, is about one fortieth the stated value of the Nasdaq 100. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:38 SCORE: 51.00 ================================================================================ Index Options Trading options on the Spiders ETF is a convenient way to trade the Standard & Poor’s (S&P) 500. But it’s not the only way. There are other option contracts listed on the S&P 500. The SPX is one of the major ones. The SPX is an index option contract. There are some very important differences between ETF options like SPY and index options like SPX. The first difference is the underlying. The underlying for ETF options is 100 shares of the ETF. The underlying for index options is the numerical value of the index. So if the S&P 500 is at 1303.50, the underlying for SPX options is 1303.50. When an SPX call option is exercised, instead of getting 100 shares of something, the exerciser gets the ITM cash value of the option times $100. Again, with SPX at 1303.50, if a 1300 call is exercised, the exerciser gets $350—that’s 1303.50 minus 1300, times $100. This is called cash settlement . Many index options are European, which means no early exercise. At expiration, any long ITM options in a trader’s inventory result in an account credit; any short ITMs result in a debit of the ITM value times $100. The settlement process for determining whether a European-style index option is in-the-money at expiration is a little different, too. Often, these indexes are a.m. settled. A.m.-settled index options will have actual expiration on the conventional Saturday following the third Friday of the month. But the final trading day is the Thursday before the expiration day. The final settlement value of the index is determined by the opening prices of the components of the index on Friday morning. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:40 SCORE: 29.00 ================================================================================ Strategies and At-Expiration Diagrams One of the great strengths of options is that there are so many different ways to use them. There are simple, straightforward strategies like buying a call. And there are complex spreads with creative names like jelly roll, guts, and iron butterfly. A spread is a strategy that involves combining an option with one or more other options or stock. Each component of the spread is referred to as a leg. Each spread has its own unique risk and reward characteristics that make it appropriate for certain market outlooks. Throughout this book, many different spreads will be discussed in depth. For now, it’s important to understand that all spreads are made up of a combination of four basic option positions: buy call, sell call, buy put, and sell put. Understanding complex option strategies requires understanding these basic positions and their common, practical uses. When learning options, it’s helpful to see what the option’s payout is if it is held until expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:41 SCORE: 43.00 ================================================================================ Buy Call Why buy the right to buy the stock when you can simply buy the stock? All option strategies have trade-offs, and the long call is no different. Whether the stock or the call is preferable depends greatly on the trader’s forecast and motivations. Consider a long call example: Buy 1 INTC June 22.50 call at 0.85. In this example, a trader is bullish on Intel (INTC). He believes Intel will rise at least 20 percent, from $22.25 per share to around $27 by June expiration, about two months from now. He is concerned, however, about downside risk and wants to limit his exposure. Instead of buying 100 shares of Intel at $22.25—a total investment of $2,225—the trader buys 1 INTC June 22.50 call at 0.85, for a total of $85. The trader is paying 0.85 for the right to buy 100 shares of Intel at $22.50 per share. If Intel is trading below the strike price of $22.50 at expiration, the call will expire and the total premium of 0.85 will be lost. Why? The trader will not exercise the right to buy the stock at a $22.50 if he can buy it cheaper in the market. Therefore, if Intel is below $22.50 at expiration, this call will expire with no value. However, if the stock is trading above the strike price at expiration, the call can be exercised, in which case the trader may purchase the stock below its trading price. Here, the call has value to the trader. The higher the stock, the more the call is worth. For the trade to be profitable, at expiration the stock must be trading above the trader’s break-even price. The break- even price for a long call is the strike price plus the premium paid—in this example, $23.35 per share. The point here is that if the call is exercised, the effective purchase price of the stock upon exercise is $23.35. The stock is literally bought at the strike price, which is $22.50, but the premium of 0.85 that the trader has paid must be taken into account. Exhibit 1.1 illustrates this example. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:42 SCORE: 18.00 ================================================================================ EXHIBIT 1.1 Long Intel call. Exhibit 1.1 is an at-expiration diagram for the Intel 22.50 call. It shows the profit and loss, or P&(L), of the option if it is held until expiration. The X-axis represents the prices at which INTC could be trading at expiration. The Y-axis represents the associated profit or loss on the position. The at- expiration diagram of any long call position will always have this same hockey-stick shape, regardless of the stock or strike. There is always a limit of loss, represented by the horizontal line, which in this case is drawn at −0.85. And there is always a line extending upward and to the right, which represents effectively a long stock position stemming from the strike. The trade-offs between a long stock position and a long call position are shown in Exhibit 1.2 . ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:43 SCORE: 21.00 ================================================================================ EXHIBIT 1.2 Long Intel call vs. long Intel stock. The thin dotted line represents owning 100 shares of Intel at $22.25. Profits are unlimited, but the risk is substantial—the stock can go to zero. Herein lies the trade-off. The long call has unlimited profit potential with limited risk. Whenever an option is purchased, the most that can be lost is the premium paid for the option. But the benefit of reduced risk comes at a cost. If the stock is above the strike at expiration, the call will always underperform the stock by the amount of the premium. Because of this trade-off, conservative traders will sometimes buy a call rather than the associated stock and sometimes buy the stock rather than the call. Buying a call can be considered more conservative when the volatility of the stock is expected to rise. Traders are willing to risk a comparatively small premium when a large price decline is feared possible. Instead, in an interest-bearing vehicle, they harbor the capital that would otherwise have been used to purchase the stock. The cost of this protection is acceptable to the trader if high-enough price advances are anticipated. In terms of percentage, much higher returns and losses are possible with the long call. If the stock is trading at $27 at expiration, as the trader in this example expected, the trader reaps a 429 percent profit on the $0.85 investment ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:45 SCORE: 29.00 ================================================================================ Sell Call Selling a call creates the obligation to sell the stock at the strike price. Why is a trader willing to accept this obligation? The answer is option premium. If the position is held until expiration without getting assigned, the entire premium represents a profit for the trader. If assignment occurs, the trader will be obliged to sell stock at the strike price. If the trader does not have a long position in the underlying stock (a naked call), a short stock position will be created. Otherwise, if stock is owned (a covered call), that stock is sold. Whether the trader has a profit or a loss depends on the movement of the stock price and how the short call position was constructed. Consider a naked call example: Sell 1 TGT October 50 call at 1.45 In this example, Target Corporation (TGT) is trading at $49.42. A trader, Sam, believes Target will continue to be trading below $50 by October expiration, about two months from now. Sam sells 1 Target two-month 50 call at 1.45, opening a short position in that series. Exhibit 1.3 will help explain the expected payout of this naked call position if it is held until expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:46 SCORE: 29.00 ================================================================================ EXHIBIT 1.3 Naked Target call. If TGT is trading below the exercise price of 50, the call will expire worthless. Sam keeps the 1.45 premium, and the obligation to sell the stock ceases to exist. If Target is trading above the strike price, the call will be in- the-money. The higher the stock is above the strike price, the more intrinsic value the call will have. As a seller, Sam wants the call to have little or no intrinsic value at expiration. If the stock is below the break-even price at expiration, Sam will still have a profit. Here, the break-even price is $51.45 —the strike price plus the call premium. Above the break-even, Sam has a loss. Since stock prices can rise to infinity (although, for the record, I have never seen this happen), the naked call position has unlimited risk of loss. Because a short stock position may be created, a naked call position must be done in a margin account. For retail traders, many brokerage firms require different levels of approval for different types of option strategies. Because the naked call position has unlimited risk, establishing it will generally require the highest level of approval—and a high margin requirement. Another tactical consideration is what Sam’s objective was when he entered the trade. His goal was to profit from the stock’s being below $50 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:47 SCORE: 51.00 ================================================================================ during this two-month period—not to short the stock. Because equity options are American exercise and can be exercised/assigned any time from the moment the call is sold until expiration, a short stock position cannot always be avoided. If assigned, the short stock position will extend Sam’s period of risk—because stock doesn’t expire. Here, he will pay one commission shorting the stock when assignment occurs and one more when he buys back the unwanted position. Many traders choose to close the naked call position before expiration rather than risk assignment. It is important to understand the fundamental difference between buying calls and selling calls. Buying a call option offers limited risk and unlimited reward. Selling a naked call option, however, has limited reward—the call premium—and unlimited risk. This naked call position is not so much bearish as not bullish . If Sam thought the stock was going to zero, he would have chosen a different strategy. Now consider a covered call example: Buy 100 shares TGT at $49.42 Sell 1 TGT October 50 call at 1.45 Unlimited and risk are two words that don’t sit well together with many traders. For that reason, traders often prefer to sell calls as part of a spread. But since spreads are strategies that involve multiple components, they have different risk characteristics from an outright option. Perhaps the most commonly used call-selling spread strategy is the covered call (sometimes called a covered write or a buy-write ). While selling a call naked is a way to take advantage of a “not bullish” forecast, the covered call achieves a different set of objectives. After studying Target Corporation, another trader, Isabel, has a neutral to slightly bullish forecast. With Target at $49.42, she believes the stock will be range-bound between $47 and $51.50 over the next two months, ending with October expiration. Isabel buys 100 shares of Target at $49.42 and sells 1 TGT October 50 call at 1.45. The implications for the covered-call strategy are twofold: Isabel must be content to own the stock at current levels, and—since she sold the right to buy the stock at $50, that is, a 50 call, to another party—she must be willing to sell the stock if the price rises to or through $50 per share. Exhibit 1.4 shows how this covered call performs if it is held until the call expires. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:48 SCORE: 46.00 ================================================================================ EXHIBIT 1.4 Target covered call. The solid kinked line represents the covered call position, and the thin, straight dotted line represents owning the stock outright. At the expiration of the call option, if Target is trading below $50 per share—the strike price —the call expires and Isabel is left with a long position of 100 shares plus $1.45 per share of expired-option premium. Below the strike, the buy-write always outperforms simply owning the stock by the amount of the premium. The call premium provides limited downside protection; the stock Isabel owns can decline $1.45 in value to $47.97 before the trade is a loser. In the unlikely event the stock collapses and becomes worthless, this limited downside protection is not so comforting. Ultimately, Isabel has $47.97 per share at risk. The trade-off comes if Target is above $50 at expiration. Here, assignment will likely occur, in which case the stock will be sold. The call can be assigned before expiration, too, causing the stock to be called away early. Because the covered call involves this obligation to sell the sock at the strike price, upside potential is limited. In this case, Isabel’s profit potential is $2.03. The stock can rise from $49.42 to $50—a $0.58 profit—plus $1.45 of option premium. Isabel does not want the stock to decline too much. Below $47.97, the trade is a loser. If the stock rises too much, the stock is sold prematurely and ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:50 SCORE: 42.00 ================================================================================ Sell Put Selling a put has many similarities to the covered call strategy. We’ll discuss the two positions and highlight the likenesses. Chapter 6 will detail the nuts and bolts of why these similarities exist. Consider an example of selling a put: Sell 1 BA January 65 put at 1.20 In this example, trader Sam is neutral to moderately bullish on Boeing (BA) between now and January expiration. He is not bullish enough to buy BA at the current market price of $69.77 per share. But if the shares dropped below $65, he’d gladly scoop some up. Sam sells 1 BA January 65 put at 1.20. The at-expiration diagram in Exhibit 1.5 shows the P&(L) of this trade if it is held until expiration. EXHIBIT 1.5 Boeing short put. At the expiration of this option, if Boeing is above $65, the put expires and Sam retains the premium of $1.20. The obligation to buy stock expires with the option. Below the strike, put owners will be inclined to exercise their option to sell the stock at $65. Therefore, those short the put, as Sam is in this example, can expect assignment. The break-even price for the position is $63.80. That is the strike price minus the option premium. If ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:51 SCORE: 46.00 ================================================================================ assigned, this is the effective purchase price of the stock. The obligation to buy at $65 is fulfilled, but the $1.20 premium collected makes the purchase effectively $63.80. Here, again, there is limited profit opportunity ($1.20 if the stock is above the strike price) and seemingly unlimited risk (the risk of potential stock ownership at $63.80) if Boeing is below the strike price. Why would a trader short a put and willingly assume this substantial risk with comparatively limited reward? There are a number of motivations that may warrant the short put strategy. In this example, Sam had the twin goals of profiting from a neutral to moderately bullish outlook on Boeing and buying it if it traded below $65. The short put helps him achieve both objectives. Much like the covered call, if the stock is above the strike at expiration, this trader reaches his maximum profit potential—in this case 1.20. And if the price of Boeing is below the strike at expiration, Sam has ownership of the stock from assignment. Here, a strike price that is lower than the current stock level is used. The stock needs to decline in order for Sam to get assigned and become long the stock. With this strategy, he was able to establish a target price at which he would buy the stock. Why not use a limit order? If the put is assigned, the effective purchase price is $63.80 even if the stock price is above this price. If the put is not assigned, the premium is kept. A consideration every trader must make before entering the short put position is how the purchase of the stock will be financed in the event the put is assigned. Traders hoping to acquire the stock will often hold enough cash in their trading account to secure the purchase of the stock. This is called a cash-secured put . In this example, Sam would hold $6,380 in his account in addition to the $120 of option premium received. This affords him enough free capital to fund the $6,500 purchase of stock the short put dictates. More speculative traders may be willing to buy the stock on margin, in which case the trader will likely need around 50 percent of the stock’s value. Some traders sell puts without the intent of ever owning the stock. They hope to profit from a low-volatility environment. Just as the short call is a not-bullish stance on the underlying, the short put is a not-bearish play. As long as the underlying is above the strike price at expiration, the option ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:53 SCORE: 37.00 ================================================================================ Buy Put Buying a put gives the holder the right to sell stock at the strike price. Of course, puts can be a part of a host of different spreads, but this chapter discusses the two most basic and common put-buying strategies: the long put and the protective put. The long put is a way to speculate on a bearish move in the underlying security, and the protective put is a way to protect a long position in the underlying security. Consider a long put example: Buy 1 SPY May 139 put at 2.30 In this example, the Spiders have had a good run up to $140.35. Trader Isabel is looking for a 10 percent correction in SPY between now and the end of May, about three months away. She buys 1 SPY May 139 put at 2.30. This put gives her the right to sell 100 shares of SPY at $139 per share. Exhibit 1.6 shows Isabel’s P&(L) if the put is held until expiration. EXHIBIT 1.6 SPY long put. If SPY is above the strike price of 139 at expiration, the put will expire and the entire premium of 2.30 will be lost. If SPY is below the strike price at expiration, the put will have value. It can be exercised, creating a short position in the Spiders at an effective price of $136.70 per share. This price ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:54 SCORE: 28.00 ================================================================================ is found by subtracting the premium paid, 2.30, from the strike price, 139. This is the point at which the position breaks even. If SPY is below $136.70 at expiration, Isabel has a profit. Profits will increase on a tick-for-tick basis, with downward movements in SPY down to zero. The long put has limited risk and substantial reward potential. An alternative for Isabel is to short the ETF at the current price of $140.35. But a short position in the underlying may not be as attractive to her as a long put. The margin requirements for short stock are significantly higher than for a long put. Put buyers must post only the premium of the put —that is the most that can be lost, after all. The margin requirement for short stock reflects unlimited loss potential. Margin requirements aside, risk is a very real consideration for a trader deciding between shorting stock and buying a put. If the trader expects high volatility, he or she may be more inclined to limit upside risk while leveraging downside profit potential by buying a put. In general, traders buy options when they expect volatility to increase and sell them when they expect volatility to decrease. This will be a common theme throughout this book. Consider a protective put example: This is an example of a situation in which volatility is expected to increase. Own 100 shares SPY at 140.35 Buy 1 SPY May139 put at 2.30 Although Isabel bought a put because she was bearish on the Spiders, a different trader, Kathleen, may buy a put for a different reason—she’s bullish but concerned about increasing volatility. In this example, Kathleen has owned 100 shares of Spiders for some time. SPY is currently at $140.35. She is bullish on the market but has concerns about volatility over the next two or three months. She wants to protect her investment. Kathleen buys 1 SPY May 139 put at 2.30. (If Kathleen bought the shares of SPY and the put at the same time, as a spread, the position would be called a married put.) Kathleen is buying the right to sell the shares she owns at $139. Effectively, it is an insurance policy on this asset. Exhibit 1.7 shows the risk profile of this new position. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:55 SCORE: 47.00 ================================================================================ EXHIBIT 1.7 SPY protective put. The solid kinked line is the protective put (put and stock), and the thin dotted line is the outright position in SPY alone, without the put. The most Kathleen stands to lose with the protective put is $3.65 per share. SPY can decline from $140.35 to $139, creating a loss of $1.35, plus the $2.30 premium spent on the put. If the stock does not fall and the insuring put hence does not come into play, the cost of the put must be recouped to justify its expense. The break-even point is $142.65. This position implies that Kathleen is still bullish on the Spiders. When traders believe a stock or ETF is going to decline, they sell the shares. Instead, Kathleen sacrifices 1.6 percent of her investment up front by purchasing the put for $2.30. She defers the sale of SPY until the period of perceived risk ends. Her motivation is not to sell the ETF; it is to hedge volatility. Once the anticipated volatility is no longer a concern, Kathleen has a choice to make. She can let the option run its course, holding it to expiration, at which point it will either expire or be exercised; or she can sell the option before expiration. If the option is out-of-the-money, it may have residual time value prior to expiration that can be recouped. If it is in- the-money, it will have intrinsic value and maybe time value as well. In this situation, Kathleen can look at this spread as two trades—one that has ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:58 SCORE: 15.00 ================================================================================ CHAPTER 2 Greek Philosophy My wife, Kathleen, is not an options trader. Au contraire. However, she, like just about everyone, uses them from time to time—though without really thinking about it. She was on eBay the other day bidding on a pair of shoes. The bid was $45 with three days left to go. She was concerned about the price rising too much and missing the chance to buy them at what she thought was a good price. She noticed, though, that someone else was selling the same shoes with a buy-it-now price of $49—a good-enough price in her opinion. Kathleen was effectively afforded a call option. She had the opportunity to buy the shoes at (the strike price of) $49, a right she could exercise until the offer expired. The biggest difference between the option in the eBay scenario and the sort of options discussed in this book is transferability. Actual options are tradable—they can be bought and sold. And it is the contract itself that has value—there is one more iteration of pricing. For example, imagine the $49 opportunity was a coupon or certificate that guaranteed the price of $49, which could be passed along from one person to another. And there was the chance that the $49-price guarantee could represent a discount on the price paid for the shoes—maybe a big discount —should the price of the shoes rise in the eBay auction. The certificate guaranteeing the $49 would have value. Anyone planning to buy the shoes would want the safety of knowing they were guaranteed not to pay more than $49 for the shoes. In fact, some people would even consider paying to buy the certificate itself if they thought the price of the shoes might rise significantly. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:59 SCORE: 67.00 ================================================================================ Price vs. Value: How Traders Use Option-Pricing Models Like in the common-life example just discussed, the right to buy or sell an underlying security—that is, an option—can have value, too. The specific value of an option is determined by supply and demand. There are several variables in an option contract, however, that can influence a trader’s willingness to demand (desire to buy) or supply (desire to sell) an option at a given price. For example, a trader would rather own—that is, there would be higher demand for—an option that has more time until expiration than a shorter-dated option, all else held constant. And a trader would rather own a call with a lower strike than a higher strike, all else kept constant, because it would give the right to buy at a lower price. Several elements contribute to the value of an option. It took academics many years to figure out exactly what those elements are. Fischer Black and Myron Scholes together pioneered research in this area at the University of Chicago. Ultimately, their work led to a Nobel Prize for Myron Scholes. Fischer Black died before he could be honored. In 1973, Black and Scholes published a paper called “The Pricing of Options and Corporate Liabilities” in the Journal of Political Economy , that introduced the Black-Scholes option-pricing model to the world. The Black-Scholes model values European call options on non-dividend-paying stocks. Here, for the first time, was a widely accepted model illustrating what goes into the pricing of an option. Option prices were no longer wild guesswork. They could now be rationalized. Soon, additional models and alterations to the Black-Scholes model were developed for options on indexes, dividend-paying stocks, bonds, commodities, and other optionable instruments. All the option-pricing models commonly in use today have slightly different means but achieve the same end: the option’s theoretical value. For American-exercise equity options, six inputs are entered into any option-pricing model to generate a theoretical value: stock price, strike price, time until expiration, interest rate, dividends, and volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:60 SCORE: 42.00 ================================================================================ Theoretical value—what a concept! A trader plugs six numbers into a pricing model, and it tells him what the option is worth, right? Well, in practical terms, that’s not exactly how it works. An option is worth what the market bears. Economists call this price discovery. The price of an option is determined by the forces of supply and demand working in a free and open market. Herein lies an important concept for option traders: the difference between price and value. Price can be observed rather easily from any source that offers option quotes (web sites, your broker, quote vendors, and so on). Value is calculated by a pricing model. But, in practice, the theoretical value is really not an output at all. It is already known: the market determines it. The trader rectifies price and value by setting the theoretical value to fall between the bid and the offer of the option by adjusting the inputs to the model. Professional traders often refer to the theoretical value as the fair value of the option. At this point, please note the absence of the mathematical formula for the Black-Scholes model (or any other pricing model, for that matter). Although the foundation of trading option greeks is mathematical, this book will keep the math to a minimum—which is still quite a bit. The focus of this book is on practical applications, not academic theory. It’s about learning to drive the car, not mastering its engineering. The trader has an equation with six inputs equaling one known output. What good is this equation? An option-pricing model helps a trader understand how market forces affect the value of an option. Five of the six inputs are dynamic; the only constant is the strike price of the option in question. If the price of the option changes, it’s because one or more of the five variable inputs has changed. These variables are independent of each other, but they can change in harmony, having either a cumulative or net effect on the option’s value. An option trader needs to be concerned with the relationship of these variables (price, time, volatility, interest). This multidimensional view of asset pricing is unique to option traders. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:61 SCORE: 100.00 ================================================================================ Delta The five figures commonly used by option traders are represented by Greek letters: delta, gamma, theta, vega, rho. The figures are referred to as option greeks. Vega, of course, is not an actual letter of the greek alphabet, but in the options vernacular, it is considered one of the greeks. The greeks are a derivation of an option-pricing model, and each Greek letter represents a specific sensitivity to influences on the option’s value. To understand concepts represented by these five figures, we’ll start with delta, which is defined in four ways: 1. The rate of change of an option value relative to a change in the underlying stock price. 2. The derivative of the graph of an option value in relation to the stock price. 3. The equivalent of underlying shares represented by an option position. 4. The estimate of the likelihood of an option expiring in-the-money. 1 Definition 1 : Delta (Δ) is the rate of change of an option’s value relative to a change in the price of the underlying security. A trader who is bullish on a particular stock may choose to buy a call instead of buying the underlying security. If the price of the stock rises by $1, the trader would expect to profit on the call—but by how much? To answer that question, the trader must consider the delta of the option. Delta is stated as a percentage. If an option has a 50 delta, its price will change by 50 percent of the change of the underlying stock price. Delta is generally written as either a whole number, without the percent sign, or as a decimal. So if an option has a 50 percent delta, this will be indicated as 0.50, or 50. For the most part, we’ll use the former convention in our discussion. Call values increase when the underlying stock price increases and vice versa. Because calls have this positive correlation with the underlying, they have positive deltas. Here is a simplified example of the effect of delta on an option: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:62 SCORE: 54.00 ================================================================================ Consider a $60 stock with a call option that has a 0.50 delta and is trading for 3.00. Considering only the delta, if the stock price increases by $1, the theoretical value of the call will rise by 0.50. That’s 50 percent of the stock price change. The new call value will be 3.50. If the stock price decreases by $1, the 0.50 delta will cause the call to decrease in value by 0.50, from 3.00 to 2.50. Puts have a negative correlation to the underlying. That is, put values decrease when the stock price rises and vice versa. Puts, therefore, have negative deltas. Here is a simplified example of the delta effect on a −0.40- delta put: As the stock rises from $60 to $61, the delta of −0.40 causes the put value to go from $2.25 to $1.85. The put decreases by 40 percent of the stock price increase. If the stock price instead declined by $1, the put value would increase by $0.40, to $2.65. Unfortunately, real life is a bit more complicated than the simplified examples of delta used here. In reality, the value of both the call and the put will likely be higher with the stock at $61 than was shown in these examples. We’ll expand on this concept later when we tackle the topic of gamma. Definition 2 : Delta can also be described another way. Exhibit 2.1 shows the value of a call option with three months to expiration at a variable stock price. As the stock price rises, the call is worth more; as the stock price declines, the call value moves toward zero. Mathematically, for any given point on the graph, the derivative will show the rate of change of the option price. The delta is the first derivative of the graph of the option price relative to the stock price . ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:63 SCORE: 58.00 ================================================================================ EXHIBIT 2.1 Call value compared with stock price. Definition 3 : In terms of absolute value (meaning that plus and minus signs are ignored), the delta of an option is between 1.00 and 0. Its price can change in tandem with the stock, as with a 1.00 delta; or it cannot change at all as the stock moves, as with a 0 delta; or anything in between. By definition, stock has a 1.00 delta—it is the underlying security. A $1 rise in the stock yields a $100 profit on a round lot of 100 shares. A call with a 0.60 delta rises by $0.60 with a $1 increase in the stock. The owner of a call representing rights on 100 shares earns $60 for a $1 increase in the underlying. It’s as if the call owner in this example is long 60 shares of the underlying stock. Delta is the option’s equivalent of a position in the underlying shares . A trader who buys five 0.43-delta calls has a position that is effectively long 215 shares—that’s 5 contracts × 0.43 deltas × 100 shares. In option lingo, the trader is long 215 deltas. Likewise, if the trader were short five 0.43-delta calls, the trader would be short 215 deltas. The same principles apply to puts. Being long 10 0.59-delta puts makes the trader short a total of 590 deltas, a position that profits or loses like being short 590 shares of the underlying stock. Conversely, if the trader were short 10 0.59-delta puts, the trader would theoretically make $590 if the stock were to rise $1 and lose $590 if the stock fell by $1—just like being long 590 shares. Definition 4 : The final definition of delta is considered the trader’s definition. It’s mathematically imprecise but is used nonetheless as a general rule of thumb by option traders. A trader would say the delta is a statistical approximation of the likelihood of the option expiring in-the- ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:65 SCORE: 56.00 ================================================================================ Dynamic Inputs Option deltas are not constants. They are calculated from the dynamic inputs of the pricing model—stock price, time to expiration, volatility, and so on. When these variables change, the changes affect the delta. These changes can be mathematically quantified—they are systematic. Understanding these patterns and other quirks as to how delta behaves can help traders use this tool more effectively. Let’s discuss a few observations about the characteristics of delta. First, call and put deltas are closely related. Exhibit 2.2 is a partial option chain of 70-day calls and puts in Rambus Incorporated (RMBS). The stock was trading at $21.30 when this table was created. In Exhibit 2.2 , the 20 calls have a 0.66 delta. EXHIBIT 2.2 RMBS Option chain with deltas. Notice the deltas of the put-call pairs in this exhibit. As a general rule, the absolute value of the call delta plus the absolute value of the put delta add up to close to 1.00. The reason for this has to do with a mathematical relationship called put-call parity, which is briefly discussed later in this chapter and described in detail in Chapter 6. But with equity options, the put-call pair doesn’t always add up to exactly 1.00. Sometimes the difference is simply due to rounding. But sometimes there are other reasons. For example, the 30-strike calls and puts in Exhibit 2.2 have deltas of 0.14 and −0.89, respectively. The absolute values of the deltas add up to 1.03. Because of the possibility of early exercise of American options, the put delta is a bit higher than the call delta would ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:67 SCORE: 41.00 ================================================================================ Moneyness and Delta The next observation is the effect of moneyness on the option’s delta. Moneyness describes the degree to which the option is in- or out-of-the- money. As a general rule, options that are in-the-money (ITM) have deltas greater than 0.50. Options that are out-of-the-money (OTM) have deltas less than 0.50. Finally, options that are at-the-money (ATM) have deltas that are about 0.50. The more in-the-money the option is, the closer to 1.00 the delta is. The more out-of-the-money, the closer the delta is to 0. But ATM options are usually not exactly 0.50. For ATMs, both the call and the put deltas are generally systematically a value other than 0.50. Typically, the call has a higher delta than 0.50 and the put has a lower absolute value than 0.50. Incidentally, the call’s theoretical value is generally greater than the put’s when the options are right at-the-money as well. One reason for this disparity between exactly at-the-money calls and puts is the interest rate. The more time until expiration, the more effect the interest rate will have, and, therefore, the higher the call’s theoretical and delta will be relative to the put. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:68 SCORE: 27.00 ================================================================================ Effect of Time on Delta In a close contest, the last few minutes of a football game are often the most exciting—not because the players run faster or knock heads harder but because one strategic element of the game becomes more and more important: time. The team that’s in the lead wants the game clock to run down with no interruption to solidify its position. The team that’s losing uses its precious time-outs strategically. The more playing time left, the less certain defeat is for the losing team. Although mathematically imprecise, the trader’s definition can help us gain insight into how time affects option deltas. The more time left until an option’s expiration, the less certain it is whether the option will be ITM or OTM at expiration. The deltas of both the ITM and the OTM options reflect that uncertainty. The more time left in the life of the option, the closer the deltas tend to gravitate to 0.50. A 0.50 delta represents the greatest level of uncertainty—a coin toss. Exhibit 2.3 shows the deltas of a hypothetical equity call with a strike price of 50 at various stock prices with different times until expiration. All other parameters are held constant. EXHIBIT 2.3 Estimated delta of 50-strike call—impact of time. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:71 SCORE: 51.00 ================================================================================ Effect of Volatility on Delta The level of volatility affects option deltas as well. We’ll discuss volatility in more detail in future chapters, but it’s important to address it here as it relates to the concept of delta. Exhibit 2.4 shows how changing the volatility percentage (explained further in Chapter 3), as opposed to the time to expiration, affects option deltas. In this table, the delta of a call with 91 days until expiration is studied. EXHIBIT 2.4 Estimated delta of 50-strike call—impact of volatility. Notice the effect that volatility has on the deltas of this option with the underlying stock at various prices. In this table, at a low volatility with the call deep in- or out-of-the-money, the delta is very large or very small, respectively. At 10 percent volatility with the stock at $58 a share, the delta is 1.00. At that same volatility level with the stock at $42 a share, the delta is 0. But at higher volatility levels, the deltas change. With the stock at $58, a 45 percent volatility gives the 50-strike call a 0.79 delta—much smaller than it was at the low volatility level. With the stock at $42, a 45-percent volatility returns a 0.30 delta for the call. Generally speaking, ITM option deltas are smaller given a higher volatility assumption, and OTM option deltas are bigger with a higher volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:73 SCORE: 88.00 ================================================================================ Gamma The strike price is the only constant in the pricing model. When the stock price moves relative to this constant, the option in question becomes more in-the-money or out-of-the-money. This means the delta changes. This isolated change is measured by the option’s gamma, sometimes called curvature . Gamma (Γ) is the rate of change of an option’s delta given a change in the price of the underlying security . Gamma is conventionally stated in terms of deltas per dollar move. The simplified examples above under Definition 1 of delta, used to describe the effect of delta, had one important piece of the puzzle missing: gamma. As the stock price moved higher in those examples, the delta would not remain constant. It would change due to the effect of gamma. The following example shows how the delta would change given a 0.04 gamma attributed to the call option. The call in this example starts as a 0.50-delta option. When the stock price increases by $1, the delta increases by the amount of the gamma. In this example, delta increases from 0.50 to 0.54, adding 0.04 deltas. As the stock price continues to rise, the delta continues to move higher. At $62, the call’s delta is 0.58. This increase in delta will affect the value of the call. When the stock price first begins to rise from $60, the option value is increasing at a rate of 50 percent—the call’s delta at that stock price. But by the time the stock is at $61, the option value is increasing at a rate of 54 percent of the stock price. To estimate the theoretical value of the call at $61, we must first estimate the average change in the delta between $60 and $61. The average delta between $60 and $61 is roughly 0.52. It’s difficult to calculate the average delta exactly because gamma is not constant; this is discussed in more detail later in the chapter. A more realistic example of call values in relation to the stock price would be as follows: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:74 SCORE: 69.00 ================================================================================ Each $1 increase in the stock shows an increase in the call value about equal to the average delta value between the two stock prices. If the stock were to decline, the delta would get smaller at a decreasing rate. As the stock price declines from $60 to $59, the option delta decreases from 0.50 to 0.46. There is an average delta of about 0.48 between the two stock prices. At $59 the new theoretical value of the call is 2.52. The gamma continues to affect the option’s delta and thereby its theoretical value as the stock continues its decline to $58 and beyond. Puts work the same way, but because they have a negative delta, when there is a positive stock-price movement the gamma makes the put delta less negative, moving closer to 0. The following example clarifies this. As the stock price rises, this put moves more and more out-of-the-money. Its theoretical value is decreasing by the rate of the changing delta. At $60, the delta is −0.40. As the stock rises to $61, the delta changes to −0.36. The average delta during that move is about −0.38, which is reflected in the change in the value of the put. If the stock price declines and the put moves more toward being in-the- money, the delta becomes more negative—that is, the put acts more like a short stock position. Here, the put value rises by the average delta value between each incremental change in the stock price. These examples illustrate the effect of gamma on an option without discussing the impact on the trader’s position. When traders buy options, they acquire positive gamma. Since gamma causes options to gain value at ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:75 SCORE: 92.00 ================================================================================ a faster rate and lose value at a slower rate, (positive) gamma helps the option buyer. A trader buying one call or put in these examples would have +0.04 gamma. Buying 10 of these options would give the trader a +0.4 gamma. When traders sell options, gamma works against them. When options lose value, they move toward zero at a slower rate. When the underlying moves adversely, gamma speeds up losses. Selling options yields a negative gamma position. A trader selling one of the above calls or puts would have −0.04 gamma per option. The effect of gamma is less significant for small moves in the underlying than it is for bigger moves. On proportionately large moves, the delta can change quite a bit, making a big difference in the position’s P&(L). In Exhibit 2.1 , the left side of the diagram showed the call price not increasing at all with advances in the stock—a 0 delta. The right side showed the option advancing in price 1-to-1 with the stock—a 1.00 delta. Between the two extremes, the delta changes. From this diagram another definition for gamma can be inferred: gamma is the second derivative of the graph of the option price relative to the stock price. Put another way, gamma is the first derivative of a graph of the delta relative to the stock price. Exhibit 2.5 illustrates the delta of a call relative to the stock price. EXHIBIT 2.5 Call delta compared with stock price. Not only does the delta change, but it changes at a changing rate. Gamma is not constant. Moneyness, time to expiration, and volatility each have an effect on the gamma of an option. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:76 SCORE: 53.00 ================================================================================ Dynamic Gamma When options are far in-the-money or out-of-the-money, they are either 1.00 delta or 0 delta. At the extremes, small changes in the stock price will not cause the delta to change much. When an option is at-the-money, it’s a different story. Its delta can change very quickly. ITM and OTM options have a low gamma. ATM options have a relatively high gamma. Exhibit 2.6 is an example of how moneyness translates into gamma on QQQ calls. EXHIBIT 2.6 Gamma of QQQ calls with QQQ at $44. With QQQ at $44, 92 days until expiration, and a constant volatility input of 19 percent, the 36- and 54-strike calls are far enough in- and out-of-the- money, respectively, that if the Qs move a small amount in either direction from the current price of $44, the movement won’t change their deltas much at all. The chances of their money status changing between now and expiration would not be significantly different statistically given a small stock price change. They have the smallest gammas in the table. The highest gammas shown here are around the ATM strike prices. (Note that because of factors not yet discussed, the strike that is exactly at-the- money may not have the highest gamma. The highest gamma is likely to occur at a slightly higher strike price.) Exhibit 2.7 shows a graph of the corresponding numbers in Exhibit 2.6 . ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:78 SCORE: 39.00 ================================================================================ At seven days until expiration, there is less time for price action in the stock to change the expected moneyness at expiration of ITMs or OTMs. ATM options, however, continue to be in play. Here, the ATM gamma is approaching 0.35. But the strikes below 41 and above 48 have 0 gamma. Similarly-priced securities that tend to experience bigger price swings may have strikes $3 away-from-the-money with seven-day gammas greater than zero. The volatility of the underlying will affect gamma, too. Exhibit 2.9 shows the same 19 percent volatility QQQ calls in contrast with a graph of the gamma if the volatility is doubled. EXHIBIT 2.9 Gamma as volatility changes. Raising the volatility assumption flattens the curve, causing ITM and OTM to have higher gamma while lowering the gamma for ATMs. Short-term ATM options with low volatility have the highest gamma. Lower gamma is found in ATMs when volatility is higher and it is lower for ITMs and OTMs and in longer-dated options. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:79 SCORE: 50.00 ================================================================================ Theta Option prices can be broken down into two parts: intrinsic value and time value. Intrinsic value is easily measurable. It is simply the ITM part of the premium. Time value, or extrinsic value, is what’s left over—the premium paid over parity for the option. All else held constant, the more time left in the life of the option, the more valuable it is—there is more time for the stock to move. And as the useful life of an option decreases, so does its time value. The decline in the value of an option because of the passage of time is called time decay, or erosion. Incremental measurements of time decay are represented by the Greek letter theta (θ). Theta is the rate of change in an option’s price given a unit change in the time to expiration . What exactly is the unit involved here? That depends. Some providers of option greeks will display thetas that represent one day’s worth of time decay. Some will show thetas representing seven days of decay. In the case of a one-day theta, the figure may be based on a seven- day week or on a week counting only trading days. The most common and, arguably, most useful display of this figure is the one-day theta based on the seven-day week. There are, after all, seven days in a week, each day of which can see an occurrence with the potential to cause a revaluation in the stock price (that is, news can come out on Saturday or Sunday). The one- day theta based on a seven-day week will be used throughout this book. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:80 SCORE: 17.00 ================================================================================ Taking the Day Out When the number of days to expiration used in the pricing model declines from, say, 32 days to 31 days, the price of the option decreases by the amount of the theta, all else held constant. But when is the day “taken out”? It is intuitive to think that after the market closes, the model is changed to reflect the passing of one day’s time. But, in fact, this change is logically anticipated and may be priced in early. In the earlier part of the week, option prices can often be observed getting cheaper relative to the stock price sometime in the middle of the day. This is because traders will commonly take the day out of their model during trading hours after the underlying stabilizes following the morning business. On Fridays and sometimes Thursdays, traders will take all or part of the weekend out. Commonly, by Friday afternoon, traders will be using Monday’s days to value their options. When option prices are seen getting cheaper on, say, a Friday, how can one tell whether this is the effect of the market taking the weekend out or a change in some other input, such as volatility? To some degree, it doesn’t matter. Remember, the model is used to reflect what the market is doing, not the other way around. In many cases, it’s logical to presume that small devaluations in option prices intraday can be attributed to the routine of the market taking the day out. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:81 SCORE: 74.00 ================================================================================ Friend or Foe? Theta can be a good thing or a bad thing, depending on the position. Theta hurts long option positions; whereas it helps short option positions. Take an 80-strike call with a theoretical value of 3.16 on a stock at $82 a share. The 32-day 80 call has a theta of 0.03. If a trader owned one of these calls, the trader’s position would theoretically lose 0.03, or $0.03, as the time until expiration change from 32 to 31 days. This trader has a negative theta position. A trader short one of these calls would have an overnight theoretical profit of $0.03 attributed to theta. This trader would have a positive theta. Theta affects put traders as well. Using all the same modeling inputs, the 32-day 80-strike put would have a theta of 0.02. A put holder would theoretically lose $0.02 a day, and a put writer would theoretically make $0.02. Long options carry with them negative theta; short options carry positive theta. A higher theta for the call than for the put of the same strike price is common when an interest rate greater than zero is used in the pricing model. As will be discussed in greater detail in the section on rho, interest causes the time value of the call to be higher than that of the corresponding put. At expiration, there is no time value left in either option. Because the call begins with more time value, its premium must decline at a faster rate than that of the put. Most modeling software will attribute the disparate rates of decline in value all to theta, whereas some modeling interfaces will make clear the distinction between the effect of time decay and the effect of interest on the put-call pair. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:82 SCORE: 41.00 ================================================================================ The Effect of Moneyness and Stock Price on Theta Theta is not a constant. As variables influencing option values change, theta can change, too. One such variable is the option’s moneyness. Exhibit 2.10 shows theoretical values (theos), time values, and thetas for 3-month options on Adobe (ADBE). In this example, Adobe is trading at $31.30 a share with three months until expiration. The more ITM a call or a put gets, the higher its theoretical value. But when studying an option’s time decay, one needs to be concerned only with the option’s time value, because intrinsic value is not subject to time decay. EXHIBIT 2.10 Adobe theos and thetas (Adobe at $31.30). The ATM options shown here have higher time value than ITM or OTM options. Hence, they have more time premium to lose in the same three- month period. ATM options have the highest rate of decay, which is reflected in higher thetas. As the stock price changes, the theta value will change to reflect its change in moneyness. If this were a higher-priced stock, say, 10 times the stock price used in this example, with all other inputs held constant, the option values, and therefore the thetas, would be higher. If this were a stock trading at $313, the 325-strike call would have a theoretical value of 16.39 and a one-day ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:84 SCORE: 43.00 ================================================================================ The Effects of Volatility and Time on Theta Stock price is not the only factor that affects theta values. Volatility and time to expiration come into play here as well. The volatility input to the pricing model has a direct relationship to option values. The higher the volatility, the higher the value of the option. Higher-valued options decay at a faster rate than lower-valued options—they have to; their time values will both be zero at expiration. All else held constant, the higher the volatility assumption, the higher the theta. The days to expiration have a direct relationship to option values as well. As the number of days to expiration decreases, the rate at which an option decays may change, depending on the relationship of the stock price to the strike price. ATM options tend to decay at a nonlinear rate—that is, they lose value faster as expiration approaches—whereas the time values of ITM and OTM options decay at a steadier rate. Consider a hypothetical stock trading at $70 a share. Exhibit 2.11 shows how the theoretical values of the 75-strike call and the 70-strike call decline with the passage of time, holding all other parameters constant. EXHIBIT 2.11 Rate of decay: ATM vs. OTM. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:86 SCORE: 21.00 ================================================================================ Vega Over the past decade or so, computers have revolutionized option trading. Options traded through an online broker are filled faster than you can say, “Oops! I meant to click on puts.” Now trading is facilitated almost entirely online by professional and retail traders alike. Market and trading information is disseminated worldwide in subseconds, making markets all the more efficient. And the tools now available to the common retail trader are very powerful as well. Many online brokers and other web sites offer high-powered tools like screeners, which allow traders to sift through thousands of options to find those that fit certain parameters. Using a screener to find ATM calls on same-priced stocks—say, stocks trading at $40 a share—can yield a result worth talking about here. One $40 stock can have a 40-strike call trading at around 0.50, while a different $40 stock can have a 40 call with the same time to expiration trading at more like 2.00. Why? The model doesn’t know the name of the company, what industry it’s in, or what its price-to-earnings ratio is. It is a mathematical equation with six inputs. If five of the inputs—the stock price, strike price, time to expiration, interest rate, and dividends—are identical for two different options but they’re trading at different prices, the difference must be the sixth variable, which is volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:87 SCORE: 95.50 ================================================================================ Implied Volatility (IV) and Vega The volatility component of option values is called implied volatility (IV). (For more on implied volatility and how it relates to vega, see Chapter 3.) IV is a percentage, although in practice the percent sign is often omitted. This is the value entered into a pricing model, in conjunction with the other variables, that returns the option’s theoretical value. The higher the volatility input, the higher the theoretical value, holding all other variables constant. The IV level can change and often does—sometimes dramatically. When IV rises or falls, option prices rise and fall in line with it. But by how much? The relationship between changes in IV and changes in an option’s value is measured by the option’s vega. Vega is the rate of change of an option’s theoretical value relative to a change in implied volatility . Specifically, if the IV rises or declines by one percentage point, the theoretical value of the option rises or declines by the amount of the option’s vega, respectively. For example, if a call with a theoretical value of 1.82 has a vega of 0.06 and IV rises one percentage point from, say, 17 percent to 18 percent, the new theoretical value of the call will be 1.88—it would rise by 0.06, the amount of the vega. If, conversely, the IV declines 1 percentage point, from 17 percent to 16 percent, the call value will drop to 1.76—that is, it would decline by the vega. A put with the same expiration month and the same strike on the same underlying will have the same vega value as its corresponding call. In this example, raising or lowering IV by one percentage point would cause the corresponding put value to rise or decline by $0.06, just like the call. An increase in IV and the consequent increase in option value helps the P&(L) of long option positions and hurts short option positions. Buying a call or a put establishes a long vega position. For short options, the opposite is true. Rising IV adversely affects P&(L), whereas falling IV helps. Shorting a call or put establishes a short vega position. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:88 SCORE: 59.50 ================================================================================ The Effect of Moneyness on Vega Like the other greeks, vega is a snapshot that is a function of multiple facets of determinants influencing option value. The stock price’s relationship to the strike price is a major determining factor of an option’s vega. IV affects only the time value portion of an option. Because ATM options have the greatest amount of time value, they will naturally have higher vegas. ITM and OTM options have lower vega values than those of the ATM options. Exhibit 2.13 shows an example of 186-day options on AT&T Inc. (T), their time value, and the corresponding vegas. EXHIBIT 2.13 AT&T theos and vegas (T at $30, 186 days to Expry, 20% IV). Note that the 30-strike calls and puts have the highest time values. This strike boasts the highest vega value, at 0.085. The lower the time premium, the lower the vega—therefore, the less incremental IV changes affect the option. Since higher-priced stocks have higher time premium (in absolute terms, not necessarily in percentage terms) they will have higher vega. Incidentally, if this were a $300 stock instead of a $30 stock, the 186-day ATMs would have a 0.850 vega, if all other model inputs remain the same. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:92 SCORE: 42.00 ================================================================================ Put-Call Parity Put and call values are mathematically bound together by an equation referred to as put-call parity. In its basic form, put-call parity states: where c = call value, PV(x) = present value of the strike price, p = put value, and s = stock price. The put-call parity assumes that options are not exercised before expiration (that is, that they are European style). This version of the put-call parity is for European options on non-dividend-paying stocks. Put-call parity can be modified to reflect the values of options on stocks that pay dividends. In practice, equity-option traders look at the equation in a slightly different way: Traders serious about learning to trade options must know put-call parity backward and forward. Why? First, by algebraically rearranging this equation, it can be inferred that synthetically equivalent positions can be established by simply adding stock to an option. Again, a put is a call; a call is a put. and For example, a long call is synthetically equal to a long stock position plus a long put on the same strike, once interest and dividends are figured in. A synthetic long stock position is created by buying a call and selling a put of the same month and strike. Understanding synthetic relationships is intrinsic to understanding options. A more comprehensive discussion of synthetic relationships and tactical considerations for creating synthetic positions is offered in Chapter 6. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:93 SCORE: 49.00 ================================================================================ Put-call parity also aids in valuing options. If put-call parity shows a difference in the value of the call versus the value of the put with the same strike, there may be an arbitrage opportunity. That translates as “riskless profit.” Buying the call and selling it synthetically (short put and short stock) could allow a profit to be locked in if the prices are disparate. Arbitrageurs tend to hold synthetic put and call prices pretty close together. Generally, only professional traders can capture these types of profit opportunities, by trading big enough positions to make very small profits (a penny or less per contract sometimes) matter. Retail traders may be able to take advantage of a disparity in put and call values to some extent, however, by buying or selling the synthetic as a substitute for the actual option if the position can be established at a better price synthetically. Another reason that a working knowledge of put-call parity is essential is that it helps attain a better understanding of how changes in the interest rate affect option values. The greek rho measures this change. Rho is the rate of change in an option’s value relative to a change in the interest rate. Although some modeling programs may display this number differently, most display a rho for the call and a rho for the put, both illustrating the sensitivity to a one-percentage-point change in the interest rate. When the interest rate rises by one percentage point, the value of the call increases by the amount of its rho and the put decreases by the amount of its rho. Likewise, when the interest rate decrease by one percentage point, the value of the call decreases by its rho and the put increases by its rho. For example, a call with a rho of 0.12 will increase $0.12 in value if the interest rate used in the model is increased by one percentage point. Of course, interest rates usually don’t rise or fall one percentage point in one day. More commonly, rates will have incremental changes of 25 basis points. That means a call with a 0.12 rho will theoretically gain $0.03 given an increase of 0.25 percentage points. Mathematically, this change in option value as a product of a change in the interest rate makes sense when looking at the formula for put-call parity. and ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:94 SCORE: 33.50 ================================================================================ But the change makes sense intuitively, too, when a call is considered as a cheaper substitute for owning the stock. For example, compare a $100 stock with a three-month 60-strike call on that same stock. Being so far ITM, there would likely be no time value in the call. If the call can be purchased at parity, which alternative would be a superior investment, the call for $40 or the stock for $100? Certainly, the call would be. It costs less than half as much as the stock but has the same reward potential; and the $60 not spent on the stock can be invested in an interest-bearing account. This interest advantage adds value to the call. Raising the interest rate increases this value, and lowering it decreases the interest component of the value of the call. A similar concept holds for puts. Professional traders often get a short- stock rebate on proceeds from a short-stock sale. This is simply interest earned on the capital received when the stock is shorted. Is it better to pay interest on the price of a put for a position that gives short exposure or to receive interest on the credit from shorting the stock? There is an interest disadvantage to owning the put. Therefore, a rise in interest rates devalues puts. This interest effect becomes evident when comparing ATM call and put prices. For example, with interest at 5 percent, three-month options on an $80 stock that pays a $0.25 dividend before option expiration might look something like this: The ATM call is higher in theoretical value than the ATM put by $0.75. That amount can be justified using put-call parity: (Here, simple interest of $1 is calculated as 80 × 0.05 × [90 / 360] = 1.) Changes in market conditions are kept in line by the put-call parity. For example, if the price of the call rises because of an increase in IV, the price of the put will rise in step. If the interest rate rises by a quarter of a percentage point, from 5 percent to 5.25 percent, the interest calculated for three months on the 80-strike will increase from $1 to $1.05, causing the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:96 SCORE: 28.00 ================================================================================ The Effect of Time on Rho The more time until expiration, the greater the effect interest rate changes will have on options. In the previous example, a 25-basis-point change in the interest rate on the 80-strike based on a three-month period caused a change of 0.05 to the interest component of put-call parity. That is, 80 × 0.0025 × (90/360) = 0.05. If a longer period were used in the example—say, one year—the effect would be more profound; it will be $0.20: 80 × 0.0025 × (360/360) = 0.20. This concept is evident when the rhos of options with different times to expiration are studied. Exhibit 2.16 shows the rhos of ATM Procter & Gamble Co. (PG) calls with various expiration months. The 750-day Long-Term Equity AnticiPation Securities (LEAPS) have a rho of 0.858. As the number of days until expiration decreases, rho decreases. The 22-day calls have a rho of only 0.015. Rho is usually a fairly insignificant factor in the value of short-term options, but it can come into play much more with long-term option strategies involving LEAPS. EXHIBIT 2.16 The effect of time on rho (Procter & Gamble @ $64.34) ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:97 SCORE: 80.00 ================================================================================ Why the Numbers Don’t Don’t Always Add Up There will be many times when studying the rho of options in an option chain will reveal seemingly counterintuitive results. To be sure, the numbers don’t always add up to what appears logical. One reason for this is rounding. Another is that traders are more likely to use simple interest in calculating value, whereas the model uses compound interest. Hard-to- borrow stocks and stocks involved in mergers and acquisitions may have put-call parities that don’t work out right. But another, more common and more significant fly in the ointment is early exercise. Since the interest input in put-call parity is a function of the strike price, it is reasonable to expect that the higher the strike price, the greater the effect of interest on option prices will be. For European options, this is true to a large extent, in terms of aggregate impact of interest on the call and put pair. Strikes below the price where the stock is trading have a higher rho associated with the call relative to the put, whereas strikes above the stock price have a higher rho associated with the put relative to the call. Essentially, the more in-the-money an option is, the higher its rho. But with European options, observing the aggregate of the absolute values of the call and put rhos would show a higher combined rho the higher the strike. With American options, the put can be exercised early. A trader will exercise a put before expiration if the alternative—being short stock and receiving a short stock rebate—is a wiser choice based on the price of the put. Professional traders may own stock as a hedge against a put. They may exercise deep ITM puts (1.00-delta puts) to avoid paying interest on capital charges related to the stock. The potential for early exercise is factored into models that price American options. Here, when puts get deeper in-the- money—that is, more apt to be exercised—the rho decreases. When the strike price is very high relative to the stock price—meaning the put is very deep ITM—and there is little or no time value left to the call or the put, the aggregate put-call rho can be zero. Rho is discussed in greater detail in Chapter 7. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:99 SCORE: 61.50 ================================================================================ Where to Find Option Greeks There are many sources from which to obtain greeks. The Internet is an excellent resource. Googling “option greeks” will display links to over four million web pages, many of which have real-time greeks or an option calculator. An option calculator is a simple interface that accepts the input of the six variables to the model and yields a theoretical value and the greeks for a single option. Some web sites devoted to option education, such as MarketTaker.com/option_modeling , have free calculators that can be used for modeling positions and using the greeks. In practice, many of the option-trading platforms commonly in use have sophisticated analytics that involve greeks. Most options-friendly online brokers provide trading platforms that enable traders to conduct comprehensive manipulations of the greeks. For example, traders can look at the greeks for their positions up or down one, two, or three standard deviations. Or they can see what happens to their position greeks if IV or time changes. With many trading platforms, position greeks are updated in real time with changes in the stock price—an invaluable feature for active traders. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:100 SCORE: 61.00 ================================================================================ Caveats with Regard to Online Greeks Often, online greeks are one click away, requiring little effort on the part of the trader. Having greeks calculated automatically online is a quick and convenient way to eyeball greeks for an option. But there is one major problem with online greeks: reliability. For active option traders, greeks are essential. There is no point in using these figures if their accuracy cannot be assured. Experienced traders can often spot these inaccuracies a proverbial mile away. When looking at greeks from an online source that does not require you to enter parameters into a model (as would be the case with professional option-trading platforms), special attention needs to be paid to the relationship of the option’s theoretical values to the bid and offer. One must be cautious if the theoretical value of the option lies outside the bid-ask spread. This scenario can exist for brief periods of time, but arbitrageurs tend to prevent this from occurring routinely. If several options in a chain all have theoretical values below the bid or above the offer, there is probably a problem with one or more of the inputs used in the model. Remember, an option-pricing model is just that: a model. It reflects what is occurring in the market. It doesn’t tell where an option should be trading. The complex changes that occur intraday in the market—taking the day or weekend out, changes in stock price, volatility, and the interest rate—are not always kept current. The user of the model must keep close watch. It’s not reasonable to expect the computer to do the thinking for you. Automatically calculated greeks can be used as a starting point. But before using these figures in the decision-making process, the trader may have to override the parameters that were used in the online calculation to make the theos line up with market prices. Professional traders will ignore online greeks altogether. They will use the greeks that are products of the inputs they entered in their trading software. It comes down to this: if you want something done right, do it yourself. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:103 SCORE: 14.00 ================================================================================ CHAPTER 3 Understanding Volatility Most option strategies involve trading volatility in one way or another. It’s easy to think of trading in terms of direction. But trading volatility? Volatility is an abstract concept; it’s a different animal than the linear trading paradigm used by most conventional market players. As an option trader, it is essential to understand and master volatility. Many traders trade without a solid understanding of volatility and its effect on option prices. These traders are often unhappily surprised when volatility moves against them. They mistake the adverse option price movements that result from volatility for getting ripped off by the market makers or some other market voodoo. Or worse, they surrender to the fact that they simply don’t understand why sometimes these unexpected price movements occur in options. They accept that that’s just the way it is. Part of what gets in the way of a ready understanding of volatility is context. The term volatility can have a few different meanings in the options business. There are three different uses of the word volatility that an option trader must be concerned with: historical volatility, implied volatility, and expected volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:108 SCORE: 13.00 ================================================================================ Standard Deviation and Historical Volatility When standard deviation is used in the context of historical volatility, it is annualized to state what the one-year volatility would be. Historical volatility is the annualized standard deviation of daily returns. This means that if a stock is trading at $100 a share and its historical volatility is 10 percent, then about 68 percent of the occurrences (closing prices) are expected to fall between $90 and $110 during a one-year period (based on recent past performance). Simply put, historical volatility shows how volatile a stock has been based on price movements that have occurred in the past. Although option traders may study HV to make informed decisions as to the value of options traded on a stock, it is not a direct function of option prices. For this, we must look to implied volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:109 SCORE: 41.50 ================================================================================ Implied Volatility Volatility is one of the six inputs of an option-pricing model. Some of the other inputs—strike price, stock price, the number of days until expiration, and the current interest rate—are easily observable. Past dividend policy allows an educated guess as to what the dividend input should be. But where can volatility be found? As discussed in Chapter 2, the output of the pricing model—the option’s theoretical value—in practice is not necessarily an output at all. When option traders use the pricing model, they commonly substitute the actual price at which the option is trading for the theoretical value. A value in the middle of the bid-ask spread is often used. The pricing model can be considered to be a complex algebra equation in which any variable can be solved for. If the theoretical value is known—which it is—it along with the five known inputs can be combined to solve for the unknown volatility. Implied volatility (IV) is the volatility input in a pricing model that, in conjunction with the other inputs, returns the theoretical value of an option matching the market price. For a specific stock price, a given implied volatility will yield a unique option value. Take a stock trading at $44.22 that has the 60-day 45-strike call at a theoretical value of $1.10 with an 18 percent implied volatility level. If the stock price remains constant, but IV rises to 19 percent, the value of the call will rise by its vega, which in this case is about 0.07. The new value of the call will be $1.17. Raising IV another point, to 20 percent, raises the theoretical value by another $0.07, to $1.24. The question is: What would cause implied volatility to change? ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:110 SCORE: 41.50 ================================================================================ Supply and Demand: Not Just a Good Idea, It’s the Law! Options are an excellent vehicle for speculation. However, the existence of the options market is better justified by the primary economic purpose of options: as a risk management tool. Hedgers use options to protect their assets from adverse price movements, and when the perception of risk increases, so does demand for this protection. In this context, risk means volatility—the potential for larger moves to the upside and downside. The relative prices of options are driven higher by increased demand for protective options when the market anticipates greater volatility. And option prices are driven lower by greater supply—that is, selling of options—when the market expects lower volatility. Like those of all assets, option prices are subject to the law of supply and demand. When volatility is expected to rise, demand for options is not limited to hedgers. Speculative traders would arguably be more inclined to buy a call than to buy the stock if they are bullish but expect future volatility to be high. Calls require a lower cash outlay. If the stock moves adversely, there is less capital at risk, but still similar profit potential. When volatility is expected to be low, hedging investors are less inclined to pay for protection. They are more likely to sell back the options they may have bought previously to recoup some of the expense. Options are a decaying asset. Investors are more likely to write calls against stagnant stocks to generate income in anticipated low-volatility environments. Speculative traders will implement option-selling strategies, such as short strangles or iron condors, in an attempt to capitalize on stocks they believe won’t move much. The rising supply of options puts downward pressure on option prices. Many traders sum up IV in two words: fear and greed . When option prices rise and fall, not because of changes in the stock price, time to expiration, interest rates, or dividends, but because of pure supply and demand, it is implied volatility that is the varying factor. There are many contributing factors to traders’ willingness to demand or supply options. Anticipation of events such as earnings reports, Federal Reserve ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:111 SCORE: 27.00 ================================================================================ announcements, or the release of other news particular to an individual stock can cause anxiety, or fear, in traders and consequently increase demand for options that causes IV to rise. IV can fall when there is complacency in the market or when the anticipated news has been announced and anxiety wanes. “Buy the rumor, sell the news” is often reflected in option implied volatility. When there is little fear of market movement, traders use options to squeeze out more profits—greed. Arbitrageurs, such as market makers who trade delta neutral—a strategy that will be discussed further in Chapters 12 and 13—must be relentlessly conscious of implied volatility. When immediate directional risk is eliminated from a position, IV becomes the traded commodity. Arbitrageurs who focus their efforts on trading volatility (colloquially called vol traders ) tend to think about bids and offers in terms of IV. In the mind of a vol trader, option prices are translated into volatility levels. A trader may look at a particular option and say it is 30 bid at 31 offer. These values do not represent the prices of the options but rather the corresponding implied volatilities. The meaning behind the trader’s remark is that the market is willing to buy implied volatility at 30 percent and sell it at 31 percent. The actual prices of the options themselves are much less relevant to this type of trader. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:112 SCORE: 32.50 ================================================================================ Should HV and IV Be the Same? Most option positions have exposure to volatility in two ways. First, the profitability of the position is usually somewhat dependent on movement (or lack of movement) of the underlying security. This is exposure to HV. Second, profitability can be affected by changes in supply and demand for the options. This is exposure to IV. In general, a long option position benefits when volatility—both historical and implied—increases. A short option position benefits when volatility—historical and implied—decreases. That said, buying options is buying volatility and selling options is selling volatility. The Relationship of HV and IV It’s intuitive that there should exist a direct relationship between the HV and IV. Empirically, this is often the case. Supply and demand for options, based on the market’s expectations for a security’s volatility, determines IV. It is easy to see why IV and HV often act in tandem. But, although HV and IV are related, they are not identical. There are times when IV and HV move in opposite directions. This is not so illogical, if one considers the key difference between the two: HV is calculated from past stock price movements; it is what has happened. IV is ultimately derived from the market’s expectation for future volatility. If a stock typically has an HV of 30 percent and nothing is expected to change, it can be reasonable to expect that in the future the stock will continue to trade at a 30 percent HV. By that logic, assuming that nothing is expected to change, IV should be fairly close to HV. Market conditions do change, however. These changes are often regular and predictable. Earnings reports are released once a quarter in many stocks, Federal Open Market Committee meetings happen regularly, and dates of other special announcements are often disclosed to the public in advance. Although the outcome of these events cannot be predicted, when they will occur often can be. It is around these widely anticipated events that HV-IV divergences often occur. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:113 SCORE: 11.00 ================================================================================ HV-IV Divergence An HV-IV divergence occurs when HV declines and IV rises or vice versa. The classic example is often observed before a company’s quarterly earnings announcement, especially when there is lack of consensus among analysts’ estimates. This scenario often causes HV to remain constant or decline while IV rises. The reason? When there is a great deal of uncertainty as to what the quarterly earnings will be, investors are reluctant to buy or sell the stock until the number is released. When this happens, the stock price movement (volatility) consolidates, causing the calculated HV to decline. IV, however, can rise as traders scramble to buy up options— bidding up their prices. When the news is out, the feared (or hoped for) move in the stock takes place (or doesn’t), and HV and IV tend to converge again. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:115 SCORE: 41.00 ================================================================================ Expected Stock Volatility Option traders must have an even greater focus on volatility, as it plays a much bigger role in their profitability—or lack thereof. Because options can create highly leveraged positions, small moves can yield big profits or losses. Option traders must monitor the likelihood of movement in the underlying closely. Estimating what historical volatility (standard deviation) will be in the future can help traders quantify the probability of movement beyond a certain price point. This leads to better decisions about whether to enter a trade, when to adjust a position, and when to exit. There is no way of knowing for certain what the future holds. But option data provide traders with tools to develop expectations for future stock volatility. IV is sometimes interpreted as the market’s estimate of the future volatility of the underlying security. That makes it a ready-made estimation tool, but there are two caveats to bear in mind when using IV to estimate future stock volatility. The first is that the market can be wrong. The market can wrongly price stocks. This mispricing can lead to a correction (up or down) in the prices of those stocks, which can lead to additional volatility, which may not be priced in to the options. Although there are traders and academics believe that the option market is fairly efficient in pricing volatility, there is a room for error. There is the possibility that the option market can be wrong. Another caveat is that volatility is an annualized figure—the annualized standard deviation. Unless the IV of a LEAPS option that has exactly one year until expiration is substituted for the expected volatility of the underlying stock over exactly one year, IV is an incongruent estimation for the future stock volatility. In practice, the IV of an option must be adjusted to represent the period of time desired. There is a common technique for deannualizing IV used by professional traders and retail traders alike. 1 The first step in this process to deannualize IV is to turn it into a one-day figure as opposed to one-year figure. This is accomplished by dividing IV by the square root of the number of trading days in a year. The number many traders use to approximate the number of ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:116 SCORE: 13.00 ================================================================================ trading days per year is 256, because its square root is a round number: 16. The formula is For example, a $100 stock that has an at-the-money (ATM) call trading at a 32 percent volatility implies that there is about a 68 percent chance that the underlying stock will be between $68 and $132 in one year’s time— that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for the volatility of the stock for one day in terms of standard deviation as a percentage of the price of the underlying is computed as follows: In one day’s time, based on an IV of 32 percent, there is a 68 percent chance of the stock’s being within 2 percent of the stock price—that’s between $98 and $102. There may be times when it is helpful for traders to have a volatility estimation for a period of time longer than one day—a week or a month, for example. This can be accomplished by multiplying the one-day volatility by the square root of the number of trading days in the relevant period. The equation is as follows: If the period in question is one month and there are 22 business days remaining in that month, the same $100 stock with the ATM call trading at a 32 percent implied volatility would have a one-month volatility of 9.38 percent. Based on this calculation for one month, it can be estimated that there is a 68 percent chance of the stock’s closing between $90.62 and $109.38 based on an IV of 32 percent. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:117 SCORE: 30.50 ================================================================================ Expected Implied Volatility Although there is a great deal of science that can be applied to calculating expected actual volatility, developing expectations for implied volatility is more of an art. This element of an option’s price provides more risk and more opportunity. There are many traders who make their living distilling direction out of their positions and trading implied volatility. To be successful, a trader must forecast IV. Conceptually, trading IV is much like trading anything else. A trader who thinks a stock is going to rise will buy the stock. A trader who thinks IV is going to rise will buy options. Directional stock traders, however, have many more analysis tools available to them than do vol traders. Stock traders have both technical analysis (TA) and fundamental analysis at their disposal. Technical Analysis There are scores, perhaps hundreds, of technical tools for analyzing stocks, but there are not many that are available for analyzing IV. Technical analysis is the study of market data, such as past prices or volume, which is manipulated in such a way that it better illustrates market activity. TA studies are usually represented graphically on a chart. Developing TA tools for IV is more of a challenge than it is for stocks. One reason is that there is simply a lot more data to manage—for each stock, there may be hundreds of options listed on it. The only practical way of analyzing options from a TA standpoint is to use implied volatility. IV is more useful than raw historical option prices themselves. Information for both IV and HV is available in the form of volatility charts, or vol charts. (Vol charts are discussed in detail in Chapter 14.) Volatility charts are essential for analyzing options because they give more complete information. To get a clear picture of what is going on with the price of an option (the goal of technical analysis for any asset), just observing the option price does not supply enough information for a trader to work with. It’s incomplete. For example, if a call rises in value, why did it rise? What greek contributed ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:118 SCORE: 39.00 ================================================================================ to its value increase? Was it delta because the underlying stock rose? Or was it vega because volatility rose? How did time decay factor in? Using a volatility chart in conjunction with a conventional stock chart (and being aware of time decay) tells the whole, complete, story. Another reason historical option prices are not used in TA is the option bid-ask spread. For most stocks, the difference between the bid and the ask is equal to a very small percentage of the stock’s price. Because options are highly leveraged instruments, their bid-ask width can equal a much higher percentage of the price. If a trader uses the last trade to graph an option’s price, it could look as if a very large percentage move has occurred when in fact it has not. For example, if the option trades a small contract size on the bid (0.80), then on the offer (0.90) it would appear that the option rose 12.5 percent in value. This large percentage move is nothing more than market noise. Using volatility data based off the midpoint-of-the-market theoretical value eliminates such noise. Fundamental Analysis Fundamental analysis can have an important role in developing expectations for IV. Fundamental analysis is the study of economic factors that affect the value of an asset in order to determine what it is worth. With stocks, fundamental analysis may include studying income statements, balance sheets, and earnings reports. When the asset being studied is IV, there are fewer hard facts available. This is where the art of analyzing volatility comes into play. Essentially, the goal is to understand the psychology of the market in relation to supply and demand for options. Where is the fear? Where is the complacency? When are news events anticipated? How important are they? Ultimately, the question becomes: what is the potential for movement in the underlying? The greater the chance of stock movement, the more likely it is that IV will rise. When unexpected news is announced, IV can rise quickly. The determination of the fundamental relevance of surprise announcements must be made quickly. Unfortunately, these questions are subjective in nature. They require the trader to apply intuition and experience on a case-by-case basis. But there ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:119 SCORE: 19.50 ================================================================================ are a few observations to be made that can help a trader make better- educated decisions about IV. Reversion to the Mean The IVs of the options on many stocks and indexes tend to trade in a range unique to those option classes. This is referred to as the mean—or average —volatility level. Some securities will have smaller mean IV ranges than others. The range being observed should be established for a period long enough to confirm that it is a typical IV for the security, not just a temporary anomaly. Traders should study IV over the most recent 6-month period. When IV has changed significantly during that period, a 12-month study may be necessary. Deviations from this range, either above or below the established mean range, will occur from time to time. When following a breakout from the established range, it is common for IV to revert back to its normal range. This is commonly called reversion to the mean among volatility watchers. The challenge is recognizing when things change and when they stay the same. If the fundamentals of the stock change in such a way as to give the options market reason to believe the stock will now be more or less volatile on an ongoing basis than it typically has been in the recent past, the IV may not revert to the mean. Instead, a new mean volatility level may be established. When considering the likelihood of whether IV will revert to recent levels after it has deviated or find a new range, the time horizon and changes in the marketplace must be taken into account. For example, between 1998 and 2003 the mean volatility level of the SPX was around 20 percent to 30 percent. By the latter half of 2006, the mean IV was in the range of 10 percent to 13 percent. The difference was that between 1998 and 2003 was the buildup of “the tech bubble,” as it was called by the financial media. Market volatility ultimately leveled off in 2003. In a later era, between the fall of 2010 and late summer of 2011 SPX implied volatility settled in to trade mostly between 12 and 20 percent. But in August 2011, as the European debt crisis heated up, a new, more volatile range between 24 and 40 percent reigned for some time. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:121 SCORE: 27.50 ================================================================================ CBOE Volatility Index ® Often traders look to the implied volatility of the market as a whole for guidance on the IV of individual stocks. Traders use the Chicago Board Options Exchange (CBOE) Volatility Index® , or VIX® , as an indicator of overall market volatility. When people talk about the market, they are talking about a broad-based index covering many stocks on many diverse industries. Usually, they are referring to the S&P 500. Just as the IV of a stock may offer insight about investors’ feelings about that stock’s future volatility, the volatility of options on the S&P 500—SPX options—may tell something about the expected volatility of the market as a whole. VIX is an index published by the Chicago Board Options Exchange that measures the IV of a hypothetical 30-day option on the SPX. A 30-day option on the SPX only truly exists once a month—30 days before expiration. CBOE computes a hypothetical 30-day option by means of a weighted average of the two nearest-term months. When the S&P 500 rises or falls, it is common to see individual stocks rise and fall in sympathy with the index. Most stocks have some degree of market risk. When there is a perception of higher risk in the market as a whole, there can consequently be a perception of higher risk in individual stocks. The rise or fall of the IV of SPX can translate into the IV of individual stocks rising or falling. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:122 SCORE: 23.50 ================================================================================ Implied Volatility and Direction Who’s afraid of falling stock prices? Logically, declining stocks cause concern for investors in general. There is confirmation of that statement in the options market. Just look at IV. With most stocks and indexes, there is an inverse relationship between IV and the underlying price. Exhibit 3.2 shows the SPX plotted against its 30-day IV, or the VIX. EXHIBIT 3.2 SPX vs. 30-day IV (VIX). The heavier line is the SPX, and the lighter line is the VIX. Note that as the price of SPX rises, the VIX tends to decline and vice versa. When the market declines, the demand for options tends to increase. Investors hedge by buying puts. Traders speculate on momentum by buying puts and speculate on a turnaround by buying calls. When the market moves higher, investors tend to sell their protection back and write covered calls or cash- secured puts. Option speculators initiate option-selling strategies. There is less fear when the market is rallying. This inverse relationship of IV to the price of the underlying is not unique to the SPX; it applies to most individual stocks as well. When a stock ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:124 SCORE: 20.50 ================================================================================ Calculating Volatility Data Accurate data are essential for calculating volatility. Many of the volatility data that are readily available are useful, but unfortunately, some are not. HV is a value that is easily calculated from publicly accessible past closing prices of a stock. It’s rather straightforward. Traders can access HV from many sources. Retail traders often have access to HV from their brokerage firm. Trading firms or clearinghouses often provide professional traders with HV data. There are some excellent online resources for HV as well. HV is a calculation with little subjectivity—the numbers add up how they add up. IV, however, can be a bit more ambiguous. It can be calculated different ways to achieve different desired outcomes; it is user-centric. Most of the time, traders consider the theoretical value to be between the bid and the ask prices. On occasion, however, a trader will calculate IV for the bid, the ask, the last trade price, or, sometimes, another value altogether. There may be a valid reason for any of these different methods for calculating IV. For example, if a trader is long volatility and aspires to reduce his position, calculating the IV for the bid shows him what IV level can be sold to liquidate his position. Firms, online data providers, and most options-friendly brokers offer IV data. Past IV data is usually displayed graphically in what is known as a volatility chart or vol chart. Current IV is often displayed along with other data right in the option chain. One note of caution: when the current IV is displayed, however, it should always be scrutinized carefully. Was the bid used in calculating this figure? What about the ask? How long ago was this calculation made? There are many questions that determine the accuracy of a current IV, and rarely are there any answers to support the number. Traders should trust only IV data they knowingly generated themselves using a pricing model. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:126 SCORE: 28.50 ================================================================================ Term Structure of Volatility Term structure of volatility—also called monthly skew or horizontal skew —is the relationship among the IVs of options in the same class with the same strike but with different expiration months. IV, again, is often interpreted as the market’s estimate of future volatility. It is reasonable to assume that the market will expect some months to be more volatile than others. Because of this, different expiration cycles can trade at different IVs. For example, if a company involved in a major product-liability lawsuit is expecting a verdict on the case to be announced in two months, the one- month IV may be low, as the stock is not expected to move much until the suit is resolved. The two-month volatility may be much higher, however, reflecting the expectations of a big move in the stock up or down, depending on the outcome. The term structure of volatility also varies with the normal ebb and flow of volatility within the business cycle. In periods of declining volatility, it is common for the month with the least amount of time until expiration, also known as the front month, to trade at a lower volatility than the back months, or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have a higher IV than the back months. Exhibit 3.3 shows historical option prices and their corresponding IVs for 32.5-strike calls on General Motors (GM) during a period of low volatility. EXHIBIT 3.3 GM term structure of volatility. In this example, no major news is expected to be released on GM, and overall market volatility is relatively low. The February 32.5 call has the lowest IV, at 32 percent. Each consecutive month has a higher IV than the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:127 SCORE: 35.50 ================================================================================ previous month. A graduated increasing or decreasing IV for each consecutive expiration cycle is typical of the term structure of volatility. Under normal circumstances, the front month is the most sensitive to changes in IV. There are two reasons for this. First, front-month options are typically the most actively traded. There is more buying and selling pressure. Their IV is subject to more activity. Second, vegas are smaller for options with fewer days until expiration. This means that for the same monetary change in an option’s value, the IV needs to move more for short- term options. Exhibit 3.4 shows the same GM options and their corresponding vegas. EXHIBIT 3.4 GM vegas. If the value of the September 32.5 calls increases by $0.10, IV must rise by 1 percentage point. If the February 32.5 calls increase by $0.10, IV must rise 3 percentage points. As expiration approaches, the vega gets even smaller. With seven days until expiration, the vega would be about 0.014. This means IV would have to change about 7 points to change the call value $0.10. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:128 SCORE: 66.00 ================================================================================ Vertical Skew The second type of skew found in option IV is vertical skew, or strike skew. Vertical skew is the disparity in IV among the strike prices within the same month for an option class. The options on most stocks and indexes experience vertical skew. As a general rule, the IV of downside options— calls and puts with strike prices lower than the at-the-money (ATM) strike —trade at higher IVs than the ATM IV. The IV of upside options—calls and puts with strike prices higher than the ATM strike—typically trade at lower IVs than the ATM IV. The downside is often simply referred to as puts and the upside as calls. The rationale for this lingo is that OTM options (puts on the downside and calls on the upside) are usually more actively traded than the ITM options. By put-call parity, a put can be synthetically created from a call, and a call can be synthetically created from a put simply by adding the appropriate long or short stock position. Exhibit 3.5 shows the vertical skew for 86-day options on Citigroup Inc. (C) on a typical day, with IVs rounded to the nearest tenth. EXHIBIT 3.5 Citigroup vertical skew. Notice the IV of the puts (downside options) is higher than that of the calls (upside options), with the 31 strike’s volatility more than 10 points higher than that of the 38 strike. Also, the difference in IV per unit change ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:129 SCORE: 51.00 ================================================================================ in the strike price is higher for the downside options than it is for the upside ones. The difference between the IV of the 31 strike is 2 full points higher than the 32 strike, which is 1.8 points higher than the 33 strike. But the 36 strike’s IV is only 1.1 points higher than the 37 strike, which is also just 1.1 points higher than the 38 strike. This incremental difference in the IV per strike is often referred to as the slope. The puts of most underlyings tend to have a greater slope to their skew than the calls. Many models allow values to be entered for the upside slope and the downside slope that mathematically increase or decrease IVs of each strike incrementally. Some traders believe the slope should be a straight line, while others believe it should be an exponentially sloped line. If the IVs were graphed, the shape of the skew would vary among asset classes. This is sometimes referred to as the volatility smile or sneer, depending on the shape of the IV skew. Although Exhibit 3.5 is a typical paradigm for the slope for stock options, bond options and other commodity options would have differently shaped skews. For example, grain options commonly have calls with higher IVs than the put IVs. Volatility skew is dependent on supply and demand. Greater demand for downside protection may cause the overall IV to rise, but it can cause the IV of puts to rise more relative to the calls or vice versa. There are many traders who make their living trading volatility skew. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:132 SCORE: 24.00 ================================================================================ Long ATM Call Kim is a trader who is bullish on the Walt Disney Company (DIS) over the short term. The time horizon of her forecast is three weeks. Instead of buying 100 shares of Disney at $35.10 per share, Kim decides to buy one Disney March 35 call at $1.10. In this example, March options have 44 days until expiration. How can Kim profit from this position? How can she lose? Exhibit 4.1 shows the profit and loss (P&(L)) for the call at different time periods. The top line is when the trade is executed; the middle, dotted line is after three weeks have passed; and the bottom, darker line is at expiration. Kim wants Disney to rise in price, which is evident by looking at the graph for any of the three time horizons. She would anticipate a loss if the stock price declines. These expectations are related to the position’s delta, but that is not the only risk exposure Kim has. As indicated by the three different lines in Exhibit 4.1 , the call loses value over time. This is called theta risk . She has other risk exposure as well. Exhibit 4.2 lists the greeks for the DIS March 35 call. EXHIBIT 4.1 P&(L) of Disney 35 call. EXHIBIT 4.2 Greeks for 35 Disney call. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:133 SCORE: 47.50 ================================================================================ Delta 0.57 Gamma0.166 Theta −0.013 Vega 0.048 Rho 0.023 Kim’s immediate directional exposure is quantified by the delta, which is 0.57. Delta is immediate directional exposure because it’s subject to change by the amount of the gamma. The positive gamma of this position helps Kim by increasing the delta as Disney rises and decreasing it as it falls. Kim, however, has time working against her—theta. At this point, she theoretically loses $0.013 per day. Since her call is close to being at-the- money, she would anticipate her theta becoming more negative as expiration approaches if Disney’s share price remains unchanged. She also has positive vega exposure. A one-percentage-point increase in implied volatility (IV) earns Kim just under $0.05. A one-point decrease costs her about $0.05. With so few days until expiration, the 35-strike call has very little rho exposure. A full one-percentage-point change in the interest rate changes her call’s value by only $0.023. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:134 SCORE: 46.00 ================================================================================ Delta Some of Kim’s risks warrant more concern than others. With this position, delta is of the greatest concern, followed by theta. Kim expects the call to rise in value and accepts the risk of decline. Delta exposure was her main rationale for establishing the position. She expects to hold it for about three weeks. Kim is willing to accept the trade-off of delta exposure for theta, which will cost her three weeks of erosion of option premium. If the anticipated delta move happens sooner than expected, Kim will have less decay. Exhibit 4.3 shows the value of her 35 call at various stock prices over time. The left column is the price of Disney. The top row is the number of days until expiration. EXHIBIT 4.3 Disney 35 call price–time matrix–value. The effect of delta is evident as the stock rises or falls. When the position is established (44 days until expiration), the change in the option price if the stock were to move from $35 to $36 is 0.62 (1.66 − 1.04). Between stock prices of $36 and $37, the option gains 0.78 (2.44 −1.66). If the stock were to decline in value from $35 to $34, the option loses 0.47 (1.04 − 0.57). The option gains value at a faster rate as the stock rises and loses value at a slower rate as the stock falls. This is the effect of gamma. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:136 SCORE: 31.00 ================================================================================ Theta Option buying is a veritable race against the clock. With each passing day, the option loses theoretical value. Refer back to Exhibit 4.3 . When three weeks pass and the time to expiration decreases from 44 days to 23, what happens to the call value? If the stock price stays around its original level, theta will be responsible for a loss of about 30 percent of the premium. If Disney is at $35 with 23 days to expiration, the call will be worth $0.73. With a big enough move in either direction, however, theta matters much less. With 23 days to expiration and Disney at $39, there is only 0.12 of time value—the premium paid over parity for the option. At that point, it is almost all delta exposure. Similarly, if the Disney stock price falls after three weeks to $33, the call will have only 0.10 of time value. Time decay is the least of Kim’s concerns if the stock makes a big move. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:137 SCORE: 49.50 ================================================================================ Vega After delta and theta, vega is the next most influential contributor to Kim’s profit or peril. With Disney at $35.10, the 1.10 premium for the 35-strike call represents $1 of time value—all of which is vulnerable to changes in IV. The option’s 1.10 value returns an IV of about 19 percent, given the following inputs: Stock: $35.10 Strike: 35 Days to expiration: 44 Interest: 5.25 percent No dividend paid during this period Consequently, the vega is 0.048. What does the 0.048 vega tell Kim? Given the preceding inputs, for each point the IV rises or falls, the option’s value gains or loses about $0.05. Some of the inputs, however, will change. Kim anticipates that Disney will rise in price. She may be right or wrong. Either way, it is unlikely that the stock will remain exactly at $35.10 to option expiration. The only certainty is that time will pass. Both price and time will change Kim’s vega exposure. Exhibit 4.5 shows the changing vega of the 35 call as time and the underlying price change. EXHIBIT 4.5 Disney 35 call price–time matrix–vega. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:138 SCORE: 38.00 ================================================================================ When comparing Exhibit 4.5 to Exhibit 4.3 , it’s easy to see that as the time value of the option declines, so does Kim’s exposure to vega. As time passes, vega gets smaller. And as the call becomes more in- or out-of-the- money, vega gets smaller. Since she plans to hold the position for around three weeks, she is not concerned about small fluctuations in IV in the interim. If indeed the rise in price that Kim anticipates comes to pass, vega becomes even less of a concern. With 23 days to expiration and DIS at $37, the call value is 2.21. The vega is $0.018. If IV decreases as the stock price rises—a common occurrence—the adverse effect of vega will be minimal. Even if IV declines by 5 points, to a historically low IV for DIS, the call loses less than $0.10. That’s less than 5 percent of the new value of the option. If dividend policy changes or the interest rate changes, the value of Kim’s call will be affected as well. Dividends are often fairly predictable. However, a large unexpected dividend payment can have a significant adverse impact on the value of the call. For example, if a surprise $3 dividend were announced, owning the stock would become greatly preferable to owning the call. This preference would be reflected in the call premium. This is a scenario that an experienced trader like Kim will realize is a possibility, although not a probability. Although she knows it can ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:140 SCORE: 15.00 ================================================================================ Rho For all intents and purposes, rho is of no concern to Kim. In recent years, interest rate changes have not been a major issue for option traders. In the Alan Greenspan years of Federal Reserve leadership, changes in the interest rate were usually announced at the regularly scheduled Federal Open Market Committee (FOMC) meetings, with but a few exceptions. Ben Bernanke, likewise, changed interest rates fairly predictably, when he made any rate changes at all. In these more stable periods, if there is no FOMC meeting scheduled during the life of the call, it’s unlikely that rates will change. Even if they do, the rho with 44 days to expiration is only 0.023. This means that if rates change by a whole percentage point—which is four times the most common incremental change—the call value will change by a little more than $0.02. In this case, this is an acceptable risk. With 23 days to expiration, the ATM 35 call has a rho of only 0.011. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:141 SCORE: 35.00 ================================================================================ Tweaking Greeks With this position, some risks are of greater concern than others. Kim may want more exposure to some greeks and less to others. What if she is concerned that her forecasted price increase will take longer than three weeks? She may want less exposure to theta. What if she is particularly concerned about a decline in IV? She may want to decrease her vega. Conversely, she may believe IV will rise and therefore want to increase her vega. Kim has many ways at her disposal to customize her greeks. All of her alternatives come with trade-offs. She can buy more calls, increasing her greek positions in exact proportion. She can buy or sell stock or options against her call, creating a spread. The simplest way to alter her exposure to option greeks is to choose a different call to buy. Instead of buying the ATM call, Kim can buy a call with a different relationship to the current stock price. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:142 SCORE: 81.50 ================================================================================ Long OTM Call Kim can reduce her exposure to theta and vega by buying an OTM call. The trade-off here is that she also reduces her immediate delta exposure. Depending on how much Kim believes Disney will rally, this may or may not be a viable trade-off. Imagine that instead of buying one Disney March 35 call, Kim buys one Disney March 37.50 call, for 0.20. There are a few observations to be made about this alternative position. First, the net premium, and therefore overall risk, is much lower, 0.20 instead of 1.10. From an expiration standpoint, the breakeven at expiration is $37.70 (the strike price plus the call premium). Since Kim plans on exiting the position after about three weeks, the exact break-even point at the expiration of the contract is irrelevant. But the concept is the same: the stock needs to rise significantly. Exhibit 4.6 shows how Kim’s concerns translate into greeks. EXHIBIT 4.6 Greeks for Disney 35 and 37.50 calls. 35 Call37.50 Call Delta 0.57 0.185 Gamma0.1660.119 Theta −0.013−0.007 Vega 0.0480.032 Rho 0.0230.007 This table compares the ATM call with the OTM call. Kim can reduce her theta to half that of the ATM call position by purchasing an OTM. This is certainly a favorable difference. Her vega is lower with the 37.50 call, too. This may or may not be a favorable difference. That depends on Kim’s opinion of IV. On the surface, the disparity in delta appears to be a highly unfavorable trade-off. The delta of the 37.50 call is less than one third of the delta of the 35 call, and the whole motive for entering into this trade is to trade direction! Although this strategy is very delta oriented, its core is more focused on gamma and theta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:143 SCORE: 95.00 ================================================================================ The gamma of the 37.50 call is about 72 percent that of the 35 call. But the theta of the 37.50 call is about half that of the 35 call. Kim is improving her gamma/theta relationship by buying the OTM, but with the call being so far out-of-the-money and so inexpensive, the theta needs to be taken with a grain of salt. It is ultimately gamma that will make or break this delta play. The price of the option is 0.20—a rather low premium. In order for the call to gain in value, delta has to go to work with help from gamma. At this point, the delta is small, only 0.185. If Kim’s forecast is correct and there is a big move upward, gamma will cause the delta to increase, and therefore also the premium to increase exponentially. The call’s sensitivity to gamma, however, is dynamic. Exhibit 4.7 shows how the gamma of the 37.50 call changes as the stock price moves over time. At any point in time, gamma is highest when the call is ATM. However, so is theta. Kim wants to reap as much benefit from gamma as possible while minimizing her exposure to theta. Ideally, she wants Disney to rally through the strike price—through the high gamma and back to the low theta. After three weeks pass, with 23 days until expiration, if Disney is at $37 a share, the gamma almost doubles, to 0.237. When the call is ATM, the delta increases at its fastest rate. As Disney rises above the strike, the gamma figures in the table begin to decline. EXHIBIT 4.7 Disney 37.50 call price–time matrix–gamma. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:144 SCORE: 44.00 ================================================================================ Gamma helps as the stock price declines, too. Exhibit 4.8 shows the effect of time and gamma on the delta of the 37.50 call. EXHIBIT 4.8 Disney 37.50 call price–time matrix–delta. The effect of gamma is readily observable, as the delta at any point in time is always higher at higher stock prices and lower at lower stock prices. Kim benefits greatly when the delta grows from its initial level of 0.185 to above 0.50—above the point of being at-the-money. If the stock moves lower, gamma helps take away the pain of the price decline by decreasing the delta. While delta, gamma, and theta occupy Kim’s thoughts, it is ultimately dollars and cents that matter. She needs to translate her study of the greeks into cold, hard cash. Exhibit 4.9 shows the theoretical values of the 37.50 call. EXHIBIT 4.9 Disney 37.50 call price–time matrix–value. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:145 SCORE: 25.00 ================================================================================ The sooner the price rise occurs, the better. It means less time for theta to eat away profits. If Kim must hold the position for the entire three weeks, she needs a good pop in the stock to make it worth her while. At a $37 share price, the call is worth about 0.50, assuming all other market influences remain constant. That’s about a 150 percent profit. At $38, Exhibit 4.9 reveals the call value to be 1.04. That’s a 420 percent profit. On one hand, it’s hard for a trader like Kim not to get excited about the prospect of making 420 percent on an 8 percent move in a stock. On the other hand, Kim has to put things in perspective. When the position is established, the call has a 0.185 delta. By the trader’s definition of delta, that means the call is estimated to have about an 18.5 percent chance of expiring in-the-money. More than four out of five times, this position will be trading below the strike at expiration. Although Kim is not likely to hold the position until expiration, this observation tells her something: she’s starting in the hole. She is more likely to lose than to win. She needs to be compensated well for her risk on the winners to make up for the more prevalent losers. Buying OTM calls can be considered more speculative than buying ITM or ATM calls. Unlike what the at-expiration diagrams would lead one to believe, OTM calls are not simply about direction. There’s a bit more to it. They are really about gamma, time, and the magnitude of the stock’s move ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:147 SCORE: 66.00 ================================================================================ Long ITM Call Kim also has the alternative to buy an ITM call. Instead of the 35 or 37.50 call, she can buy the 32.50. The 32.50 call shares some of the advantages the 37.50 call has over the 35 call, but its overall greek characteristics make it a very different trade from the two previous alternatives. Exhibit 4.10 shows a comparison of the greeks of the three different calls. EXHIBIT 4.10 Greeks for Disney 32.50, 35, and 37.50 calls. Like the 37.50 call, the 32.50 has a lower gamma, theta, and vega than the ATM 35-strike call. Because the call is ITM, it has a higher delta: 0.862. In this example, Kim can buy the 32.50 call for 3. That’s 0.40 over parity (3 − [35.10 − 32.50] = 0.40). There is not much time value, but more than the 37.50 call has. Thus, theta is of some concern. Ultimately, the ITMs have 0.40 of time value to lose compared with the 0.20 of the OTM calls. Vega is also of some concern, but not as much as in the other alternatives because the vega of the 32.50 is lower than the 35s or the 37.50s. Gamma doesn’t help much as the stock rallies—it will get smaller as the stock price rises. Gamma will, however, slow losses somewhat if the stock declines by decreasing delta at an increasing rate. In this case, the greek of greatest consequence is delta—it is a more purely directional play than the other alternatives discussed. Exhibit 4.11 shows the matrix of the delta of the 32.50 call. EXHIBIT 4.11 Disney 32.50 call price–time matrix–delta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:150 SCORE: 58.00 ================================================================================ Long ATM Put The beauty of the free market is that two people can study all the available information on the same stock and come up with completely different outlooks. First of all, this provides for entertaining television on the business-news channels when the network juxtaposes an outspoken bullish analyst with an equally unreserved bearish analyst. But differing opinions also make for a robust marketplace. Differing opinions are the oil that greases the machine that is price discovery. From a market standpoint, it’s what makes the world go round. It is possible that there is another trader, Mick, in the market studying Disney, who arrives at the conclusion that the stock is overpriced. Mick believes the stock will decline in price over the next three weeks. He decides to buy one Disney March 35 put at 0.80. In this example, March has 44 days to expiration. Mick initiates this long put position to gain downside exposure, but along with his bearish position comes option-specific risk and opportunity. Mick is buying the same month and strike option as Kim did in the first example of this chapter: the March 35 strike. Despite the different directional bias, Mick’s position and Kim’s position share many similarities. Exhibit 4.13 offers a comparison of the greeks of the Disney March 35 call and the Disney March 35 put. EXHIBIT 4.13 Greeks for Disney 35 call and 35 put. Call Put Delta 0.57 −0.444 Gamma0.1660.174 Theta −0.013−0.009 Vega 0.0480.048 Rho 0.023−0.015 The first comparison to note is the contrasting deltas. The put delta is negative, in contrast to the call delta. The absolute value of the put delta is close to 1.00 minus the call delta. The put is just slightly OTM, so its delta ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:151 SCORE: 47.00 ================================================================================ is just under 0.50, while that of the call is just over 0.50. The disparate, yet related deltas represent the main difference between these two trades. The difference between the gamma of the 35 put and that of the corresponding call is fairly negligible: 0.174 versus 0.166, respectively. The gamma of this ATM put will enter into the equation in much the same way as the gamma of the ATM call. The put’s negative delta will become more negative as the stock declines, drawing closer to −1.00. It will get less negative as the stock price rises, drawing closer to zero. Gamma is important here, because it helps the delta. Delta, however, still remains the most important greek. Exhibit 4.14 illustrates how the 35 put delta changes as time and price change. EXHIBIT 4.14 Disney 35 put price–time matrix–delta. Since this put is ATM, it starts out with a big enough delta to offer the directional exposure Mick desires. The delta can change, but gamma ensures that it always changes in Mick’s favor. Exhibit 4.15 shows how the value of the 35 put changes with the stock price. EXHIBIT 4.15 Disney 35 put price–time matrix–value. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:152 SCORE: 42.00 ================================================================================ Over time, a decline of only 10 percent in the stock yields high percentage returns. This is due to the leveraged directional nature of this trade—delta. While the other greeks are not of primary concern, they must be monitored. At the onset, the 0.80 premium is all time value and, therefore subject to the influences of time decay and volatility. This is where trading greeks comes into play. Conventional trading wisdom says, “Cut your losses early, and let your profits run.” When trading a stock, that advice is intellectually easy to understand, although psychologically difficult to follow. Buyers of options, especially ATM options, must follow this advice from the standpoint of theta. Options are decaying assets. The time premium will be zero at expiration. ATMs decay at an increasing nonlinear rate. Exiting a long position before getting too close to expiration can cut losses caused by an increasing theta. When to cut those losses, however, will differ from trade to trade, situation to situation, and person to person. When buying options, accepting some loss of premium due to time decay should be part of the trader’s plan. It comes with the territory. In this example, Mick is willing to accept about three weeks of erosion. Mick needs to think about what his put will be worth, not just if the underlying rises or falls but also if it doesn’t move at all. At the time the position is ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:153 SCORE: 60.00 ================================================================================ established, the theta is 0.009, just under a penny. If Disney share price is unchanged when three weeks pass, his theta will be higher. Exhibit 4.16 shows how thetas and theoretical values change over time if DIS stock remains at $35.10. EXHIBIT 4.16 Disney 35 put—thetas and theoretical values. Mick needs to be concerned not only about what the theta is now but what it will be when he plans on exiting the position. His plan is to exit the trade in about three weeks, at which point the put theta will be −0.013. If he amortizes his theta over this three-week period, he theoretically loses an average of about 0.01 a day during this time if nothing else changes. The average daily theta is calculated here by subtracting the value of the put at 23 days to expiration from its value when the trade was established to find the loss of premium attributed to time decay, then dividing by the number of days until expiration. Since the theta doesn’t change much over the first three weeks, Mick can eyeball the theta rather easily. As expiration approaches and theta begins to grow more quickly, he’ll need to do the math. At nine days to expiration, the theoretical value of Mick’s put is about 0.35, assuming all other variables are held constant. By that time, he will have lost 0.45 (0.80 − 0.35) due to erosion over the 35-day period he held the position if the stock hasn’t moved. Mick’s average daily theta during that period is about 0.0129 (0.45 ÷ 35). The more time he holds the trade, the greater a concern is theta. Mick must weigh his assessment of the likelihood of the option’s gaining value from delta against the risk of erosion. If he holds the trade for 35 days, he must make 0.0129 on average per day from delta to offset theta losses. If the forecast is not realized within the expected time frame or if the forecast changes, Mick needs to act fast to curtail average daily theta losses. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:154 SCORE: 108.00 ================================================================================ Finding the Right Risk Mick could lower the theta of his position by selecting a put with a greater number of days to expiration. This alternative has its own set of trade-offs: lower gamma and higher vega than the 44-day put. He could also select an ITM put or an OTM put. Like Kim’s call alternatives, the OTM put would have less exposure to time decay, lower vega, lower gamma, and a lower delta. It would have a lower premium, too. It would require a bigger price decline than the ATM put and would be more speculative. The ITM put would also have lower theta, vega, and gamma, but it would have a higher delta. It would take on more of the functionality of a short stock position in much the same way that Kim’s ITM call alternative did for a long stock position. In its very essence, however, an option trade, ITM or otherwise, is still fundamentally different than a stock trade. Stock has a 1.00 delta. The delta of a stock never changes, so it has zero gamma. Stock is not subject to time decay and has no volatility component to its pricing. Even though ITM options have deltas that approach 1.00 and other greeks that are relatively low, they have two important differences from an equity. The first is that the greeks of options are dynamic. The second is the built-in leverage feature of options. The relationship of an option’s strike price to the stock price can change constantly. Options that are ITM now may be OTM tomorrow and vice versa. Greeks that are not in play at the moment may be later. Even if there is no time value in the option now because it is so far away-from-the- money, there is the potential for time premium to become a component of the option’s price if the stock moves closer to the strike price. Gamma, theta, and vega always have the potential to come into play. Since options are leveraged by nature, small moves in the stock can provide big profits or big losses. Options can also curtail big losses if used for hedging. Long option positions can reap triple-digit percentage gains quickly with a favorable move in the underlying. Even though 100 percent of the premium can be lost just as easily, one option contract will have far less nominal exposure than a similar position in the stock. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:155 SCORE: 109.00 ================================================================================ It’s All About Volatility What are Kim and Mick really trading? Volatility. The motivation for buying an option as opposed to buying or shorting the stock is volatility. To some degree, these options have exposure to both flavors of volatility— implied volatility and historical volatility (HV). The positions in each of the examples have positive vega. Their values are influenced, in part, by IV. Over time, IV begins to lose its significance if the option is no longer close to being at-the-money. The main objective of each of these trades is to profit from the volatility of the stock’s price movement, called future stock volatility or future realized volatility. The strategies discussed in this chapter are contingent on volatility being one directional. The bigger the move in the trader’s forecasted direction the better. Volatility in the form of an adverse directional move results in a decline in premium. The gamma in these long option positions makes volatility in the right direction more beneficial and volatility in the wrong direction less costly. This phenomenon is hardly unique to the long call and the long put. Although some basic strategies, such as the ones studied in this chapter, depend on a particular direction, many don’t. Except for interest rate strategies and perhaps some arbitrage strategies, all option trades are volatility trades in one way or another. In general, option strategies can be divided into two groups: volatility-buying strategies and volatility-selling strategies. The following is a breakdown of common option strategies into categories of volatility-buying strategies and volatility-selling strategies: Volatility-Selling Strategies Volatility-Buying Strategies Short Call, Short Put, Covered Call, Covered Put, Bull Call Spread, Bear Call Spread, Bull Put Spread, Bear Put Spread, Short Straddle, Short Strangle, Guts, Ratio Call Spread, Calendar, Butterfly, Iron Butterfly, Broken-Wing Butterfly, Condor, Iron Condor, Diagonals, Double Diagonals, Risk Reversals/Collars. Long Call, Long Put, Bull Call Spread, Bear Call Spread, Bull Put Spread, Bear Put Spread, Long Straddle, Long Strangle, Guts, Back Spread, Calendar, Butterfly, Iron Butterfly, Broken-Wing Butterfly, Condor, Iron Condor, Diagonals, Double Diagonals, Risk Reversals/Collars. Long option strategies appear in the volatility-buying group because they have positive gamma and positive vega. Short option strategies appear in ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:157 SCORE: 19.00 ================================================================================ Direction Neutral, Direction Biased, and Direction Indifferent As typically traded, volatility-selling option strategies are direction neutral. This means that the position has the greatest results if the underlying price remains in a range—that is, neutral. Although some option-selling strategies —for example, a naked put—may have a positive or negative delta in the short term, profit potential is decidedly limited. This means that if traders are expecting a big move, they are typically better off with option-buying strategies. Option-buying strategies can be either direction biased or direction indifferent. Direction-biased strategies have been shown throughout this chapter. They are delta trades. Direction-indifferent strategies are those that benefit from increased volatility in the underlying but where the direction of the move is irrelevant to the profitability of the trade. Movement in either direction creates a winner. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:158 SCORE: 29.00 ================================================================================ Are You a Buyer or a Seller? The question is: which is better, selling volatility or buying volatility? I have attended option seminars with instructors (many of whom I regard with great respect) teaching that volatility-selling strategies, or income- generating strategies, are superior to buying options. I also know option gurus that tout the superiority of buying options. The answer to the question of which is better is simple: it’s all a matter of personal preference. When I began trading on the floor of Chicago Board Options Exchange (CBOE) in the 1990s, I quickly became aware of a dichotomy among my market-making peers. Those making markets on the floor of the exchange at that time were divided into two groups: teenie buyers and teenie sellers. Teenie Buyers Before options traded in decimals (dollars and cents) like they do today, the lowest price increment in which an option could be traded was one sixteenth of a dollar—a teenie . Teenie buyers were market makers who would buy back OTM options at one sixteenth to eliminate short positions. They would sometimes even initiate long OTM option positions at a teenie, too. The focus of the teenie-buyer school of thought was the fact that long options have unlimited reward, while short options have unlimited risk. An option purchased so far OTM that it was offered at one sixteenth is unlikely to end up profitable, but it’s an inexpensive lottery ticket. At worst, the trader can only lose a teenie. Teenie buyers felt being short OTM options that could be closed by paying a sixteenth was an unreasonable risk. Teenie Sellers Teenie sellers, however, focused on the fact that options offered at one sixteenth were far enough OTM that they were very likely to expire worthless. This appears to be free money, unless the unexpected occurs, in which case potential losses can be unlimited. Teenie sellers would routinely save themselves $6.25 (one sixteenth of a dollar per contract representing 100 shares) by selling their long OTMs at a teenie to close the position. They sometimes would even initiate short OTM contracts at one sixteenth. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:159 SCORE: 10.00 ================================================================================ These long-option or short-option biases hold for other types of strategies as well. Volatility-selling positions, such as the iron condor, can be constructed to have limited risk. The paradigm for these strategies is they tend to produce winners more often than not. But when the position loses, the trader loses more than he would stand to profit if the trade worked out favorably. Herein lies the issue of preference. Long-option traders would rather trade Babe Ruth–style. For years, Babe Ruth was the record holder for the most home runs. At the same time, he was also the record holder for the most strikeouts. The born fighters that are option buyers accept the fact that they will have more strikeouts, possibly many more strikeouts, than winning trades. But the strategy dictates that the profit on one winner more than makes up for the string of small losers. Short-option traders, conversely, like to have everything cool and copacetic. They like the warm and fuzzy feeling they get from the fact that month after month they tend to generate winners. The occasional loser that nullifies a few months of profits is all part of the game. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:160 SCORE: 17.50 ================================================================================ Options and the Fair Game There may be a statistical advantage to buying stock as opposed to shorting stock, because the market has historically had a positive annualized return over the long run. A statistical advantage to being either an option buyer or an option seller, however, should not exist in the long run, because the option market prices IV. Assuming an overall efficient market for pricing volatility into options, there should be no statistical advantage to systematically buying or selling options. 1 Consider a game consisting of one six-sided die. Each time a one, two, or three is rolled, the house pays the player $1. Each time a four, five, or six is rolled, the house pays zero. What is the most a player would be willing to pay to play this game? If the player paid nothing, the house would be at a tremendous disadvantage, paying $1 50 percent of the time and nothing the other 50 percent of the time. This would not be a fair game from the house’s perspective, as it would collect no money. If the player paid $1, the player would get his dollar back when one, two, or three came up. Otherwise, he would lose his dollar. This is not a fair game from the player’s perspective. The chances of winning this game are 3 out of 6, or 50–50. If this game were played thousands of times, one would expect to receive $1 half the time and receive nothing the other half of the time. The average return per roll one would expect to receive would be $0.50, that’s ($1 × 50 percent + $0 × 50 percent). This becomes a fair game with an entrance fee of $0.50. Now imagine a similar game in which a six-sided die is rolled. This time if a one is rolled, the house pays $1. If any other number is rolled, the house pays nothing. What is a fair price to play this game? The same logic and the same math apply. There is a percent chance of a one coming up and the player receiving $1. And there is a percent chance of each of the other five numbers being rolled and the player receiving nothing. Mathematically, this translates to: percent percent). Fair value for a chance to play this game is about $0.1667 per roll. The fair game concept applies to option prices as well. The price of the game, or in this case the price of the option, is determined by the market in ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:163 SCORE: 26.00 ================================================================================ CHAPTER 5 An Introduction to Volatility-Selling Strategies Along with death and taxes, there is one other fact of life we can all count on: the time value of all options ultimately going to zero. What an alluring concept! In a business where expected profits can be thwarted by an unexpected turn of events, this is one certainty traders can count on. Like all certainties in the financial world, there is a way to profit from this fact, but it’s not as easy as it sounds. Alas, the potential for profit only exists when there is risk of loss. In order to profit from eroding option premiums, traders must implement option-selling strategies, also known as volatility-selling strategies. These strategies have their own set of inherent risks. Selling volatility means having negative vega—the risk of implied volatility rising. It also means having negative gamma—the risk of the underlying being too volatile. This is the nature of selling volatility. The option-selling trader does not want the underlying stock to move—that is, the trader wants the stock to be less volatile. That is the risk. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:166 SCORE: 50.00 ================================================================================ Greeks and Income Generation With volatility-selling strategies (sometimes called income-generating strategies), greeks are often overlooked. Traders simply dismiss greeks as unimportant to this kind of trade. There is some logic behind this reasoning. Time decay provides the profit opportunity. In order to let all of time premium erode, the position must be held until expiration. Interim changes in implied volatility are irrelevant if the position is held to term. The gamma-theta loses some significance if the position is held until expiration, too. The position has either passed the break-even point on the at-expiration diagram, or it has not. Incremental daily time decay–related gains are not the ultimate goal. The trader is looking for all the time premium, not portions of it. So why do greeks matter to volatility sellers? Greeks allow traders to be flexible. Consider short-term-momentum stock traders. The traders buy a stock because they believe it will rise over the next month. After one week, if unexpected bearish news is announced causing the stock to break through its support lines, the traders have a decision to make. Short-term speculative traders very often choose to cut their losses and exit the position early rather than risk a larger loss hoping for a recovery. Volatility-selling option traders are often faced with the same dilemma. If the underlying stays in line with the traders’ forecast, there is little to worry about. But if the environment changes, the traders have to react. Knowing the greeks for a position can help traders make better decisions if they plan to close the position before expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:167 SCORE: 17.00 ================================================================================ Naked Call A naked call is when a trader shorts a call without having stock or other options to cover or protect it. Since the call is uncovered, it is one of the riskier trades a trader can make. Recall the at-expiration diagram for the naked call from Chapter 1, Exhibit 1.3 : Naked TGT Call. Theoretically, there is limited reward and unlimited risk. Yet there are times when experienced traders will justify making such a trade. When a stock has been trading in a range and is expected to continue doing so, traders may wait until it is near the top of the channel, where there is resistance, and then short a call. For example, a trader, Brendan, has been studying a chart of Johnson & Johnson (JNJ). Brendan notices that for a few months the stock has trading been in a channel between $60 and $65. As he observes Johnson & Johnson beginning to approach the resistance level of $65 again, he considers selling a call to speculate on the stock not rising above $65. Before selling the call, Brendan consults other technical analysis tools, like ADX/DMI, to confirm that there is no trend present. ADX/DMI is used by some traders as a filter to determine the strength of a trend and whether the stock is overbought or oversold. In this case, the indicator shows no strong trend present. Brendan then performs due diligence. He studies the news. He looks for anything specific that could cause the stock to rally. Is the stock a takeover target? Brendan finds nothing. He then does earnings research to find out when they will be announced, which is not for almost two more months. Next, Brendan pulls up an option chain on his computer. He finds that with the stock trading around $64 per share, the market for the November 65 call (expiring in four weeks) is 0.66 bid at 0.68 offer. Brendan considers when Johnson & Johnson’s earnings report falls. Although recent earnings have seldom been a major concern for Johnson & Johnson, he certainly wants to sell an option expiring before the next earnings report. The November fits the mold. Brendan sells ten of the November 65 calls at the bid price of 0.66. Brendan has a rather straightforward goal. He hopes to see Johnson & Johnson shares remain below $65 between now and expiration. If he is ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:168 SCORE: 20.00 ================================================================================ right, he stands to make $660. If he is wrong? Exhibit 5.1 shows how Brendan’s calls hold up if they are held until expiration. EXHIBIT 5.1 Naked Johnson & Johnson call at expiration. Considering the risk/reward of this trade, Brendan is rightfully concerned about a big upward move. If the stock begins to rally, he must be prepared to act fast. Brendan must have an idea in advance of what his pain threshold is. In other words, at what price will he buy back his calls and take a loss if Johnson & Johnson moves adversely? He decides he will buy all 10 of his calls back at 1.10 per contract if the trade goes against him. (1.10 is an arbitrary price used for illustrative purposes. The actual price will vary, based on the situation and the risk tolerance of the trader. More on when to take profits and losses is discussed in future chapters.) He may choose to enter a good-till-canceled (GTC) stop-loss order to buy back his calls. Or he may choose to monitor the stock and enter the order when he sees the calls offered at 1.10—a mental stop order. What Brendan needs to know is: How far can the stock price advance before the calls are at 1.10? Brendan needs to examine the greeks of this trade to help answer this question. Exhibit 5.2 shows the hypothetical greeks for the position in this example. EXHIBIT 5.2 Greeks for short Johnson & Johnson 65 call (per contract). ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:169 SCORE: 67.00 ================================================================================ Delta −0.34 Gamma−0.15 Theta 0.02 Vega −0.07 The short call has a negative delta. It also has negative gamma and vega, but it has positive time decay (theta). As Johnson & Johnson ticks higher, the delta increases the nominal value of the call. Although this is not a directional trade per se, delta is a crucial element. It will have a big impact on Brendan’s expectations as to how high the stock can rise before he must take his loss. First, Brendan considers how much the option price can move before he covers. The market now is 0.66 bid at 0.68 offer. To buy back his calls at 1.10, they must be offered at 1.10. The difference between the offer now and the offer price at which Brendan will cover is 0.42 (that’s 1.10 − 0.68). Brendan can use delta to convert the change in the ask prices into a stock price change. To do so, Brendan divides the change in the option price by the delta. The −0.34 delta indicates that if JNJ rises $1.24, the calls should be offered at 1.10. Brendan takes note that the bid-ask spreads are typically 0.01 to 0.03 wide in near-term Johnson & Johnson options trading under 1.00. This is not necessarily the case in other option classes. Less liquid names have wider spreads. If the spreads were wider, Brendan would have more slippage. Slippage is the difference between the assumed trade price and the actual price of the fill as a product of the bid-ask spread. It’s the difference between theory and reality. If the bid-ask spread had a typical width of, say, 0.70, the market would be something more like 0.40 bid at 1.10 offer. In this case, if the stock moved even a few cents higher, Brendan could not buy his calls back at his targeted exit price of 1.10. The tighter markets provide lower transaction costs in the form of lower slippage. Therefore, there is more leeway if the stock moves adversely when there are tighter bid-ask option spreads. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:170 SCORE: 38.00 ================================================================================ But just looking at delta only tells a part of the story. In reality, the delta does not remain constant during the price rise in Johnson & Johnson but instead becomes more negative. Initially, the delta is −0.34 and the gamma is −0.15. After a rise in the stock price, the delta will be more negative by the amount of the gamma. To account for the entire effect of direction, Brendan needs to take both delta and gamma into account. He needs to estimate the average delta based on gamma during the stock price move. The formula for the change in stock price is Taking into account the effect of gamma as well as delta, Johnson & Johnson needs to rise only $1.01, in order for Brendan’s calls to be offered at his stop-loss price of 1.10. While having a predefined price point to cover in the event the underlying rises is important, sometimes traders need to think on their feet. If material news is announced that changes the fundamental outlook for the stock, Brendan will have to adjust his plan. If the news leads Brendan to become bullish on the stock, he should exit the trade at once, taking a small loss now instead of the bigger loss he would expect later. If the trader is uncertain as to whether to hold or close the position, the Would I Do It Now? rule is a useful rule of thumb. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:171 SCORE: 30.00 ================================================================================ Would I Do It Now? Rule To follow this rule, ask yourself, “If I did not already have this position, would I do it now? Would I establish the position at the current market prices, given the current market scenario?” If the answer is no, then the solution is simple: Exit the trade. For example, if after one week material news is released and Johnson & Johnson is trading higher, at $64.50 per share, and the November 65 call is trading at 0.75, Brendan must ask himself, based on the price of the stock and all known information, “If I were not already short the calls, would I short them now at the current price of 0.75, with the stock trading at $64.50?” Brendan’s opinion of the stock is paramount in this decision. If, for example, based on the news that was announced he is now bullish, he would likely not want to sell the calls at 0.75—he only gets $0.09 more in option premium and the stock is 0.50 closer to the strike. If, however, he is not bullish, there is more to consider. Theta can be of great use in decision making in this situation. As the number of days until expiration decreases and the stock approaches $65 (making the option more at-the-money), Brendan’s theta grows more positive. Exhibit 5.3 shows the theta of this trade as the underlying rises over time. EXHIBIT 5.3 Theta of Johnson & Johnson. When the position is first established, positive theta comforts Brendan by showing that with each passing day he gets a little closer to his goal—to have the 65 calls expire out-of-the-money (OTM) and reap a profit of the entire 66-cent premium. Theta becomes truly useful if the position begins to move against him. As Johnson & Johnson rises, the trade gets more ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:172 SCORE: 44.00 ================================================================================ precarious. His negative delta increases. His negative gamma increases. His goal becomes more out of reach. In conjunction with delta and gamma, theta helps Brendan decide whether the risk is worth the reward. In the new scenario, with the stock at $64.50, Brendan would collect $18 a day (1.80 × 10 contracts). Is the risk of loss in the short run worth earning $18 a day? With Johnson & Johnson at $64.50, would Brendan now short 10 calls at 0.75 to collect $18 a day, knowing that each day may bring a continued move higher in the stock? The answer to this question depends on Brendan’s assessment of the risk of the underlying continuing its ascent. As time passes, if the stock remains closer to the strike, the daily theta rises, providing more reward. Brendan must consider that as theta—the reward— rises, so does gamma: a risk factor. A small but noteworthy risk is that implied volatility could rise. The negative vega of this position would, then, adversely affect the profitability of this trade. It will make Brendan’s 1.10 cover-point approach faster because it makes the option more expensive. Vega is likely to be of less consequence because it would ultimately take the stock’s rising though the strike price for the trade to be a loser at expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:173 SCORE: 25.00 ================================================================================ Short Naked Puts Another trader, Stacie, has also been studying Johnson & Johnson. Stacie believes Johnson & Johnson is on its way to test the $65 resistance level yet again. She believes it may even break through $65 this time, based on strong fundamentals. Stacie decides to sell naked puts. A naked put is a short put that is not sold in conjunction with stock or another option. With the stock around $64, the market for the November 65 put is 1.75 bid at 1.80. Stacie likes the fact that the 65 puts are slightly in-the-money (ITM) and thus have a higher delta. If her price rise comes sooner than expected, the high delta may allow her to take a profit early. Stacie sells 10 puts at 1.75. In the best-case scenario, Stacie retains the entire 1.75. For that to happen, she will need to hold this position until expiration and the stock will have to rise to be trading above the 65 strike. Logically, Stacie will want to do an at-expiration analysis. Exhibit 5.4 shows Stacie’s naked put trade if she holds it until expiration. EXHIBIT 5.4 Naked Johnson & Johnson put at expiration. While harvesting the entire premium as a profit sounds attractive, if Stacie can take the bulk of her profit early, she’ll be happy to close the position and eliminate her risk—nobody ever went broke taking a profit. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:174 SCORE: 72.00 ================================================================================ Furthermore, she realizes that her outlook may be wrong: Johnson & Johnson may decline. She may have to close the position early—maybe for a profit, maybe for a loss. Stacie also needs to study her greeks. Exhibit 5.5 shows the greeks for this trade. EXHIBIT 5.5 Greeks for short Johnson & Johnson 65 put (per contract). Delta 0.65 Gamma−0.15 Theta 0.02 Vega −0.07 The first item to note is the delta. This position has a directional bias. This bias can work for or against her. With a positive 0.65 delta per contract, this position has a directional sensitivity equivalent to being long around 650 shares of the stock. That’s the delta × 100 shares × 10 contracts. Stacie’s trade is not just a bullish version of Brendan’s. Partly because of the size of the delta, it’s different—specific directional bias aside. First, she will handle her trade differently if it is profitable. For example, if over the next week or so Johnson & Johnson rises $1, positive delta and negative gamma will have a net favorable effect on Stacie’s profitability. Theta is small in comparison and won’t have too much of an effect. Delta/gamma will account for a decrease in the put’s theoretical value of about $0.73. That’s the estimated average delta times the stock move, or [0.65 + (–0.15/2)] × 1.00. Stacie’s actual profit would likely be less than 0.73 because of the bid-ask spread. Stacie must account for the fact that the bid-ask is 0.05 wide (1.75– 1.80). Because Stacie would buy to close this position, she should consider the 0.73 price change relative to the 1.80 offer, not the 1.75 trade price— that is, she factors in a nickel of slippage. Thus, she calculates, that the puts will be offered at 1.07 (that’s 1.80 − 0.73) when the stock is at $65. That is a gain of $0.68. In this scenario, Stacie should consider the Would I Do It Now? rule to guide her decision as to whether to take her profit early or hold the position until expiration. Is she happy being short ten 65 puts at 1.07 with Johnson & Johnson at $65? The premium is lower now. The anticipated move has already occurred, and she still has 28 days left in the option that could allow ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:175 SCORE: 35.00 ================================================================================ for the move to reverse itself. If she didn’t have the trade on now, would she sell ten 65 puts at 1.07 with Johnson & Johnson at $65? Based on her original intention, unless she believes strongly now that a breakout through $65 with follow-through momentum is about to take place, she will likely take the money and run. Stacie also must handle this trade differently from Brendan in the event that the trade is a loser. Her trade has a higher delta. An adverse move in the underlying would affect Stacie’s trade more than it would Brendan’s. If Johnson & Johnson declines, she must be conscious in advance of where she will cover. Stacie considers both how much she is willing to lose and what potential stock-price action will cause her to change her forecast. She consults a stock chart of Johnson & Johnson. In this example, we’ll assume there is some resistance developing around $64 in the short term. If this resistance level holds, the trade becomes less attractive. The at-expiration breakeven is $63.25, so the trade can still be a winner if Johnson & Johnson retreats. But Stacie is looking for the stock to approach $65. She will no longer like the risk/reward of this trade if it looks like that price rise won’t occur. She makes the decision that if Johnson & Johnson bounces off the $64 level over the next couple weeks, she will exit the position for fear that her outlook is wrong. If Johnson & Johnson drifts above $64, however, she will ride the trade out. In this example, Stacie is willing to lose 1.00 per contract. Without taking into account theta or vega, that 1.00 loss in the option should occur at a stock price of about $63.28. Theta is somewhat relevant here. It helps Stacie’s potential for profit as time passes. As time passes and as the stock rises, so will theta, helping her even more. If the stock moves lower (against her) theta helps ease the pain somewhat, but the further in-the-money the put, the lower the theta. Vega can be important here for two reasons: first, because of how implied volatility tends to change with market direction, and second, because it can be read as an indication of the market’s expectations. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:176 SCORE: 74.00 ================================================================================ The Double Whammy With the stock around $64, there is a negative vega of about seven cents. As the stock moves lower, away from the strike, the vega gets a bit smaller. However, the market conditions that would lead to a decline in the price of Johnson & Johnson would likely cause implied volatility (IV) to rise. If the stock drops, Stacie would have two things working against her—delta and vega—a double whammy. Stacie needs to watch her vega. Exhibit 5.6 shows the vega of Stacie’s put as it changes with time and direction. EXHIBIT 5.6 Johnson & Johnson 65 put vega. If after one week passes Johnson & Johnson gaps lower to, say, $63.00 a share, the vega will be 0.043 per contract. If IV subsequently rises 5 points as a result of the stock falling, vega will make Stacie’s puts theoretically worth 21.5 cents more per contract. She will lose $215 on vega (that’s 0.043 vega × 5 volatility points × 10 contracts) plus the adverse delta/gamma move. A gap opening will cause her to miss the opportunity to stop herself out at her target price entirely. Even if the stock drifts lower, her targeted stop-loss price will likely come sooner than expected, as the option price will likely increase both by delta/gamma and vega resulting from rising volatility. This can cause her to have to cover sooner, which leaves less room for error. With this trade, increases in IV due to market direction can make it feel as if the delta is greater than it actually is as the market declines. Conversely, IV softening makes it feel as if the delta is smaller than it is as the market rises. The second reason IV has importance for this trade (as for most other strategies) is that it can give some indication of how much the market thinks the stock can move. If IV is higher than normal, the market perceives there ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:177 SCORE: 29.00 ================================================================================ to be more risk than usual of future volatility. The question remains: Is the higher premium worth the risk? The answer to this question is subjective. Part of the answer is based on Stacie’s assessment of future volatility. Is the market right? The other part is based on Stacie’s risk tolerance. Is she willing to endure the greater price swings associated with the potentially higher volatility? This can mean getting whipsawed, which is exiting a position after reaching a stop-loss point only to see the market reverse itself. The would-be profitable trade is closed for a loss. Higher volatility can also mean a higher likelihood of getting assigned and acquiring an unwanted long stock position. Cash-Secured Puts There are some situations where higher implied volatility may be a beneficial trade-off. What if Stacie’s motivation for shorting puts was different? What if she would like to own the stock, just not at the current market price? Stacie can sell ten 65 puts at 1.75 and deposit $63,250 in her trading account to secure the purchase of 1,000 shares of Johnson & Johnson if she gets assigned. The $63,250 is the $65 per share she will pay for the stock if she gets assigned, minus the 1.75 premium she received for the put × $100 × 10 contracts. Because the cash required to potentially purchase the stock is secured by cash sitting ready in the account, this is called a cash-secured put. Her effective purchase price if assigned is $63.25—the same as her breakeven at expiration. The idea with this trade is that if Johnson & Johnson is anywhere under $65 per share at expiration, she will buy the stock effectively at $63.25. If assigned, the time premium of the put allows her to buy the stock at a discount compared with where it is priced when the trade is established, $64. The higher the time premium—or the higher the implied volatility—the bigger the discount. This discount, however, is contingent on the stock not moving too much. If it is above $65 at expiration she won’t get assigned and therefore can only profit a maximum of 1.75 per contract. If the stock is below $63.25 at expiration, the time premium no longer represents a discount, in fact, the trade becomes a loser. In a way, Stacie is still selling volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:178 SCORE: 59.50 ================================================================================ Covered Call The problem with selling a naked call is that it has unlimited exposure to upside risk. Because of this, many traders simply avoid trading naked calls. A more common, and some would argue safer, method of selling calls is to sell them covered. A covered call is when calls are sold and stock is purchased on a share- for-share basis to cover the unlimited upside risk of the call. For each call that is sold, 100 shares of the underlying security are bought. Because of the addition of stock to this strategy, covered calls are traded with a different motivation than naked calls. There are clearly many similarities between these two strategies. The main goal for both is to harvest the premium of the call. The theta for the call is the same with or without the stock component. The gamma and vega for the two strategies are the same as well. The only difference is the stock. When stock is added to an option position, the net delta of the position is the only thing affected. Stock has a delta of one, and all its other greeks are zero. The pivotal point for both positions is the strike price. That’s the point the trader wants the stock to be above or below at expiration. With the naked call, the maximum payout is reaped if the stock is below the strike at expiration, and there is unlimited risk above the strike. With the covered call, the maximum payout is reaped if the stock is above the strike at expiration. If the stock is below the strike at expiration, the risk is substantial—the stock can potentially go to zero. Putting It on There are a few important considerations with the covered call, both when putting on, or entering, the position and when taking off, or exiting, the trade. The risk/reward implications of implied volatility are important in the trade-planning process. Do I want to get paid more to assume more potential risk? More speculative traders like the higher premiums. More conservative (investment-oriented) covered-call sellers like the low implied risk of low-IV calls. Ultimately, a main focus of a covered call is the option ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:179 SCORE: 35.00 ================================================================================ premium. How fast can it go to zero without the movement hurting me? To determine this, the trader must study both theta and delta. The first step in the process is determining which month and strike call to sell. In this example, Harley-Davidson Motor Company (HOG) is trading at about $69 per share. A trader, Bill, is neutral to slightly bullish on Harley- Davidson over the next three months. Exhibit 5.7 shows a selection of available call options for Harley-Davidson with corresponding deltas and thetas. EXHIBIT 5.7 Harley-Davidson calls. In this example, the May 70 calls have 85 days until expiration and are 2.80 bid. If Harley-Davidson remained at $69 until May expiration, the 2.80 premium would represent a 4 percent profit over this 85-day period (2.80 ÷ 69). That’s an annualized return of about 17 percent ([0.04 / 85)] × 365). Bill considers his alternatives. He can sell the April (57-day) 70 calls at 2.20 or the March (22-day) 70 calls at 0.85. Since there is a different number of days until expiration, Bill needs to compare the trades on an apples-to-apples basis. For this, he will look at theta and implied volatility. Presumably, the March call has a theta advantage over the longer-term choices. The March 70 has a theta of 0.032, while the April 70’s theta is 0.026 and the May 70’s is 0.022. Based on his assessment of theta, Bill would have the inclination to sell the March. If he wants exposure for 90 days, when the March 70 call expires, he can roll into the April 70 call and then the May 70 call (more on this in subsequent chapters). This way Bill can continue to capitalize on the nonlinear rate of decay through May. Next, Bill studies the IV term structure for the Harley-Davidson ATMs and finds the March has about a 19.2 percent IV, the April has a 23.3 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:180 SCORE: 74.50 ================================================================================ percent IV, and the May has a 23 percent IV. March is the cheapest option by IV standards. This is not necessarily a favorable quality for a short candidate. Bill must weigh his assessment of all relevant information and then decide which trade is best. With this type of a strategy, the benefits of the higher theta can outweigh the disadvantages of selling the lower IV. In this case, Bill may actually like selling the lower IV. He may infer that the market believes Harley-Davidson will be less volatile during this period. So far, Bill has been focusing his efforts on the 70 strike calls. If he trades the March 70 covered call, he will have a net delta of 0.588 per contract. That’s the negative 0.412 delta from shorting the call plus the 1.00 delta of the stock. His indifference point if the trade is held until expiration is $70.85. The indifference point is the point at which Bill would be indifferent as to whether he held only the stock or the covered call. This is figured by adding the strike price of $70 to the 0.85 premium. This is the effective sale price of the stock if the call is assigned. If Bill wants more potential for upside profit, he could sell a higher strike. He would have to sell the April or May 75, since the March 75s are a zero bid. This would give him a higher indifference point, and the upside profits would materialize quickly if HOG moved higher, since the covered-call deltas would be higher with the 75 calls. The April 75 covered-call net delta is 0.796 per contract (the stock delta of 1.00 minus the 0.204 delta of the call). The May 75 covered-call delta is 0.751. But Bill is neutral to only slightly bullish. In this case, he’d rather have the higher premium—high theta is more desirable than high delta in this situation. Bill buys 1,000 shares of Harley-Davidson at $69 and sells 10 Harley-Davidson March 70 calls at 0.85. Bill also needs to plan his exit. To exit, he must study two things: an at- expiration diagram and his greeks. Exhibit 5.8 shows the P&(L) at expiration of the Harley-Davidson March 70 covered call. Exhibit 5.9 shows the greeks. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:181 SCORE: 45.00 ================================================================================ EXHIBIT 5.8 Harley-Davidson covered call. EXHIBIT 5.9 Greeks for Harley-Davidson covered call (per contract). Delta 0.591 Gamma−0.121 Theta 0.032 Vega −0.066 Taking It Off If the trade works out perfectly for Bill, 22 days from now Harley-Davidson will be trading right at $70. He’d profit on both delta and theta. If the trade isn’t exactly perfect, but still good, Harley-Davidson will be anywhere above $68.15 in 22 days. It’s the prospect that the trade may not be so good at March expiration that occupies Bill’s thoughts, but a trader has to hope for the best and plan for the worst. If it starts to trend, Bill needs to react. The consequences to the stock’s trending to the upside are not quite so dire, although he might be somewhat frustrated with any lost opportunity above the indifference point. It’s the downside risk that Bill will more vehemently guard against. First, the same IV/vega considerations exist as they did in the previous examples. In the event the trade is closed early, IV/vega may help or hinder profitability. A rise in implied volatility will likely accompany a decline in ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:182 SCORE: 47.00 ================================================================================ the stock price. This can bring Bill to his stop-loss sooner. Delta versus theta however, is the major consideration. He will plan his exit price in advance and cover when the planned exit price is reached. There are more moving parts with the covered call than a naked option. If Bill wants to close the position early, he can leg out, meaning close only one leg of the trade (the call or the stock) at a time. If he legs out of the trade, he’s likely to close the call first. The motivation for exiting a trade early is to reduce risk. A naked call is hardly less risky than a covered call. Another tactic Bill can use, and in this case will plan to use, is rolling the call. When the March 70s expire, if Harley-Davidson is still in the same range and his outlook is still the same, he will sell April calls to continue the position. After the April options expire, he’ll plan to sell the Mays. With this in mind, Bill may consider rolling into the Aprils before March expiration. If it is close to expiration and Harley-Davidson is trading lower, theta and delta will both have devalued the calls. At the point when options are close to expiration and far enough OTM to be offered close to zero, say 0.05, the greeks and the pricing model become irrelevant. Bill must consider in absolute terms if it is worth waiting until expiration to make 0.05. If there is a lot of time until expiration, the answer is likely to be no. This is when Bill will be apt to roll into the Aprils. He’ll buy the March 70s for a nickel, a dime, or maybe 0.15 and at the same time sell the Aprils at the bid. This assumes he wants to continue to carry the position. If the roll is entered as a single order, it is called a calendar spread or a time spread. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:183 SCORE: 48.00 ================================================================================ Covered Put The last position in the family of basic volatility-selling strategies is the covered put, sometimes referred to as selling puts and stock. In a covered put, a trader sells both puts and stock on a one-to-one basis. The term covered put is a bit of a misnomer, as the strategy changes from limited risk to unlimited risk when short stock is added to the short put. A naked put can produce only losses until the stock goes to zero—still a substantial loss. Adding short stock means that above the strike gains on the put are limited, while losses on the stock are unlimited. The covered put functions very much like a naked call. In fact, they are synthetically equal. This concept will be addressed further in the next chapter. Let’s looks at another trader, Libby. Libby is an active trader who trades several positions at once. Libby believes the overall market is in a range and will continue as such over the next few weeks. She currently holds a short stock position of 1,000 shares in Harley-Davidson. She is becoming more neutral on the stock and would consider buying in her short if the market dipped. She may consider entering into a covered-put position. There is one caveat: Libby is leaving for a cruise in two weeks and does not want to carry any positions while she is away. She decides she will sell the covered put and actively manage the trade until her vacation. Libby will sell 10 Harley-Davidson March (22-day) 70 puts at 1.85 against her short 1,000 shares of Harley-Davidson, which is trading at $69 per share. She knows that her maximum profit if the stock declines and assignment occurs will be $850. That’s 0.85 × $100 × 10 contracts. Win or lose, she will close the position in two weeks when there are only eight days until expiration. To trade this covered put she needs to watch her greeks. Exhibit 5.10 shows the greeks for the Harley-Davidson 70-strike covered put. EXHIBIT 5.10 Greeks for Harley-Davidson covered put (per contract). Delta −0.419 Gamma−0.106 Theta 0.031 Vega −0.066 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:184 SCORE: 33.00 ================================================================================ Libby is really focusing on theta. It is currently about $0.03 per day but will increase if the put stays close-to-the-money. In two weeks, the time premium will have decayed significantly. A move downward will help, too, as the −0.419 delta indicates. Exhibit 5.11 displays an array of theoretical values of the put at eight days until expiration as the stock price changes. EXHIBIT 5.11 HOG 70 put values at 8 days to expiry. As long as Harley-Davidson stays below the strike price, Libby can look at her put from a premium-over-parity standpoint. Below the strike, the intrinsic value of the put doesn’t matter too much, because losses on intrinsic value are offset by gains on the stock. For Libby, all that really matters is the time value. She sold the puts at 0.85 over parity. If Harley- Davidson is trading at $68 with eight days to go, she can buy her puts back for 0.12 over parity. That’s a 73-cent profit, or $730 on her 10 contracts. This doesn’t account for any changes in the time value that may occur as a result of vega, but vega will be small with Harley-Davidson at $68 and eight days to go. At this point, she would likely close down the whole position—buying the puts and buying the stock—to take a profit on a position that worked out just about exactly as planned. Her risk, though, is to the upside. A big rally in the stock can cause big losses. From a theoretical standpoint, losses are potentially unlimited with this type of trade. If the stock is above the strike, she needs to have a mental stop order in mind and execute the closing order with discipline. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:187 SCORE: 40.50 ================================================================================ Put-Call Parity Essentials Before the creation of the Black-Scholes model, option pricing was hardly an exact science. Traders had only a few mathematical tools available to compare the relative prices of options. One such tool, put-call parity, stems from the fact that puts and calls on the same class sharing the same month and strike can have the same functionality when stock is introduced. For example, traders wanting to own a stock with limited risk can buy a married put: long stock and a long put on a share-for-share basis. The traders have infinite profit potential, and the risk of the position is limited below the strike price of the option. Conceptually, long calls have the same risk/reward profile—unlimited profit potential and limited risk below the strike. Exhibit 6.1 is an overview of the at-expiration diagrams of a married put and a long call. EXHIBIT 6.1 Long call vs. long stock + long put (married put). Married puts and long calls sharing the same month and strike on the same security have at-expiration diagrams with the same shape. They have the same volatility value and should trade around the same implied volatility (IV). Strategically, these two positions provide the same service to a trader, but depending on margin requirements, the married put may require more capital to establish, because the trader must buy not just the option but also the stock. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:188 SCORE: 34.00 ================================================================================ The stock component of the married put could be purchased on margin. Buying stock on margin is borrowing capital to finance a stock purchase. This means the trader has to pay interest on these borrowed funds. Even if the stock is purchased without borrowing, there is opportunity cost associated with the cash used to pay for the stock. The capital is tied up. If the trader wants to use funds to buy another asset, he will have to borrow money, which will incur an interest obligation. Furthermore, if the trader doesn’t invest capital in the stock, the capital will rest in an interest-bearing account. The trader forgoes that interest when he buys a stock. However the trader finances the purchase, there is an interest cost associated with the transaction. Both of these positions, the long call and the married put, give a trader exposure to stock price advances above the strike price. The important difference between the two trades is the value of the stock below the strike price—the part of the trade that is not at risk in either the long call or the married put. On this portion of the invested capital, the trader pays interest with the married put (whether actually or in the form of opportunity cost). This interest component is a pricing consideration that adds cost to the married put and not the long call. So if the married put is a more expensive endeavor than the long call because of the interest paid on the investment portion that is below the strike, why would anyone buy a married put? Wouldn’t traders instead buy the less expensive—less capital intensive—long call? Given the additional interest expense, they would rather buy the call. This relates to the concept of arbitrage. Given two effectively identical choices, rational traders will choose to buy the less expensive alternative. The market as a whole would buy the calls, creating demand which would cause upward price pressure on the call. The price of the call would rise until its interest advantage over the married put was gone. In a robust market with many savvy traders, arbitrage opportunities don’t exist for very long. It is possible to mathematically state the equilibrium point toward which the market forces the prices of call and put options by use of the put-call parity. As shown in Chapter 2, the put-call parity states ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:190 SCORE: 21.00 ================================================================================ Dividends Another difference between call and married-put values is dividends. A call option does not extend to its owner the right to receive a dividend payment. Traders, however, who are long a put and long stock are entitled to a dividend if it is the corporation’s policy to distribute dividends to its shareholders. An adjustment must be made to the put-call parity to account for the possibility of a dividend payment. The equation must be adjusted to account for the absence of dividends paid to call holders. For a dividend-paying stock, the put-call parity states The interest advantage and dividend disadvantage of owning a call is removed from the market by arbitrageurs. Ultimately, that is what is expressed in the put-call parity. It’s a way to measure the point at which the arbitrage opportunity ceases to exist. When interest and dividends are factored in, a long call is an equal position to a long put paired with long stock. In options nomenclature, a long put with long stock is a synthetic long call. Algebraically rearranging the above equation: The interest and dividend variables in this equation are often referred to as the basis. From this equation, other synthetic relationships can be algebraically derived, like the synthetic long put. A synthetic long put is created by buying a call and selling (short) stock. The at-expiration diagrams in Exhibit 6.2 show identical payouts for these two trades. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:191 SCORE: 49.00 ================================================================================ EXHIBIT 6.2 Long put vs. long call + short stock. The concept of synthetics can become more approachable when studied from the perspective of delta as well. Take the 50-strike put and call listed on a $50 stock. A general rule of thumb in the put-call pair is that the call delta plus the put delta equals 1.00 when the signs are ignored. If the 50 put in this example has a −0.45 delta, the 50 call will have a 0.55 delta. By combining the long call (0.55 delta) with short stock (–1.00 delta), we get a synthetic long put with a −0.45 delta, just like the actual put. The directional risk is the same for the synthetic put and the actual put. A synthetic short put can be created by selling a call of the same month and strike and buying stock on a share-for-share basis (i.e., a covered call). This is indicated mathematically by multiplying both sides of the put-call parity equation by −1: The at-expiration diagrams, shown in Exhibit 6.3 , are again conceptually the same. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:192 SCORE: 36.00 ================================================================================ EXHIBIT 6.3 Short put vs. short call + long stock. A short (negative) put is equal to a short (negative) call plus long stock, after the basis adjustment. Consider that if the put is sold instead of buying stock and selling a call, the interest that would otherwise be paid on the cost of the stock up to the strike price is a savings to the put seller. To balance the equation, the interest benefit of the short put must be added to the call side (or subtracted from the put side). It is the same with dividends. The dividend benefit of owning the stock must be subtracted from the call side to make it equal to the short put side (or added to the put side to make it equal the call side). The same delta concept applies here. The short 50-strike put in our example would have a 0.45 delta. The short call would have a −0.55 delta. Buying one hundred shares along with selling the call gives the synthetic short put a net delta of 0.45 (–0.55 + 1.00). Similarly, a synthetic short call can be created by selling a put and selling (short) one hundred shares of stock. Exhibit 6.4 shows a conceptual overview of these two positions at expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:194 SCORE: 49.00 ================================================================================ Comparing Synthetic Calls and Puts The common thread among the synthetic positions explained above is that, for a put-call pair, long options have synthetic equivalents involving long options, and short options have synthetic equivalents involving short options. After accounting for the basis, the four basic synthetic option positions are: Because a call or put position is interchangeable with its synthetic position, an efficient market will ensure that the implied volatility is closely related for both. For example, if a long call has an IV of 25 percent, the corresponding put should have an IV of about 25 percent, because the long put can easily be converted to a synthetic long call and vice versa. The greeks will be similar for synthetically identical positions, too. The long options and their synthetic equivalents will have positive gamma and vega with negative theta. The short options and their synthetics will have negative gamma and vega with positive theta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:195 SCORE: 113.00 ================================================================================ American-Exercise Options Put-call parity was designed for European-style options. The early exercise possibility of American-style options gums up the works a bit. Because a call (put) and a synthetic call (put) are functionally the same, it is logical to assume that the implied volatility and the greeks for both will be exactly the same. This is not necessarily true with American-style options. However, put-call parity may still be useful with American options when the limitations of the equation are understood. With at-the-money American- exercise options, the differences in the greeks for a put-call pair are subtle. Exhibit 6.5 is a comparison of the greeks for the 50-strike call and the 50- strike put with the underlying at $50 and 66 days until expiration. EXHIBIT 6.5 Greeks for a 50-strike put-call pair on a $50 stock. Call Put Delta 0.5540.457 Gamma0.0750.078 Theta 0.0200.013 Vega 0.0840.084 The examples used earlier in this chapter in describing the deltas of synthetics were predicated on the rule of thumb that the absolute values of call and put deltas add up to 1.00. To be a bit more realistic, consider that because of American exercise, the absolute delta values of put-call pairs don’t always add up to 1.00. In fact, Exhibit 6.5 shows that the call has closer to a 0.554 delta. The put struck at the same price then has a 0.457 delta. By selling 100 shares against the long call, we can create a combined- position delta (call delta plus stock delta) that is very close to the put’s delta. The delta of this synthetic put is −0.446 (0.554 − 1.00). The delta of a put will always be similar to the delta of its corresponding synthetic put. This is also true with call–synthetic-call deltas. This relationship mathematically is ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:196 SCORE: 62.00 ================================================================================ This holds true whether the options are in-, at-, or out-of-the-money. For example, with a stock at $54, the 50-put would have a −0.205 delta and the call would have a 0.799 delta. Selling 100 shares against the call to create the synthetic put yields a net delta of −0.201. If long or short stock is added to a call or put to create a synthetic, delta will be the only greek affected. With that in mind, note the other greeks displayed in Exhibit 6.5 —especially theta. Proportionally, the biggest difference in the table is in theta. The disparity is due in part to interest. When the effects of the interest component outweigh the effects of the dividend, the time value of the call can be higher than the time value of the put. Because the call must lose more premium than the put by expiration, the theta of the call must be higher than the theta of the put. American exercise can also cause the option prices in put-call parity to not add up. Deep in-the-money (ITM) puts can trade at parity while the corresponding call still has time value. The put-call equation can be unbalanced. The same applies to calls on dividend-paying stocks as the dividend date approaches. When the date is imminent, calls can trade close to parity while the puts still have time value. The role of dividends will be discussed further in Chapter 8. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:197 SCORE: 26.00 ================================================================================ Synthetic Stock Not only can synthetic calls and puts be derived by manipulation of put-call parity, but synthetic positions for the other security in the equation—stock —can be derived, as well. By isolating stock on one side of the equation, the formula becomes After accounting for interest and dividends, buying a call and selling a put of the same strike and time to expiration creates the equivalent of a long stock position. This is called a synthetic stock position, or a combo. After accounting for the basis, the equation looks conceptually like this: This is easy to appreciate when put-call parity is written out as it is here. It begins to make even more sense when considering at-expiration diagrams and the greeks. Exhibit 6.6 illustrates a long stock position compared with a long call combined with a short put position. EXHIBIT 6.6 Long stock vs. long call + short put. A quick glance at these two strategies demonstrates that they are the same, but think about why. Consider the synthetic stock position if both options are held until expiration. The long call gives the trader the right to buy the stock at the strike price. The short put gives the trader the obligation ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:198 SCORE: 82.50 ================================================================================ to buy the stock at the same strike price. It doesn’t matter what the strike price is. As long as the strike is the same for the call and the put, the trader will have a long position in the underlying at the shared strike at expiration when exercise or assignment occurs. The options in this example are 50-strike options. At expiration, the trader can exercise the call to buy the underlying at $50 if the stock is above the strike. If the underlying is below the strike at expiration, he’ll get assigned on the put and buy the stock at $50. If the stock is bought, whether by exercise or assignment, the effective price of the potential stock purchase, however, is not necessarily $50. For example, if the trader bought one 50-strike call at 3.50 and sold one 50-strike put at 1.50, he will effectively purchase the underlying at $52 upon exercise or assignment. Why? The trader paid a net of $2 to get a long position in the stock synthetically (3.50 of call premium debited minus 1.50 of put premium credited). Whether the call or the put is ITM, the effective purchase price of the stock will always be the strike price plus or minus the cost of establishing the synthetic, in this case, $52. The question that begs to be asked is: would the trader rather buy the stock or pay $2 to have the same market exposure as long stock? Arbitrageurs in the market (with the help of the put-call parity) ensure that neither position—long stock or synthetic long stock—is better than the other. For example, assume a stock is trading at $51.54. With 71 days until expiration, 26.35 IV, a 5 percent interest rate, and no dividends, the 50- strike call is theoretically worth 3.50, and the 50-strike put is theoretically worth 1.50. Exhibit 6.7 charts the synthetic stock versus the actual stock when there are 71 days until expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:199 SCORE: 8.00 ================================================================================ EXHIBIT 6.7 Long stock and synthetic long stock with 71 days to expiration. Looking at this exhibit, it appears that being long the actual stock outperforms being long the stock synthetically. If the stock is purchased at $51.54, it need only rise a penny higher to profit (in the theoretical world where traders do not pay commissions on transactions). If the synthetic is purchased for $2, the stock needs to rise $0.46 to break even—an apparent disadvantage. This figure, however, does not include interest. The synthetic stock offers the same risk/reward as actually being long the stock. There is a benefit, from the perspective of interest, to paying only $2 for this exposure rather than $51.54. The interest benefit here is about $0.486. We can find this number by calculating the interest as we did earlier in the chapter. Interest, again, is computed as the strike price times the interest rate times the number of days to expiration divided by the number of days in a year. The formula is as follows: Inputting the numbers from this example: The $0.486 of interest is about equal to the $0.46 disparity between the diagrams of the stock and the synthetic stock with 71 days until expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:200 SCORE: 9.00 ================================================================================ The difference is due mainly to rounding and the early-exercise potential of the American put. In mathematical terms The synthetic long stock is approximately equal to the long stock position when considering the effect of interest. The two lines in Exhibit 6.7 — representing stock and synthetic stock—would converge with each passing day as the calculated interest decreases. This equation works as well for a synthetic short stock position; reversing the signs reveals the synthetic for short stock. Or, in this case, Shorting stock at $51.54 is about equal to selling the 50 call and buying the 50 put for a $2 credit based on the interest of 0.486 computed on the 50 strike. Again, the $0.016 disparity between the calculated interest and the actual difference between the synthetic value and the stock price is a function of rounding and early exercise. More on this in the “Conversions and Reversals” section. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:202 SCORE: 72.00 ================================================================================ Conversions and Reversals When calls and puts are combined to create synthetic stock, the main differences are the interest rate and dividends. This is important because the risks associated with interest and dividends can be isolated, and ultimately traded, when synthetic stock is combined with the underlying. There are two ways to combine synthetic stock with its underlying security: a conversion and a reversal. Conversion A conversion is a three-legged position in which a trader is long stock, short a call, and long a put. The options share the same month and strike price. By most metrics, this is a very flat position. A trader with a conversion is long the stock and, at the same time, synthetically short the same stock. Consider this from the perspective of delta. In a conversion, the trader is long 1.00 deltas (the long stock) and short very close to 1.00 deltas (the synthetic short stock). Conversions have net flat deltas. The following is a simple example of a typical conversion and the corresponding deltas of each component. Short one 35-strike call:−0.63 delta Long one 35-strike put:−0.37 delta Long 100 shares: 1.00 delta 0.00 delta The short call contributes a negative delta to the position, in this case, −0.63. The long put also contributes a negative delta, −0.37. The combined delta of the synthetic stock is −1.00 in this example, which is like being short 100 shares of stock. When the third leg of the spread is added, the long 100 shares, it counterbalances the synthetic. The total delta for the conversion is zero. Most of the conversion’s other greeks are pretty flat as well. Gamma, theta, and vega are similar for the call and the put in the conversion, because they have the same expiration month and strike price. Because the trader is selling one option and buying another—a call and a put, respectively—with the same month and strike, the greeks come very close ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:203 SCORE: 35.00 ================================================================================ to offsetting each other. For all intents and purposes, the trader is out of the primary risks of the position as measured by greeks when a position is converted. Let’s look at a more detailed example. A trader executes the following trade (for the purposes of this example, we assume the stock pays no dividend and the trade is executed at fair value): Sell one 71-day 50 call at 3.50 Buy one 71-day 50 put at 1.50 Buy 100 shares at $51.54 The trader buys the stock at $51.54 and synthetically sells the stock at $52. The synthetic price is computed as −3.50 + 1.50 − 50. Therefore, the stock is sold synthetically at $0.46 over the actual stock price. Exhibit 6.8 shows the analytics for the conversion. EXHIBIT 6.8 Conversion greeks. This position has very subtle sensitivity to the greeks. The net delta for the spread has a very slightly negative bias. The bias is so small it is negligible to most traders, except professionals trading very large positions. Why does this negative delta bias exist? Mathematically, the synthetic’s delta can be higher with American options than with their European counterparts because of the possibility of early exercise of the put. This anomaly becomes more tangible when we consider the unique directional risk associated with this trade. In this example, the stock is synthetically sold at $0.46 over the price at which the stock is bought. If the stock declines significantly in value before expiration, the put will, at some point, trade at parity while the call loses all its time value. In this scenario, the value of the synthetic stock will be short at effectively the same price as the actual stock price. For example, if the stock declines to $35 per share then the numbers are as follows: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:204 SCORE: 40.00 ================================================================================ or With American options, a put this far in-the-money with less than 71 days until expiry will be all intrinsic value. Interest, in this case, will not factor into the put’s value, because the put can be exercised. By exercising the put, both the long stock leg and the long put leg can be closed for even money, leaving only the theoretically worthless call. The stock-synthetic spread is sold at 0.46 and essentially bought at zero when the put is exercised. If the put is exercised before expiration, the profit potential is 0.46 minus the interest calculated between the trade date and the day the put is exercised. If, however, the conversion is held until expiration, the $0.46 is negated by the $0.486 of interest incurred from holding long stock over the entire 71- day period, hence the trader’s desire to see the stock decline before expiration, and thus the negative bias toward delta. This is, incidentally, why the synthetic price (0.46 over the stock price) does not exactly equal the calculated value of the interest (0.486). The trader can exercise the put early if the stock declines and capitalize on the disparity between the interest calculated when the conversion was traded and the actual interest calculation given the shorter time frame. The model values the synthetic at a little less than the interest value would indicate—in this case $0.46 instead of $0.486. The gamma of this trade is fairly negligible. The theta is slightly positive. Rho is the figure that deserves the most attention. Rho is the change in an option’s price given a change in the interest rate. The −0.090 rho of the conversion indicates that if the interest rate rises one percentage point, the position as a whole loses $0.09. Why? The financing of the position gets more expensive as the interest rate rises. The trader would have to pay more in interest to carry the long stock. In this example, if interest rises by one percentage point, the synthetic stock, which had an effective short price of $0.46 over the price of the long stock before the interest rate increase, will be $0.55 over the price of the long stock afterward. If, however, the interest rate declines by one percentage point, the trader profits $0.09, as the synthetic is repriced by the market to $0.37 over the stock price. The lower the interest rate, the less expensive it is to ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:205 SCORE: 24.00 ================================================================================ finance the long stock. This is proven mathematically by put-call parity. Negative rho indicates a bearish position on the interest rate; the trader wants it to go lower. Positive rho is a bullish interest rate position. But a one-percentage-point change in the interest rate in one day is a big and uncommon change. The question is: is rho relevant? That depends on the type of position and the type of trader. A 0.090 rho would lead to a 0.0225 profit-and-loss (P&(L)) change per one lot conversion on a 25-basis- point, or quarter percent, change. That’s just $2.25 per spread. This incremental profit or loss, however, can be relevant to professional traders like market makers. They trade very large positions with the aspiration of making small incremental profits on each trade. A market maker with a 5,000-lot conversion would stand to make or lose $11,250, given a quarter- percentage-point change in interest rate and a 0.090 rho. The Mind of a Market Maker Market makers are among the only traders who can trade conversions and reversals profitably, because of the size of their trades and the fact that they can buy the bid and sell the offer. Market makers often attempt to leg into and out of conversions (and reversals). Given the conversion in this example, a market maker may set out to sell calls and in turn buy stock to hedge the call’s delta risk (this will be covered in Chapters 12 and 17), then buy puts and the rest of the stock to create a balanced conversion: one call to one put to one hundred shares. The trader may try to put on the conversion in the previous example for a total of $0.50 over the price of the long stock instead of the $0.46 it’s worth. He would then try to leg out of the trade for less, say $0.45 over the stock, with the goal of locking in a $0.05 profit per spread on the whole trade. Reversal A reversal, or reverse conversion, is simply the opposite of the conversion: buy call, sell put, and sell (short) stock. A reversal can be executed to close a conversion, or it can be an opening transaction. Using the same stock and options as in the previous example, a trader could establish a reversal as follows: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:206 SCORE: 9.00 ================================================================================ Buy one 71-day 50 call at 3.50 Sell one 71-day 50 put at 1.50 Sell 100 shares at 51.54 The trader establishes a short position in the stock at $51.54 and a long synthetic stock position effectively at $52.00. He buys the stock synthetically at $0.46 over the stock price, again assuming the trade can be executed at fair value. With the reversal, the trader has a bullish position on interest rates, which is indicated by a positive rho. In this example, the rho for this position is 0.090. If interest rates rise one percentage point, the synthetic stock (which the trader is long) gains nine cents in value relative to the stock. The short stock rebate on the short stock leg earns more interest at a higher interest rate. If rates fall one percentage point, the synthetic long stock loses $0.09. The trader earns less interest being short stock given a lower interest rate. With the reversal, the fact that the put can be exercised early is a risk. Since the trader is short the put and short stock, he hopes not to get assigned. If he does, he misses out on the interest he planned on collecting when he put on the reversal for $0.46 over. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:207 SCORE: 38.00 ================================================================================ Pin Risk Conversions and reversals are relatively low-risk trades. Rho and early exercise are relevant to market makers and other arbitrageurs, but they are among the lowest-risk positions they are likely to trade. There is one indirect risk of conversions and reversals that can be of great concern to market makers around expiration: pin risk. Pin risk is the risk of not knowing for certain whether an option will be assigned. To understand this concept, let’s revisit the mind of a market maker. Recall that market makers have two primary functions: 1. Buy the bid or sell the offer. 2. Manage risk. When institutional or retail traders send option orders to an exchange (through a broker), market makers are usually the ones with whom they trade. Customers sell the bid; the market makers buy the bid. Customers buy the offer; the market makers sell the offer. The first and arguably easier function of market makers is accomplished whenever a marketable order is sent to the exchange. Managing risk can get a bit hairy. For example, once the market makers buy April 40 calls, their first instinct is to hedge by selling stock to become delta neutral. Market makers are almost always delta neutral, which mitigates the direction risk. The next step is to mitigate theta, gamma, and vega risk by selling options. The ideal options to sell are the same calls that were bought—that is, get out of the trade. The next best thing is to sell the April 40 puts and sell more stock. In this case, the market makers have established a reversal and thereby have very little risk. If they can lock in the reversal for a small profit, they have done their job. What happens if the market makers still have the reversal in inventory at expiration? If the stock is above the strike price—40, in this case—the puts expire, the market makers exercise the calls, and the short stock is consequently eliminated. The market makers are left with no position, which is good. They’re delta neutral. If the stock is below 40, the calls expire, the puts get assigned, and the short stock is consequently eliminated. Again, no position. But what if the stock is exactly at $40? Should the calls ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:208 SCORE: 54.00 ================================================================================ be exercised? Will the puts get assigned? If the puts are assigned, the traders are left with no short stock and should let the calls expire without exercising so as not to have a long delta position after expiration. If the puts are not assigned, they should exercise the calls to get delta flat. It’s also possible that only some of the puts will be assigned. Because they don’t know how many, if any, of the puts will be assigned, the market makers have pin risk. To avoid pin risk, market makers try to eliminate their position if they have conversions or reversals close to expiration. Boxes and Jelly Rolls There are two other uses of synthetic stock positions that form conventional strategies: boxes and rolls. Boxes When long synthetic stock is combined with short synthetic stock on the same underlying within the same expiration cycle but with a different strike price, the resulting position is known as a box. With a box, a trader is synthetically both long and short the stock. The two positions, for all intents and purposes, offset each other directionally. The risk of stock-price movement is almost entirely avoided. A study of the greeks shows that the delta is close to zero. Gamma, theta, vega, and rho are also negligible. Here’s an example of a 60–70 box for April options: Short 1 April 60 call Long 1 April 60 put Long 1 April 70 call Short 1 April 70 put In this example, the trader is synthetically short the 60-strike and, at the same time, synthetically long the 70-strike. Exhibit 6.9 shows the greeks. EXHIBIT 6.9 Box greeks. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:209 SCORE: 31.00 ================================================================================ Aside from the risks associated with early exercise implications, this position is just about totally flat. The near-1.00 delta on the long synthetic stock struck at 60 is offset by the near-negative-1.00 delta of the short synthetic struck at 70. The tiny gammas and thetas of both combos are brought closer to zero when they are spread against each another. Vega is zero. And the bullish interest rate sensitivity of the long combo is nearly all offset by the bearish interest sensitivity of the short combo. The stock can move, time can pass, volatility and interest can change, and there will be very little effect on the trader’s P&(L). The question is: Why would someone trade a box? Market makers accumulate positions in the process of buying bids and selling offers. But they want to eliminate risk. Ideally, they try to be flat the strike —meaning have an equal number of calls and puts at each strike price, whether through a conversion or a reversal. Often, they have a conversion at one strike and a reversal at another. The stock positions for these cancel each other out and the trader is left with only the four option legs—that is, a box. They can eliminate pin risk on both strikes by trading the box as a single trade to close all four legs. Another reason for trading a box has to do with capital. Borrowing and Lending Money The first thing to consider is how this spread is priced. Let’s look at another example of a box, the October 50–60 box. Long 1 October 60 call Short 1 October 60 put Short 1 October 70 call Long 1 October 70 put ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:210 SCORE: 28.00 ================================================================================ A trader with this position is synthetically long the stock at $60 and short the stock at $70. That sounds like $10 in the bank. The question is: How much would a trader be willing to pay for the right to $10? And for how much would someone be willing to sell it? At face value, the obvious answer is that the equilibrium point is at $10, but there is one variable that must be factored in: time. In this example, assume that the October call has 90 days until expiration and the interest rate is 6 percent. A rational trader would not pay $10 today for the right to have $10 90 days from now. That would effectively be like loaning the $10 for 90 days and not receiving interest—A losing proposition! The trader on the other side of this box would be happy to enter into the spread for $10. He would have interest-free use of $10 for 90 days. That’s free money! Certainly, there is interest associated with the cost of carrying the $10. In this case, the interest would be $0.15. This $0.15 is discounted from the price of the $10 box. In fact, the combined net value of the options composing the box should be about 9.85 —with differences due mainly to rounding and the early exercise possibility for American options. A trader buying this box—that is, buying the more ITM call and more ITM put—would expect to pay $0.15 below the difference between the strike prices. Fair value for this trade is $9.85. The seller of this box—the trader selling the meatier options and buying the cheaper ones—would concede up to $0.15 on the credit. Jelly Rolls A jelly roll, or simply a roll, is also a spread with four legs and a combination of two synthetic stock trades. In a box, the difference between the synthetics is the strike price; in a roll, it’s the contract month. Here’s an example: Long 1 April 50 call Short 1 April 50 put Short 1 May 50 call Long 1 May 50 put ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:211 SCORE: 38.00 ================================================================================ The options in this spread all share the same strike price, but they involve two different months—April and May. In this example, the trader is long synthetic stock in April and short synthetic stock in May. Like the conversion, reversal, and box, this is a mostly flat position. Delta, gamma, theta, vega, and even rho have only small effects on a jelly roll, but like the others, this spread serves a purpose. A trader with a conversion or reversal can roll the option legs of the position into a month with a later expiration. For example, a trader with an April 50 conversion in his inventory (short the 50 call, long the 50 put, long stock) can avoid pin risk as April expiration approaches by trading the roll from the above example. The long April 50 call and short April 50 put cancel out the current option portion of the conversion leaving only the stock. Selling the May 50 calls and buying the May 50 puts reestablishes the conversion a month farther out. Another reason for trading a roll has to do with interest. The roll in this example has positive exposure to rho in April and negative exposure to rho in May. Based on a trader’s expectations of future changes in interest rates, a position can be constructed to exploit opportunities in interest. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:217 SCORE: 44.00 ================================================================================ Rho and Interest Rates Rho is a measurement of the sensitivity of an option’s value to a change in the interest rate. To understand how and why the interest rate is important to the value of an option, recall the formula for put-call parity stated in Chapter 6. Call + Strike − Interest = Put + Stock 1 From this formula, it’s clear that as the interest rate rises, put prices must fall and call prices must rise to keep put-call parity balanced. With a little algebra, the equation can be restated to better illustrate this concept: and If interest rates fall, and Rho helps quantify this relationship. Calls have positive rho, and puts have negative rho. For example, a call with a rho of +0.08 will gain $0.08 with each one-percentage-point rise in interest rates and fall $0.08 with each one-percentage-point fall in interest rates. A put with a rho of −0.08 will lose $0.08 with each one-point rise and gain $0.08 in value with a one- point fall. The effect of changes in the interest variable of put-call parity on call and put values is contingent on three factors: the strike price, the interest rate, and the number of days until expiration. Interest = Strike×Interest Rate×(Days to Expiration/365) 2 Interest, for our purposes, is a function of the strike price. The higher the strike price, the greater the interest and, consequently the more changes in the interest rate will affect the option. The higher the interest rate is, the higher the interest variable will be. Likewise, the more time to expiration, ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:218 SCORE: 44.00 ================================================================================ the greater the effect of interest. Rho measures an option’s sensitivity to the end results of these three influences. To understand how changes in interest affect option prices, consider a typical at-the-money (ATM) conversion on a non-dividend-paying stock. Short 1 May 50 call at 1.92 Long 1 May 50 put at 1.63 Long 100 shares at $50 With 43 days until expiration at a 5 percent interest rate, the interest on the 50 strike will be about $0.29. Put-call parity ensures that this $0.29 shows up in option prices. After rearranging the equation, we get In this example, both options are exactly ATM. There is no intrinsic value. Therefore, the difference between the extrinsic values of the call and the put must equal interest. If one option were in-the-money (ITM), the intrinsic value on the left side of the equation would be offset by the Stock − Strike on the right side. Still, it would be the difference in the time value of the call and put that equals the interest variable. This is shown by the fact that the synthetic stock portion of the conversion is short at $50.29 (call − put + strike). This is $0.29 above the stock price. The synthetic stock equals the Stock + Interest, or Certainly, if the interest rate were higher, the interest on the synthetic stock would be a higher number. At a 6 percent interest rate, the effective short price of the synthetic stock would be about $50.35. The call would be valued at about 1.95, and the put would be 1.60—a net of $0.35. A one-percentage-point rise in the interest rate causes the synthetic stock position to be revalued by $0.06—a $0.03 gain in the call value and a $0.03 decline in the put. Therefore, by definition, the call has a +0.03 rho and the put has a −0.03 rho. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:219 SCORE: 24.00 ================================================================================ Rho and Time The time component of interest has a big impact on the magnitude of an option’s rho, because the greater the number of days until expiration, the greater the interest. Long-term options will be more sensitive to changes in the interest rate and, therefore, have a higher rho. Take a stock trading at about $120 per share. The July, October, and January ATM calls have the following rhos with the interest rate at 5.5 percent. Option Rho July (38-day) 120 calls+0.068 October (130-day) 120 calls+0.226 January (221-day) 120 calls+0.385 If interest rates rise 25 basis points, or a quarter of a percentage point, the July calls with only 38 days until expiration will gain very little: only $0.017 (0.068 × 0.25). The October 120 calls with 130 days until expiration gain more: $0.057 (0.226 × 0.25). The January calls that have 221 days until they expire make $0.096 theoretically (0.385 × 0.25). If all else is held constant, the more time to expiration, the higher the option’s rho, and therefore, the more interest will affect the option’s value. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:221 SCORE: 45.00 ================================================================================ LEAPS Options buyers have time working against them. With each passing day, theta erodes the value of their assets. Buying a long-term option, or a LEAPS, helps combat erosion because long-term options can decay at a slower rate. In environments where there is interest rate uncertainty, however, LEAPS traders have to think about more than the rate of decay. Consider two traders: Jason and Susanne. Both are bullish on XYZ Corp. (XYZ), which is trading at $59.95 per share. Jason decides to buy a May 60 call at 1.60, and Susanne buys a LEAPS 60 call at 7.60. In this example, May options have 44 days until expiration, and the LEAPS have 639 days. Both of these trades are bullish, but the traders most likely had slightly different ideas about time, volatility, and interest rates when they decided which option to buy. Exhibit 7.1 compares XYZ short-term at-the-money calls with XYZ LEAPS ATM calls. EXHIBIT 7.1 XYZ short-term call vs. LEAPS call. To begin with, it appears that Susanne was allowing quite a bit of time for her forecast to be realized—almost two years. Jason, however, was looking for short-term price appreciation. Concerns about time decay may have been a motivation for Susanne to choose a long-term option—her theta of 0.01 is half Jason’s, which is 0.02. With only 44 days until expiration, the theta of Jason’s May call will begin to rise sharply as expiration draws near. But the trade-off of lower time decay is lower gamma. At the current stock price, Susanne has a higher delta. If the XYZ stock price rises $2, the gamma of the May call will cause Jason’s delta to creep higher than Susanne’s. At $62, the delta for the May 60s would be about 0.78, whereas ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:222 SCORE: 65.50 ================================================================================ the LEAPS 60 call delta is about 0.77. This disparity continues as XYZ moves higher. Perhaps Susanne had implied volatility (IV) on her mind as well as time decay. These long-term ATM LEAPS options have vegas more than three times the corresponding May’s. If IV for both the May and the LEAPS is at a yearly low, LEAPS might be a better buy. A one- or two-point rise in volatility if IV reverts to its normal level will benefit the LEAPS call much more than the May. Theta, delta, gamma, and vega are typical considerations with most trades. Because this option is long term, in addition to these typical considerations, Susanne needs to take a good hard look at rho. The LEAPS rho is significantly higher than that of its short-term counterpart. A one- percentage-point change in the interest rate will change Susanne’s P&(L) by $0.64—that’s about 8.5 percent of the value of her option—and she has nearly two years of exposure to interest rate fluctuations. Certainly, when the Federal Reserve Board has great concerns about growth or inflation, rates can rise or fall by more than one percentage point in one year’s time. It is important to understand that, like the other greeks, rho is a snapshot at a particular price, volatility level, interest rate, and moment in time. If interest rates were to fall by one percentage point today, it would cause Susanne’s call to decline in value by $0.64. If that rate drop occurred over the life of the option, it would have a much smaller effect. Why? Rate changes closer to expiration have less of an effect on option values. Assume that on the trade date, when the LEAPS has 639 days until expiration, interest rates fall by 25 basis points. The effect will be a decline in the value of the call of 0.16—one-fourth of the 0.638 rho. If the next rate cut occurs six months later, the rho of the LEAPS will be smaller, because it will have less time until expiration. In this case, after six months, the rho will be only 0.46. Another 25-basis-point drop will hurt the call by $0.115. After another six months, the option will have a 0.26 rho. Another quarter- point cut costs Susanne only $0.065. Any subsequent rate cuts in ensuing months will have almost no effect on the now short-term option value. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:223 SCORE: 29.50 ================================================================================ Pricing in Interest Rate Moves In the same way that volatility can get priced in to an option’s value, so can the interest rate. When interest rates are expected to rise or fall, those expectations can be reflected in the prices of options. Say current interest rates are at 8 percent, but the Fed has announced that the economy is growing at too fast of a pace and that it may raise interest rates at the next Federal Open Market Committee meeting. Analysts expect more rate hikes to follow. The options with expiration dates falling after the date of the expected rate hikes will have higher interest rates priced in. In this situation, the higher interest rates in the longer-dated options will be evident when entering parameters into the model. Take options on Already Been Chewed Bubblegum Corp. (ABC). A trader, Kyle, enters parameters into the model for ABC options and notices that the prices don’t line up. To get the theoretical values of the ATM calls for all the expiration months to sit in the middle of the actual market values, Kyle may have to tinker with the interest rate inputs. Assume the following markets for the ATM 70-strike calls in ABC options: Calls Puts Aug 70 calls1.75–1.851.30–1.40 Sep 70 calls2.65–2.751.75–1.85 Dec 70 calls4.70–4.902.35–2.45 Mar 70 calls6.50–6.702.65–2.75 ABC is at $70 a share, has a 20 percent IV in all months, and pays no dividend. August expiration is one month away. Entering the known inputs for strike price, stock price, time to expiration, volatility, and dividend and using an 8 percent interest rate yields the following theoretical values for ABC options: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:224 SCORE: 20.00 ================================================================================ The theoretical values, in bold type, are those that don’t line up in the middle of the call and put markets. These values are wrong. The call theoretical values are too low, and the put theoretical values are too high. They are the product of an interest rate that is too low being applied to the model. To generate values that are indicative of market prices, Kyle must change the interest input to the pricing model to reflect the market’s expectations of future interest rate changes. Using new values for the interest rate yields the following new values: After recalculating, the theoretical values line up in the middle of the call and put markets. Using higher interest rates for the longer expirations raises the call values and lowers the put values for these months. These interest rates were inferred from, or backed out of, the option-market prices by use of the option-pricing model. In practice, it may take some trial and error to find the correct interest values to use. In times of interest rate uncertainty, rho can be an important factor in determining which strategy to select. When rates are generally expected to continue to rise or fall over time, they are normally priced in to the options, as shown in the previous example. When there is no consensus among analysts and traders, the rates that are priced in may change as economic data are made available. This can cause a revision of option values. In long- term options that have higher rhos, this is a bona fide risk. Short-term ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:226 SCORE: 49.00 ================================================================================ Trading Rho While it’s possible to trade rho, most traders forgo this niche for more dynamic strategies with greater profitability. The effects of rho are often overshadowed by the more profound effects of the other greeks. The opportunity to profit from rho is outweighed by other risks. For most traders, rho is hardly ever even looked at. Because LEAPS have higher rho values than corresponding short-term options, it makes sense that these instruments would be appropriate for interest-rate plays. But even with LEAPS, rho exposure usually pales in comparison with that of delta, theta, and vega. It is not uncommon for the rho of a long-term option to be 5 to 8 percent of the option’s value. For example, Exhibit 7.2 shows a two-year LEAPS on a $70 stock with the following pricing-model inputs and outputs: EXHIBIT 7.2 Long 70-strike LEAPS call. The rho is +0.793, or about 5.8 percent of the call value. That means a 25- basis-point rise in rates contributes to only a 20-cent profit on the call. That’s only about 1.5 percent of the call’s value. On one hand, 1.5 percent is not a very big profit on a trade. On the other hand, if there are more rate rises at following Fed meetings, the trader can expect further gains on rho. Even if the trader is compelled to wait until the next Fed meeting to make another $0.20—or less, as rho will get smaller as time passes—from a second 25-basis-point rate increase, other influences will diminish rho’s significance. If over the six-week period between Fed meetings, the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:227 SCORE: 61.00 ================================================================================ underlying declines by just $0.60, the $0.40 that the trader hoped to make on rho is wiped out by delta loss. With the share price $0.60 lower, the 0.760 delta costs the trade about $0.46. Furthermore, the passing of six weeks (42 days) will lead to a loss of about $0.55 from time decay because of the −0.013 theta. There is also the risk from the fat vegas associated with LEAPS. A 1.5 percent drop in implied volatility completely negates any hopes of rho profits. Aside from the possibility that delta, theta, and vega may get in the way of profits, the bid-ask spread with these long-term options tends to be wider than with their short-term counterparts. If the bid-ask spread is more than $0.40 wide, which is often the case with LEAPS, rho profits are canceled out by this cost of doing business. Buying the offer and selling the bid negative scalps away potential profits. With LEAPS, rho is always a concern. It will contribute to prosperity or peril and needs to be part of the trade plan from forecast to implementation. Buying or selling a LEAPS call or put, however, is not a practical way to speculate on interest rates. To take a position on interest rates in the options market, risk needs to be distilled down to rho. The other greeks need to be spread off. This is accomplished only through the conversions, reversals, and jelly rolls described in Chapter 6. However, the bid-ask can still be a hurdle to trading these strategies for non–market makers. Generally, rho is a greek that for most traders is important to understand but not practical to trade. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:229 SCORE: 32.00 ================================================================================ CHAPTER 8 Dividends and Option Pricing Much of this book studies how to break down and trade certain components of option prices. This chapter examines the role of dividends in the pricing structure. There is no greek symbol that measures an option’s sensitivity to changes in the dividend. And in most cases, dividends are not “traded” by means of options in the same way that volatility, interest, and other option price influences are. Dividends do, though, affect option prices, and therefore a trader’s P&(L), so they deserve attention. There are some instances where dividends provide ample opportunity to the option trader, and there some instances where a change in dividend policy can have desirable, or undesirable, effects on the bottom line. Despite the fact that dividends do not technically involve greeks, they need to be monitored in much the same way as do delta, gamma, theta, vega, and rho. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:232 SCORE: 25.00 ================================================================================ Dividends and Option Pricing The preceding discussion demonstrated how dividends affect stock traders. There’s one problem: we’re option traders! Option holders or writers do not receive or pay dividends, but that doesn’t mean dividends aren’t relevant to the pricing of these securities. Observe the behavior of a conversion or a reversal before and after an ex-dividend date. Assuming the stock opens unchanged on the ex-date, the relationship of the price of the synthetic stock to the actual stock price will change. Let’s look at an example to explore why. At the close on the day before the ex-date of a stock paying a $0.25 dividend, a trader has an at-the-money (ATM) conversion. The stock is trading right at $50 per share. The 50 puts are worth 2.34, and the 50 calls are worth 2.48. Before the ex-date, the trader is Long 100 shares at $50 Long one 50 put at 2.34 Short one 50 call at 2.48 Here, the trader is long the stock at $50 and short stock synthetically at $50.14—50 + (2.48 − 2.34). The trader is synthetically short $0.14 over the price at which he is long the stock. Assume that the next morning the stock opens unchanged. Since this is the ex-date, that means the stock opens at $49.75—$0.25 lower than the previous day’s close. The theoretical values of the options will change very little. The options will be something like 2.32 for the put and 2.46 for the call. After the ex-date, the trader is Long 100 shares at $49.75 Long one 50 put at 2.32 Short one 50 call at 2.46 Each option is two cents lower. Why? The change in the option prices is due to theta. In this case, it’s $0.02 for each option. The synthetic stock is still short from an effective price of $50.14. With the stock at $49.75, the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:234 SCORE: 38.00 ================================================================================ Dividends and Early Exercise As the ex-date approaches, in-the-money (ITM) calls on equity options can often be found trading at parity, regardless of the dividend amount and regardless of how far off expiration is. This seems counterintuitive. What about interest? What about dividends? Normally, these come into play in option valuation. But option models designed for American options take the possibility of early exercise into account. It is possible to exercise American-style calls and exchange them for the underlying stock. This would give traders, now stockholders, the right to the dividend—a right for which they would not be eligible as call holders. Because of the impending dividend, the call becomes an exercise just before the ex-date. For this reason, the call can trade for parity before the ex-date. Let’s look at an example of a reversal on a $70 stock that pays a $0.40 dividend. The options in this reversal have 24 days until expiration, which makes the interest on the 60 strike roughly $0.20, given a 5 percent interest rate. The day before the ex-date, a trader has the following position at the stated prices: Short 100 shares at $70 Long one 60 call at 10.00 Short one 60 put at 0.05 To understand how American calls work just before the ex-date, it is helpful first to consider what happens if the trader holds the position until the ex-date. Making the assumption that the stock is unchanged on the ex- dividend date, it will open at $69.60, lower by the amount of the dividend— in this case, $0.40. The put, being so far out-of-the-money (OTM) as to have a negligible delta, will remain unchanged. But what about the call? With no dividend left in the stock, the put call-parity states In this case, ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:235 SCORE: 43.00 ================================================================================ Before the ex-date, the model valued the call at parity. Now it values the same call at $0.25 over parity (9.85 − [69.60 − 60]). Another way to look at this is that the time value of the call is now made up of the interest plus the put premium. Either way, that’s a gain of $0.25 on the call. That sounds good, but because the trader is short stock, if he hasn’t exercised, he will owe the $0.40 dividend—a net loss of $0.15. The new position will be Short 100 shares at $69.60 Owe $0.40 dividend Long one 60 call at 9.85 Short one 60 put at 0.05 At the end of the trading day before the ex-date, this trader must exercise the call to capture the dividend. By doing so, he closes two legs of the trade —the call and the stock. The $10 call premium is forfeited, the stock that is short at $70 is bought at $60 (from the call exercise) for a $10 profit. The transaction leads to neither a profit nor a loss. The purpose of exercising is to avoid the $0.15 loss ($0.25 gain in call time value minus the $0.40 loss in dividends owed). The other way the trader could achieve the same ends is to sell the long call and buy in the short stock. This is tactically undesirable because the trader may have to sell the bid in the call and buy the offer in the stock. Furthermore, when legging a trade in this manner, there is the risk of slippage. If the call is sold first, the stock can move before the trader has a chance to buy it at the necessary price. It is generally better and less risky to exercise the call rather than leg out of the trade. In this transaction, the trader begins with a fairly flat position (short stock/long synthetic stock) and ends with a short put that is significantly out-of-the-money. For all intents and purposes, exercising the call in this trade is like synthetically selling the put. But at what price? In this case, it’s $0.15. This again is the cost benefit of saving $0.40 by avoiding the dividend obligation versus the $0.25 gain in call time value. Exercising the call is effectively like selling the put at 0.15 in this example. If the dividend is lower or the interest is higher, it may not be worth it to the trader to exercise the call to capture the dividend. How do traders know if their calls should be exercised? ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:236 SCORE: 23.00 ================================================================================ The traders must do the math before each ex-dividend date in option classes they trade. The traders have to determine if the benefit from exercising—or the price at which the synthetic put is essentially being sold —is more or less than the price at which they can sell the put. The math used here is adopted from put-call parity: This shows the case where the traders can effectively synthetically sell the put (by exercising) for more than the current put value. Tactically, it’s appropriate to use the bid price for the put in this calculation since that is the price at which the put can be sold. In this case, the traders would be inclined to not exercise. It would be theoretically more beneficial to sell the put if the trader is so inclined. Here, the traders, from a valuation perspective, are indifferent as to whether or not to exercise. The question then is simply: do they want to sell the put at this price? Professionals and big retail traders who are long (ITM) calls—whether as part of a reversal, part of another type of spread, or because they are long the calls outright—must do this math the day before each ex-dividend date to maximize profits and minimize losses. Not exercising, or forgetting to exercise, can be a costly mistake. Traders who are short ITM dividend- paying calls, however, can reap the benefits of those sleeping on the job. It works both ways. Traders who are long stock and short calls at parity before the ex-date may stand to benefit if some of the calls do not get assigned. Any shares of long stock remaining on the ex-date will result in the traders receiving dividends. If the dividends that will be received are greater in value than the interest that will subsequently be paid on the long stock, the traders may stand reap an arbitrage profit because of long call holders’ forgetting to exercise. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:237 SCORE: 23.00 ================================================================================ Dividend Plays The day before an ex-dividend date in a stock, option volume can be unusually high. Tens of thousands of contracts sometimes trade in names that usually have average daily volumes of only a couple thousand. This spike in volume often has nothing to do with the market’s opinion on direction after the dividend. The heavy trading has to do with the revaluation of the relationship of exercisable options to the underlying expected to occur on the ex-dividend date. Traders that are long ITM calls and short ITM calls at another strike just before an ex-dividend date have a potential liability and a potential benefit. The potential liability is that they can forget to exercise. This is a liability over which the traders have complete control. The potential benefit is that some of the short calls may not get assigned. If traders on the other side of the short calls (the longs) forget to exercise, the traders that are short the call make out by not having to pay the dividend on short stock. Professionals and big retail traders who have very low transaction costs will sometimes trade ITM call spreads during the afternoon before an ex- dividend date. This consists of buying one call and selling another call with a different strike price. Both calls in the dividend-play strategy are ITM and have corresponding puts with little or no value (to be sure, the put value is less than the dividend minus the interest). The traders trade the spreads, fairly indifferent as to whether they buy or sell the spreads, in hope of skating—or not getting assigned—on some of their short calls. The more they don’t get assigned the better. This usually occurs in options that have high open interest, meaning there are a lot of outstanding contracts already. The more contracts in existence, the better the possibility of someone forgetting to exercise. The greatest volume also tends to occur in the front month. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:238 SCORE: 21.00 ================================================================================ Strange Deltas Because American calls become an exercise possibility when the ex-date is imminent, the deltas can sometimes look odd. When the calls are trading at parity, they have a 1.00 delta. They are a substitute for the stock. They, in fact, will be stock if and when they are exercised just before the ex-date. But if the puts still have some residual time value, they may also have a small delta, of 0.05 or perhaps more. In this unique scenario, the delta of the synthetic can be greater than +1.00 or less than −1.00. It is not uncommon to see the absolute values of the call and put deltas add up to 1.07 or 1.08. When the dividend comes out of the options model on the ex-date, synthetics go back to normal. The delta of the synthetic again approaches 1.00. Because of the out-of-whack deltas, delta-neutral traders need to take extra caution in their analytics when ex- dates are near. A little common sense should override what the computer spits out. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:239 SCORE: 10.00 ================================================================================ Inputting Dividend Data into the Pricing Model Often dividend payments are regular and predictable. With many companies, the dividend remains constant quarter after quarter. Some corporations have a track record of incrementally increasing their dividends every year. Some companies pay dividends in a very irregular fashion, by paying special dividends that are often announced as a surprise to investors. In a truly capitalist society, there are no restrictions and no rules on when, whether, or how corporations pay dividends to their shareholders. Unpredictability of dividends, though, can create problems in options valuation. When a company has a constant, reasonably predictable dividend, there is not a lot of guesswork. Take Exelon Corp. (EXC). From November 2008 to the time of this writing, Exelon has paid a regular quarterly dividend of $0.525. During that period, a trader has needed simply to enter 0.525 into the pricing calculator for all expected future dividends to generate the theoretical value. Based on recent past performance, the trader could feel confident that the computed analytics were reasonably accurate. If the trader believed the company would continue its current dividend policy, there would be little options-related dividend risk—unless things changed. When there is uncertainty about when future dividends will be paid in what amounts, the level of dividend-related risk begins to increase. The more uncertainty, the more risk. Let’s examine an interesting case study: General Electric (GE). For a long time, GE was a company that has had a history of increasing its dividends at fairly regular intervals. In fact, there was more than a 30- year stretch in which GE increased its dividend every year. During most of the first decade of the 2000s, increases in GE’s dividend payments were around one to six cents and tended to occur toward the end of December, after December expiration. The dividends were paid four times per year but not exactly quarterly. For several years, the ex-dates were in February, June, September, and December. Option traders trading GE options had a pretty ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:243 SCORE: 13.00 ================================================================================ Good and Bad Dates with Models Using an incorrect date for the ex-date in option pricing can lead to unfavorable results. If the ex-dividend date is not known because it has yet to be declared, it must be estimated and adjusted as need be after it is formally announced. Traders note past dividend history and estimate the expected dividend stream accordingly. Once the dividend is declared, the ex-date is known and can be entered properly into the pricing model. Not executing due diligence to find correct known ex-dates can lead to trouble. Using a bad date in the model can yield dubious theoretical values that can be misleading or worse—especially around the expiration. Say a call is trading at 2.30 the day before the ex-date of a $0.25 dividend, which happens to be thirty days before expiration. The next day, of course, the stock may have moved higher or lower. Assume for illustrative purposes, to compare apples to apples as it were, that the stock is trading at the same price—in this case, $76. If the trader is using the correct date in the model, the option value will adjust to take into account the effect of the dividend expiring, or reaching its ex-date, when the number of days to expiration left changes from 30 to 29. The call trading postdividend will be worth more relative to the same stock price. If the dividend date the trader is using in the model is wrong, say one day later than it should be, the dividend will still be an input of the theoretical value. The calculated value will be too low. It will be wrong. Exhibit 8.1 compares the values of a 30-day call on the ex-date given the right and the wrong dividend. EXHIBIT 8.1 Comparison of 30-day call values ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:244 SCORE: 20.00 ================================================================================ At the same stock price of $76 per share, the call is worth $0.13 more after the dividend is taken out of the valuation. Barring any changes in implied volatility (IV) or the interest rate, the market prices of the options should reflect this change. A trader using an ex-date in the model that is farther in the future than the actual ex-date will still have the dividend as part of the generated theoretical value. With the ex-date just one day later, the call would be worth 2.27. The difference in option value is due to the effect of theta—in this case, $0.03. With a bad date, the value of 2.27 would likely be significantly below market price, causing the market value of the option to look more expensive than it actually is. If the trader did not know the date was wrong, he would need to raise IV to make the theoretical value match the market. This option has a vega of 0.08, which translates into a difference of about two IV points for the theoretical values 2.43 and 2.27. The trader would perceive the call to be trading at an IV two points higher than the market indicates. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:245 SCORE: 15.00 ================================================================================ Dividend Size It’s not just the date but also the size of the dividend that matters. When companies change the amount of the dividend, options prices follow in step. In 2004, when Microsoft (MSFT) paid a special dividend of $3 per share, there were unexpected winners and losers in the Microsoft options. Traders who were long calls or short puts were adversely affected by this change in dividend policy. Traders with short calls or long puts benefited. With long- term options, even less anomalous changes in the size of the dividend can have dramatic effects on options values. Let’s study an example of how an unexpected rise in the quarterly dividend of a stock affects a long call position. Extremely Yellow Zebra Corp. (XYZ) has been paying a quarterly dividend of $0.10. After a steady rise in stock price to $61 per share, XYZ declares a dividend payment of $0.50. It is expected that the company will continue to pay $0.50 per quarter. A trader, James, owns the 528-day 60-strike calls, which were trading at 9.80 before the dividend increase was announced. Exhibit 8.2 compares the values of the long-term call using a $0.10 quarterly dividend and using a $0.50 quarterly dividend. EXHIBIT 8.2 Effect of change in quarterly dividend on call value. This $0.40 dividend increase will have a big effect on James’s calls. With 528 days until expiration, there will be six dividends involved. Because ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:246 SCORE: 10.00 ================================================================================ James is long the calls, he loses 1.52 per option. If, however, he were short the calls, 1.52 would be his profit on each option. Put traders are affected as well. Another trader, Marty, is long the 60- strike XYZ puts. Before the dividend announcement, Marty was running his values with a $0.10 dividend, giving his puts a value of 5.42. Exhibit 8.3 compares the values of the puts with a $0.10 quarterly dividend and with a $0.50 quarterly dividend. EXHIBIT 8.3 Effect of change in quarterly dividend on put value. When the dividend increase is announced, Marty will benefit. His puts will rise because of the higher dividend by $0.66 (all other parameters held constant). His long-term puts with six quarters of future expected dividends will benefit more than short-term XYZ puts of the same strike would. Of course, if he were short the puts, he would lose this amount. The dividend inputs to a pricing model are best guesses until the dates and amounts are announced by the company. How does one find dividend information? Regularly monitoring the news and press releases on the companies one trades is a good way to stay up to date on dividend information, as well as other company news. Dividend announcements are widely disseminated by the major news services. Most companies also have an investor-relations phone number and section on their web sites where dividend information can be found. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:248 SCORE: 19.00 ================================================================================ CHAPTER 9 Vertical Spreads Risk—it is the focal point around which all trading revolves. It may seem as if profit should be occupying this seat, as most important to trading options, but without risk, there would be no profit! As traders, we must always look for ways to mitigate, eliminate, preempt, and simply avoid as much risk as possible in our pursuit of success without diluting opportunity. Risk must be controlled. Trading vertical spreads takes us one step further in this quest. The basic strategies discussed in Chapters 4 and 5 have strengths when compared with pure linear trading in the equity markets. But they have weaknesses, too. Consider the covered call, one of the most popular option strategies. A covered call is best used as an augmentation to an investment plan. It can be used to generate income on an investment holding, as an entrance strategy into a stock, or as an exit strategy out of a stock. But from a trading perspective, one can often find better ways to trade such a forecast. If the forecast on a stock is neutral to moderately bullish, accepting the risk of stock ownership is often unwise. There is always the chance that the stock could collapse. In many cases, this is an unreasonable risk to assume. To some extent, we can make the same case for the long call, short put, naked call, and the like. In certain scenarios, each of these basic strategies is accompanied with unwanted risks that serve no beneficial purpose to the trader but can potentially cause harm. In many situations, a vertical spread is a better alternative to these basic spreads. Vertical spreads allow a trader to limit potential directional risk, limit theta and vega risk, free up margin, and generally manage capital more efficiently. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:250 SCORE: 51.00 ================================================================================ Bull Call Spread A bull call spread is a long call combined with a short call that has a higher strike price. Both calls are on the same underlying and share the same expiration month. Because the purchased call has a lower strike price, it costs more than the call being sold. Establishing the trade results in a debit to the trader’s account. Because of this debit, it’s called a debit spread. Below is an example of a bull call spread on Apple Inc. (AAPL): In this example, Apple is trading around $391. With 40 days until February expiration, the trader buys the 395–405 call spread for a net debit of $4.40, or $440 in actual cash. Or one could simply say the trader paid $4.40 for the 395–405 call. Consider the possible outcomes if the spread is held until expiration. Exhibit 9.1 shows an at-expiration diagram of the bull call spread. EXHIBIT 9.1 AAPL bull call spread. Before discussing the greeks, consider the bull call spread from an at- expiration perspective. Unlike the long call, which has two possible ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:251 SCORE: 86.50 ================================================================================ outcomes at expiration—above or below the strike—this spread has three possibilities: below both strikes, between the strikes, or above both strikes. In this example, if Apple is below $395 at expiration, both calls expire worthless. The rights and obligations of the options are gone, as is the cash spent on the trade. In this case, the entire debit of $4.40 is lost. If Apple is between the strikes at expiration, the 405-strike call expires worthless. The trader is long stock at an effective price of $399.40. This is the $395-strike price at which the stock would be purchased if the call is exercised, plus the $4.40 premium spent on the spread. The break-even price of the trade is $399.40. If Apple is above $399.40 at expiration, the trade is profitable; below $399.40, it is a loser. The aptly named bull call spread requires the stock to rise to reach its profit potential. But unlike an outright long call, profits are capped with the spread. If Apple is above $405 at expiration, both calls are in-the-money (ITM). If the 395-strike calls are exercised, the trader buys 100 shares of Apple at $395 and these shares, in turn, would be sold at $405 when the 405-strike calls are assigned, for a $10 gain per share. Subtract from that $10 the $4.40 debit spent on the trade and the net profit is $5.60 per share. There are some other differences between the 395–405 call spread and the outright purchase of the 395 call. The absolute risk is lower. To buy the 395-strike call costs 14.60, versus 4.40 for the spread—a big difference. Because the debit is lower, the margin for the spread is lower at most option-friendly brokers, as well. If we dig a little deeper, we find some other differences between the bull call spread and the outright call. Long options are haunted by the specter of time. Because the spread involves both a long and a short option, the time- decay risk is lower than that associated with owning an option outright. Implied volatility (IV) risk is lower, too. Exhibit 9.2 compares the greeks of the long 395 call with those of the 395–405 call spread. EXHIBIT 9.2 Apple call versus bull call spread (Apple @ $391). 395 Call395–405 Call Delta 0.484 0.100 Gamma0.00970.0001 Theta −0.208−0.014 Vega 0.513 0.020 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:252 SCORE: 113.00 ================================================================================ The positive deltas indicate that both positions are bullish, but the outright call has a higher delta. Some of the 395 call’s directional sensitivity is lost when the 405 call is sold to make a spread. The negative delta of the 405 call somewhat offsets the positive delta of the 395 call. The spread delta is only about 20 percent of the outright call’s delta. But for a trader wanting to focus on trading direction, the smaller delta can be a small sacrifice for the benefit of significantly reduced theta and vega. Theta spread’s risk is about 7 percent that of the outright. The spread’s vega risk is also less than 4 percent that of the outright 395 call. With the bull call spread, a trader can spread off much of the exposure to the unwanted risks and maintain a disproportionately higher greeks in the wanted exposure (delta). These relationships change as the underlying moves higher. Remember, at-the-money (ATM) options have the greatest sensitivity to theta and vega. With Apple sitting at around the long strike, gamma and vega have their greatest positive value, and theta has its most negative value. Exhibit 9.3 shows the spread greeks given other underlying prices. EXHIBIT 9.3 AAPL 395–405 bull call spread. As the stock moves higher toward the 405 strike, the 395 call begins to move away from being at-the-money, and the 405 call moves toward being at-the-money. The at-the-money is the dominant strike when it comes to the characteristics of the spread greeks. Note the greeks position when the underlying is directly between the two strike prices: The long call has ceased to be the dominant influence on these metrics. Both calls influence the analytics pretty evenly. The time-decay risk has been entirely spread off. The volatility risk is mostly spread off. Gamma remains a minimal concern. When the greeks of the two calls balance each other, the result is a directional play. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:253 SCORE: 92.00 ================================================================================ As AAPL continues to move closer to the 405-strike, it becomes the at- the-money option, with the dominant greeks. The gamma, theta, and vega of the 405 call outweigh those of the ITM 395 call. Vega is more negative. Positive theta now benefits the trade. The net gamma of the spread has turned negative. Because of the negative gamma, the delta has become smaller than it was when the stock was at $400. This means that the benefit of subsequent upward moves in the stock begins to wane. Recall that there is a maximum profit threshold with a vertical spread. As the stock rises beyond $405, negative gamma makes the delta smaller and time decay becomes less beneficial. But at this point, the delta has done its work for the trader who bought this spread when the stock was trading around $395. The average delta on a move in the stock from $395 to $405 is about 0.10 in this case. When the stock is at the 405 strike, the characteristics of the trade are much different than they are when the stock is at the 395 strike. Instead of needing movement upward in the direction of the delta to combat the time decay of the long calls, the position can now sit tight at the short strike and reap the benefits of option decay. The key with this spread, and with all vertical spreads, is that the stock needs to move in the direction of the delta to the short strike. Strengths and Limitations There are many instances when a bull call spread is superior to other bullish strategies, such as a long call, and there are times when it isn’t. Traders must consider both price and time. A bull call spread will always be cheaper than the outright call purchase. That’s because the cost of the long-call portion of the spread is partially offset by the premium of the higher-strike short call. Spending less for the same exposure is always a better choice, but the exposure of the vertical is not exactly the same as that of the long call. The most obvious trade-off is the fact that profit is limited. For smaller moves—up to the price of the short strike—vertical spreads tend to be better trades than outright call purchases. Beyond the strike? Not so much. But time is a trade-off, too. There have been countless times that I have talked with new traders who bought a call because they thought the stock ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:254 SCORE: 54.00 ================================================================================ was going up. They were right and still lost money. As the adage goes, timing is everything. The more time that passes, the more advantageous the lower-theta vertical spread becomes. When held until expiration, a vertical spread can be a better trade than an outright call in terms of percentage profit. In the previous example, when Apple is at $391 with 40 days until expiration, the 395 call is worth 14.60 and the spread is worth 4.40. If Apple were to rise to be trading at $405 at expiration, the call rises to be worth 10, for a loss of 4.60 on the 14.60 debit paid. The spread also is worth 10. It yields a gain of about 127 percent on the initial $4.40 per share debit. But look at this same trade if the move occurs before expiration. If Apple rallies to $405 after only a couple weeks, the outcome is much different. With four weeks still left until expiration, the 395 call is worth 19.85 with the underlying at $405. That’s a 36 percent gain on the 14.60. The spread is worth 5.70. That’s a 30 percent gain. The vertical spread must be held until expiration to reap the full benefits, which it accomplishes through erosion of the short option. The long-call-only play (with a significantly larger negative theta) is punished severely by time passing. The long call benefits more from a quick move in the underlying. And of course, if the stock were to rise to a price greater than $405, in a short amount of time—the best of both worlds for the outright call—the outright long 395 call would be emphatically superior to the spread. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:255 SCORE: 58.00 ================================================================================ Bear Call Spread The next type of vertical spread is called a bear call spread . A bear call spread is a short call combined with a long call that has a higher strike price. Both calls are on the same underlying and share the same expiration month. In this case, the call being sold is the option of higher value. This call spread results in a net credit when the trade is put on and, therefore, is called a credit spread. The bull call spread and the bear call spread are two sides of the same coin. The difference is that with the bull call spread, one is buying the call spread, and with the bear call spread, one is selling the call spread. An example of a bear call spread can be shown using the same trade used earlier. Here we are selling one AAPL February (40-day) 395 call at 14.60 and buying the 405 call at 10.20. We are selling the 395–405 call at $4.40 per share, or $440. Exhibit 9.4 is an at-expiration diagram of the trade. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:256 SCORE: 51.00 ================================================================================ EXHIBIT 9.4 Apple bear call spread. The same three at-expiration outcomes are possible here as with the bull call spread: the stock can be above both strikes, between both strikes, or below both strikes. If the stock is below both strikes at expiration, both calls will expire worthless. The rights and obligations cease to exist. In this case, the entire credit of $440 is profit. If AAPL is between the two strike prices at expiration, the 395-strike call will be in-the-money. The short call will get assigned and result in a short stock position at expiration. The break-even price falls at $399.40—the short strike plus the $4.40 net premium. This is the price at which the stock will effectively be sold if assignment occurs. If Apple is above both strikes at expiration, it means both calls are in-the- money. Stock is sold at $395 because of assignment and bought back at $405 through exercise. This leads to a loss of $10 per share on the negative scalp. Factoring in the $4.40-per-share credit makes the net loss only $5.60 per share with AAPL above $405 at February expiration. Just as the at-expiration diagram is the same but reversed, the greeks for this call spread will be similar to those in the bull call spread example except for the positive and negative signs. See Exhibit 9.5 . EXHIBIT 9.5 Apple 395–405 bear call spread. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:257 SCORE: 53.00 ================================================================================ A credit spread is commonly traded as an income-generating strategy. The idea is simple: sell the option closer-to-the-money and buy the more out-of- the-money (OTM) option—that is, sell volatility—and profit from nonmovement (above a certain point). In this example, with Apple at $391, a neutral to slightly bearish trader would think about selling this spread at 4.40 in hopes that the stock will remain below $395 until expiration. The best-case scenario is that the stock is below $395 at expiration and both options expire, resulting in a $4.40-per-share profit. The strategy profits as long as Apple is under its break-even price, $399.40, at expiration. But this is not so much a bearish strategy as it is a nonbullish strategy. The maximum gain with a credit spread is the premium received, in this case $4.40 per share. Traders who thought AAPL was going to decline sharply would short it or buy a put. If they thought it would rise sharply, they’d use another strategy. From a greek perspective, when the trade is executed it’s very close to its highest theta price point—the 395 short strike price. This position theoretically collects $0.90 a day with Apple at around $395. As time passes, that theta rises. The key is that the stock remains at around $395 until the short option is just about worthless. The name of the game is sit and wait. Although the delta is negative, traders trading this spread to generate income want the spread to expire worthless so they can pocket the $4.40 per share. If Apple declines, profits will be made on delta, and theta profits will be foregone later. All that matters is the break-even point. Essentially, the idea is to sell a naked call with a maximum potential loss. Sell the 395s and buy the 405s for protection. If the underlying decreases enough in the short term and significant profits from delta materialize, it is logical to consider closing the spread early. But it often makes more sense to close part of the spread. Consider ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:258 SCORE: 10.00 ================================================================================ that the 405-strike call is farther out-of-the-money and will lose its value before the 395 call. Say that after two weeks a big downward move occurs. Apple is trading at $325 a share; the 405s are 0.05 bid at 0.10, and the 395s are 0.50 bid at 0.55. At this point, the lion’s share of the profits can be taken early. A trader can do so by closing only the 395 calls. Closing the 395s to eliminate the risk of negative delta and gamma makes sense. But does it make sense to close the 405s for 0.05? Usually not. Recouping this residual value accomplishes little. It makes more sense to leave them in your position in case the stock rebounds. If the stock proves it can move down $70; it can certainly move up $70. Because the majority of the profits were taken on the 395 calls, holding on to the 405s is like getting paid to own calls. In scenarios where a big move occurs and most of the profits can be taken early, it’s often best to hold the long calls, just in case. It’s a win-win situation. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:259 SCORE: 49.00 ================================================================================ Credit and Debit Spread Similarities The credit call spread and the debit call spread appear to be exactly opposite in every respect. Many novice traders perceive credit spreads to be fundamentally different from debit spreads. That is not necessarily so. Closer study reveals that these two are not so different after all. What if Apple’s stock price was higher when the trade was put on? What if the stock was at $405? First, the spread would have had more value. The 395 and 405 calls would both be worth more. A trader could have sold the spread for a $5.65-per-share credit. The at-expiration diagram would look almost the same. See Exhibit 9.6 . EXHIBIT 9.6 Apple bear call spread initiated with Apple at $405. Because the net premium is much higher in this example, the maximum gain is more—it is $5.65 per share. The breakeven is $400.65. The price points on the at-expiration diagram, however, have nothing to do with the greeks. The analytics from Exhibit 9.5 are the same either way. The motivation for a trader selling this call spread, which has both options in-the-money, is different from that for the typical income generator. When the spread is sold in this context, the trader is buying volatility. Long gamma, long vega, negative theta. The trader here has a ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:261 SCORE: 45.00 ================================================================================ Bear Put Spread There is another way to take a bearish stance with vertical spreads: the bear put spread. A bear put spread is a long put plus a short put that has a lower strike price. Both puts are on the same underlying and share the same expiration month. This spread, however, is a debit spread because the more expensive option is being purchased. Imagine that a stock has had a good run-up in price. The chart shows a steady march higher over the past couple of months. A study of technical analysis, though, shows that the run-up may be pausing for breath. An oscillator, such as slow stochastics, in combination with the relative strength index (RSI), indicates that the stock is overbought. At the same time, the average directional movement index (ADX) confirms that the uptrend is slowing. For traders looking for a small pullback, a bear put spread can be an excellent strategy. The goal is to see the stock drift down to the short strike. So, like the other members of the vertical spread family, strike selection is important. Let’s look at an example of ExxonMobil (XOM). After the stock has rallied over a two-month period to $80.55, a trader believes there will be a short-term temporary pullback to $75. Instead of buying the June 80 puts for 1.75, the trader can buy the 75–80 put spread of the same month for 1.30 because the 75 put can be sold for 0.45. 1 In this example, the June put has 40 days until expiration. Exhibit 9.7 illustrates the payout at expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:262 SCORE: 33.00 ================================================================================ EXHIBIT 9.7 ExxonMobil bear put spread. If the trader is wrong and ExxonMobil is still above 80 at expiry, both puts expire and the 1.30 premium is lost. If ExxonMobil is between the two strikes, the 80 puts are ITM, resulting in an exercise, and the 75 puts are OTM and expire. The net effect is short stock at an effective price of $78.70. The effective sale price is found by taking the price at which the short stock is established when the puts are exercised—$80—minus the net 1.30 paid for the spread. This is the spread’s breakeven at expiration. If the trader is right and ExxonMobil is below both strikes at expiration, both puts are ITM, and the result is a 3.70 profit and no position. Why a 3.70 profit? The 80 puts are exercised, making the trader short at $80, and the 75 puts are assigned, so the short is bought back at $75 for a positive stock scalp of $5. Including the 1.30 debit for the spread in the profit and loss (P&(L)), the net profit is $3.70 per share when the stock is below both strikes at expiration. This is a bearish trade. But is the bear put spread necessarily a better trade than buying an outright ATM put? No. The at-expiration diagram makes this clear. Profits are limited to $3.70 per share. This is an important difference. But because in this particular example, the trader expects the stock to retrace only to around $75, the benefits of lower cost and lower theta and vega risk can be well worth the trade-off of limited profit. The trader’s ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:263 SCORE: 89.00 ================================================================================ objectives are met more efficiently by buying the spread. The goal is to profit from the delta move down from $80 to $75. Exhibit 9.8 shows the differences between the greeks of the outright put and the spread when the trade is put on with ExxonMobil at $80.55. EXHIBIT 9.8 ExxonMobil put vs. bear put spread (ExxonMobil @ $80.55). 80 Put75–80 Put Delta −0.445−0.300 Gamma+0.080+0.041 Theta −0.018−0.006 Vega +0.110+0.046 As in the call-spread examples discussed previously, the spread delta is smaller than the outright put’s. It appears ironic that the spread with the smaller delta is a better trade in this situation, considering that the intent is to profit from direction. But it is the relative differences in the greeks besides delta that make the spread worthwhile given the trader’s goal. Gamma, theta, and vega are proportionately much smaller than the delta in the spread than in the outright put. While the spread’s delta is two thirds that of the put, its gamma is half, its theta one third, and its vega around 42 percent of the put’s. Retracements such as the one called for by the trader in this example can happen fast, sometimes over the course of a week or two. It’s not necessarily bad if this move occurs quickly. If ExxonMobil drops by $5 right away, the short delta will make the position profitable. Exhibit 9.9 shows how the spread position changes as the stock declines from $80 to $75. EXHIBIT 9.9 75–80 bear put spread as ExxonMobil declines. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:264 SCORE: 46.00 ================================================================================ The delta of this trade remains negative throughout the stock’s descent to $75. Assuming the $5 drop occurs in one day, a delta averaging around −0.36 means about a 1.80 profit, or $180 per spread, for the $5 move (0.36 times $5 times 100). This is still a far cry from the spread’s $3.70 potential profit. Although the stock is at $75, the maximum profit potential has yet to be reached, and it won’t be until expiration. How does the rest of the profit materialize? Time decay. The price the trader wants the stock to reach is $75, but the assumption here is that the move happens very fast. The trade went from being a long- volatility play—long gamma and vega—to a short-vol play: short gamma and vega. The trader wanted movement when the stock was at $80 and wants no movement when the stock is at $75. When the trade changes characteristics by moving from one strike to another, the trader has to reconsider the stock’s outlook. The question is: if I didn’t have this position on, would I want it now? The trader has a choice to make: take the $180 profit—which represents a 138 percent profit on the 1.30 debit—or wait for theta to do its thing. The trader looking for a retracement would likely be inclined to take a profit on the trade. Nobody ever went broke taking a profit. But if the trader thinks the stock will sit tight for the remaining time until expiration, he will be happy with this income-generating position. Although the trade in the last, overly simplistic example did not reap its full at-expiration potential, it was by no means a bad trade. Holding the spread until expiration is not likely to be part of a trader’s plan. Buying the 80 put outright may be a better play if the trader is expecting a fast move. It would have a bigger delta than the spread. Debit and credit spreads can be used as either income generators or as delta plays. When they’re used as delta plays, however, time must be factored in. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:265 SCORE: 55.00 ================================================================================ Bull Put Spread The last of the four vertical spreads is a bull put spread. A bull put spread is a short put with one strike and a long put with a lower strike. Both puts are on the same underlying and in the same expiration cycle. A bull put spread is a credit spread because the more expensive option is being sold, resulting in a net credit when the position is established. Using the same options as in the bear put example: With ExxonMobil at $80.55, the June 80 puts are sold for 1.75 and the June 75 puts are bought at 0.45. The trade is done for a credit of 1.30. Exhibit 9.10 shows the payout of this spread if it is held until expiration. EXHIBIT 9.10 ExxonMobil bull put spread. The sale of this spread generates a 1.30 net credit, which is represented by the maximum profit to the right of the 80 strike. With ExxonMobil above $80 per share at expiration, both options expire OTM and the premium is all profit. Between the two strike prices, the 80 put expires in the money. If the ITM put is still held at expiration, it will be assigned. Upon assignment, ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:266 SCORE: 88.00 ================================================================================ the put becomes long stock, profiting with each tick higher up to $80, or losing with each tick lower to $75. If the 80 put is assigned, the effective price of the long stock will be $78.70. The assignment will “hit your sheets” as a buy at $80, but the 1.30 credit lowers the effective net cost to $78.70. If the stock is below $75 at option expiration, both puts will be ITM. This is the worst case scenario, because the higher-struck put was sold. At expiration, the 80 puts would be assigned, the 75 puts exercised. That’s a negative scalp of $5 on the resulting stock. The initial credit lessens the pain by 1.30. The maximum possible loss with ExxonMobil below both strikes at expiration is $3.70 per spread. The spread in this example is the flip side of the bear put spread of the previous example. Instead of buying the spread, as with the bear put, the spread in this case is sold. Exhibit 9.11 shows the analytics for the bull put spread. EXHIBIT 9.11 Greeks for ExxonMobil 75–80 bull put spread. Instead of having a short delta, as with the bear spread, the bull spread is long delta. There is negative theta with positive gamma and vega as XOM approaches the long strike—the 75s, in this case. There is also positive theta with negative gamma and vega around the short strike—the 80s. Exhibit 9.11 shows the characteristics that define the vertical spread. If one didn’t know which particular options were being traded here, this could almost be a table of greeks for either a 75–80 bull put spread or a 75–80 bull call spread. Like the other three verticals, this spread can be a delta play or a theta play. A bullish trader may sell the spread if both puts are in-the-money. Imagine that XOM is trading at around $75. The spread will have a positive ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:267 SCORE: 56.50 ================================================================================ 0.364 delta, positive gamma, and negative theta. The spread as a whole is a decaying asset. It needs the underlying to rally to combat time decay. A bullish trader may also sell this spread if XOM is between the two strikes. In this case, with XOM at, say, $77, the delta is +0.388, and all other greeks are negligible. At this particular price point in the underlying, the trader has almost pure leveraged delta exposure. But this trade would be positioned for only a small move, not much above $80. A speculator wanting to trade direction for a small move while eliminating theta and vega risks achieves her objectives very well with a vertical spread. A bullish-to-neutral trader would be inclined to sell this spread if ExxonMobil were around $80 or higher. Day by day, the 1.30 premium would start to come in. With 40 days until expiration, theta would be small, only 0.004. But if the stock remained at $80, this ATM put would begin decaying faster and faster. The objective of trading this spread for a neutral trader is selling future realized volatility—selling gamma to earn theta. A trader can also trade a vertical spread to profit from IV. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:268 SCORE: 95.00 ================================================================================ Verticals and Volatility The IV component of a vertical spread, although small compared with that of an outright call or put, is still important—especially for large traders with low margin and low commissions who can capitalize on small price changes efficiently. Whether it’s a call spread or a put spread, a credit spread or a debit spread, if the underlying is at the short option’s strike, the spread will have a net negative vega. If the underlying is at the long option’s strike, the spread will have positive vega. Because of this characteristic, there are three possible volatility plays with vertical spreads: speculating on IV changes when the underlying remains constant, profiting from IV changes resulting from movement of the underlying, and special volatility situations. Vertical spreads offer a limited-risk way to speculate on volatility changes when the underlying remains fairly constant. But when the intent of a vertical spread is to benefit from vega, one must always consider the delta —it’s the bigger risk. Chapter 13 discusses ways to manage this risk by hedging with stock, a strategy called delta-neutral trading. Non-delta-neutral traders may speculate on vol with vertical spreads by assuming some delta risk. Traders whose forecast is vega bearish will sell the option with the strike closest to where the underlying is trading—that is, the ATM option—and buy an OTM strike. Traders would lean with their directional bias by choosing either a call spread or a put spread. As risk managers, the traders balance the volatility stance being taken against the additional risk of delta. Again, in this scenario, delta can hurt much more than help. In the ExxonMobil bull put spread example, the trader would sell the 80- strike put if ExxonMobil were around $80 a share. In this case, if the stock didn’t move as time passed, theta would benefit from historical volatility being’s low—that is, from little stock movement. At first, the benefit would be only 0.004 per day, speeding up as expiration nears. And if implied volatility decreased, the trader would profit 0.04 for every 1 percent decline in IV. Small directional moves upward help a little. But in the long run, ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:269 SCORE: 66.00 ================================================================================ those profits are leveled off by the fact that theta gets smaller as the stock moves higher above $80—more profit on direction, less on time. For the delta player, bull call spreads and bull put spreads have a potential added benefit that stems from the fact that IV tends to decrease as stocks rise and increase when stocks fall. This offers additional opportunity to the bull spread player. With the bull call spread or the bull put spread, the trader gains on positive delta with a rally. Once the underlying comes close to the short option’s strike, vega is negative. If IV declines, as might be anticipated, there is a further benefit of vega profits on top of delta profits. If the underlying declines, the trader loses on delta. But the pain can potentially be slightly lessened by vega profits. Vega will get positive as the underlying approaches the long strike, which will benefit from the firming of IV that often occurs when the stock drops. But this dual benefit is paid for in the volatility skew. In most stocks or indexes, the lower strikes—the ones being bought in a bull spread—have higher IVs than the higher strikes, which are being sold. Then there are special market situations in which vertical spreads that benefit from volatility changes can be traded. Traders can trade vertical spreads to strategically position themselves for an expected volatility change. One example of such a situation is when a stock is rumored to be a takeover target. A natural instinct is to consider buying calls as an inexpensive speculation on a jump in price if the takeover is announced. Unfortunately, the IV of the call is often already bid up by others with the same idea who were quicker on the draw. Buying a call spread consisting of a long ITM call and a short OTM call can eliminate immediate vega risk and still provide wanted directional exposure. Certainly, with this type of trade, the trader risks being wrong in terms of direction, time, and volatility. If and when a takeover bid is announced, it will likely be for a specific price. In this event, the stock price is unlikely to rise above the announced takeover price until either the deal is consummated or a second suitor steps in and offers a higher price to buy the company. If the takeover is a “cash deal,” meaning the acquiring company is tendering cash to buy the shares, the stock will usually sit in a very tight range below the takeover price for a long time. In this event, implied volatility will often drop to very low levels. Being short an ATM call when ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:271 SCORE: 67.00 ================================================================================ The Interrelations of Credit Spreads and Debit Spreads Many traders I know specialize in certain niches. Sometimes this is because they find something they know well and are really good at. Sometimes it’s because they have become comfortable and don’t have the desire to try anything new. I’ve seen this strategy specialization sometimes with traders trading credit spreads and debit spreads. I’ve had serial credit spread traders tell me credit spreads are the best trades in the world, much better than debit spreads. Habitual debit spread traders have likewise said their chosen spread is the best. But credit spreads and debit spreads are not so different. In fact, one could argue that they are really the same thing. Conventionally, credit-spread traders have the goal of generating income. The short option is usually ATM or OTM. The long option is more OTM. The traders profit from nonmovement via time decay. Debit-spread traders conventionally are delta-bet traders. They buy the ATM or just out-of-the- money option and look for movement away from or through the long strike to the short strike. The common themes between the two are that the underlying needs to end up around the short strike price and that time has to pass to get the most out of either spread. With either spread, movement in the underlying may be required, depending on the relationship of the underlying price to the strike prices of the options. And certainly, with a credit spread or debit spread, if the underlying is at the short strike, that option will have the most premium. For the trade to reach the maximum profit, it will need to decay. For many retail traders, debit spreads and credit spreads begin to look even more similar when margin is considered. Margin requirements can vary from firm to firm, but verticals in retail accounts at option-friendly brokerage firms are usually margined in such a way that the maximum loss is required to be deposited to hold the position (this assumes Regulation T margining). For all intents and purposes, this can turn the trader’s cash position from a credit into a debit. From a cash perspective, all vertical spreads are spreads that require a debit under these margin requirements. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:273 SCORE: 55.00 ================================================================================ Building a Box Two traders, Sam and Isabel, share a joint account. They have each been studying Johnson & Johnson (JNJ), which is trading at around $63.35 per share. Sam and Isabel, however, cannot agree on direction. Sam thinks Johnson & Johnson will rise over the next five weeks, and Isabel believes it will decline during that period. Sam decides to buy the January 62.50 −65 call spread (January has 38 days until expiration in this example). Sam can buy this spread for 1.28. His maximum risk is 1.28. This loss occurs if Johnson & Johnson is below $62.50 at expiration, leaving both calls OTM. His maximum gain is 1.22, realized if Johnson & Johnson is above $65 (65–62.50–1.28). With Johnson & Johnson at $63.35, Sam’s delta is long 0.29 and his other greeks are about flat. Isabel decides to buy the January 62.50–65 put spread for a debit of 1.22. Isabel’s biggest potential loss is 1.22, incurred if Johnson & Johnson is above $65 a share at expiration, leaving both puts OTM. Her maximum possible profit is 1.28, realized if the stock is below $62.50 at option expiration. With Johnson & Johnson at $63.35, Isabel has a delta that is short around 0.27 and is nearly flat gamma, theta, and vega. Collectively, if both Sam and Isabel hold their trades until expiration, it’s a zero-sum game. With Johnson & Johnson below $62.50, Sam loses his investment of 1.28, but Isabel profits. She cancels out Sam’s loss by making 1.28. Above $65, Sam makes 1.22 while Isabel loses the same amount, canceling out Sam’s gains. Between the two strikes, Sam has gains on his 62.50 call and Isabel has gains on her 65 put. The gains on the two options will total 2.50, the combined total spent on the spreads—another draw. EXHIBIT 9.12 Sam’s long call spread in Johnson & Johnson. 62.50–65 Call Spread Delta +0.290 Gamma+0.001 Theta −0.004 Vega +0.006 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:274 SCORE: 69.00 ================================================================================ EXHIBIT 9.13 Isabel’s long put spread in Johnson & Johnson. 62.50–65 Put Spread Delta −0.273 Gamma−0.001 Theta +0.005 Vega −0.006 These two spreads were bought for a combined total of 2.50. The collective position, composed of the four legs of these two spreads, forms a new strategy altogether. The two traders together have created a box. This box, which is empty of both profit and loss, is represented by greeks that almost entirely offset each other. Sam’s positive delta of 0.29 is mostly offset by Isabel’s −0.273 delta. Gamma, theta, and vega will mostly offset each other, too. Chapter 6 described a box as long synthetic stock combined with short synthetic stock having a different strike price but the same expiration month. It can also be defined, however, as two vertical spreads: a bull (bear) call spread plus a bear (bull) put spread with the same strike prices and expiration month. The value of a box equals the present value of the distance between the two strike prices (American-option models will also account for early exercise potential in the box’s value). This 2.50 box, with 38 days until expiration at a 1 percent interest rate, has less than a penny of interest affecting its value. Boxes with more time until expiration will have a higher interest rate component. If there was one year until expiration, the combined value of the two verticals would equal 2.475. This is simply the distance between the strikes minus interest (2.50–[2.50 × 0.01]). Credit spreads are often made up of OTM options. Traders betting against a stock rising through a certain price tend to sell OTM call spreads. For a stock at $50 per share, they might sell the 55 calls and buy the 60 calls. But because of the synthetic relationship that verticals have with one another, the traders could buy an ITM put spread for the same exposure, after ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:276 SCORE: 33.00 ================================================================================ Verticals and Beyond Traders who want to take full advantage of all that options have to offer can do so strategically by trading spreads. Vertical spreads truncate directional risk compared with strategies like the covered call or single-legged option trades. They also reduce option-specific risk, as indicated by their lower gamma, theta, and vega. But lowering risk both in absolute terms and in the greeks has a trade-off compared with buying options: limited profit potential. This trade-off can be beneficial, depending on the trader’s forecast. Debit spreads and credit spreads can be traded interchangeably to achieve the same goals. When a long (short) call spread is combined with a long (short) put spread, the product is a box. Chapter 10 describes other ways vertical spreads can be combined to form positions that achieve different trading objectives. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:279 SCORE: 13.00 ================================================================================ Condors and Butterflies The “wing spread” family is a set of option strategies that is very popular, particularly among experienced traders. These strategies make it possible for speculators to accomplish something they could not possibly do by just trading stocks: They provide a means to profit from a truly neutral market in a security. Stocks that don’t move one iota can earn profits month after month for income-generating traders who trade these strategies. These types of spreads have a lot of moving parts and can be intimidating to newcomers. At their heart, though, they are rather straightforward break- even analysis trades that require little complex math to maintain. A simple at-expiration diagram reveals in black and white the range in which the underlying stock must remain in order to have a profitable position. However, applying the greeks and some of the mathematics discussed in previous chapters can help a trader understand these strategies on a deeper level and maximize the chance of success. This chapter will discuss condors and butterflies and how to put them into action most effectively. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:281 SCORE: 70.00 ================================================================================ Condor A condor is a four-legged option strategy that enables a trader to capitalize on volatility—increased or decreased. Traders can trade long or short iron condors. Long Condor Long one call (put) with strike A; short one call (put) with a higher strike, B; short one call (put) at strike C, which is higher than B; and long one call (put) at strike D, which is higher than C. The distance between strike price A and B is equal to the distance between strike C and strike D. The options are all on the same security, in the same expiration cycle, and either all calls or all puts. Long Condor Example Buy 1 XYZ November 70 call (A) Sell 1 XYZ November 75 call (B) Sell 1 XYZ November 90 call (C) Buy 1 XYZ November 95 call (D) Short Condor Short one call (put) with strike A; long one call (put) with a higher strike, B; long one call (put) with a strike, C, that is higher than B; and short one call (put) with a strike, D, that is higher than C. The options must be on the same security, in the same expiration cycle, and either all calls or all puts. The differences in strike price between the vertical spread of strike prices A and B and the strike prices of the vertical spread of strikes C and D are equal. Short Condor Example Sell 1 XYZ November 70 call (A) Buy 1 XYZ November 75 call (B) Buy 1 XYZ November 90 call (C) Sell 1 XYZ November 95 call (D) ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:282 SCORE: 88.00 ================================================================================ Iron Condor An iron condor is similar to a condor, but with a mix of both calls and puts. Essentially, the condor and iron condor are synthetically the same. Short Iron Condor Long one put with strike A; short one put with a higher strike, B; short one call with an even higher strike, C; and long one call with a still higher strike, D. The options are on the same security and in the same expiration cycle. The put credit spread has the same distance between the strike prices as the call credit spread. Short Iron Condor Example Buy 1 XYZ November 70 put (A) Sell 1 XYZ November 75 put (B) Sell 1 XYZ November 90 call (C) Buy 1 XYZ November 95 call (D) Long Iron Condor Short one put with strike A; long one put with a higher strike, B; long one call with an even higher strike, C; and short one call with a still higher strike, D. The options are on the same security and in the same expiration cycle. The put debit spread (strikes A and B) has the same distance between the strike prices as the call debit spread (strikes C and D). Long Iron Condor Example Sell 1 XYZ November 70 put (A) Buy 1 XYZ November 75 put (B) Buy 1 XYZ November 90 call (C) Sell 1 XYZ November 95 call (D) ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:283 SCORE: 72.00 ================================================================================ Butterflies Butterflies are wing spreads similar to condors, but there are only three strikes involved in the trade—not four. Long Butterfly Long one call (put) with strike A; short two calls (puts) with a higher strike, B; and long one call (put) with an even higher strike, C. The options are on the same security, in the same expiration cycle, and are either all calls or all puts. The difference in price between strikes A and B equals that between strikes B and C. Long Butterfly Example Buy 1 XYZ December 50 call (A) Sell 2 XYZ December 60 call (B) Buy 1 XYZ December 70 call (C) Short Butterfly Short one call (put) with strike A; long two calls (puts) with a higher strike, B; and short one call (put) with an even higher strike, C. The options are on the same security, in the same expiration cycle, and are either all calls or all puts. The vertical spread made up of the options with strike A and strike B has the same distance between the strike prices of the vertical spread made up of the options with strike B and strike C. Short Butterfly Example Sell 1 XYZ December 50 call Buy 2 XYZ December 60 call Sell 1 XYZ December 70 call ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:284 SCORE: 77.00 ================================================================================ Iron Butterflies Much like the relationship of the condor to the iron condor, a butterfly has its synthetic equal as well: the iron butterfly. Short Iron Butterfly Long one put with strike A; short one put with a higher strike, B; short one call with strike B; long one call with a strike higher than B, C. The options are on the same security and in the same expiration cycle. The distances between the strikes of the put spread and between the strikes of the call spread are equal. Short Iron Butterfly Example Buy 1 XYZ December 50 put (A) Sell 1 XYZ December 60 put (B) Sell 1 XYZ December 60 call (B) Buy 1 XYZ December 70 call (C) Long Iron Butterfly Short one put with strike A; long one put with a higher strike, B; long one call with strike B; short one call with a strike higher than B, C. The options are on the same security and in the same expiration cycle. The distances between the strikes of the put spread and between the strikes of the call spread are equal. The put debit spread has the same distance between the strike prices as the call debit spread. Long Iron Butterfly Example Sell 1 XYZ December 50 put Buy 1 XYZ December 60 put Buy 1 XYZ December 60 call Sell 1 XYZ December 70 call These spreads were defined in terms of both long and short for each strategy. Whether the spread is classified as long or short depends on whether it was established at a credit or a debit. Debit condors or butterflies ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:285 SCORE: 34.00 ================================================================================ are considered long spreads. And credit condors or butterflies are considered short spreads. The words long and short mean little, though in terms of the spread as a whole. The important thing is which strikes have long options and which have short options. A call debit spread is synthetically equal to a put credit spread on the same security, with the same expiration month and strike prices. That means a long condor is synthetically equal to a short iron condor, and a long butterfly is synthetically equal to a short iron butterfly, when the same strikes are used. Whichever position is constructed, the best- case scenario is to have debit spreads expire with both options in-the-money (ITM) and credit spreads expire with both options out-of-the-money (OTM). Many retail traders prefer trading these spreads for the purpose of generating income. In this case, a trader would sell the guts, or middle strikes, and buy the wings, or outer strikes. When a trader is short the guts, low realized volatility is usually the objective. For long butterflies and short iron butterflies, the stock needs to be right at the middle strike for the maximum payout. For long condors and short iron condors, the stock needs to be between the short strikes at expiration for maximum payout. In both instances, the wings are bought to limit potential losses of the otherwise naked options. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:286 SCORE: 37.00 ================================================================================ Long Butterfly Example A trader, Kathleen, has been studying United Parcel Service (UPS), which is trading at around $70.65. She believes UPS will trade sideways until July expiration. Kathleen buys the July 65–70–75 butterfly for 2.00. She executes the following legs: Kathleen looks at her trade as two vertical spreads, the 65–70 bull (debit) call spread and the 70–75 bear (credit) call spread. Intuitively, she would want UPS to be at or above $70 at expiration for her bull call spread to have maximum value. But she has the seemingly conflicting goal of also wanting UPS to be at or below $70 to get the most from her 70–75 bear call spread. The ideal price for the stock to be trading at expiration in this example is right at $70 per share—the best of both worlds. The at-expiration diagram, Exhibit 10.1 , shows the profit or loss of all possible outcomes at expiration. EXHIBIT 10.1 UPS 65–70–75 butterfly. If the price of UPS shares declines below $65 at expiration, all these calls will expire. The entire 2.00 spent on the trade will be lost. If UPS is above $65 at expiration, the 65 call will be ITM and will be exercised. The call ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:287 SCORE: 37.00 ================================================================================ will profit like a long position in 100 shares of the underlying. The maximum profit is reached if UPS is at $70 at expiration. Kathleen makes a 5.00 profit from $65 to $70 on her 65 calls. But because she paid 2.00 initially for the spread, her net profit at $70 is just 3.00. If UPS is above $70 a share at expiration in this example, the two 70 calls will be assigned. The assignment of one call will offset the long stock acquired by the 65 calls being exercised. Assignment of the other call will create a short position in the underlying. That short position loses as UPS moves higher up to $75 a share, eating away at the 3.00 profit. If UPS is above $75 at expiration, the 75 call can be exercised to buy back the short stock position that resulted from the 70’s being assigned. The loss on the short stock between $70 and $75 will cost Kathleen 5.00, stripping her of her 3.00 profit and giving her a net loss of 2.00 to boot. End result? Above $75 at expiration, she has no position in the underlying and loses 2.00. A butterfly is a break-even analysis trade . This name refers to the idea that the most important considerations in this strategy are the breakeven points. The at-expiration diagram, Exhibit 10.2 , shows the break-even prices for this trade. EXHIBIT 10.2 UPS 65–70–75 butterfly breakevens. If the position is held until expiration and UPS is between $65 and $70 at that time, the 65 calls are exercised, resulting in long stock. The effective purchase price of that stock is $67. That’s the strike price plus the cost of ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:288 SCORE: 36.00 ================================================================================ the spread; that’s the lower break-even price. The other break-even is at $73. The net short position of 100 shares resulting from assignment of the 70 call loses more as the stock rises between $70 and $75. The entire 3.00 profit realized at the $70 share price is eroded when the stock reaches $73. Above $73, the trade produces a loss. Kathleen’s trading objective is to profit from UPS trading between $67 and $73 at expiration. The best-case scenario is that it declines only slightly from its price of $70.65 when the trade is established, to $70 per share. Alternatives Kathleen had other alternative positions she could have traded to meet her goals. An iron butterfly with the same strike prices would have shown about the same risk/reward picture, because the two positions are synthetically equivalent. But there may, in some cases, be a slight advantage to trading the iron butterfly over the long butterfly. The iron butterfly uses OTM put options instead of ITM calls, meaning the bid-ask spreads may be tighter. This means giving up less edge to the liquidity providers. She could have also bought a condor or sold an iron condor. With condor- family spreads, there is a lower maximum profit potential but a wider range in which that maximum payout takes place. For example, Kathleen could have executed the following legs to establish an iron condor: Essentially, Kathleen would be selling two credit spreads: the July 60–65 put spread for 0.30 and the July 75–80 call spread for 0.35. Exhibit 10.3 shows the payout at expiration of the UPS July 60–65–75–80 iron condor. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:289 SCORE: 39.00 ================================================================================ EXHIBIT 10.3 UPS 60–65–75–80 iron condor. Although the forecast and trading objectives may be similar to those for the butterfly, the payout diagram reveals some important differences. First, the maximum loss is significantly higher with a condor or iron condor. In this case, the maximum loss is 4.35. This unfortunate situation would occur if UPS were to drop to below $60 or rise above $80 by expiration. Below $60, the call spread expires, netting 0.35. But the put spread is ITM. Kathleen would lose a net of 4.70 on the put spread. The gain on the call spread combined with the loss on the put spread makes the trade a loser of 4.35 if the stock is below $60 at expiration. Above $80, the put spread is worthless, earning 0.30, but the call spread is a loser by 4.65. The gain on the put spread plus the loss on the call spread is a net loser of 4.35. Between $65 and $75, all options expire and the 0.65 credit is all profit. So far, this looks like a pretty lousy alternative to the butterfly. You can lose 4.35 but only make 0.65! Could there be any good reason for making this trade? Maybe. The difference is wiggle room. The breakevens are 2.65 wider in each direction with the iron condor. Exhibit 10.4 shows these prices on the graph. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:291 SCORE: 10.00 ================================================================================ Keys to Success No matter which trade is more suitable to Kathleen’s risk tolerance, the overall concept is the same: profit from little directional movement. Before Kathleen found a stock on which to trade her spread, she will have sifted through myriad stocks to find those that she expects to trade in a range. She has a few tools in her trading toolbox to help her find good butterfly and condor candidates. First, Kathleen can use technical analysis as a guide. This is a rather straightforward litmus test: does the stock chart show a trending, volatile stock or a flat, nonvolatile stock? For the condor, a quick glance at the past few months will reveal whether the stock traded between $65 and $75. If it did, it might be a good iron condor candidate. Although this very simplistic approach is often enough for many traders, those who like lots of graphs and numbers can use their favorite analyses to confirm that the stock is trading in a range. Drawing trendlines can help traders to visualize the channel in which a stock has been trading. Knowing support and resistance is also beneficial. The average directional movement index (ADX) or moving average converging/diverging (MACD) indicator can help to show if there is a trend present. If there is, the stock may not be a good candidate. Second, Kathleen can use fundamentals. Kathleen wants stocks with nothing on their agendas. She wants to avoid stocks that have pending events that could cause their share price to move too much. Events to avoid are earnings releases and other major announcements that could have an impact on the stock price. For example, a drug stock that has been trading in a range because it is awaiting Food and Drug Administration (FDA) approval, which is expected to occur over the next month, is not a good candidate for this sort of trade. The last thing to consider is whether the numbers make sense. Kathleen’s iron condor risks 4.35 to make 0.65. Whether this sounds like a good trade depends on Kathleen’s risk tolerance and the general environment of UPS, the industry, and the market as a whole. In some environments, the 0.65/4.35 payout-to-risk ratio makes a lot of sense. For other people, other stocks, and other environments, it doesn’t. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:292 SCORE: 60.00 ================================================================================ Greeks and Wing Spreads Much of this chapter has been spent on how wing spreads perform if held until expiration, and little has been said of option greeks and their role in wing spreads. Greeks do come into play with butterflies and condors but not necessarily the same way they do with other types of option trades. The vegas on these types of spreads are smaller than they are on many other types of strategies. For a typical nonprofessional trader, it’s hard to trade implied volatility with condors or butterflies. The collective commissions on the four legs, as well as margin and capital considerations, put these out of reach for active trading. Professional traders and retail traders subject to portfolio margining are better equipped for volatility trading with these spreads. The true strength of wing spreads, however, is in looking at them as break-even analysis trades much like vertical spreads. The trade is a winner if it is on the correct side of the break-even price. Wing spreads, however, are a combination of two vertical spreads, so there are two break-even prices. One of the verticals is guaranteed to be a winner. The stock can be either higher or lower at expiration—not both. In some cases, both verticals can be winners. Consider an iron condor. Instead of reaping one premium from selling one OTM call credit spread, iron condor sellers double dip by additionally selling an OTM put credit spread. They collect a double credit, but only one of the credit spreads can be a loser at expiration. The trader, however, does have to worry about both directions independently. There are two ways for greeks and volatility analysis to help traders trade wing spreads. One of them involves using delta and theta as tools to trade a directional spread. The other uses implied volatility in strike selection decisions. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:293 SCORE: 26.00 ================================================================================ Directional Butterflies Trading a butterfly can be an excellent way to establish a low-cost, relatively low-risk directional trade when a trader has a specific price target in mind. For example, a trader, Ross, has been studying Walgreen Co. (WAG) and believes it will rise from its current level of $33.50 to $36 per share over the next month. Ross buys a butterfly consisting of all OTM January calls with 31 days until expiration. He executes the following legs: As a directional trade alternative, Ross could have bought just the January 35 call for 1.15. As a cheaper alternative, he could have also bought the 35– 36 bull call spread for 0.35. In fact, Ross actually does buy the 35–36 spread, but he also sells the January 36–37 call spread at 0.25 to reduce the cost of the bull call spread, investing only a dime. The benefit of lower cost, however, comes with trade-offs. Exhibit 10.5 compares the bull call spread with a bullish butterfly. EXHIBIT 10.5 Bull call spread vs. bull butterfly (Walgreen Co. at $33.50). ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:294 SCORE: 74.00 ================================================================================ The butterfly has lower nominal risk—only 0.10 compared with 0.35 for the call spread. The maximum reward is higher in nominal terms, too—0.90 versus 0.65. The trade-off is what is given up. With both strategies, the goal is to have Walgreen Co. at $36 around expiration. But the bull call spread has more room for error to the upside. If the stock trades a lot higher than expected, the butterfly can end up being a losing trade. Given Ross’s expectations in this example, this might be a risk he is willing to take. He doesn’t expect Walgreen Co. to close right at $36 on the expiration date. It could happen, but it’s unlikely. However, he’d have to be wildly wrong to have the trade be a loser on the upside. It would be a much larger move than expected for the stock to rise significantly above $36. If Ross strongly believes Walgreen Co. can be around $36 at expiration, the cost benefit of 0.10 vs. 0.35 may offset the upside risk above $37. As a general rule, directional butterflies work well in trending, low-volatility stocks. When Ross monitors his butterfly, he will want to see the greeks for this position as well. Exhibit 10.6 shows the trade’s analytics with Walgreen Co. at $33.50. EXHIBIT 10.6 Walgreen Co. 35–36–37 butterfly greeks (stock at $33.50, 31 days to expiration). Delta +0.008 Gamma−0.004 Theta +0.001 Vega −0.001 When the trade is first put on, the delta is small—only +0.008. Gamma is slightly negative and theta is very slightly positive. This is important information if Walgreen Co.’s ascent happens sooner than Ross planned. The trade will show just a small profit if the stock jumps to $36 per share right away. Ross’s theoretical gain will be almost unnoticeable. At $36 per share, the position will have its highest theta, which will increase as expiration approaches. Ross will have to wait for time to pass to see the trade reach its full potential. This example shows the interrelation between delta and theta. We know from an at-expiration analysis that if Walgreen Co. moves from $33.50 to $36, the butterfly’s profit will be 0.90 (the spread of $1 minus the 0.10 ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:295 SCORE: 27.00 ================================================================================ initial debit). If we distribute the 0.90 profit over the 2.50 move from $33.50 to $36, the butterfly gains about 0.36 per dollar move in Walgreen Co. (0.90/(36 − 33.50). This implies a delta of about 0.36. But the delta, with 31 days until expiration and Walgreen Co. at $33.50, is only 0.008, and because of negative gamma this delta will get even smaller as Walgreen Co. rises. Butterflies, like the vertical spreads of which they are composed, can profit from direction but are never purely directional trades. Time is always a factor. It is theta, working in tandem with delta, that contributes to profit or peril. A bearish butterfly can be constructed as well. One would execute the trade with all OTM puts or all ITM calls. The concept is the same: sell the guts at the strike at which the stock is expected to be trading at expiration, and buy the wings for protection. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:297 SCORE: 19.50 ================================================================================ Three Looks at the Condor Strike selection is essential for a successful condor. If strikes are too close together or two far apart, the trade can become much less attractive. Strikes Too Close The QQQs are options on the ETFs that track the Nasdaq 100 (QQQ). They have strikes in $1 increments, giving traders a lot to choose from. With QQQ trading at around $55.95, consider the 54–55–57–58 iron condor. In this example, with 31 days until expiration, the following legs can be executed: In this trade, the maximum profit is 0.63. The maximum risk is 0.37. This isn’t a bad profit-to-loss ratio. The break-even price on the downside is $54.37 and on the upside is $57.63. That’s a $3.26 range—a tight space for a mover like the QQQ to occupy in a month. The ETF can drop about only 2.8 percent or rise 3 percent before the trade becomes a loser. No one needs any fancy math to show that this is likely a losing proposition in the long run. While choosing closer strikes can lead to higher premiums, the range can be so constricting that it asphyxiates the possibility of profit. Strikes Too Far Strikes too far apart can make for impractical trades as well. Exhibit 10.7 shows an options chain for the Dow Jones Industrial Average Index (DJX). These prices are from around 2007 when implied volatility (IV) was historically low, making the OTM options fairly low priced. In this example, DJX is around $135.20 and there are 51 days until expiration. EXHIBIT 10.7 Options chain for DJIA. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:299 SCORE: 25.00 ================================================================================ This would be a great trade if it weren’t for the prices one would have to accept to put it on. First, the 120 puts are offered at 0.25 and the 123 puts are 0.25 bid. This means that the put spread would be sold at zero! The maximum risk is 3.00, and the maximum gain is zero. Not a really good risk/reward. The 142–145 call spread isn’t much better: it can be sold for a dime. At the time, again a low-volatility period, many traders probably felt it was unlikely that the DJX will rise 5 percent in a 51-day period. Some traders may have considered trading a similarly priced iron condor (though of course they’d have to require some small credit for the risk). A little over a year later the DJX was trading around 50 percent lower. Traders must always be vigilant of the possibility of volatility, even unexpected volatility and structure their risk/reward accordingly. Most traders would say the risk/reward of this trade isn’t worth it. Strikes too far apart have a greater chance of success, but the payoff just isn’t there. Strikes with High Probabilities of Success So how does a trader find the happy medium of strikes close enough together to provide rich premiums but far enough apart to have a good chance of success? Certainly, there is something to be said for looking at the prices at which a trade can be done and having a subjective feel for whether the underlying is likely to move outside the range of the break- even prices. A little math, however, can help quantify this likelihood and aid in the decision-making process. Recall that IV is read by many traders to be the market’s consensus estimate of future realized volatility in terms of annualized standard deviation. While that is a mouthful to say—or in this case, rather, an eyeful to read—when broken down it is not quite as intimidating as it sounds. Consider a simplified example in which an underlying security is trading at $100 a share and the implied volatility of the at-the-money (ATM) options is 10 percent. That means, from a statistical perspective, that if the expected return for the stock is unchanged, the one-year standard deviations are at $90 and $110. 1 In this case, there is about a 68 percent chance of the stock trading between $90 and $110 one year from now. IV then is useful information to a trader who wants to quantify the chances of an iron ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:300 SCORE: 38.50 ================================================================================ condor’s expiring profitable, but there are a few adjustments that need to be made. First, because with an iron condor the idea is to profit from net short option premium, it usually makes more sense to sell shorter-term options to profit from higher rates of time decay. This entails trading condors composed of one- or two-month options. The IV needs to be deannualized and converted to represent the standard deviation of the underlying at expiration. The first step is to compute the one-day standard deviation. This is found by dividing the implied volatility by the square root of the number of trading days in a year, then multiplying by the square root of the number of trading days until expiration. The result is the standard deviation (σ) at the time of expiration stated as a percent. Next, multiply that percentage by the price of the underlying to get the standard deviation in absolute terms. The formula 2 for calculating the shorter-term standard deviation is as follows: This value will be added to or subtracted from the price of the underlying to get the price points at which the approximate standard deviations fall. Consider an example using options on the Standard & Poor’s 500 Index (SPX). With 50 days until expiration, the SPX is at 1241 and the implied volatility is 23.2 percent. To find strike prices that are one standard deviation away from the current index price, we need to enter the values into the equation. We first need to know how many actual trading days are in the 50-day period. There are 35 business days during this particular 50- day period (there is one holiday and seven weekend days). We now have all the data we need to calculate which strikes to sell. The lower standard deviation is 1134.55 (1241 − 106.45) and the upper is 1347.45 (1241 + 106.45). This means there would be about a 68 percent chance of SPX ending up between 1134.55 and 1347.45 at expiration. In this example, to have about a two-thirds chance of success, one would sell the 1135 puts and the 1350 calls as part of the iron condor. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:301 SCORE: 22.50 ================================================================================ Being Selective There is about a two-thirds chance of the underlying staying between the upper and lower standard deviation points and about a one-third chance it won’t. Reasonably good odds. But the maximum loss of an iron condor will be more than the maximum profit potential. In fact, the max-profit-to-max- loss ratio is usually less than 1 to 3. For every $1 that can be made, often $4 or $5 will be at risk. The pricing model determines fair value of an option based on the implied volatility set by the market. Again, many traders consider IV to be the market’s consensus estimate of future realized volatility. Assuming the market is generally right and options are efficiently priced, in the long run, future stock volatility should be about the same as the implied volatility from options prices. That means that if all of your options trades are executed at fair value, you are likely to break even in the long run. The caveat is that whether the options market is efficient or not, retail or institutional traders cannot generally execute trades at fair value. They have to sell the bid (sell below theoretical value) and buy the offer (buy above theoretical value). This gives the trade a statistical disadvantage, called giving up the edge, from an expected return perspective. Even though you are more likely to win than to lose with each individual trade when strikes are sold at the one-standard-deviation point, the edge given up to the market in conjunction with the higher price tag on losers makes the trade a statistical loser in the long run. While this means for certain that the non-market-making trader is at a constant disadvantage, trading condors and butterflies is no different from any other strategy. Giving up the edge is the plight of retail and institutional traders. To profit in the long run, a trader needs to beat the market, which requires careful planning, selectivity, and risk management. Savvy traders trade iron condors with strikes one standard deviation away from the current stock price only when they think there is more than a two- thirds chance of market neutrality. In other words, if you think the market will be less volatile than the prices in the options market imply, sell the iron condor or trade another such premium-selling strategy. As discussed above, this opinion should reflect sound judgment based on some combination of ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:302 SCORE: 30.00 ================================================================================ technical analysis, fundamental analysis, volatility analysis, feel, and subjectivity. A Safe Landing for an Iron Condor Although traders can’t control what the market does, they can control how they react to the market. Assume a trader has done due diligence in studying a stock and feels it is a qualified candidate for a neutral strategy. With the stock at $90, a 16.5 percent implied volatility, and 41 days until expiration, the standard deviation is about 5. The trader sells the following iron condor: With the stock at $90, directly between the two short strikes, the trade is direction neutral. The maximum profit is equal to the total premium taken in, which in this case is $800. The maximum loss is $4,200. There is about a two-thirds chance of retaining the $800 at expiration. After one week, the overall market begins trending higher on unexpected bullish economic news. This stock follows suit and is now trading at $93, and concern is mounting that the rally will continue. The value of the spread now is about 1.10 per contract (we ignore slippage from trading on the bid- ask spreads of the four legs of the spread). This means the trade has lost $300 because it would cost $1,100 to buy back what the trader sold for a total of $800. One strategy for managing this trade looking forward is inaction. The philosophy is that sometimes these trades just don’t work out and you take your lumps. The philosophy is that the winners should outweigh the losers over the long term. For some of the more talented and successful traders with a proven track record, this may be a viable strategy, but there are more active options as well. A trader can either close the spread or adjust it. The two sets of data that must be considered in this decision are the prices of the individual options and the greeks for the trade. Exhibit 10.8 shows the new data with the stock at $93. EXHIBIT 10.8 Greeks for iron condor with stock at $93. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:303 SCORE: 28.00 ================================================================================ The trade is no longer neutral, as it was when the underlying was at $90. It now has a delta of −2.54, which is like being short 254 shares of the underlying. Although the more time that passes the better—as indicated by the +0.230 theta—delta is of the utmost concern. The trader has now found himself short a market that he thinks may rally. Closing the entire position is one alternative. To be sure, if you don’t have an opinion on the underlying, you shouldn’t have a position. It’s like making a bet on a sporting event when you don’t really know who you think will win. The spread can also be dismantled piecemeal. First, the 85 puts are valued at $0.07 each. Buying these back is a no-brainer. In the event the stock does retrace, why have the positive delta of that leg working against you when you can eliminate the risk inexpensively now? The 80 puts are worthless, offered at 0.05, presumably. There is no point in trying to sell these. If the market does turn around, they may benefit, resulting in an unexpected profit. The 80 and 85 puts are the least of his worries, though. The concern is a continuing rally. Clearly, the greater risk is in the 95–100 call spread. Closing the call spread for a loss eliminates the possibility of future losses and may be a wise choice, especially if there is great uncertainty. Taking a small loss now of only around $300 is a better trade than risking a total loss of $4,200 when you think there is a strong chance of that total loss occurring. But if the trader is not merely concerned that the stock will rally but truly believes that there is a good chance it will, the most logical action is to position himself for that expected move. Although there are many ways to accomplish this, the simplest way is to buy to close the 95 calls to eliminate the position at that strike. This eliminates the short delta from the 95 calls, ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:305 SCORE: 45.00 ================================================================================ The Retail Trader versus the Pro Iron condors are very popular trades among retail traders. These days one can hardly go to a cocktail party and mention the word options without hearing someone tell a story about an iron condor on which he’s made a bundle of money trading. Strangely, no one ever tells stories about trades in which he has lost a bundle of money. Two of the strengths of this strategy that attract retail traders are its limited risk and high probability of success. Another draw of this type of strategy is that the iron condor and the other wing spreads offer something truly unique to the retail trader: a way to profit from stocks that don’t move. In the stock-trading world, the only thing that can be traded is direction— that is, delta. The iron condor is an approachable way for a nonprofessional to dabble in nonlinear trading. The iron condor does a good job in eliminating delta—unless, of course, the stock moves and gamma kicks in. It is efficient in helping income-generating retail traders accomplish their goals. And when a loss occurs, although it can be bigger than the potential profits, it is finite. But professional option traders, who have access to lots of capital and have very low commissions and margin requirements, tend to focus their efforts in other directions: they tend to trade volatility. Although iron condors are well equipped for profiting from theta when the stock cooperates, it is also possible to trade implied volatility with this strategy. The examples of iron condors, condors, iron butterflies, and butterflies presented in this chapter so far have for the most part been from the perspective of the neutral trader: selling the guts and buying the wings. A trader focusing on vega in any of these strategies may do just the opposite —buy the guts and sell the wings—depending on whether the trader is bullish or bearish on volatility. Say a trader, Joe, had a bullish outlook on volatility in Salesforce.com (CRM). Joe could sell the following condor 100 times. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:306 SCORE: 61.50 ================================================================================ In this example, February is 59 days from expiration. Exhibit 10.10 shows the analytics for this trade with CRM at $104.32. EXHIBIT 10.10 Salesforce.com condor ( Salesforce.com at $104.32). As expected with the underlying centered between the two middle strikes, delta and gamma are about flat. As Salesforce.com moves higher or lower, though, gamma and, consequently, delta will change. As the stock moves closer to either of the long strikes, gamma will become more positive, causing the delta to change favorably for Joe. Theta, however, is working against him with Salesforce.com at $104.32, costing $150 a day. In this instance, movement is good. Joe benefits from increased realized volatility. The best-case scenario would be if Salesforce.com moves through either of the long strikes to, or through, either of the short strikes. The prime objective in this example, though, is to profit from a rise in IV. The position has a positive vega. The position makes or loses $400 with every point change in implied volatility. Because of the proportion of theta risk to vega risk, this should be a short-term play. If Joe were looking for a small rise in IV, say five points, the move would have to happen within 13 calendar days, given the vega and theta figures. The vega gain on a rise of five vol points would be $2,000, and the theta loss over 13 calendar days would be $1,950. If there were stock movement associated with the IV increase, that delta/gamma gain would offset some of the havoc that theta wreaked on the option premiums. However, if Joe traded a strategy like a condor as a vol play, he would likely expect a bigger ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:310 SCORE: 36.00 ================================================================================ Calendar Spreads Definition : A calendar spread, sometimes called a time spread or a horizontal spread , is an option strategy that involves buying one option and selling another option with the same strike price but with a different expiration date. At-expiration diagrams do a calendar-spread trader little good. Why? At the expiration of the short-dated option, the trader is left with another option that may have time value. To estimate what the position will be worth when the short-term option expires, the value of the long-term option must be analyzed using the greeks. This is true of the variants of the calendar— double calendars, diagonals, and double diagonals—as well. This chapter will show how to analyze strategies that involve options with different expirations and discuss how and when to use them. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:311 SCORE: 63.00 ================================================================================ Buying the Calendar The calendar spread and all its variations are commonly associated with income-generating spreads. Using calendar spreads as income generators is popular among retail and professional traders alike. The process involves buying a longer-term at-the-money option and selling a shorter-term at-the- money (ATM) option. The options must be either both calls or both puts. Because this transaction results in a net debit—the longer-term option being purchased has a higher premium than the shorter-term option being sold— this is referred to as buying the calendar. The main intent of buying a calendar spread for income is to profit from the positive net theta of the position. Because the shorter-term ATM option decays at a faster rate than the longer-term ATM option, the net theta is positive. As for most income spreads, the ideal outcome occurs when the underlying is at the short strike (in this case, shared strike) when the shorter-term option expires. At this strike price, the long option has its highest value, while the short option expires without the trader’s getting assigned. As long as the underlying remains close to the strike price, the value of the spread rises as time passes, because the short option decreases in value faster than the long option. For example, a trader, Richard, watches Bed Bath & Beyond Inc. (BBBY) on a regular basis. Richard believes that Bed Bath & Beyond will trade in a range around $57.50 a share (where it is trading now) over the next month. Richard buys the January–February 57.50 call calendar for 0.80. Assuming January has 25 days until expiration and February has 53 days, Richard will execute the following trade: Richard’s best-case scenario occurs when the January calls expire at expiration and the February calls retain much of their value. If Richard created an at-expiration P&(L) diagram for his position, he’d have trouble because of the staggered expiration months. A general representation would look something like Exhibit 11.1 . ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:312 SCORE: 40.00 ================================================================================ EXHIBIT 11.1 Bed Bath & Beyond January–February 57.50 calendar. The only point on the diagram that is drawn with definitive accuracy is the maximum loss to the downside at expiration of the January call. The maximum loss if Bed Bath & Beyond falls low enough is 0.80—the debit paid for the spread. If Bed Bath & Beyond is below $57.50 at January expiration, the January 57.50 call expires worthless, and the February 57.50 call may or may not have residual value. If Bed Bath & Beyond declines enough, the February 57.50 call can lose all of its value, even with residual time until expiration. If the stock falls enough, the entire 0.80 debit would be a loss. If Bed Bath & Beyond is above $57.50 at January expiration, the January 57.50 call will be trading at parity. It will be a negative-100-delta option, imitating short stock. If Bed Bath & Beyond is trading high enough, the February 57.50 call will become a positive-100-delta option trading at parity plus the interest calculated on the strike. The February deep-in-the- money option would imitate long stock. At a 2 percent interest rate, interest on the 57.50 strike is about 0.17. Therefore, Richard would essentially have a short stock position from $57.50 from the January 57.50 call and would be essentially long stock from $57.50 plus 0.28 from the February call. The maximum loss to the upside is about 0.63 (0.80 − 0.17). The maximum loss if Bed Bath & Beyond is trading over $57.50 at expiration is only an estimate that assumes there is no time value and that ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:313 SCORE: 39.00 ================================================================================ interest and dividends remain constant. Ultimately, the maximum loss will be 0.80, the premium paid, if there is no time value or carry considerations. The maximum profit is gained if Bed Bath & Beyond is at $57.50 at expiration. At this price, the February 57.50 call is worth the most it can be worth without having the January 57.50 call assigned and creating negative deltas to the upside. But how much precisely is the maximum profit? Richard would have to know what the February 57.50 call would be worth with Bed Bath & Beyond stock trading at $57.50 at February expiration before he can know the maximum profit potential. Although Richard can’t know for sure at what price the calls will be trading, he can use a pricing model to estimate the call’s value. Exhibit 11.2 shows analytics at January expiration. EXHIBIT 11.2 Bed Bath & Beyond January–February 57.50 call calendar greeks at January expiration. With an unchanged implied volatility of 23 percent, an interest rate of two percent, and no dividend payable before February expiration, the February 57.50 calls would be valued at 1.53 at January expiration. In this best-case scenario, therefore, the spread would go from 0.80, where Richard purchased it, to 1.53, for a gain of 91 percent. At January expiration, with Bed Bath & Beyond at $57.50, the January call would expire; thus, the spread is composed of just the February 57.50 call. Let’s now go back in time and see how Richard figured this trade. Exhibit 11.3 shows the position when the trade is established. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:314 SCORE: 61.00 ================================================================================ EXHIBIT 11.3 Bed Bath & Beyond January–February 57.50 call calendar. A small and steady rise in the stock price with enough time to collect theta is the recipe for success in this trade. As time passes, delta will flatten out if Bed Bath & Beyond is still right at-the-money. The delta of the January call that Richard is short will move closer to exactly −0.50. The February call delta moves toward exactly +0.50. Gamma and theta will both rise if Bed Bath & Beyond stays around the strike. As expiration approaches, there is greater risk if there is movement and greater reward if there is not. Vega is positive because the long-term option with the higher vega is the long leg of the spread. When trading calendars for income, implied volatility (IV) must be considered as a possible threat. Because it is Richard’s objective to profit from Bed Bath & Beyond being at $57.50 at expiration, he will try to avoid vega risk by checking that the implied volatility of the February call is in the lower third of the 12-month range. He will also determine if there are any impending events that could cause IV to change. The less likely IV is to drop, the better. If there is an increase in IV, that may benefit the profitability of the trade. But a rise in IV is not really a desired outcome for two reasons. First, a rise in IV is often more pronounced in the front month than in the months farther out. If this happens, Richard can lose more on the short call than he makes on the long call. Second, a rise in IV can indicate anxiety and therefore a greater possibility for movement in the underlying stock. Richard doesn’t want IV to rock the boat. “Buy low, stay low” is his credo. Rho is positive also. A rise in interest rates benefits the position because the long-term call is helped by the rise more than the short call is hurt. With ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:315 SCORE: 58.00 ================================================================================ only a one-month difference between the two options, rho is very small. Overall, rho is inconsequential to this trade. There is something curious to note about this trade: the gamma and the vega. Calendar spreads are the one type of trade where gamma can be negative while vega is positive, and vice versa. While it appears—at least on the surface—that Richard wants higher IV, he certainly wants low realized volatility. Bed Bath & Beyond January–February 57.50 Put Calendar Richard’s position would be similar if he traded the January–February 57.50 put calendar rather than the call calendar. Exhibit 11.4 shows the put calendar. EXHIBIT 11.4 Bed Bath & Beyond January–February 57.50 put calendar. The premium paid for the put spread is 0.75. A huge move in either direction means a loss. It is about the same gamma/theta trade as the 57.50 call calendar. At expiration, with Bed Bath & Beyond at $57.50 and IV unchanged, the value of the February put would be 1.45—a 93 percent gain. The position is almost exactly the same as the call calendar. The biggest difference is that the rho is negative, but that is immaterial to the trade. As with the call spread, being short the front-month option means negative gamma and positive theta; being long the back month means positive vega. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:316 SCORE: 27.00 ================================================================================ Managing an Income-Generating Calendar Let’s say that instead of trading a one-lot calendar, Richard trades it 20 times. His trade in this case is His total cash outlay is $1,600 ($80 times 20). The greeks for this trade, listed in Exhibit 11.5 , are also 20 times the size of those in Exhibit 11.3 . EXHIBIT 11.5 20-Lot Bed Bath & Beyond January–February 57.50 call calendar. Note that Richard has a +0.18 delta. This means he’s long the equivalent of about 18 shares of stock—still pretty flat. A gamma of −0.72 means that if Bed Bath & Beyond moves $1 higher, his delta will be starting to get short; and if it moves $1 lower he will be longer, long 90 deltas. Richard can use the greeks to get a feel for how much the stock can move before negative gamma causes a loss. If Bed Bath & Beyond starts trending in either direction, Richard may need to react. His plan is to cover his deltas to continue the position. Say that after one week Bed Bath & Beyond has dropped $1 to $56.50. Richard will have collected seven days of theta, which will have increased slightly from $18 per day to $20 per day. His average theta during that time is about $19, so Richard’s profit attributed to theta is about $133. With a big-enough move in either direction, Richard’s delta will start working against him. Since he started with a delta of +0.18 on this 20-lot ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:317 SCORE: 47.00 ================================================================================ spread and a gamma of −0.72, one might think that his delta would increase to 0.90 with Bed Bath & Beyond a dollar lower (18 − [−0.072 × 1.00]). But because a week has passed, his delta would actually get somewhat more positive. The shorter-term call’s delta will get smaller (closer to zero) at a faster rate compared to the longer-term call because it has less time to expiration. Thus, the positive delta of the long-term option begins to outweigh the negative delta of the short-term option as time passes. In this scenario, Richard would have almost broken even because what would be lost on stock price movement, is made up for by theta gains. Richard can sell about 100 shares of Bed Bath & Beyond to eliminate his immediate directional risk and stem further delta losses. The good news is that if Bed Bath & Beyond declines more after this hedge, the profit from the short stock offsets losses from the long delta. The bad news is that if BBBY rebounds, losses from the short stock offset gains from the long delta. After Richard’s hedge trade is executed, his delta would be zero. His other greeks remain unchanged. The idea is that if Bed Bath & Beyond stays at its new price level of $56.50, he reaps the benefits of theta increasing with time from $18 per day. Richard is accepting the new price level and any profits or losses that have occurred so far. He simply adjusts his directional exposure to a zero delta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:318 SCORE: 49.50 ================================================================================ Rolling and Earning a “Free” Call Many traders who trade income-generating strategies are conservative. They are happy to sell low IV for the benefits afforded by low realized volatility. This is the problem-avoidance philosophy of trading. Due to risk aversion, it’s common to trade calendar spreads by buying the two-month option and selling the one-month option. This can allow traders to avoid buying the calendar in earnings months, and it also means a shorter time horizon, signifying less time for something unwanted to happen. But there’s another school of thought among time-spread traders. There are some traders who prefer to buy a longer-term option—six months to a year—while selling a one-month option. Why? Because month after month, the trader can roll the short option to the next month. This is a simple tactic that is used by market makers and other professional traders as well as savvy retail traders. Here’s how it works. XYZ stock is trading at $60 per share. A trader has a neutral outlook over the next six months and decides to buy a calendar. Assuming that July has 29 days until expiration and December has 180, the trader will take the following position: The initial debit here is 2.55. The goal is basically the same as for any time spread: collect theta without negative gamma spoiling the party. There is another goal in these trades as well: to roll the spread. At the end of month one, if the best-case scenario occurs and XYZ is sitting at $60 at July expiration, the July 60 call expires. The December 60 call will then be worth 3.60, assuming all else is held constant. The positive theta of the short July call gives full benefits as the option goes from 1.45 to zero. The lower negative theta of the December call doesn’t bite into profits quite as much as the theta of a short-term call would. The profit after month one is 1.05. Profit is derived from the December call, worth 3.60 at July expiry, minus the 2.55 initial spread debit. This works out to about a 41 percent return. The profit is hardly as good as it ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:319 SCORE: 32.00 ================================================================================ would have been if a short-term, less expensive August 60 call were the long leg of this spread. Rolling the Spread The July–December spread is different from short-term spreads, however. When the Julys expire, the August options will have 29 days until expiration. If volatility is still the same, XYZ is still at $60, and the trader’s forecast is still neutral, the 29-day August 60 calls can be sold for 1.45. The trader can either wait until the Monday after July expiration and then sell the August 60s, or when the Julys are offered at 0.05 or 0.10, he can buy the Julys and sell the Augusts as a spread. In either case, it is called rolling the spread. When the August expires, he can sell the Septembers, and so on. The goal is to get a credit month after month. At some point, the aggregate credit from the call sales each month is greater than the price initially paid for the long leg of the spread, thus eliminating the original net debit. Exhibit 11.6 shows how the monthly credits from selling the one- month calls aggregate over time. EXHIBIT 11.6 A “free” call. After July has expired, 1.45 of premium is earned. After August expiration, the aggregate increases to 2.90. When the September calls, which have 36 days until expiration, are sold, another 1.60 is added to the total premium collected. Over three months—assuming the stock price, volatility, and the other inputs don’t change—this trader collects a total of 4.50. That’s 0.50 more than the price originally paid for the December 60 call leg of the spread. At this point, he effectively owns the December call for free. Of course, this call isn’t really free; it’s earned. It’s paid for with risk and maybe a few sleepless nights. At this point, even if the stock and, consequently, the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:320 SCORE: 46.00 ================================================================================ December call go to zero, the position is still a profitable trade because of the continued month-to-month rolling. This is now a no-lose situation. When the long call of the spread has been paid for by rolling, there are three choices moving forward: sell it, hold it, or continue writing calls against it. If the trader’s opinion calls for the stock to decline, it’s logical to sell the December call and take the residual value as profit. In this case, over three months the trade will have produced 4.50 in premium from the sale of three consecutive one-month calls, which is more than the initial purchase price of the December call. At September expiration, the premium that will be received for selling the December call is all profit, plus 0.50, which is the aggregate premium minus the initial cost of the December call. If the outlook is for the underlying to rise, it makes sense to hold the call. Any appreciation in the value of the call resulting from delta gains as the underlying moves higher is good—$0.50 plus whatever the call can be sold for. If the forecast is for XYZ to remain neutral, it’s logical to continue selling the one-month call. Because the December call has been financed by the aggregate short call premiums already, additional premiums earned by writing calls are profit with “free” protection. As long as the short is closed at its expiration, the risk of loss is eliminated. This is the general nature of rolling calls in a calendar spread. It’s a beautiful plan when it works! The problem is that it is incredibly unlikely that the stock will stay right at $60 per share for five months. It’s almost inevitable that it will move at some point. It’s like a game of Russian roulette. At some point it’s going to be a losing proposition—you just don’t know when. The benefit of rolling is that if the trade works out for a few months in a row, the long call is paid for and the risk of loss is covered by aggregate profits. If we step outside this best-case theoretical world and consider what is really happening on a day-to-day basis, we can gain insight on how to manage this type of trade when things go wrong. Effectively, a long calendar is a typical gamma/theta trade. Negative gamma hurts. Positive theta helps. If we knew which way the stock was going, we would simply buy or sell stock to adjust to get long or short deltas. But, unfortunately, we don’t. Our ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:323 SCORE: 32.00 ================================================================================ Selling the Front, Buying the Back If for a particular stock, the February ATM calls are trading at 50 volatility and the May ATM calls are trading at 35 volatility, a vol-calendar trader would buy the Mays and sell the Februarys. Sounds simple, right? The devil is in the details. We’ll look at an example and then discuss some common pitfalls with vol-trading calendars. George has been studying the implied volatility of a $164.15 stock. George notices that front-month volatility has been higher than that of the other months for a couple of weeks. There is nothing in the news to indicate immediate risk of extraordinary movement occurring in this example. George sees that he can sell the 22-day July 165 calls at a 45 percent IV and buy the 85-day September 165 calls at a 38 percent IV. George would like to buy the calendar spread, because he believes the July ATM volatility will drop down to around 38, where the September is trading. If he puts on this trade, he will establish the following position: What are George’s risks? Because he would be selling the short-term ATM option, negative gamma could be a problem. The greeks for this trade, shown in Exhibit 11.7 , confirm this. The negative gamma means each dollar of stock price movement causes an adverse change of about 0.09 to delta. The spread’s delta becomes shorter when the stock rises and longer when the stock falls. Because the position’s delta is long 0.369 from the start, some price appreciation may be welcomed in the short term. The stock advance will yield profits but at a diminishing rate, as negative gamma reduces the delta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:324 SCORE: 32.50 ================================================================================ EXHIBIT 11.7 10-lot July–September 165 call calendar. But just looking at the net position greeks doesn’t tell the whole story. It is important to appreciate the fact that long calendar spreads such as this have long vegas. In this case, the vega is +1.522. But what does this number really mean? This vega figure means that if IV rises or falls in both the July and the September calls by the same amount, the spread makes or loses $152 per vol point. George’s plan, however, is to see the July’s volatility decline to converge with the September’s. He hopes the volatilities of the two months will move independently of each other. To better gauge his risk, he needs to look at the vega of each option. With the stock at $164.15 the vegas are as follows: If George is right and July volatility declines 8 points, from 46 to 38, he will make $1,283 ($1.604 × 100 × 8). There are a couple of things that can go awry. First, instead of the volatilities converging, they can diverge further. Implied volatility is a slave to the whims of the market. If the July IV continues to rise while the September IV stays the same, George loses $160 per vol point. The second thing that can go wrong is the September IV declining along with the July IV. This can lead George into trouble, too. It depends the extent to which the September volatility declines. In this example, the vega of the September leg is about twice that of the July leg. That means that if the July volatility loses eight points while the September volatility declines four points, profits from the July calls will be negated by losses from the September calls. If the September volatility falls even more, the trade is a loser. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:325 SCORE: 38.00 ================================================================================ IV is a common cause of time-spread failure for market makers. When i in the front month rises, the volatility of the back-months sometimes does as well. When this happens, it’s often because market makers who sold front-month options to retail or institutional buyers buy the back-month options to hedge their short-gamma risk. If the market maker buys enough back-month options, he or she will accumulate positive vega. But when the market sells the front-month volatility back to the market makers, the back months drop, too, because market makers no longer need the back months for a hedge. Traders should study historical implied volatility to avoid this pitfall. As is always the case with long vega strategies, there is a risk of a decline in IV. Buying long-term options with implied volatility in the lower third of the 12-month IV range helps improve the chances of success, since the volatility being bought is historically cheap. This can be tricky, however. If a trader looks back on a chart of IV for an option class and sees that over the past six months it has ranged between 20 and 30 but nine months ago it spiked up to, say, 55, there must be a reason. This solitary spike could be just an anomaly. To eliminate the noise from volatility charts, it helps to filter the data. News stories from that time period and historical stock charts will usually tell the story of why volatility spiked. Often, it is a one-time event that led to the spike. Is it reasonable to include this unique situation when trying to get a feel for the typical range of implied volatility? Usually not. This is a judgment call that needs to be made on a case-by-case basis. The ultimate objective of this exercise is to determine: “Is volatility cheap or expensive?” ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:326 SCORE: 40.50 ================================================================================ Buying the Front, Selling the Back All trading is based on the principle of “buy low, sell high”—even volatility trading. With time spreads, we can do both at once, but we are not limited to selling the front and buying the back. When short-term options are trading at a lower IV than long-term ones, there may be an opportunity to sell the calendar. If the IV of the front month is 17 and the back-month IV is 25, for example, it could be a wise trade to buy the front and sell the back. But selling time spreads in this manner comes with its own unique set of risks. First, a short calendar’s greeks are the opposite of those of a long calendar. This trade has negative theta with positive gamma. A sideways market hurts this position as negative theta does its damage. Each day of carrying the position is paid for with time decay. The short calendar is also a short-vega trade. At face value, this implies that a drop in IV leads to profit and that the higher the IV sold in the back month, the better. As with buying a calendar, there are some caveats to this logic. If there is an across-the-board decline in IV, the net short vega will lead to a profit. But an across-the-board drop in volatility, in this case, is probably not a realistic expectation. The front month tends to be more sensitive to volatility. It is a common occurrence for the front month to be “cheap” while the back month is “expensive.” The volatilities of the different months can move independently, as they can when one buys a time spread. There are a couple of scenarios that might lead to the back-month volatility’s being higher than the front month. One is high complacency in the short term. When the market collectively sells options in expectation of lackluster trading, it generally prefers to sell the short-term options. Why? Higher theta. Because the trade has less time until expiration, the trade has a shorter period of risk. Because of this, selling pressure can push down IV in the front-month options more than in the back. Again, the front month is more sensitive to changes in implied volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:327 SCORE: 22.50 ================================================================================ Because volatility has peaks and troughs, this can be a smart time to sell a calendar. The focus here is in seeing the “cheap” front month rise back up to normal levels, not so much in seeing the “expensive” back month fall. This trade is certainly not without risk. If the market doesn’t move, the negative theta of the short calendar leads to a slow, painful death for calendar sellers. Another scenario in which the back-month volatility can trade higher than the front is when the market expects higher movement after the expiration of the short-term option but before the expiration of the long-term option. Situations such as the expectation of the resolution of a lawsuit, a product announcement, or some other one-time event down the road are opportunities for the market to expect such movement. This strategy focuses on the back-month vol coming back down to normal levels, not on the front-month vol rising. This can be a more speculative situation for a volatility trade, and more can go wrong. The biggest volatility risk in selling a time spread is that what goes up can continue to go up. The volatility disparity here is created by hedgers and speculators favoring long-term options, hence pushing up the volatility, in anticipation of a big future stock move. As the likely date of the anticipated event draws near, more buyers can be attracted to the market, driving up IV even further. Realized volatility can remain low as investors and traders lie in wait. This scenario is doubly dangerous when volatility rises and the stock doesn’t move. A trader can lose on negative theta and lose on negative vega. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:328 SCORE: 71.00 ================================================================================ A Directional Approach Calendar spreads are often purchased when the outlook for the underlying is neutral. Sell the short-term ATM option; buy the long-term ATM option; collect theta. But with negative gamma, these trades are never really neutral. The delta is constantly changing, becoming more positive or negative. It’s like a rubber band: at times being stretched in either direction but always demanding a pull back to the strike. When the strike price being traded is not ATM, calendar spreads can be strategically traded as directional plays. Buying a calendar, whether using calls or puts, where the strike price is above the current stock price is a bullish strategy. With calls, the positive delta of the long-term out-of-the-money (OTM) call will be greater than the negative delta of the short-term OTM call. For puts, the positive delta of the short-term in-the-money (ITM) put will be greater than the negative delta of the long-term ITM put. Just the opposite applies if the strike price is below the current stock price. The negative delta of the short-term ITM call is greater than the positive delta of the long-term ITM call. The negative delta of the long-term OTM put is greater than the positive delta of the short-term OTM put. When the position starts out with either a positive or negative delta, movement in the direction of the delta is necessary for the trade to be profitable. Negative gamma is also an important strategic consideration. Stock-price movement is needed, but not too much. Buying calendar spreads is like playing outfield in a baseball game. To catch a fly ball, an outfielder must focus on both distance and timing. He must gauge how far the ball will be hit and how long it will take to get there. With calendars, the distance is the strike price—that’s where the stock needs to be—and the time is the expiration day of the short month’s option: that’s when it needs to be at the target price. For example, with Wal-Mart (WMT) at $48.50, a trader, Pete, is looking for a rise to about $50 over the next five or six weeks. Pete buys the August–September call calendar. In this example, August has 39 days until expiration and September has 74 days. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:329 SCORE: 44.00 ================================================================================ Exactly what does 50 cents buy Pete? The stock price sitting below the strike price means a net positive delta. This long time spread also has positive theta and vega. Gamma is negative. Exhibit 11.8 shows the specifics. EXHIBIT 11.8 10-lot Wal-Mart August–September 50 call calendar. The delta of this trade, while positive, is relatively small with 39 days left until August expiration. It’s not rational to expect a quick profit if the stock advances faster than expected. But ultimately, a rise in stock price is the goal. In this example, Wal-Mart needs to rise to $50, and timing is everything. It needs to be at that price in 39 days. In the interim, a move too big and too fast in either direction hurts the trade because of negative gamma. Starting with Wal-Mart at $48.50, delta/gamma problems are worse to the downside. Exhibit 11.9 shows the effects of stock price on delta, gamma, and theta. EXHIBIT 11.9 Stock price movement and greeks. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:330 SCORE: 40.00 ================================================================================ If Wal-Mart moves lower, the delta gets more positive, racking up losses at a higher rate. To add to Pete’s woes, theta becomes less of a benefit as the stock drifts lower. At $47 a share, theta is about flat. With Wal-Mart trading even lower than $47, the positive theta of the August call is overshadowed by the negative theta of the September. Theta can become negative, causing the position to lose value as time passes. A big move to the upside doesn’t help either. If Wal-Mart rises just a bit, the −0.323 gamma only lessens the benefit of the 0.563 delta. But above $50, negative gamma begins to cause the delta to become increasingly negative. Theta begins to wither away at higher stock prices as well. The place to be is right at $50. The delta is flat and theta is highest. As long as Wal-Mart finds its way up to this price by the third Friday of August, life is good for Pete. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:331 SCORE: 57.00 ================================================================================ The In-or-Out Crowd Pete could just as well have traded the Aug–Sep 50 put calendar in this situation. If he’d been bearish, he could have traded either the Aug–Sep 45 call spread or the Aug–Sep 45 put spread. Whether bullish or bearish, as mentioned earlier, the call calendar and the put calendar both function about the same. When deciding which to use, the important consideration is that one of them will be in-the-money and the other will be OTM. Whether you have an ITM spread or an OTM spread has potential implications for the success of the trade. The bid-ask spreads tend to be wider for higher-delta, ITM options. Because of this, it can be more expensive to enter into an ITM calendar. Why? Trading options with wider markets requires conceding more edge. Take the following options series: By buying the May 50 calls at 3.20, a trader gives up 0.10 of theoretical edge (3.20 is 0.10 higher than the theoretical value). Buying the put at 1.00 means buying only 0.05 over theoretical. Because a calendar is a two-legged spread, the double edge given up by trading the wider markets of two in-the-money options can make the out-of- the-money spread a more attractive trade. The issue of wider markets is compounded when rolling the spread. Giving up a nickel or a dime each month can add up, especially on nominally low-priced spreads. It can cut into a high percentage of profits. Early assignment can complicate ITM calendars made up of American options, as dividends and interest can come into play. The short leg of the spread could get assigned before the expiration date as traders exercise calls to capture the dividend. Short ITM puts may get assigned early because of interest. Although assignment is an undesirable outcome for most calendar spread traders, getting assigned on the short leg of the calendar spread may not necessarily create a significantly different trade. If a long put calendar, for ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:333 SCORE: 76.00 ================================================================================ Double Calendars Definition : A double calendar spread is the execution of two calendar spreads that have the same months in common but have two different strike prices. Example Sell 1 XYZ February 70 call Buy 1 XYZ March 70 call Sell 1 XYZ February 75 call Buy 1 XYZ March 75 call Double calendars can be traded for many reasons. They can be vega plays. If there is a volatility-time skew, a double calendar is a way to take a position without concentrating delta or gamma/theta risk at a single strike. This spread can also be a gamma/theta play. In that case, there are two strikes, so there are two potential focal points to gravitate to (in the case of a long double calendar) or avoid (in the case of a short double calendar). Selling the two back-month strikes and buying the front-month strikes leads to negative theta and positive gamma. The positive gamma creates favorable deltas when the underlying moves. Positive or negative deltas can be covered by trading the underlying stock. With positive gamma, profits can be racked up by buying the underlying to cover short deltas and subsequently selling the underlying to cover long deltas. Buying the two back-month strikes and selling the front-month strikes creates negative gamma and positive theta, just as in a conventional calendar. But the underlying stock has two target price points to shoot for at expiration to achieve the maximum payout. Often double calendars are traded as IV plays. Many times when they are traded as IV plays, traders trade the lower-strike spread as a put calendar and the higher-strike spread a call calendar. In that case, the spread is sometimes referred to as a strangle swap . Strangles are discussed in Chapter 15. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:334 SCORE: 30.00 ================================================================================ Two Courses of Action Although there may be many motivations for trading a double calendar, there are only two courses of action: buy it or sell it. While, for example, the trader’s goal may be to capture theta, buying a double calendar comes with the baggage of the other greeks. Fully understanding the interrelationship of the greeks is essential to success. Option traders must take a holistic view of their positions. Let’s look at an example of buying a double calendar. In this example, Minnesota Mining & Manufacturing (MMM) has been trading in a range between about $85 and $97 per share. The current price of Minnesota Mining & Manufacturing is $87.90. Economic data indicate no specific reasons to anticipate that Minnesota Mining & Manufacturing will deviate from its recent range over the next month—that is, there is nothing in the news, no earnings anticipated, and the overall market is stable. August IV is higher than October IV by one volatility point, and October implied volatility is in line with 30-day historical volatility. There are 38 days until August expiration, and 101 days until October expiration. The Aug–Oct 85–90 double calendar can be traded at the following prices: Much like a traditional calendar spread, the price points cannot be definitively plotted on a P&(L) diagram. What is known for certain is that at August expiration, the maximum loss is $3,200. While it’s comforting to know that there is limited loss, losing the entire premium that was paid for the spread is an outcome most traders would like to avoid. We also know the maximum gains occur at the strike prices; but not exactly what the maximum profit can be. Exhibit 11.10 provides an alternative picture of the position that is useful in managing the trade on a day-to-day basis. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:335 SCORE: 34.00 ================================================================================ EXHIBIT 11.10 10-lot Minnesota Mining & Manufacturing Aug–Oct 85– 90 double call calendar. These numbers are a good representation of the position’s risk. Knowing that long calendars and long double calendars have maximum losses at the expiration of the short-term option equal to the net premiums paid, the max loss in this example is 3.20. Break-even prices are not relevant to this position because they cannot be determined with any certainty. What is important is to get a feel for how much movement can hurt the position. To make $19 a day in theta, a −0.468 gamma must be accepted. In the long run, $1 of movement is irrelevant. In fact, some movement is favorable because the ideal point for MMM to be at, at August expiration is either $85 or $90. So while small moves are acceptable, big moves are of concern. The negative gamma is an illustration of this warning. The other risk besides direction is vega. A positive 1.471 vega means the calendar makes or loses about $147 with each one-point across-the-board change in implied volatility. Implied volatility is a risk in all calendar trades. Volatility was one of the criteria studied when considering this trade. Recall that the August IV was one point higher than the October and that the October IV was in line with the 30-day historical volatility at inception of the trade. Considering the volatility data is part of the due diligence when considering a calendar or a double calendar. First, the (slightly) more expensive options (August) are being sold, and the cheaper ones are being bought (October). A study of the company reveals no news to lead one to believe that Minnesota Mining & Manufacturing should move at a higher realized volatility than it currently is in this example. Therefore, the front ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:337 SCORE: 45.00 ================================================================================ Diagonals Definition : A diagonal spread is an option strategy that involves buying one option and selling another option with a different strike price and with a different expiration date. Diagonals are another strategy in the time spread family. Diagonals enable a trader to exploit opportunities similar to those exploited by a calendar spread, but because the options in a diagonal spread have two different strike prices, the trade is more focused on delta. The name diagonal comes from the fact that the spread is a combination of a horizontal spread (two different months) and a vertical spread (two different strikes). Say it’s 22 days until January expiration and 50 days until February expiration. Apple Inc. (AAPL) is trading at $405.10. Apple has been in an uptrend heading toward the peak of its six-month range, which is around $420. A trader, John, believes that it will continue to rise and hit $420 again by February expiration. Historical volatility is 28 percent. The February 400 calls are offered at a 32 implied volatility and the January 420 calls are bid on a 29 implied volatility. John executes the following diagonal: Exhibit 11.11 shows the analytics for this trade. EXHIBIT 11.11 Apple January–February 400–420 call diagonal. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:338 SCORE: 16.00 ================================================================================ From the presented data, is this a good trade? The answer to this question is contingent on whether the position John is taking is congruent with his view of direction and volatility and what the market tells him about these elements. John is bullish up to August expiration, and the stock in this example is in an uptrend. Any rationale for bullishness may come from technical or fundamental analysis, but techniques for picking direction, for the most part, are beyond the scope of this book. Buying the lower strike in the February option gives this trade a more positive delta than a straight calendar spread would have. The trader’s delta is 0.255, or the equivalent of about 25.5 shares of Apple. This reflects the trader’s directional view. The volatility is not as easy to decipher. A specific volatility forecast was not stated above, but there are a few relevant bits of information that should be considered, whether or not the trader has a specific view on future volatility. First, the historical volatility is 28 percent. That’s lower than either the January or the February calls. That’s not ideal. In a perfect world, it’s better to buy below historical and sell above. To that point, the February option that John is buying has a higher volatility than the January he is selling. Not so good either. Are these volatility observations deal breakers? ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:339 SCORE: 50.00 ================================================================================ A Good Ex-Skews It’s important to take skew into consideration. Because the January calls have a higher strike price than the February calls, it’s logical for them to trade at a lower implied volatility. Is this enough to justify the possibility of selling the lower volatility? Consider first that there is some margin for error. The bid-ask spreads of each of the options has a volatility disparity. In this case, both the January and February calls are 10 cents wide. That means with a January vega of 0.34 the bid-ask is about 0.29 vol points wide. The Februarys have a 0.57 vega. They are about 0.18 vol points wide. That accounts for some of the disparity. Natural vertical skew accounts for the rest of the difference, which is acceptable as long as the skew is not abnormally pronounced. As for other volatility considerations, this diagonal has the rather unorthodox juxtaposition of positive vega and negative gamma seen with other time spreads. The trader is looking for a move upward, but not a big one. As the stock rises and Apple moves closer to the 420 strike, the positive delta will shrink and the negative gamma will increase. In order to continue to enjoy profits as the stock rises, John may have to buy shares of Apple to keep his positive delta. The risk here is that if he buys stock and Apple retraces, he may end up negative scalping stock. In other words, he may sell it back at a lower price than he bought it. Using stock to adjust the delta in a negative-gamma play can be risky business. Gamma scalping is addressed further in Chapter 13. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:340 SCORE: 64.00 ================================================================================ Making the Most of Your Options The trader from the previous example had a time-spread alternative to the diagonal: John could have simply bought a traditional time spread at the 420 strike. Recall that calendars reap the maximum reward when they are at the shared strike price at expiration of the short-term option. Why would he choose one over the other? The diagonal in that example uses a lower-strike call in the February than a straight 420 calendar spread and therefore has a higher delta, but it costs more. Gamma, theta, and vega may be slightly lower with the in-the-money call, depending on how far from the strike price the ITM call is and how much time until expiration it has. These, however, are less relevant differences. The delta of the February 400 call is about 0.57. The February 420 call, however, has only a 0.39 delta. The 0.18 delta difference between the calls means the position delta of the time spread will be only about 0.07 instead of about 0.25 of the diagonal—a big difference. But the trade-off for lower delta is that the February 420 call can be bought for 12.15. That means a lower debit paid—that means less at risk. Conversely, though there is greater risk with the diagonal, the bigger delta provides a bigger payoff if the trader is right. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:341 SCORE: 56.00 ================================================================================ Double Diagonals A double diagonal spread is the simultaneous trading of two diagonal spreads: one call spread and one put spread. The distance between the strikes is the same in both diagonals, and both have the same two expiration months. Usually, the two long-term options are more out-of-the-money than the two shorter-term options. For example Buy 1 XYZ May 70 put Sell 1 XYZ March 75 put Sell 1 XYZ March 85 call Buy 1 XYZ May 90 call Like many option strategies, the double diagonal can be looked at from a number of angles. Certainly, this is a trade composed of two diagonal spreads—the March–May 70–75 put and the March–May 85–90 call. It is also two strangles—buying the May 70–90 strangle and selling the March 75–85 strangle. One insightful way to look at this spread is as an iron condor in which the guts are March options and the wings are May options. Trading a double diagonal like this one, rather than a typically positioned iron condor, can offer a few advantages. The first advantage, of course, is theta. Selling short-term options and buying long-term options helps the trader reap higher rates of decay. Theta is the raison d’être of the iron condor. A second advantage is rolling. If the underlying asset stays in a range for a long period of time, the short strangle can be rolled month after month. There may, in some cases, also be volatility-term-structure discrepancies on which to capitalize. A trader, Paul, is studying JPMorgan (JPM). The current stock price is $49.85. In this example, JPMorgan has been trading in a pretty tight range over the past few months. Paul believes it will continue to do so over the next month. Paul considers the following trade: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:342 SCORE: 40.00 ================================================================================ Paul considers volatility. In this example, the JPMorgan ATM call, the August 50 (which is not shown here), is trading at 22.9 percent implied volatility. This is in line with the 20-day historical volatility, which is 23 percent. The August IV appears to be reasonably in line with the September volatility, after accounting for vertical skew. The IV of the August 52.50 calls is 1.5 points above that of the September 55 calls and the August 47.50 put IV is 1.6 points below the September 45 put IV. It appears that neither month’s volatility is cheap or expensive. Exhibit 11.12 shows the trade’s greeks. EXHIBIT 11.12 10-lot JPMorgan August–September 45–47.50–52.50–55 double diagonal. The analytics of this trade are similar to those of an iron condor. Immediate directional risk is almost nonexistent, as indicated by the delta. But gamma and theta are high, even higher than they would be if this were a straight September iron condor, although not as high as if this were an August iron condor. Vega is positive. Surely, if this were an August or a September iron condor, vega would be negative. In this example, Paul is indifferent as to whether vega is positive or negative because IV is fairly priced in terms of historical volatility and term structure. In fact, to play it close to the vest, Paul probably wants the smallest vega possible, in case of an IV move. Why take on the risk? The motivation for Paul’s double diagonal was purely theta. The volatilities were all in line. And this one-month spread can’t be rolled. If Paul were interested in rolling, he could have purchased longer-term ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:348 SCORE: 20.00 ================================================================================ Trading Implied Volatility Many of the strategies covered so far have been option-selling strategies. Some had a directional bias; some did not. Most of the strategies did have a primary focus on realized volatility—especially selling it. These short volatility strategies require time. The reward of low stock volatility is theta. In general, most of the strategies previously covered were theta trades in which negative gamma was an unpleasant inconvenience to be dealt with. Moving forward, much of the remainder of this book will involve more in-depth discussions of trading both realized and implied volatility (IV), with a focus on the harmonious, and sometimes disharmonious, relationship between the two types. Much attention will be given to how IV trades in the option market, describing situations in which volatility moves are likely to occur and how to trade them. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:349 SCORE: 15.00 ================================================================================ Direction Neutral versus Direction Indifferent In the world of nonlinear trading, there are two possible nondirectional views of the underlying asset: direction neutral and direction indifferent. Direction neutral means the trader believes the stock will not trend either higher or lower. The trader is neutral in his or her assessment of the future direction of the asset. Short iron condors, long time spreads, and out-of-the- money (OTM) credit spreads are examples of direction-neutral strategies. These strategies generally have deltas close to zero. Because of negative gamma, movement is the bane of the direction-neutral trade. Direction indifferent means the trader may desire movement in the underlying but is indifferent as to whether that movement is up or down. Some direction-indifferent trades are almost completely insulated from directional movement, with a focus on interest or dividends instead. Examples of these types of trades are conversions, reversals, and boxes, which are described in Chapter 6, as well as dividend plays, which are described in Chapter 8. Other direction-indifferent strategies are long option strategies that have positive gamma. In these trades, the focus is on movement, but the direction of that movement is irrelevant. These are plays that are bullish on realized volatility. Yet other direction-indifferent strategies are volatility plays from the perspective of IV. These are trades in which the trader’s intent is to take a bullish or bearish position in IV. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:350 SCORE: 66.50 ================================================================================ Delta Neutral To be truly direction neutral or direction indifferent means to have a delta equal to zero. In other words, there are no immediate gains if the underlying moves incrementally higher or lower. This zero-delta method of trading is called delta-neutral trading . A delta-neutral position can be created from any option position simply by trading stock to flatten out the delta. A very basic example of a delta- neutral trade is a long at-the-money (ATM) call with short stock. Consider a trade in which we buy 20 ATM calls that have a 50 delta and sell stock on a delta-neutral ratio. Buy 20 50-delta calls (long 1,000 deltas) Short 1,000 shares (short 1,000 deltas) In this position, we are long 1,000 deltas from the calls (20 × 50) and short 1,000 deltas from the short sale of stock. The net delta of the position is zero. Therefore, the immediate directional exposure has been eliminated from the trade. But intuitively, there are other opportunities for profit or loss with this trade. The addition of short stock to the calls will affect only the delta, not the other greeks. The long calls have positive gamma, negative theta, and positive vega. Exhibit 12.1 is a simplified representation of the greeks for this trade. EXHIBIT 12.1 20-lot delta-neutral long call. With delta not an immediate concern, the focus here is on gamma, theta, and vega. The +1.15 vega indicates that each one-point change in IV makes or loses $115 for this trade. Yet there is more to the volatility story. Each day that passes costs the trader $50 in time decay. Holding the position for ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:351 SCORE: 58.00 ================================================================================ an extended period of time can produce a loser even if IV rises. Gamma is potentially connected to the success of this trade, too. If the underlying moves in either direction, profit from deltas created by positive gamma may offset the losses from theta. In fact, a big enough move in either direction can produce a profitable trade, regardless of what happens to IV. Imagine, for a moment, that this trade is held until expiration. If the stock is below the strike price at this point, the calls expire. The resulting position is short 1,000 shares of stock. If the stock is above the strike price at expiration, the calls can be exercised, creating 2,000 shares of long stock. Because the trade is already short 1,000 shares, the resulting net position is long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock moves in either direction the greater the profit potential. The underlying has to move far enough above or below the strike price to allow the beneficial gains from buying or selling stock to cover the option premium lost from time decay. If the trade is held until expiration, the underlying needs to move far enough to cover the entire premium spent on the calls. The solid lines forming a V in Exhibit 12.2 conceptually illustrate the profit or loss for this delta-neutral long call at expiration. EXHIBIT 12.2 Profit-and-loss diagram for delta-neutral long-call trade. Because of gamma, some deltas will be created by movement of the underlying before expiration. Gamma may lead to this being a profitable ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:353 SCORE: 14.00 ================================================================================ Why Trade Delta Neutral? A few years ago, I was teaching a class on option trading. Before the seminar began, I was talking with one of the students in attendance. I asked him what he hoped to learn in the class. He said that he was really interested in learning how to trade delta neutral. When I asked him why he was interested in that specific area of trading, he replied, “I hear that’s where all the big money is made!” This observation, right or wrong, probably stems from the fact that in the past most of the trading in this esoteric discipline has been executed by professional traders. There are two primary reasons why the pros have dominated this strategy: high commissions and high margin requirements for retail traders. Recently, these two reasons have all but evaporated. First, the ultracompetitive world of online brokers has driven commissions for retail traders down to, in some cases, what some market makers pay. Second, the oppressive margin requirements that retail option traders were subjected to until 2007 have given way to portfolio margining. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:354 SCORE: 31.00 ================================================================================ Portfolio Margining Customer portfolio margining is a method of calculating customer margin in which the margin requirement is based on the “up and down risk” of the portfolio. Before the advent of portfolio margining, retail traders were subject to strategy-based margining, also called Reg. T margining, which in many cases required a significantly higher amount of capital to carry a position than portfolio margining does. With portfolio margining, highly correlated securities can be offset against each other for purposes of calculating margin. For example, SPX options and SPY options—both option classes based on the Standard & Poor’s 500 Index—can be considered together in the margin calculation. A bearish position in one and a bullish position in the other may partially offset the overall risk of the portfolio and therefore can help to reduce the overall margin requirement. With portfolio margining, many strategies are margined in such a way that, from the point of view of this author, they are subject to a much more logical means of risk assessment. Strategy-based margining required traders of some strategies, like a protective put, to deposit significantly more capital than one could possibly lose by holding the position. The old rules require a minimum margin of 50 percent of the stock’s value and up to 100 percent of the put premium. A portfolio-margined protective put may require only a fraction of what it would with strategy-based margining. Even though Reg. T margining is antiquated and sometimes unreasonable, many traders must still abide by these constraints. Not all traders meet the eligibility requirements to qualify for portfolio-based margining. There is a minimum account balance for retail traders to be eligible for this treatment. A broker may also require other criteria to be met for the trader to benefit from this special margining. Ultimately, portfolio margining allows retail traders to be margined similarly to professional traders. There are some traders, both professional and otherwise, who indeed have made “big money,” as the student in my class said, trading delta neutral. But, to be sure, there are successful and unsuccessful traders in many areas ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:356 SCORE: 30.00 ================================================================================ Trading Implied Volatility With a typical option, the sensitivity of delta overshadows that of vega. To try and profit from a rise or fall in IV, one has to trade delta neutral to eliminate immediate directional sensitivity. There are many strategies that can be traded as delta-neutral IV strategies simply by adding stock. Throughout this chapter, I will continue using a single option leg with stock, since it provides a simple yet practical example. It’s important to note that delta-neutral trading does not refer to a specific strategy; it refers to the fact that the trader is indifferent to direction. Direction isn’t being traded, volatility is. Volatility trading is fundamentally different from other types of trading. While stocks can rise to infinity or decline to zero, volatility can’t. Implied volatility, in some situations, can rise to lofty levels of 100, 200, or even higher. But in the long-run, these high levels are not sustainable for most stocks. Furthermore, an IV of zero means that the options have no extrinsic value at all. Now that we have established that the thresholds of volatility are not as high as infinity and not as low as zero, where exactly are they? The limits to how high or low IV can go are not lines in the sand. They are more like tides that ebb and flow, but normally come up only so far onto the beach. The volatility of an individual stock tends to trade within a range that can be unique to that particular stock. This can be observed by studying a chart of recent volatility. When IV deviates from the range, it is typical for it to return to the range. This is called reversion to the mean , which was discussed in Chapter 3. IV can get stretched in either direction like a rubber band but then tends to snap back to its original shape. There are many examples of situations where reversion to the mean enters into trading. In some, volatility temporarily dips below the typical range, and in some, it rises beyond the recent range. One of the most common examples is the rush and the crush. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:357 SCORE: 12.00 ================================================================================ The Rush and the Crush In this situation, volatility rises before and falls after a widely anticipated news announcement, of earnings, for instance, or of a Food and Drug Administration (FDA) approval. In this situation, option buyers rush in and bid up IV. The more uncertainty—the more demand for insurance—the higher vol rises. When the event finally occurs and the move takes place or doesn’t, volatility gets crushed. The crush occurs when volatility falls very sharply—sometimes 10 points, 20 points, or more—in minutes. Traders with large vega positions appreciate the appropriateness of the term crush all too well. Volatility traders also affectionately refer to this sudden drop in IV by saying that volatility has gotten “whacked.” In order to have a feel for whether implied volatility is high or low for a particular stock, you need to know where it’s been. It’s helpful to have an idea of where realized volatility is and has been, too. To be sure, one analysis cannot be entirely separate from the other. Studying both implied and realized volatility and how they relate is essential to seeing the big picture. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:359 SCORE: 11.50 ================================================================================ Volatility Selling Susie Seller, a volatility trader, studies semiconductor stocks. Exhibit 12.3 shows the volatilities of a $50 chip stock. The circled area shows what happened before and after second-quarter earnings were reported in July. The black line is the IV, and the gray is the 30-day historical. EXHIBIT 12.3 Chip stock volatility before and after earnings reports. Source : Chart courtesy of iVolatility.com In mid-July, Susie did some digging to learn that earnings were to be announced on July 24, after the close. She was careful to observe the classic rush and crush that occurred to varying degrees around the last three earnings announcements, in October, January, and April. In each case, IV firmed up before earnings only to get crushed after the report. In mid-to-late July, she watched as IV climbed to the mid-30s (the rush) just before earnings. As the stock lay in wait for the report, trading came to a proverbial screeching halt, sending realized volatility lower, to about 13 percent. Susie waited for the end of the day just before the report to make her move. Before the closing bell, the stock was at $50. Susie sold 20 one- month 50-strike calls at 2.10 (a 35 volatility) and bought 1,100 shares of the underlying stock at $50 to become delta neutral. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:360 SCORE: 38.00 ================================================================================ Exhibit 12.4 shows Susie’s position. EXHIBIT 12.4 Delta-neutral short ATM call, long stock position. Her delta was just about flat. The delta for the 50 calls was 0.54 per contract. Selling a 20-lot creates 10.80 short deltas for her overall position. After buying 1,100 shares, she was left long 0.20 deltas, about the equivalence of being long 20 shares. Where did her risk lie? Her biggest concern was negative gamma. Without even seeing a chart of the stock’s price, we can see from the volatility chart that this stock can have big moves on earnings. In October, earnings caused a more than 10-point jump in realized volatility, to its highest level during the year shown. Whether the stock rose or fell is irrelevant. Either event means risk for a premium seller. The positive theta looks good on the surface, but in fact, theta provided Susie with no significant benefit. Her plan was “in and out and nobody gets hurt.” She got into the trade right before the earnings announcement and out as soon as implied volatility dropped off. Ideally, she’d like to hold these types of trades for less than a day. The true prize is vega. Susie was looking for about a 10-point drop in IV, which this option class had following the October and January earnings reports. April had a big drop in IV, as well, of about eight or nine points. Ultimately, what Susie is looking for is reversion to the mean. She gauges the normal level of volatility by observing where it is before and after the surges caused by earnings. From early November to mid- to late- December, the stock’s IV bounced around the 25 percent level. In the month of February, the IV was around 25. After the drop-off following April earnings and through much of May, the IV was closer to 20 percent. In June, IV was just above 25. Susie surmised from this chart that when no ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:361 SCORE: 30.50 ================================================================================ earnings event is pending, this stock’s options typically trade at about a 25 percent IV. Therefore, anticipating a 10-point decline from 35 was reasonable, given the information available. If Susie gets it right, she stands to make $1,150 from vega (10 points × 1.15 vegas × 100). As we can see from the right side of the volatility chart in Exhibit 12.3 , Susie did get it right. IV collapsed the next morning by just more than ten points. But she didn’t make $1,150; she made less. Why? Realized volatility (gamma). The jump in realized volatility shown on the graph is a function of the fact that the stock rallied $2 the day after earnings. Negative gamma contributed to negative deltas in the face of a rallying market. This negative delta affected some of Susie’s potential vega profits. So what was Susie’s profit? On this trade she made $800. The next morning at the open, she bought back the 50-strike calls at 2.80 (25 IV) and sold the stock at $52. To compute her actual profit, she compared the prices of the spread when entering the trade with the prices of the spread when exiting. Exhibit 12.5 shows the breakdown of the trade. EXHIBIT 12.5 Profit breakdown of delta-neutral trade. After closing the trade, Susie knew for sure what she made or lost. But there are many times when a trader will hold a delta-neutral position for an extended period of time. If Susie hadn’t closed her trade, she would have looked at her marks to see her P&(L) at that point in time. Marks are the prices at which the securities are trading in the actual market, either in real time or at end of day. With most online brokers’ trading platforms or options-trading software, real-time prices are updated dynamically and always at their fingertips. The profit or loss is, then, calculated automatically by comparing the actual prices of the opening transaction with the current marks. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:362 SCORE: 68.00 ================================================================================ What Susie will want to know is why she made $800. Why not more? Why not less, for that matter? When trading delta neutral, especially with more complex trades involving multiple legs, a manual computation of each leg of the spread can be tedious. And to be sure, just looking at the profit or loss on each leg doesn’t provide an explanation. Susie can see where her profits or losses came from by considering the profit or loss for each influence contributing to the option’s value. Exhibit 12.6 shows the breakdown. EXHIBIT 12.6 Profit breakdown by greek. Delta Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40 profit attributable to that initial delta. Gamma As the stock rose, the negative delta of the position increased as a result of negative gamma. The delta of the stock remained the same, but the negative delta of the 50 call grew by the amount of the gamma. Deriving an exact P&(L) attributable to gamma is difficult because gamma is a dynamic metric: as the stock price changes, so can the gamma. This calculation assumes that gamma remains constant. Therefore, the gamma calculation here provides only an estimate. The initial position gamma of −1.6 means the delta decreases by 3.2 with a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then, would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But she wasn’t short 3.2 deltas for the whole $2. She started out with zero deltas attributable to gamma and ended up being 3.2 shorter from gamma over that $2 move. Therefore, if she assumes her negative delta from gamma grew steadily from 0 to −3.2, she can estimate her average delta loss over that move by dividing by 2. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:365 SCORE: 45.50 ================================================================================ The Imprecision of Estimation It is important to notice that the P&(L) found by adding up the P&(L)’s from the greeks is slightly different from the actual P&(L). There are a couple of reasons for this. First, the change in delta resulting from gamma is only an estimate, because gamma changes as the stock price changes. For small moves in the underlying, the gamma change is less significant, but for larger moves, the rate of change of the gamma can be bigger, and it can be nonlinear. For example, as an option moves from being at-the-money (ATM) to being out-of-the-money (OTM), its gamma decreases. But as the option becomes more OTM, its gamma decreases at a slower rate. Another reason that the P&(L) from the greeks is different from the actual P&(L) is that the greeks are derived from the option-pricing model and are therefore theoretical values and do not include slippage. Furthermore, the volatility input in this example is rounded a bit for simplicity. For example, a volatility of 25 actually yielded a theoretical value of 2.796, while the call was bought at 2.80. Because some options trade at minimum price increments of a nickel, and none trade in fractions of a penny, IV is often rounded. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:367 SCORE: 10.00 ================================================================================ Volatility Buying This same earnings event could have been played entirely differently. A different trader, Bobby Buyer, studied the same volatility chart as Susie. It is shown again here as Exhibit 12.7 . Bobby also thought there would be a rush and crush of IV, but he decided to take a different approach. EXHIBIT 12.7 Chip stock volatility before and after earnings reports. Source : Chart courtesy of iVolatility.com About an hour before the close of business on July 21, just three days before earnings announcements, Bobby saw that he could buy volatility at 30 percent. In Bobby’s opinion, volatility seemed cheap with earnings so close. He believed that IV could rise at least five points over the next three days. Note that we have the benefit of 20/20 hindsight in the example. Near the end of the trading day, the stock was at $49.70. Bobby bought 20 33-day 50-strike calls at 1.75 (30 volatility) and sold short 1,000 shares of the underlying stock at $49.70 to become delta neutral. Exhibit 12.8 shows Bobby’s position. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:368 SCORE: 26.00 ================================================================================ EXHIBIT 12.8 Delta-neutral long call, short stock position. With the stock at $49.70, the calls had +0.51 delta per contract, or +10.2 for the 20-lot. The short sale of 1,000 shares got Bobby as close to delta- neutral as possible without trading an odd lot in the stock. The net position delta was +0.20, or about the equivalent of being long 20 shares of stock. Bobby’s objective in this case is to profit from an increase in implied volatility leading up to earnings. While Susie was looking for reversion to the mean, Bobby hoped for a further divergence. For Bobby, positive gamma looked like a good thing on the surface. However, his plan was to close the position just before earnings were released—before the vol crush and before the potential stock-price move. With realized volatility already starting to drop off at the time the trade was put on, gamma offered little promise of gain. As fate would have it, IV did indeed increase. At the end of the day before the July earnings report, IV was trading at 35 percent. Bobby closed his trade by selling his 20-lot of the 50 calls at 2.10 and buying his 1,000 shares of stock back at $50. Exhibit 12.9 shows the P&(L) for each leg of the spread. EXHIBIT 12.9 Profit breakdown. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:369 SCORE: 37.00 ================================================================================ The calls earned Bobby a total of $700, while the stock lost $300. Of course, with this type of trade, it is not relevant which leg was a winner and which a loser. All that matters is the bottom line. The net P&(L) on the trade was a gain of $400. The gain in this case was mostly a product of IV’s rising. Exhibit 12.10 shows the P&(L) per greek. EXHIBIT 12.10 Profit breakdown by greek. Delta The position began long 0.20 deltas. The 0.30-point rise earned Bobby a 0.06 point gain in delta per contract. Gamma Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P& (L) in this example, assuming gamma remained constant. A 0.30 rise in the stock price multiplied by the 1.8 gamma means that with the stock at $50, Bobby was long an additional 0.54 deltas. We can estimate that over the course of the 0.30 rise in the stock price, Bobby was long an average of 0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is a gain of about 0.08 (0.27 × 0.30). Theta Bobby held this trade for three days. His total theta cost him 1.92 or $192. Vega The biggest contribution to Bobby’s profit on this trade was made by the spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position vega earned him 6.00, or $600. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:373 SCORE: 44.00 ================================================================================ Trading Realized Volatility So far, we’ve discussed many option strategies in which realized volatility is an important component of the trade. And while the management of these positions has been the focus of much of the discussion, the ultimate gain or loss for many of these strategies has been from movement in a single direction. For example, with a long call, the higher the stock rallies the better. But increases or decreases in realized volatility do not necessarily have an exclusive relationship with direction. Recall that realized volatility is the annualized standard deviation of daily price movements. Take two similarly priced stocks that have had a net price change of zero over a one-month period. Stock A had small daily price changes during that period, rising $0.10 one day and falling $0.10 the next. Stock B went up or down by $5 each day for a month. In this rather extreme example, Stock B was much more volatile than Stock A, regardless of the fact that the net price change for the period for both stocks was zero. A stock’s volatility—either high or low volatility—can be capitalized on by trading options delta neutral. Simply put, traders buy options delta neutral when they believe a stock will have more movement and sell options delta neutral when they believe a stock will move less. Delta-neutral option sellers profit from low volatility through theta. Every day that passes in which the loss from delta/gamma movement is less than the gain from theta is a winning day. Traders can adjust their deltas by hedging. Delta-neutral option buyers exploit volatility opportunities through a trading technique called gamma scalping. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:374 SCORE: 76.00 ================================================================================ Gamma Scalping Intraday trading is seldom entirely in one direction. A stock may close higher or lower, even sharply higher or lower, on the day, but during the day there is usually not a steady incremental rise or fall in the stock price. A typical intraday stock chart has peaks and troughs all day long. Delta- neutral traders who have gamma don’t remain delta neutral as the underlying price changes, which inevitably it will. Delta-neutral trading is kind of a misnomer. In fact, it is gamma trading in which delta-neutral traders engage. For long-gamma traders, the position delta gets more positive as the underlying moves higher and more negative as the underlying moves lower. An upward move in the underlying increases positive deltas, resulting in exponentially increasing profits. But if the underlying price begins to retrace downward, the gain from deltas can be erased as quickly as it was racked up. To lock in delta gains, a trader can adjust the position to delta neutral again by selling short stock to cover long deltas. If the stock price declines after this adjustment, losses are curtailed thanks to the short stock. In fact, the delta will become negative as the underlying price falls, leading to growing profits. To lock in profits again, the trader buys stock to cover short deltas to once again become delta neutral. The net effect is a stock scalp. Positive gamma causes the delta-neutral trader to sell stock when the price rises and buy when the stock falls. This adds up to a true, realized profit. So positive gamma is a money-making machine, right? Not so fast. As in any business, the profits must be great enough to cover expenses. Theta is the daily cost of running this gamma- scalping business. For example, a trader, Harry, notices that the intraday price swings in a particular stock have been increasing. He takes a bullish position in realized volatility by buying 20 off the 40-strike calls, which have a 50 delta, and selling stock on a delta-neutral ratio. Buy 20 40-strike calls (50 delta) (long 1,000 deltas) Short 1,000 shares at $40 (short 1,000 deltas) ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:375 SCORE: 48.00 ================================================================================ The immediate delta of this trade is flat, but as the stock moves up or down, that will change, presenting gamma-scalping opportunities. Gamma scalping is the objective here. The position greeks in Exhibit 13.1 show the relationship of the two forces involved in this trade: gamma and theta. EXHIBIT 13.1 Greeks for 20-lot delta-neutral long call. The relationship of gamma to theta in this sort of trade is paramount to its success. Gamma-scalping plays are not buy-and-hold strategies. This is active trading. These spreads need to be monitored intraday to take advantage of small moves in the underlying security. Harry will sell stock when the underlying rises and buy it when the underlying falls, taking a profit with each stock trade. The goal for each day that passes is to profit enough from positive gamma to cover the day’s theta. But that’s not always as easy as it sounds. Let’s study what happens the first seven days after this hypothetical trade is executed. For the purposes of this example, we assume that gamma remains constant and that the trader is content trading odd lots of stock. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:376 SCORE: 20.00 ================================================================================ Day One The first day proves to be fairly volatile. The stock rallies from $40 to $42 early in the day. This creates a positive position delta of 5.60, or the equivalent of being long about 560 shares. At $42, Harry covers the position delta by selling 560 shares of the underlying stock to become delta neutral again. Later in the day, the market reverses, and the stock drops back down to $40 a share. At this point, the position is short 5.60 deltas. Harry again adjusts the position, buying 560 shares to get flat. The stock then closes right at $40. The net result of these two stock transactions is a gain of $1,070. How? The gamma scalp minus the theta, as shown below. The volatility of day one led to it being a profitable day. Harry scalped 560 shares for a $2 profit, resulting from volatility in the stock. If the stock hadn’t moved as much, the delta would have been smaller, and the dollar amount scalped would have been smaller, leading to an exponentially smaller profit. If there had been more volatility, profits would have been exponentially larger. It would have led to a bigger bite being taken out of the market. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:377 SCORE: 12.00 ================================================================================ Day Two The next day, the market is a bit quieter. There is a $0.40 drop in the price of the stock, at which point the position delta is short 1.12. Harry buys 112 shares at $39.60 to get delta neutral. Following Harry’s purchase, the stock slowly drifts back up and is trading at $40 near the close. Harry decides to cover his deltas and sell 112 shares at $40. It is common to cover all deltas at the end of the day to get back to being delta neutral. Remember, the goal of gamma scalping is to trade volatility, not direction. Starting the next trading day with a delta, either positive or negative, means an often unwanted directional bias and unwanted directional risk. Tidying up deltas at the end of the day to get neutral is called going home flat. Today was not a banner day. Harry did not quite have the opportunity to cover the decay. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:378 SCORE: 30.00 ================================================================================ Day Three On this day, the market trends. First, the stock rises $0.50, at which point Harry sells 140 shares of stock at $40.50 to lock in gains from his delta and to get flat. However, the market continues to rally. At $41 a share, Harry is long another 1.40 deltas and so sells another 140 shares. The rally continues, and at $41.50 he sells another 140 shares to cover the delta. Finally, at the end of the day, the stock closes at $42 a share. Harry sells a final 140 shares to get flat. There was not any literal scalping of stock today. It was all selling. Nonetheless, gamma trading led to a profitable day. As the stock rose from $40 to $40.50, 140 deltas were created from positive gamma. Because the delta was zero at $40 and 140 at $40.50, the estimated average delta is found by dividing 140 in half. This estimated average delta multiplied by the $0.50 gain on the stock equals a $35 profit. The delta was zero after the adjustment made at $40.50, when 140 shares were sold. When the stock reached $41, another $35 was reaped from the average delta of 70 over the $0.50 move. This process was repeated every time the stock rose $0.50 and the delta was covered. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:382 SCORE: 24.00 ================================================================================ Art and Science Although this was a very simplified example, it was typical of how a profitable week of gamma scalping plays out. This stock had a pretty volatile week, and overall the week was a winner: there were four losing days and three winners. The number of losing days includes the weekends. Weekends and holidays are big hurdles for long-gamma traders because of the theta loss. The biggest contribution to this being a winning week was made by the gap open on day four. Part of the reason was the sheer magnitude of the move, and part was the fact that the deltas weren’t covered too soon, as they had been on day three. In a perfect world, a long-gamma trader will always buy the low of the day and sell the high of the day when covering deltas. This, unfortunately, seldom happens. Long-gamma traders are very often wrong when trading stock to cover deltas. Being wrong can be okay on occasion. In fact, it can even be rewarding. Day three was profitable despite the fact that 140 shares were sold at $40.50, $41, and $41.50. The stock closed at $42; the first three stock trades were losers. Harry sold stock at a lower price than the close. But the position still made money because of his positive gamma. To be sure, Harry would like to have sold all 560 shares at $42 at the end of the day. The day’s profits would have been significantly higher. The problem is that no one knows where the stock will move next. On day three, if the stock had topped out at $40.50 and Harry did not sell stock because he thought it would continue higher, he would have missed an opportunity. Gamma scalping is not an exact science. The art is to pick spots that capture the biggest moves possible without missing opportunities. There are many methods traders have used to decide where to cover deltas when gamma scalping: the daily standard deviation, a fixed percentage of the stock price, a fixed nominal value, covering at a certain time of day, “market feel.” No system appears to be absolutely better than another. This is where it gets personal. Finding what works for you, and what works for the individual stocks you trade, is the art of this science. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:383 SCORE: 51.00 ================================================================================ Gamma, Theta, and Volatility Clearly, more volatile stocks are more profitable for gamma scalping, right? Well . . . maybe. Recall that the higher the implied volatility, the lower the gamma and the higher the theta of at-the-money (ATM) options. In many cases, the more volatile a stock, the higher the implied volatility (IV). That means that a volatile stock might have to move more for a trader to scalp enough stock to cover the higher theta. Let’s look at the gamma-theta relationship from another perspective. In this example, for 0.50 of theta, Harry could buy 2.80 gamma. This relationship is based on an assumed 25 percent implied volatility. If IV were 50 percent, theta for this 20 lot would be higher, and the gamma would be lower. At a volatility of 50, Harry could buy 1.40 gammas for 0.90 of theta. The gamma is more expensive from a theta perspective, but if the stock’s statistical volatility is significantly higher, it may be worth it. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:384 SCORE: 38.50 ================================================================================ Gamma Hedging Knowing that the gamma and theta figures of Exhibit 13.1 are derived from a 25 percent volatility assumption offers a benchmark with which to gauge the potential profitability of gamma trading the options. If the stock’s standard deviation is below 25 percent, it will be difficult to make money being long gamma. If it is above 25 percent, the play becomes easier to trade. There is more scalping opportunity, there are more opportunities for big moves, and there are more likely to be gaps in either direction. The 25 percent volatility input not only determines the option’s theoretical value but also helps determine the ratio of gamma to theta. A 25 percent or higher realized volatility in this case does not guarantee the trade’s success or failure, however. Much of the success of the trade has to do with how well the trader scalps stock. Covering deltas too soon leads to reduced profitability. Covering too late can lead to missed opportunities. Trading stock well is also important to gamma sellers with the opposite trade: sell calls and buy stock delta neutral. In this example, a trader will sell 20 ATM calls and buy stock on a delta-neutral ratio. This is a bearish position in realized volatility. It is the opposite of the trade in the last example. Consider again that 25 percent IV is the benchmark by which to gauge potential profitability. Here, if the stock’s volatility is below 25, the chances of having a profitable trade are increased. Above 25 is a bit more challenging. In this simplified example, a different trader, Mary, plays the role of gamma seller. Over the same seven-day period as before, instead of buying calls, Mary sold a 20 lot. Exhibit 13.2 shows the analytics for the trade. For the purposes of this example, we assume that gamma remains constant and the trader is content trading odd lots of stock. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:386 SCORE: 25.00 ================================================================================ Day One This was one of the volatile days. The stock rallied from $40 to $42 early in the day and had fallen back down to $40 by the end of the day. Big moves like this are hard to trade as a short-gamma trader. As the stock rose to $42, the negative delta would have been increasing. That means losses were adding up at an increasing rate. The only way to have stopped the hemorrhaging of money as the stock continued to rise would have been to buy stock. Of course, if Mary buys stock and the stock then declines, she has a loser. Let’s assume the best-case scenario. When the stock reached $42 and she had a −560 delta, Mary correctly felt the market was overbought and would retrace. Sometimes, the best trades are the ones you don’t make. On this day, Mary traded no stock. When the stock reached $40 a share at the end of the day, she was back to being delta neutral. Theta makes her a winner today. Because of the way Mary handled her trade, the volatility of day one was not necessarily an impediment to it being profitable. Again, the assumption is that Mary made the right call not to negative scalp the stock. Mary could have decided to hedge her negative gamma when the stock reach $42 and the position delta was at −$560 by buying stock and then selling it at $40. There are a number of techniques for hedging deltas resulting from negative gamma. The objective of hedging deltas is to avoid losses from the stock trending in one direction and creating increasingly adverse deltas but not to overtrade stock and negative scalp. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:388 SCORE: 12.00 ================================================================================ Day Three Day three saw the stock price trending. It slowly drifted up $2. There would have been some judgment calls throughout this day. Again, delta-neutral trades are for active traders. Prepare to watch the market much of the day if implementing this kind of strategy. When the stock was at $41 a share, Mary decided to guard against further advances in stock price and hedged her delta. At that point, the position would have had a −2.80 delta. She bought 280 shares at $41. As the day progressed, the market proved Mary to be right. The stock rose to $42 giving the position a delta of −2.80 again. She covered her deltas at the end of the day by buying another 280 shares. Covering the negative deltas to get flat at $41 proved to be a smart move today. It curtailed an exponentially growing delta and let Mary take a smaller loss at $41 and get a fresh start. While the day was a loser, it would have been $280 worse if she had not purchased stock at $41 before the run- up to $42. This is evidenced by the fact that she made a $280 profit on the 280 shares of stock bought at $41, since the stock closed at $42. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:389 SCORE: 34.00 ================================================================================ Day Four Day four offered a rather unpleasant surprise. This was the day that the stock gapped open $4 lower. This is the kind of day short-gamma traders dread. There is, of course, no right way to react to this situation. The stock can recover, heading higher; it can continue lower; or it can have a dead-cat bounce, remaining where it is after the fall. Staring at a quite contrary delta of 11.20, Mary was forced to take action by selling stock. But how much stock was the responsible amount to sell for a pure short-gamma trader not interested in trading direction? Selling 1,120 shares would bring the position back to being delta neutral, but the only way the trade would stay delta neutral would be if the stock stayed right where it was. Hedging is always a difficult call for short-gamma traders. Long-gamma traders are taking a profit on deltas with every stock trade that covers their deltas. Short-gamma traders are always taking a loss on delta. In this case, Mary decided to cover half her deltas by selling 560 shares. The other 560 deltas represent a loss, too; it’s just not locked in. Here, Mary made the conscious decision not to go home flat. On the one hand, she was accepting the risk of the stock continuing its decline. On the other hand, if she had covered the whole delta, she would have been accepting the risk of the stock moving in either direction. Mary felt the stock would regain some of its losses. She decided to lead the stock a little, going into the weekend with a positive delta bias. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:391 SCORE: 12.00 ================================================================================ Day Seven This was the quiet day of the week, and a welcome respite. On this day, the stock rose just $0.25. The rise in price helped a bit. Mary was still long 560 deltas from Friday. Negative gamma took only a small bite out of her profit. The P&(L) can be broken down into the profit attributable to the starting delta of the trade, the estimated loss from gamma, and the gain from theta. Mary ends these seven days of trading worse off than she started. What went wrong? The bottom line is that she sold volatility on an asset that proved to be volatile. A $4 drop in price of a $42 dollar stock was a big move. This stock certainly moved at more than 25 percent volatility. Day four alone made this trade a losing proposition. Could Mary have done anything better? Yes. In a perfect world, she would not have covered her negative deltas on day 3 by buying 280 shares at $41 and another 280 at $42. Had she not, this wouldn’t have been such a bad week. With the stock ending at $38.25, she lost $1,050 on the 280 shares she bought at $42 ($3.75 times 280) and lost $770 on the 280 shares bought at $41 ($2.75 times 280). Then again, if the stock had continued higher, rising beyond $42, those would have been good buys. Mary can’t beat herself up too much for protecting herself in a way that made sense at the time. The stock’s $2 rally is more to blame than the fact that she hedged her deltas. That’s the risk of selling volatility: the stock may prove to be volatile. If the stock had not made such a move, she wouldn’t have faced the dilemma of whether or not to hedge. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:392 SCORE: 20.00 ================================================================================ Conclusions The same stock during the same week was used in both examples. These two traders started out with equal and opposite positions. They might as well have made the trade with each other. And although in this case the vol buyer (Harry) had a pretty good week and the vol seller (Mary) had a not- so-good week, it’s important to notice that the dollar value of the vol buyer’s profit was not the same as the dollar value of the vol seller’s loss. Why? Because each trader hedged his or her position differently. Option trading is not a zero-sum game. Option-selling delta-neutral strategies work well in low-volatility environments. Small moves are acceptable. It’s the big moves that can blow you out of the water. Like long-gamma traders, short-gamma traders have many techniques for covering deltas when the stock moves. It is common to cover partial deltas, as Mary did on day four of the last example. Conversely, if a stock is expected to continue along its trajectory up or down, traders will sometimes overhedge by buying more deltas (stock) than they are short or selling more than they are long, in anticipation of continued price rises. Daily standard deviation derived from implied volatility is a common measure used by short-gamma players to calculate price points at which to enter hedges. Market feel and other indicators are also used by experienced traders when deciding when and how to hedge. Each trader must find what works best for him or her. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:393 SCORE: 41.00 ================================================================================ Smileys and Frowns The trade examples in this chapter have all involved just two components: calls and stock. We will explore delta-neutral strategies in other chapters that involve more moving parts. Regardless of the specific makeup of the position, the P&(L) of each individual leg is not of concern. It is the profitability of the position as a whole that matters. For example, after a volatile move in a stock occurs, a positive-gamma trader like Harry doesn’t care whether the calls or the stock made the profit on the move. The trader would monitor the net delta that was produced—positive or negative—and cover accordingly. The process is the same for a negative-gamma trader. In either case, it is gamma and delta that need to be monitored closely. Gamma can make or break a trade. P&(L) diagrams are helpful tools that offer a visual representation of the effect of gamma on a position. Many option-trading software applications offer P&(L) graphing applications to study the payoff of a position with the days to expiration as an adjustable variable to study the same trade over time. P&(L) diagrams for these delta-neutral positions before the options’ expiration generally take one of two shapes: a smiley or a frown. The shape of the graph depends on whether the position gamma is positive or negative. Exhibit 13.3 shows a typical positive-gamma trade. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:395 SCORE: 24.00 ================================================================================ EXHIBIT 13.4 The effect of time on P&(L). As time passes, the reduction in profit is reflected by the center point of the graph dipping farther into negative territory. That is the effect of time decay. The long options will have lost value at that future date with the stock still at the same price (all other factors held constant). Still, a move in either direction can lead to a profitable position. Ultimately, at expiration, the payoff takes on a rigid kinked shape. In the delta-neutral long call examples used in this chapter the position becomes net long stock if the calls are in-the-money at expiration or net short stock if they are out-of-the-money and only the short stock remains. Volatility, as well, would move the payoff line vertically. As IV increases, the options become worth more at each stock price, and as IV falls, they are worth less, assuming all other factors are held constant. A delta-neutral short-gamma play would have a P&(L) diagram quite the opposite of the smiley-faced long-gamma graph. Exhibit 13.5 shows what is called the short-gamma frown. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:397 SCORE: 25.00 ================================================================================ A decrease in value of the options from time decay causes an increase in profitability. This profit potential pinnacles at the center (strike) price at expiration. Rising IV will cause a decline in profitability at each stock price point. Declining IV will raise the payout on the Y axis as profitability increases at each price point. Smileys and frowns are a mere graphical representation of the technique discussed in this chapter: buying and selling realized volatility. These P& (L) diagrams are limited, because they show the payout only of stock-price movement. The profitability of direction-indifferent and direction-neutral trading is also influenced by time and implied volatility. These actively traded strategies are best evaluated on a gamma-theta basis. Long-gamma traders strive each day to scalp enough to cover the day’s theta, while short- gamma traders hope to keep the loss due to adverse movement in the underlying lower than the daily profit from theta. The strategies in this chapter are the same ones traded in Chapter 12. The only difference is the philosophy. Ultimately, both types of volatility are being traded using these and other option strategies. Implied and realized volatility go hand in hand. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:398 SCORE: 14.50 ================================================================================ CHAPTER 14 Studying Volatility Charts Implied and realized volatility are both important to option traders. But equally important is to understand how the two interact. This relationship is best studied by means of a volatility chart. Volatility charts are invaluable tools for volatility traders (and all option traders for that matter) in many ways. First, volatility charts show where implied volatility (IV) is now compared with where it’s been in the past. This helps a trader gauge whether IV is relatively high or relatively low. Vol charts do the same for realized volatility. The realized volatility line on the chart answers three questions: Have the past 30 days been more or less volatile for the stock than usual? What is a typical range for the stock’s volatility? How much volatility did the underlying historically experience in the past around specific recurring events? When IV lines and realized volatility lines are plotted on the same chart, the divergences and convergences of the two spell out the whole volatility story for those who know how to read it. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:400 SCORE: 17.50 ================================================================================ 1. Realized Volatility Rises, Implied Volatility Rises The first volatility chart pattern is that in which both IV and realized volatility rise. In general, this kind of volatility chart can line up three ways: implied can rise more than realized volatility; realized can rise more than implied; or they can both rise by about the same amount. The chart below shows implied volatility rising at a faster rate than realized vol. The general theme in this case is that the stock’s price movement has been getting more volatile, and the option prices imply even higher volatility in the future. This specific type of volatility chart pattern is commonly seen in active stocks with a lot of news. Stocks du jour, like some Internet stocks during the tech bubble of the late 1990s, story stocks like Apple (AAPL) around the release of the iPhone in 2007, have rising volatilities, with the IV outpacing the realized volatility. Sometimes individual stocks and even broad market indexes and exchange-traded funds (ETFs) see this pattern, when the market is declining rapidly, like in the summer of 2011. A delta-neutral long-volatility position bought at the beginning of May, according to Exhibit 14.1 , would likely have produced a winner. IV took off, and there were sure to be plenty of opportunities to profit from gamma with realized volatility gaining strength through June and July. EXHIBIT 14.1 Realized volatility rises, implied volatility rises. Source : Chart courtesy of iVolatility.com ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:401 SCORE: 43.00 ================================================================================ Looking at the right side of the chart, in late July, with IV at around 50 percent and realized vol at around 35 percent, and without the benefit of knowing what the future will bring, it’s harder to make a call on how to trade the volatility. The IV signals that the market is pricing a higher future level of stock volatility into the options. If the market is right, gamma will be good to have. But is the price right? If realized volatility does indeed catch up to implied volatility—that is, if the lines converge at 50 or realized volatility rises above IV—a trader will have a good shot at covering theta. If it doesn’t, gamma will be very expensive in terms of theta, meaning it will be hard to cover the daily theta by scalping gamma intraday. The question is: why is IV so much higher than realized? If important news is expected to be released in the near future, it may be perfectly reasonable for the IV to be higher, even significantly higher, than the stock’s realized volatility. One big move in the stock can produce a nice profit, as long as theta doesn’t have time to work its mischief. But if there is no news in the pipeline, there may be some irrational exuberance—in the words of ex-Fed chairman Alan Greenspan—of option buyers rushing to acquire gamma that is overvalued in terms of theta. In fact, a lack of expectation of news could indicate a potential bearish volatility play: sell volatility with the intent of profiting from daily theta and a decline in IV. This type of play, however, is not for the fainthearted. No one can predict the future. But one thing you can be sure of with this ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:402 SCORE: 12.50 ================================================================================ trade: you’re in for a wild ride. The lines on this chart scream volatility. This means that negative-gamma traders had better be good and had better be right! In this situation, hedgers and speculators in the market are buying option volatility of 50 percent, while the stock is moving at 35 percent volatility. Traders putting on a delta-neutral volatility-selling strategy are taking the stance that this stock will not continue increasing in volatility as indicated by option prices; specifically, it will move at less than 50 percent volatility —hopefully a lot less. They are taking the stance that the market’s expectations are wrong. Instead of realized and implied volatility both trending higher, sometimes there is a sharp jump in one or the other. When this happens, it could be an indication of a specific event that has occurred (realized volatility) or news suddenly released of an expected event yet to come (implied volatility). A sharp temporary increase in IV is called a spike, because of its pointy shape on the chart. A one-day surge in realized volatility, on the other hand, is not so much a volatility spike as it is a realized volatility mesa. Realized volatility mesas are shown in Exhibit 14.2 . EXHIBIT 14.2 Volatility mesas. Source : Chart courtesy of iVolatility.com The patterns formed by the gray line in the circled areas of the chart shown below are the result of typical one-day surges in realized volatility. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:404 SCORE: 32.00 ================================================================================ 2. Realized Volatility Rises, Implied Volatility Remains Constant This chart pattern can develop from a few different market conditions. One scenario is a one-time unanticipated move in the underlying that is not expected to affect future volatility. Once the news is priced into the stock, there is no point in hedgers’ buying options for protection or speculators’ buying options for a leveraged bet. What has happened has happened. There are other conditions that can cause this type of pattern to materialize. In Exhibit 14.3 , the IV was trading around 25 for several months, while the realized volatility was lagging. With hindsight, it makes perfect sense that something had to give—either IV needed to fall to meet realized, or realized would rise to meet market expectations. Here, indeed, the latter materialized as realized volatility had a steady rise to and through the 25 level in May. Implied, however remained constant. EXHIBIT 14.3 Realized volatility rises, implied volatility remains constant. Source : Chart courtesy of iVolatility.com Traders who were long volatility going into the May realized-vol rise probably reaped some gamma benefits. But those who got in “too early,” buying in January or February, would have suffered too great of theta losses before gaining any significant profits from gamma. Time decay (theta) can inflict a slow, painful death on an option buyer. By studying this chart in hindsight, it is clear that options were priced too high for a gamma scalper to have a fighting chance of covering the daily theta before the rise in May. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:406 SCORE: 12.50 ================================================================================ 3. Realized Volatility Rises, Implied Volatility Falls This chart pattern can manifest itself in different ways. In this scenario, the stock is becoming more volatile, and options are becoming cheaper. This may seem an unusual occurrence, but as we can see in Exhibit 14.4 , volatility sometimes plays out this way. This chart shows two different examples of realized vol rising while IV falls. EXHIBIT 14.4 Realized volatility rises, implied volatility falls. Source : Chart courtesy of iVolatility.com The first example, toward the left-hand side of the chart, shows realized volatility trending higher while IV is trending lower. Although fundamentals can often provide logical reasons for these volatility changes, sometimes they just can’t. Both implied and realized volatility are ultimately a function of the market. There is a normal oscillation to both of these figures. When there is no reason to be found for a volatility change, it might be an opportunity. The potential inefficiency of volatility pricing in the options market sometimes creates divergences such as this one that vol traders scour the market in search of. In this first example, after at least three months of IV’s trading marginally higher than realized volatility, the two lines converge and then cross. The ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:407 SCORE: 38.50 ================================================================================ point at which these lines meet is an indication that IV may be beginning to get cheap. First, it’s a potentially beneficial opportunity to buy a lower volatility than that at which the stock is actually moving. The gamma/theta ratio would be favorable to gamma scalpers in this case, because the lower cost of options compared with stock fluctuations could lead to gamma profits. Second, with IV at 35 at the first crossover on this chart, IV is dipping down into the lower part of its four-month range. One can make the case that it is getting cheaper from a historical IV standpoint. There is arguably an edge from the perspective of IV to realized volatility and IV to historical IV. This is an example of buying value in the context of volatility. Furthermore, if the actual stock volatility is rising, it’s reasonable to believe that IV may rise, too. In hindsight we see that this did indeed occur in Exhibit 14.4 , despite the fact that realized volatility declined. The example circled on the right-hand side of the chart shows IV declining sharply while realized volatility rises sharply. This is an example of the typical volatility crush as a result of an earnings report. This would probably have been a good trade for long volatility traders—even those buying at the top. A trader buying options delta neutral the day before earnings are announced in this example would likely lose about 10 points of vega but would have a good chance to more than make up for that loss on positive gamma. Realized volatility nearly doubled, from around 28 percent to about 53 percent, in a single day. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:408 SCORE: 13.00 ================================================================================ 4. Realized Volatility Remains Constant, Implied Volatility Rises Exhibit 14.5 shows that the stock is moving at about the same volatility from the beginning of June to the end of July. But during that time, option premiums are rising to higher levels. This is an atypical chart pattern. If this was a period leading up to an anticipated event, like earnings, one would anticipate realized volatility falling as the market entered a wait-and-see mode. But, instead, statistical volatility stays the same. This chart pattern may indicate a potential volatility-selling opportunity. If there is no news or reason for IV to have risen, it may simply be high tide in the normal ebb and flow of volatility. EXHIBIT 14.5 Realized volatility remains constant, implied volatility rises. Source : Chart courtesy of iVolatility.com In this example, the historical volatility oscillates between 20 and 24 for nearly two months (the beginning of June through the end of July) as IV rises from 24 to over 30. The stock price is less volatile than option prices indicate. If there is no news to be dug up on the stock to lead one to believe there is a valid reason for the IV’s trading at such a level, this could be an opportunity to sell IV 5 to 10 points higher than the stock volatility. The ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:410 SCORE: 24.50 ================================================================================ 5. Realized Volatility Remains Constant, Implied Volatility Remains Constant This volatility chart pattern shown in Exhibit 14.6 is typical of a boring, run-of-the-mill stock with nothing happening in the news. But in this case, no news might be good news. EXHIBIT 14.6 Realized volatility remains constant, implied volatility remains constant. Source : Chart courtesy of iVolatility.com Again, the gray is realized volatility and the black line is IV. It’s common for IV to trade slightly above or below realized volatility for extended periods of time in certain assets. In this example, the IV has traded in the high teens from late January to late July. During that same time, realized volatility has been in the low teens. This is a prime environment for option sellers. From a gamma/theta standpoint, the odds favor short-volatility traders. The gamma/theta ratio provides an edge, setting the stage for theta profits to outweigh negative- gamma scalping. Selling calls and buying stock delta neutral would be a trade to look at in this situation. But even more basic strategies, such as time spreads and iron condors, are appropriate to consider. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:412 SCORE: 16.00 ================================================================================ 6. Realized Volatility Remains Constant, Implied Volatility Falls Exhibit 14.7 shows two classic implied-realized convergences. From mid- September to early November, realized volatility stayed between 22 and 25. In mid-October the implied was around 33. Within the span of a few days, the implied vol collapsed to converge with the realized at about 22. EXHIBIT 14.7 Realized volatility remains constant, implied volatility falls. Source : Chart courtesy of iVolatility.com There can be many catalysts for such a drop in IV, but there is truly only one reason: arbitrage. Although it is common for a small difference between implied and realized volatility—1 to 3 points—to exist even for extended periods, bigger disparities, like the 7- to 10-point difference here cannot exist for that long without good reason. If, for example, IV always trades significantly above the realized volatility of a particular underlying, all rational market participants will sell options because they have a gamma/theta edge. This, in turn, forces options prices lower until volatility prices come into line and the arbitrage opportunity no longer exists. In Exhibit 14.7 , from mid-March to mid-May a similar convergence took place but over a longer period of time. These situations are often the result ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:414 SCORE: 16.00 ================================================================================ 7. Realized Volatility Falls, Implied Volatility Rises This setup shown in Exhibit 14.8 should now be etched into the souls of anyone who has been reading up to this point. It is, of course, the picture of the classic IV rush that is often seen in stocks around earnings time. The more uncertain the earnings, the more pronounced this divergence can be. EXHIBIT 14.8 Realized volatility falls, implied volatility rises. Source : Chart courtesy of iVolatility.com Another classic vol divergence in which IV rises and realized vol falls occurs in a drug or biotech company when a Food and Drug Administration (FDA) decision on one of the company’s new drugs is imminent. This is especially true of smaller firms without big portfolios of drugs. These divergences can produce a huge implied–realized disparity of, in some cases, literally hundreds of volatility points leading up to the announcement. Although rising IV accompanied by falling realized volatility can be one of the most predictable patterns in trading, it is ironically one of the most difficult to trade. When the anticipated news breaks, the stock can and often will make a big directional move, and in that case, IV can and likely will get crushed. Vega and gamma work against each other in these situations, as ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:416 SCORE: 10.50 ================================================================================ 8. Realized Volatility Falls, Implied Volatility Remains Constant This volatility shift can be marked by a volatility convergence, divergence, or crossover. Exhibit 14.9 shows the realized volatility falling from around 30 percent to about 23 percent while IV hovers around 25. The crossover here occurs around the middle of February. EXHIBIT 14.9 Realized volatility falls, implied volatility remains constant. Source : Chart courtesy of iVolatility.com The relative size of this volatility change makes the interpretation of the chart difficult. The last half of September saw around a 15 percent decline in realized volatility. The middle of October saw a one-day jump in realized of about 15 points. Historical volatility has had several dynamic moves that were larger and more abrupt than the seven-point decline over this six-week period. This smaller move in realized volatility is not necessarily an indication of a volatility event. It could reflect some complacency in the market. It could indicate a slow period with less trading, or it could simply be a natural contraction in the ebb and flow of volatility causing the calculation of recent stock-price fluctuations to wane. What is important in this interpretation is how the options market is reacting to the change in the volatility of the stock—where the rubber hits ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:417 SCORE: 27.00 ================================================================================ the road. The market’s apparent assessment of future volatility is unchanged during this period. When IV rises or falls, vol traders must look to the underlying stock for a reason. The options market reacts to stock volatility, not the other way around. Finding fundamental or technical reasons for surges in volatility is easier than finding specific reasons for a decline in volatility. When volatility falls, it is usually the result of a lack of news, leading to less price action. In this example, probably nothing happened in the market. Consequently, the stock volatility drifted lower. But it fell below the lowest IV level seen for the six- month period leading up to the crossover. It was probably hard to take a confident stance in volatility immediately following the crossover. It is difficult to justify selling volatility when the implied is so cheap compared with its historic levels. And it can be hard to justify buying volatility when the options are priced above the stock volatility. The two-week period before the realized line moved beneath the implied line deserves closer study. With the IV four or five points lower than the realized volatility in late January, traders may have been tempted to buy volatility. In hindsight, this trade might have been profitable, but there was surely no guarantee of this. Success would have been greatly contingent on how the traders managed their deltas, and how well they adapted as realized volatility fell. During the first half of this period, the stock volatility remained above implied. For an experienced delta-neutral trader, scalping gamma was likely easy money. With the oscillations in stock price, the biggest gamma- scalping risk would have been to cover too soon and miss out on opportunities to take bigger profits. Using the one-day standard deviation based on IV (described in Chapter 3) might have produced early covering for long-gamma traders. Why? Because in late January, the standard deviation derived from IV was lower than the actual standard deviation of the stock being traded. In the latter half of the period being studied, the end of February on this chart, using the one- day standard deviation based on IV would have produced scalping that was too late. This would have led to many missed opportunities. Traders entering hedges at regular nominal intervals—every $0.50, for example—would probably have needed to decrease the interval as volatility ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:419 SCORE: 11.50 ================================================================================ 9. Realized Volatility Falls, Implied Volatility Falls This final volatility-chart permutation incorporates a fall of both realized and IV. The chart in Exhibit 14.10 clearly represents the slow culmination of a highly volatile period. This setup often coincides with news of some scary event’s being resolved—a law suit settled, unpopular upper management leaving, rumors found to be false, a happy ending to political issues domestically or abroad, for example. After a sharp sell-off in IV, from 75 to 55, in late October, marking the end of a period of great uncertainty, the stock volatility began a steady decline, from the low 50s to below 25. IV fell as well, although it remained a bit higher for several months. EXHIBIT 14.10 Realized volatility falls, implied volatility falls. Source : Chart courtesy of iVolatility.com In some situations where an extended period of extreme volatility appears to be coming to an end, there can be some predictability in how IV will react. To be sure, no one knows what the future holds, but when volatility starts to wane because a specific issue that was causing gyrations in the stock price is resolved, it is common, and intuitive, for IV to fall with the stock volatility. This is another type of example of reversion to the mean. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:425 SCORE: 41.00 ================================================================================ The Basic Long Straddle The long straddle is an option strategy to use when a trader is looking for a big move in a stock but is uncertain which direction it will move. Technically, the Commodity Channel Index (CCI), Bollinger bands, or pennants are some examples of indicators which might signal the possibility of a breakout. Or fundamental data might call for a revaluation of the stock based on an impending catalyst. In either case, a long straddle, is a way for traders to position themselves for the expected move, without regard to direction. In this example, we’ll study a hypothetical $70 stock poised for a breakout. We’ll buy the one-month 70 straddle for 4.25. Exhibit 15.1 shows the payout of the straddle at expiration. EXHIBIT 15.1 At-expiration diagram for a long straddle. At expiration, with the stock at $70, neither the call nor the put is in-the- money. The straddle expires worthless, leaving a loss of 4.25 in its wake from erosion. If, however, the stock is above or below $70, either the call or the put will have at least some value. The farther the stock price moves ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:426 SCORE: 68.00 ================================================================================ from the strike price in either direction, the higher the net value of the options. Above $70, the call has value. If the underlying is at $74.25 at expiration, the put will expire worthless, but the call will be worth 4.25—the price initially paid for the straddle. Above this break-even price, the trade is a winner, and the higher, the better. Below $70, the put has value. If the underlying is at $65.75 at expiration, the call expires, and the put is worth 4.25. Below this breakeven, the straddle is a winner, and the lower, the better. Why It Works In this basic example, if the underlying is beyond either of the break-even points at expiration, the trade is a winner. The key to understanding this is the fact that at expiration, the loss on one option is limited—it can only fall to zero—but the profit potential on the other can be unlimited. In practice, most active traders will not hold a straddle until expiration. Even if the trade is not held to term, however, movement is still beneficial —in fact, it is more beneficial, because time decay will not have depleted all the extrinsic value of the options. Movement benefits the long straddle because of positive gamma. But movement is a race against the clock—a race against theta. Theta is the cost of trading the long straddle. Only pay it for as long as necessary. When the stock’s volatility appears poised to ebb, exit the trade. Exhibit 15.2 shows the P&(L) of the straddle both at expiration and at the time the trade was made. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:427 SCORE: 49.00 ================================================================================ EXHIBIT 15.2 Long straddle P&(L) at initiation and expiration. Because this is a short-term at-the-money (ATM) straddle, we will assume for simplicity that it has a delta of zero. 1 When the trade is consummated, movement can only help, as indicated by the dotted line on the exhibit. This is the classic graphic representation of positive gamma— the smiley face. When the stock moves higher, the call gains value at an increasing rate while the put loses value at a decreasing rate. When the stock moves lower, the put gains at an increasing rate while the call loses at a decreasing rate. This is positive gamma. This still may not be an entirely fair representation of how profits are earned. The underlying is not required to move continuously in one direction for traders to reap gamma profits. As described in Chapter 13, traders can scalp gamma by buying and selling stock to offset long or short deltas created by movement in the underlying. When traders scalp gamma, they lock in profits as the stock price oscillates. The potential for gamma scalping is an important motivation for straddle buyers. Gamma scalping a straddle gives traders the chance to profit from a stock that has dynamic price swings. It should be second nature to volatility traders to understand that theta is the trade-off of gamma scalping. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:428 SCORE: 92.50 ================================================================================ The Big V Gamma and theta are not alone in the straddle buyer’s thoughts. Vega is a major consideration for a straddle buyer, as well. In a straddle, there are two long options of the same strike, which means double the vega risk of a single-leg trade at that strike. With no short options in this spread, the implied-volatility exposure is concentrated. For example, if the call has a vega of 0.05, the put’s vega at that same strike will also be about 0.05. This means that buying one straddle gives the trader exposure of around 10 cents per implied volatility (IV) point. If IV rises by one point, the trader makes $10 per one-lot straddle, $20 for two points, and so on. If IV falls one point, the trader loses $10 per straddle, $20 for two points, and so on. Traders who want maximum positive exposure to volatility find it in long straddles. This strategy is a prime example of the marriage of implied and realized volatility. Traders who buy straddles because they are bullish on realized volatility will also have bullish positions in implied volatility—like it or not. With this in mind, traders must take care to buy gamma via a straddle that it is not too expensive in terms of the implied volatility. A winning gamma trade can quickly become a loser because of implied volatility. Likewise, traders buying straddles to speculate on an increase in implied volatility must take the theta risk of the trade very seriously. Time can eat away all a trade’s vega profits and more. Realized and implied exposure go hand in hand. The relationship between gamma and vega depends on, among other things, the time to expiration. Traders have some control over the amount of gamma relative to the amount of vega by choosing which expiration month to trade. The shorter the time until expiration, the higher the gammas and the lower the vegas of ATM options. Gamma traders may be better served by buying short-term contracts that coincide with the period of perceived high stock volatility. If the intent of the straddle is to profit from vega, the choice of the month to trade depends on which month’s volatility is perceived to be too high or too low. If, for example, the front-month IV looks low compared with historical IV, current and historical realized volatility, and the expected future volatility, but the back months’ IVs are higher and more in line with these other metrics, there would be no point in buying the back-month ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:430 SCORE: 33.00 ================================================================================ Trading the Long Straddle Option trading is all about optimizing the statistical chances of success. A long-straddle trade makes the most sense if traders think they can make money on both implied volatility and gamma. Many traders make the mistake of buying a straddle just before earnings are announced because they anticipate a big move in the stock. Of course, stock-price action is only half the story. The option premium can be extraordinarily expensive just before earnings, because the stock move is priced into the options. This is buying after the rush and before the crush. Although some traders are successful specializing in trading earnings, this is a hard way to make money. Ideally, the best time to buy volatility is before the move is priced in— that is, before everyone else does. This is conceptually the same as buying a stock in anticipation of bullish news. Once news comes out, the stock rallies, and it is often too late to participate in profits. The goal is to get in at the beginning of the trend, not the end—the same goal as in trading volatility. As in analyzing a stock, fundamental and technical tools exist for analyzing volatility—namely, news and volatility charts. For fundamentals, buy the rumor, sell the news applies to the rush and crush of implied volatility. Previous chapters discussed fundamental events that affect volatility; be prepared to act fast when volatility-changing situations present themselves. With charts, the elementary concept of buy low, sell high is obvious, yet profound. Review Chapter 14 for guidance on reading volatility charts. With all trading, getting in is easy. It’s managing the position, deciding when to hedge and when to get out that is the tricky part. This is especially true with the long straddle. Straddles are intended to be actively managed. Instead of waiting for a big linear move to evolve over time, traders can take profits intermittently through gamma scalping. Furthermore, they hold the trade only as long as gamma scalping appears to be a promising opportunity. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:431 SCORE: 26.50 ================================================================================ Legging Out There are many ways to exiting a straddle. In the right circumstances, legging out is the preferred method. Instead of buying and selling stock to lock in profits and maintain delta neutrality, traders can reduce their positions by selling off some of the calls or puts that are part of the straddle. In this technique, when the underlying rises, traders sell as many calls as needed to reduce the delta to zero. As the underlying falls, they sell enough puts to reduce their position to zero delta. As the stock oscillates, they whittle away at the position with each hedging transaction. This serves the dual purpose of taking profits and reducing risk. A trader, Susan, has been studying Acme Brokerage Co. (ABC). Susan has noticed that brokerage stocks have been fairly volatile in recent past. Exhibit 15.3 shows an analysis of Acme’s volatility over the past 30 days. EXHIBIT 15.3 Acme Brokerage Co. volatility. Stock Price Realized VolatilityFront-Month Implied Volatility 30-day high $78.6630-day high 47%30-day high 55% 30-day low $66.9430-day low 36%30-day low 34% Current px $74.80Current vol 36%Current vol 36% During this period, Acme stock ranged more than $11 in price. In this example, Acme’s volatility is a function of interest rate concerns and other macroeconomic issues affecting the brokerage industry as a whole. As the stock price begins to level off in the latter half of the 30-day period, realized volatility begins to ebb. The front month’s IV recedes toward recent lows as well. At this point, both realized and implied volatility converge at 36 percent. Although volatility is at its low for the past month, it is still relatively high for a brokerage stock under normal market conditions. Susan does not believe that the volatility plaguing this stock is over. She believes that an upcoming scheduled Federal Reserve Board announcement will lead to more volatility. She perceives this to be a volatility-buying opportunity. Effectively, she wants to buy volatility on the dip. Susan pays 5.75 for 20 July 75-strike straddles. Exhibit 15.4 shows the analytics of this trade with four weeks until expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:432 SCORE: 35.00 ================================================================================ EXHIBIT 15.4 Analytics for long 20 Acme Brokerage Co. 75-strike straddles. As with any trade, the risk is that the trader is wrong. The risk here is indicated by the −2.07 theta and the +3.35 vega. Susan has to scalp an average of at least $207 a day just to break even against the time decay. And if IV continues to ebb down to a lower, more historically normal, level, she needs to scalp even more to make up for vega losses. Effectively, Susan wants both realized and implied volatility to rise. She paid 36 volatility for the straddle. She wants to be able to sell the options at a higher vol than 36. In the interim, she needs to cover her decay just to break even. But in this case, she thinks the stock will be volatile enough to cover decay and then some. If Acme moves at a volatility greater than 36, her chances of scalping profitably are more favorable than if it moves at less than 36 vol. The following is one possible scenario of what might have happened over two weeks after the trade was made. Week One During the first week, the stock’s volatility tapered off a bit more, but implied volatility stayed firm. After some oscillation, the realized volatility ended the week at 34 percent while IV remained at 36 percent. Susan was able to scalp stock reasonably well, although she still didn’t cover her seven days of theta. Her stock buys and sells netted a gain of $1,100. By the end of week one, the straddle was 5.10 bid. If she had sold the straddle at the market, she would have ended up losing $200. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:433 SCORE: 49.50 ================================================================================ Susan decided to hold her position. Toward the end of week two, there would be the Federal Open Market Committee (FOMC) meeting. Week Two The beginning of the week saw IV rise as the event drew near. By the close on Tuesday, implied volatility for the straddle was 40 percent. But realized volatility continued its decline, which meant Susan was not able to scalp to cover the theta of Saturday, Sunday, Monday, and Tuesday. But, the straddle was now 5.20 bid, 0.10 higher than it had been on previous Friday. The rising IV made up for most of the theta loss. At this point, Susan could have sold her straddle to scratch her trade. She would have lost $1,100 on the straddle [(5.20 − 5.75) × 20] but made $1,100 by scalping gamma in the first week. Susan decided to wait and see what the Fed chairman had to say. By week’s end, the trade had proved to be profitable. After the FOMC meeting, the stock shot up more than $4 and just as quickly fell. It continued to bounce around a bit for the rest of the week. Susan was able to lock in $5,200 from stock scalps. After much gyration over this two-week period, the price of Acme stock incidentally returned to around the same price it had been at when Susan bought her straddle: $74.50. As might have been expected after the announcement, implied volatility softened. By Friday, IV had fallen to 30. Realized volatility was sharply higher as a result of the big moves during the week that were factored into the 30-day calculation. With seven more days of decay and a lower implied volatility, the straddle was 3.50 bid at midafternoon on Friday. Susan sold her 20-lot to close the position. Her profit for week two was $2,000. What went into Susan’s decision to close her position? Susan had two objectives: to profit from a rise in implied volatility and to profit from a rise ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:434 SCORE: 19.50 ================================================================================ in realized volatility. The rise in IV did indeed occur, but not immediately. By Tuesday of the second week, vega profits were overshadowed by theta losses. Gamma was the saving grace with this trade. The bulk of the gain occurred in week two when the Fed announcement was made. Once that event passed, the prospects for covering theta looked less attractive. They were further dimmed by the sharp drop in implied volatility from 40 to 30. In this hypothetical scenario, the trade ended up profitable. This is not always the case. Here the profit was chiefly produced by one or two high- volatility days. Had the stock not been unusually volatile during this time, the trade would have been a certain loser. Even though implied volatility had risen four points by Tuesday of the second week, the trade did not yield a profit. The time decay of holding two options can make long straddles a tough strategy to trade. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:435 SCORE: 47.00 ================================================================================ Short Straddle Definition : Selling one call and one put in the same option class, in the same expiration cycle, and with the same strike price. Just as buying a straddle is a pure way to buy volatility, selling a straddle is a way to short it. When a trader’s forecast calls for lower implied and realized volatility, a straddle generates the highest returns of all volatility- selling strategies. Of course, with high reward necessarily comes high risk. A short straddle is one of the riskiest positions to trade. Let’s look at a one-month 70-strike straddle sold at 4.25. The risk is easily represented graphically by means of a P&(L) diagram. Exhibit 15.5 shows the risk and reward of this short straddle. EXHIBIT 15.5 Short straddle P&(L) at initiation and expiration. If the straddle is held until expiration and the underlying is trading below the strike price, the short put is in-the-money (ITM). The lower the stock, the greater the loss on the +1.00 delta from the put. The trade as a whole ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:436 SCORE: 86.00 ================================================================================ will be a loser if the underlying is below the lower of the two break-even points—in this case $65.75. This point is found by subtracting the premium received from the strike. Before expiration, negative gamma adversely affects profits as the underlying falls. The lower the underlying is trading below the strike price, the greater the drain on P&(L) due to the positive delta of the short put. It is the same proposition if the underlying is above $70 at expiration. But in this case, it is the short call that would be in-the-money. The higher the underlying price, the more the −1.00 delta adversely impacts P&(L). If at expiration the underlying is above the higher breakeven, which in this case is $74.25 (the strike plus the premium), the trade is a loser. The higher the underlying, the worse off the trade. Before expiration, negative gamma creates negative deltas as the underlying climbs above the strike, eating away at the potential profit, which is the net premium received. The best-case scenario is that the underlying is right at $70 at the closing bell on expiration Friday. In this situation, neither option is ITM, meaning that the 4.25 premium is all profit. In reaping the maximum profit, both time and price play roles. If the position is closed before expiration, implied volatility enters into the picture as well. It’s important to note that just because neither option is ITM if the underlying is right at $70 at expiration, it doesn’t mean with certainty that neither option will be assigned. Sometimes options that are ATM or even out-of-the-money (OTM) get assigned. This can lead to a pleasant or unpleasant surprise the Monday morning following expiration. The risk of not knowing whether or not you will be assigned—that is, whether or not you have a position in the underlying security—is a risk to be avoided. It is the goal of every trader to remove unnecessary risk from the equation. Buying the call and the put for 0.05 or 0.10 to close the position is a small price to pay when one considers the possibility of waking up Monday morning to find a loss of hundreds of dollars per contract because a position you didn’t even know you owned had moved against you. Most traders avoid this risk, referred to as pin risk, by closing short options before expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:437 SCORE: 20.00 ================================================================================ The Risks with Short Straddles Looking at an at-expiration diagram or even analyzing the gamma/theta relationship of a short straddle may sometimes lead to a false sense of comfort. Sometimes it looks as if short straddles need a pretty big move to lose a lot of money. So why are they definitely among the riskiest strategies to trade? That is a matter of perspective. Option trading is about risk management. Dealing with a proverbial train wreck every once in a while is part of the game. But the big disasters can end one’s trading career in an instant. Because of its potential—albeit sometimes small potential—for a colossal blowup, the short straddle is, indeed, one of the riskiest positions one can trade. That said, it has a place in the arsenal of option strategies for speculative traders. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:438 SCORE: 98.50 ================================================================================ Trading the Short Straddle A short straddle is a trade for highly speculative traders who think a security will trade within a defined range and that implied volatility is too high. While a long straddle needs to be actively traded, a short straddle needs to be actively monitored to guard against negative gamma. As adverse deltas get bigger because of stock price movement, traders have to be on alert, ready to neutralize directional risk by offsetting the delta with stock or by legging out of the options. To be sure, with a short straddle, every stock trade locks in a loss with the intent of stemming future losses. The ideal situation is that the straddle is held until expiration and expires with the underlying right at $70 with no negative-gamma scalping. Short-straddle traders must take a longer-term view of their positions than long-straddle traders. Often with short straddles, it is ultimately time that provides the payout. While long straddle traders would be inclined to watch gamma and theta very closely to see how much movement is required to cover each day’s erosion, short straddlers are more inclined to focus on the at-expiration diagram so as not to lose sight of the end game. There are some situations that are exceptions to this long-term focus. For example, when implied volatility gets to be extremely high for a particular option class relative to both the underlying stock’s volatility and the historical implied volatility, one may want to sell a straddle to profit from a fall in IV. This can lead to leveraged short-term profits if implied volatility does, indeed, decline. Because of the fact that there are two short options involved, these straddles administer a concentrated dose of negative vega. For those willing to bet big on a decline in implied volatility, a short straddle is an eager croupier. These trades are delta neutral and double the vega of a single-leg trade. But they’re double the gamma, too. As with the long straddle, realized and implied volatility levels are both important to watch. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:439 SCORE: 20.00 ================================================================================ Short-Straddle Example For this example, a trader, John, has been watching Federal XYZ Corp. (XYZ) for a year. During the 12 months that John has followed XYZ, its front-month implied volatility has typically traded at around 20 percent, and its realized volatility has fluctuated between 15 and 20 percent. The past 30 days, however, have been a bit more volatile. Exhibit 15.6 shows XYZ’s recent volatility. EXHIBIT 15.6 XYZ volatility. Stock Price Realized VolatilityFront-Month Implied Volatility 30-day high $111.7130-day high 26%30-day high 30% 30-day low $102.0530-day low 21%30-day low 24% Current px $104.75Current vol 22%Current vol 26% The stock volatility has begun to ease, trading now at a 22 volatility compared with the 30-day high of 26, but still not down to the usual 15-to- 20 range. The stock, in this scenario, has traded in a channel. It currently lies in the lower half of its recent range. Although the current front-month implied volatility is in the lower half of its 30-day range, it’s historically high compared with the 20 percent level that John has been used to seeing, and it’s still four points above the realized volatility. John believes that the conditions that led to the recent surge in volatility are no longer present. His forecast is for the stock volatility to continue to ease and for implied volatility to continue its downtrend as well and revert to its long-term mean over the next week or two. John sells 10 September 105 straddles at 5.40. Exhibit 15.7 shows the greeks for this trade. EXHIBIT 15.7 Greeks for short XYZ straddle. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:440 SCORE: 44.50 ================================================================================ The goal here is for implied volatility to fall to around 20. If it does, John makes $1,254 (6 vol points × 2.09 vega). He also thinks theta gains will outpace gamma losses. The following is a two-week examination of one possible outcome for John’s trade. Week One The first week in this example was a profitable one, but it came with challenges. John paid for his winnings with a few sleepless nights. On the Monday following his entry into the trade, the stock rose to $106. While John collected a weekend’s worth of time decay, the $1.25 jump in stock price ate into some of those profits and naturally made him uneasy about the future. At this point, John was sitting on a profit, but his position delta began to grow negative, to around −1.22 [(–1.18 × 1.25) + 0.26]. For a $104.75 stock, a move of $1.25—or just over 1 percent—is not out of the ordinary, but it put John on his guard. He decided to wait and see what happened before hedging. The following day, the rally continued. The stock was at $107.30 by noon. His delta was around −3. In the face of an increasingly negative delta, John weighed his alternatives: He could buy back some of his calls to offset his delta, which would have the added benefit of reducing his gamma as well. He could buy stock to flatten out. Lastly, he could simply do nothing and wait. John felt the stock was overbought and might retrace. He also still believed volatility would fall. He decided to be patient and enter a stop order to buy all of his deltas at $107.50 in case the stock continued trending up. The XYZ shares closed at $107.45 that day. This time inaction proved to be the best action. The stock did retrace. Week one ended with Federal XYZ back down around $105.50. The IV of the straddle was at 23. The straddle finished up week one offered at $4.10. Week Two The future was looking bright at the start of week two until Wednesday. Wednesday morning saw XYZ gap open to $109. When you have a short straddle, a $3.50 gap move in the underlying tends to instantly give you a ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:441 SCORE: 25.00 ================================================================================ sinking feeling in the pit of your stomach. But the damage was truly not that bad. The offer in the straddle was 4.75, so the position was still a winner if John bought it back at this point. Gamma/delta hurt. Theta helped. A characteristic that enters into this trade is volatility’s changing as a result of movement in the stock price. Despite the fact that the stock gapped $3.50 higher, implied volatility fell by 1 percent, to 22. This volatility reaction to the underlying’s rise in price is very common in many equity and index options. John decided to close the trade. Nobody ever went broke taking a profit. The trade in this example was profitable. Of course, this will not always be the case. Sometimes short straddles will be losers—sometimes big ones. Big moves and rising implied volatility can be perilous to short straddles and their writers. If the XYZ stock in the previous example had gapped up to $115—which is not an unreasonable possibility—John’s trade would have been ugly. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:442 SCORE: 30.00 ================================================================================ Synthetic Straddles Straddles are the pet strategy of certain professional traders who specialize in trading volatility. In fact, in the mind of many of these traders, a straddle is all there is. Any single-legged trade can be turned into a straddle synthetically simply by adding stock. Chapter 6 discussed put-call parity and showed that, for all intents and purposes, a put is a call and a call is a put. For the most part, the greeks of the options in the put-call pair are essentially the same. The delta is the only real difference. And, of course, that can be easily corrected. As a matter of perspective, one can make the case that buying two calls is essentially the same as buying a call and a put, once stock enters into the equation. Take a non-dividend-paying stock trading at $40 a share. With 60 days until expiration, a 25 volatility, and a 4 percent interest rate, the greeks of the 40-strike calls and puts of the straddle are as follows: Essentially, the same position can be created by buying one leg of the spread synthetically. For example, in addition to buying one 40 call, another 40 call can be purchased along with shorting 100 shares of stock to create a 40 put synthetically. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:443 SCORE: 46.00 ================================================================================ Combined, the long call and the synthetic long put (long call plus short stock) creates a synthetic straddle. A long synthetic straddle could have similarly been constructed with a long put and a long synthetic call (long put plus long stock). Furthermore, a short synthetic straddle could be created by selling an option with its synthetic pair. Notice the similarities between the greeks of the two positions. The synthetic straddle functions about the same as a conventional straddle. Because the delta and gamma are nearly the same, the up-and-down risk is nearly the same. Time and volatility likewise affect the two trades about the same. The only real difference is that the synthetic straddle might require a bit more cash up front, because it requires buying or shorting the stock. In practice, straddles will typically be traded in accounts with retail portfolio margining or professional margin requirements (which can be similar to retail portfolio margining). So the cost of the long stock or margin for short stock is comparatively small. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:444 SCORE: 58.00 ================================================================================ Long Strangle Definition : Buying one call and one put in the same option class, in the same expiration cycle, but with different strike prices. Typical long strangles involve an OTM call and an OTM put. A strangle in which an ITM call and an ITM put are purchased is called a long guts strangle. A long strangle is similar to a long straddle in many ways. They both require buying a call and a put on the same class in the same expiration month. They are both buying volatility. There are, however, some functional differences. These differences stem from the fact that the options have different strike prices. Because there is distance between the strike prices, from an at-expiration perspective, the underlying must move more for the trade to show a profit. Exhibit 15.8 illustrates the payout of options as part of a long strangle on a $70 stock. The graph is much like that of Exhibit 15.1 , which shows the payout of a long straddle. But the net cost here is only 1.00, compared with 4.25 for the straddle with the same time and volatility inputs. The cost is lower because this trade consists of OTM options instead of ATM options. The breakdown is as follows: ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:445 SCORE: 80.00 ================================================================================ EXHIBIT 15.8 Long strangle at-expiration diagram. The underlying has a bit farther to go by expiration for the trade to have value. If the underlying is above $75 at expiration, the call is ITM and has value. If the underlying is below $65 at expiration, the put is ITM and has value. If the underlying is between the two strike prices at expiration both options expire and the 1.00 premium is lost. An important difference between a straddle and a strangle is that if a strangle is held until expiration, its break-even points are farther apart than those of a comparable straddle. The 70-strike straddle in Exhibit 15.1 had a lower breakeven of $65.75 and an upper break-even of $74.25. The comparable strangle in this example has break-even prices of $64 and $76. But what if the strangle is not held until expiration? Then the trade’s greeks must be analyzed. Intuitively, two OTM options (or ITM ones, for that matter) will have lower gamma, theta, and vega than two comparable ATM options. This has a two-handed implication when comparing straddles and strangles. On the one hand, from a realized volatility perspective, lower gamma means the underlying must move more than it would have to for a straddle to produce the same dollar gain per spread, even intraday. But on the other hand, lower theta means the underlying doesn’t have to move as much to cover decay. A lower nominal profit but a higher percentage profit is generally reaped by strangles as compared with straddles. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:447 SCORE: 64.50 ================================================================================ Long-Strangle Example Let’s return to Susan, who earlier in this chapter bought a straddle on Acme Brokerage Co. (ABC). Acme currently trades at $74.80 a share with current realized volatility at 36 percent. The stock’s volatility range for the past month was between 36 and 47. The implied volatility of the four-week options is 36 percent. The range over the past month for the IV of the front month has been between 34 and 55. As in the long-straddle example earlier in this chapter, there is a great deal of uncertainty in brokerage stocks revolving around interest rates, credit- default problems, and other economic issues. An FOMC meeting is expected in about one week’s time about whose possible actions analysts’ estimates vary greatly, from a cut of 50 basis points to no cut at all. Add a pending earnings release to the docket, and Susan thinks Acme may move quite a bit. In this case, however, instead of buying the 75-strike straddle, Susan pays 2.35 for 20 one-month 70–80 strangles. Exhibit 15.9 compares the greeks of the long ATM straddle with those of the long strangle. EXHIBIT 15.9 Long straddle versus long strangle. The cost of the strangle, at 2.35, is about 40 percent of the cost of the straddle. Of course, with two long options in each trade, both have positive gamma and vega and negative theta, but the exposure to each metric is less with the strangle. Assuming the same stock-price action, a strangle would ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:448 SCORE: 57.50 ================================================================================ enjoy profits from movement and losses from lack of movement that were similar to those of a straddle—just nominally less extreme. For example, if Acme stock rallies $5, from $74.80 to $79.80, the gamma of the 75 straddle will grow the delta favorably, generating a gain of 1.50, or about 25 percent. The 70–80 strangle will make 1.15 from the curvature of the delta–almost a 50 percent gain. With the straddle and especially the strangle, there is one more detail to factor in when considering potential P&L: IV changes due to stock price movement. IV is likely to fall as the stock rallies and rise as the stock declines. The profits of both the long straddle and the long strangle would likely be adversely affected by IV changes as the stock rose toward $79.80. And because the stock would be moving away from the straddle strike and toward one of the strangle strikes, the vegas would tend to become more similar for the two trades. The straddle in this example would have a vega of 2.66, while the strangle’s vega would be 2.67 with the underlying at $79.80 per share. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:449 SCORE: 82.00 ================================================================================ Short Strangle Definition : Selling one call and one put in the same option class, in the same expiration cycle, but with different strike prices. Typically, an OTM call and an OTM put are sold. A strangle in which an ITM call and an ITM put are sold is called a short guts strangle. A short strangle is a volatility-selling strategy, like the short straddle. But with the short strangle, the strikes are farther apart, leaving more room for error. With these types of strategies, movement is the enemy. Wiggle room is the important difference between the short-strangle and short-straddle strategies. Of course, the trade-off for a higher chance of success is lower option premium. Exhibit 15.10 shows the at-expiration diagram of a short strangle sold at 1.00, using the same options as in the diagram for the long strangle. EXHIBIT 15.10 Short strangle at-expiration diagram. Note that if the underlying is between the two strike prices, the maximum gain of 1.00 is harvested. With the stock below $65 at expiration, the short put is ITM, with a +1.00 delta. If the stock price is below the lower breakeven of $64 (the put strike minus the premium), the trade is a loser. The lower the stock, the bigger the loss. If the underlying is above $75, the ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:450 SCORE: 58.00 ================================================================================ short call is ITM, with a −1.00 delta. If the stock is above the upper breakeven of $76 (the call strike plus the premium), the trade is a loser. The higher the stock, the bigger the loss. Intuitively, the signs of the greeks of this strangle should be similar to those of a short straddle—negative gamma and vega, positive theta. That means that increased realized volatility hurts. Rising IV hurts. And time heals all wounds—unless, of course, the wounds caused by gamma are greater than the net premium received. This brings us to an important philosophical perspective that emphasizes the differences between long straddles and strangles and their short counterparts. Losses from rising vega are temporary; the time value of all options will be zero at expiration. But gamma losses can be permanent and profound. These short strategies have limited profit potential and unlimited loss potential. Although short-term profits (or losses) can result from IV changes, the real goal here is to capture theta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:451 SCORE: 39.50 ================================================================================ Short-Strangle Example Let’s revisit John, a Federal XYZ (XYZ) trader. XYZ is at $104.75 in this example, with an implied volatility of 26 percent and a stock volatility of 22. Both implied and realized volatility are higher than has been typical during the past twelve months. John wants to sell volatility. In this example, he believes the stock price will remain in a fairly tight range, causing realized volatility to revert to its normal level, in this case between 15 and 20 percent. He does everything possible to ensure success. This includes scanning the news headlines on XYZ and its financials for a reason not to sell volatility. Playing devil’s advocate with oneself can uncover unforeseen yet valid reasons to avoid making bad trades. John also notes the recent price range, which has been between $111.71 and $102.05 over the past month. Once John commits to an outlook on the stock, he wants to set himself up for maximum gain if he’s right and, for that matter, to maximize his chances of being right. In this case, he decides to sell a strangle to give himself as much margin for error as possible. He sells 10 three-week 100–110 strangles at 1.80. Exhibit 15.11 compares the greeks of this strangle with those of the 105 straddle. EXHIBIT 15.11 Short straddle vs. short strangle. As expected, the strangle’s greeks are comparable to the straddle’s but of less magnitude. If John’s intention were to capture a drop in IV, he’d be ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:452 SCORE: 70.50 ================================================================================ better off selling the bigger vega of the straddle. Here, though, he wants to see the premium at zero at expiration, so the strangle serves his purposes better. What he is most concerned about are the breakevens—in this case, 98.20 and 111.8. The straddle has closer break-even points, of $99.60 and $110.40. Despite the fact that in this case, John is not really trading the greeks or IV per se, they still play an important role in his trade. First, he can use theta to plan the best strangle to trade. In this case, he sells the three-week strangle because it has the highest theta of the available months. The second month strangle has a −0.71 theta, and the third month has a −0.58 theta. With strangles, because the options are OTM, this disparity in theta among the tradable months may not always be the case. But for this trade, if he is still bearish on realized volatility after expiration, John can sell the next month when these options expire. Certainly, he will monitor his risk by watching delta and gamma. These are his best measures of directional exposure. He will consider implied volatility in the decision-making process, too. An implied volatility significantly higher than the realized volatility can be a red flag that the market expects something to happen, but there’s a bigger payoff if there is no significant volatility. An IV significantly lower than the realized can indicate the risk of selling options too cheaply: the premium received is not high enough, based on how much the stock has been moving. Ideally, the IV should be above the realized volatility by between 2 and 20 percent, perhaps more for highly speculative traders. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:457 SCORE: 21.00 ================================================================================ Ratio Spreads The simplest versions of these strategies used by retail traders, institutional traders, proprietary traders, and others are referred to as ratio spreads . In ratio spreads, options are bought and sold in quantities based on a ratio. For example, a 1:3 spread is when one option is bought (or sold) and three are sold (or bought)—a ratio of one to three. This kind of ratio spread would be called a “one-by-three.” However, some option positions can get a lot more complicated. Market makers and other professional traders manage a complex inventory of long and short options. These types of strategies go way beyond simple at- expiration diagrams. This chapter will discuss the two most common types of ratio spreads—backspreads and ratio vertical spreads—and also the delta-neutral position management of market makers and other professional traders. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:458 SCORE: 59.00 ================================================================================ Backspreads Definition : An option strategy consisting of more long options than short options having the same expiration month. Typically, the trader is long calls (or puts) in one series of options and short a fewer number of calls (or puts) in another series with the same expiration month in the same option class. Some traders, such as market makers, refer generically to any delta-neutral long-gamma position as a backspread. Shades of Gray In its simplest form, trading a backspread is trading a one-by-two call or put spread and holding it until expiration in hopes that the underlying stock’s price will make a big move, particularly in the more favorable direction. But holding a backspread to expiration as described has its challenges. Let’s look at a hypothetical example of a backspread held to term and its at- expiration diagram. With the stock at $71 and one month until March expiration: In this example, there is a credit of 3.20 from the sale of the 70 call and a debit of 1.10 for each of the two 75 calls. This yields a total net credit of 1.00 (3.20 − 1.10 − 1.10). Let’s consider how this trade performs if it is held until expiration. If the stock falls below $70 at expiration, all the calls expire and the 1.00 credit is all profit. If the stock is between $70 and $75 at expiration, the 70 call is in-the-money (ITM) and the −1.00 delta starts racking up losses above the breakeven of $71 (the strike plus the credit). At $75 a share this trade suffers its maximum potential loss of $4. If the stock is above $75 at expiration, the 75 calls are ITM. The net delta of +1.00, resulting from the +2.00 deltas of the 75 calls along with the −1.00 delta of the 70 call, makes money as the stock rises. To the upside, the trade is profitable once the stock is at a high enough price for the gain on the two 75 calls to make up ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:459 SCORE: 37.00 ================================================================================ for the loss on the 70 call. In this case, the breakeven is $79 (the $4 maximum potential loss plus the strike price of 75). While it’s good to understand this at-expiration view of this trade, this diagram is a bit misleading. What does the trader of this spread want to have happen? If the trader is bearish, he could find a better way to trade his view than this, which limits his gains to 1.00—he could buy a put. If the trader believes the stock will make a volatile move in either direction, the backspread offers a decidedly limited opportunity to the downside. A straddle or strangle might be a better choice. And if the trader is bullish, he would have to be very bullish for this trade to make sense. The underlying needs to rise above $79 just to break even. If instead he just bought 2 of the 75 calls for 1.10, the maximum risk would be 2.20 instead of 4, the breakeven would be $77.20 instead of $79, and profits at expiration would rack up twice as fast above the breakeven, since the trader is net long two calls instead of one. Why would a trader ever choose to trade a backspread? EXHIBIT 16.1 Backspread at expiration. The backspread is a complex spread that can be fully appreciated only when one has a thorough knowledge of options. Instead of waiting patiently until expiration, an experienced backspreader is more likely to gamma scalp intermittent opportunities. This requires trading a large enough position to make scalping worthwhile. It also requires appropriate margining (either professional-level margin requirements or retail portfolio margining). For ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:460 SCORE: 50.00 ================================================================================ example, this 1:2 contract backspread has a delta of −0.02 and a gamma of +0.05. Fewer than 10 deltas could be scalped if the stock moves up and down by one point. It becomes a more practical trade as the position size increases. Of course, more practical doesn’t necessarily guarantee it will be more profitable. The market must cooperate! Backspread Example Let’s say a 20:40 contract backspread is traded. (Note : In trader lingo this is still called a one-by-two; it is just traded 20 times.) The spread price is still 1.00 credit per contract; in this case, that’s $2,000. But with this type of trade, the spread price is not the best measure of risk or reward, as it is with some other kinds of spreads. Risk and reward are best measured by delta, gamma, theta, and vega. Exhibit 16.2 shows this trade’s greeks. EXHIBIT 16.2 Greeks for 20:40 backspread with the underlying at $71. Backspreads are volatility plays. This spread has a +1.07 vega with the stock at $71. It is, therefore, a bullish implied volatility (IV) play. The IV of the long calls, the 75s, is 30 percent, and that of the 70s is 32 percent. Much as with any other volatility trade, traders would compare current implied volatility with realized volatility and the implied volatility of recent past and consider any catalysts that might affect stock volatility. The objective is to buy an IV that is lower than the expected future stock volatility, based on all available data. The focus of traders of this backspread is not the dollar credit earned. They are more interested in buying a 30 volatility—that’s the focus. But the 75 calls’ IV is not the only volatility figure to consider. The short options, the 70s, have implied volatility of 32 percent. Because of their ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:461 SCORE: 76.50 ================================================================================ lower strike, the IV is naturally higher for the 70 calls. This is vertical skew and is described in Chapter 3. The phenomenon of lower strikes in the same option class and with the same expiration month having higher IV is very common, although it is not always the case. Backspreads usually involve trading vertical skew. In this spread, traders are buying a 30 volatility and selling a 32 volatility. In trading the skew, the traders are capturing two volatility points of what some traders would call edge by buying the lower volatility and selling the higher. Based on the greeks in Exhibit 16.2 , the goal of this trade appears fairly straightforward: to profit from gamma scalping and rising IV. But, sadly, what appears to be straightforward is not. Exhibit 16.3 shows the greeks of this trade at various underlying stock prices. EXHIBIT 16.3 70–75 backspread greeks at various stock prices. Notice how the greeks change with the stock price. As the stock price moves lower through the short strike, the 70 strike calls become the more relevant options, outweighing the influence of the 75s. Gamma and vega become negative, and theta becomes positive. If the stock price falls low enough, this backspread becomes a very different position than it was with the stock price at $71. Instead of profiting from higher implied and realized volatility, the spread needs a lower level of both to profit. This has important implications. First, gamma traders must approach the backspread a little differently than they would most spreads. The backspread traders must keep in mind the dynamic greeks of the position. With a trade like a long straddle, in which there are no short options, traders scalping gamma simply buy to cover short deltas as the stock falls and sell to cover long deltas as the stock rises. The only risks are that the stock may not move enough to cover theta or that the traders may cover deltas too soon to maximize profits. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:462 SCORE: 48.50 ================================================================================ With the backspread, the changing gamma adds one more element of risk. In this example, buying stock to flatten out delta as the stock falls can sometimes be a premature move. Traders who buy stock may end up with more long deltas than they bargained for if the stock falls into negative- gamma territory. Exhibit 16.3 shows that with the stock at $68, the delta for this trade is −2.50. If the traders buy 250 shares at $68, they will be delta neutral. If the stock subsequently falls to $62 a share, instead of being short 1.46 deltas, as the figure indicates, they will be long 1.04 because of the 250 shares they bought. These long deltas start to hurt as the stock continues lower. Backspreaders must therefore anticipate stock movements to avoid overhedging. The traders in this example may decide to lean short if the stock shows signs of weakness. Leaning short means that if the delta is −2.50 at $68 a share, the traders may decide to underhedge by buying just 100 or 200 shares. If the stock continues to fall and negative gamma kicks in, this gives the traders some cushion to the downside. The short delta of the position moves closer to being flat as the stock falls. Because there is a long strike and a short strike in this delta-neutral position, trading ratio spreads is like trading a long and a short volatility position at the same time. Trading backspreads is not an exact science. The stock has just as good a chance of rising as it does of falling, and if it does rise and the traders have underhedged at $68, they will not participate in all the gains they would have if they had fully hedged by buying 250 shares of stock. If trading were easy, everyone would do it! Backspreaders must also be conscious of the volatility of each leg of the spread. There is an inherent advantage in this example to buying the lower volatility of the 75 calls and selling the higher volatility of the 70 calls. But there is also implied risk. Equity prices and IV tend to have an inverse relationship. When stock prices fall—especially if the drop happens quickly —IV will often rise. When stock prices rise, IV often falls. In this backspread example, as the stock price falls to or through the short strike, vega becomes negative in the face of a potentially rising IV. As the stock price rises into positive vega turf, there is the risk of IV’s declining. A dynamic volatility forecast should be part of a backspread-trading plan. One of the volatility questions traders face in this example is whether the two- ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:464 SCORE: 52.00 ================================================================================ Ratio Vertical Spreads Definition : An option strategy consisting of more short options than long options having the same expiration month. Typically, the trader is short calls (or puts) in one series of options and long a fewer number of calls (or puts) in another series in the same expiration month on the same option class. A ratio vertical spread, like a backspread, involves options struck at two different prices—one long strike and one short. That means that it is a volatility strategy that may be long or short gamma or vega depending on where the underlying price is at the time. The ratio vertical spread is effectively the opposite of a backspread. Let’s study a ratio vertical using the same options as those used in the backspread example. With the stock at $71 and one month until March expiration: In this case, we are buying one ITM call and selling two OTM calls. The relationship of the stock price to the strike price is not relevant to whether this spread is considered a ratio vertical spread. Certainly, all these options could be ITM or OTM at the time the trade is initiated. It is also not important whether the trade is done for a debit or a credit. If the stock price, time to expiration, volatility, or number of contracts in the ratio were different, this could just as easily been a credit ratio vertical. Exhibit 16.4 illustrates the payout of this strategy if both legs of the 1:2 contract are still open at expiration. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:465 SCORE: 46.00 ================================================================================ EXHIBIT 16.4 Short ratio spread at expiration. This strategy is a mirror image of the backspread discussed previously in this chapter. With limited risk to the downside, the maximum loss to the trade is the initial debit of 1 if the stock is below $70 at expiration and all the calls expire. There is a maximum profit potential of 4 if the stock is at the short strike at expiration. There is unlimited loss potential, since a short net delta is created on the upside, as one short 75 call is covered by the long 70 call, and one is naked. The breakevens are at $71 and $79. Low Volatility With the stock at $71, gamma and vega are both negative. Just as the backspread was a long volatility play at this underlying price, this ratio vertical is a short-vol play here. As in trading a short straddle, the name of the game is low volatility—meaning both implied and realized. This strategy may require some gamma hedging. But as with other short volatility delta-neutral trades, the fewer the negative scalps, the greater the potential profit. Delta covering should be implemented in situations where it looks as if the stock will trend deep into negative-gamma territory. Murphy’s Law of trading dictates that delta covering will likely be wrong at least as often as it is right. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:466 SCORE: 44.50 ================================================================================ Ratio Vertical Example Let’s examine a trade of 20 contracts by 40 contracts. Exhibit 16.5 shows the greeks for this ratio vertical. EXHIBIT 16.5 Short ratio vertical spread greeks. Before we get down to the nitty-gritty of the mechanics and management of this trade—the how—let’s first look at the motivations for putting the trade on—the why. For the cost of 1.00 per spread, this trader gets a leveraged position if the stock rises moderately. The profits max out with the stock at the short-strike target price—$75—at expiration. Another possible profit engine is IV. Because of negative vega, there is the chance of taking a quick profit if IV falls in the interim. But short-term losses are possible, too. IV can rise, or negative gamma can hurt the trader. Ultimately, having naked calls makes this trade not very bullish. A big move north can really hurt. Basically, this is a delta-neutral-type short-volatility play that wins the most if the stock is at $75 at expiration. One would think about making this trade if the mechanics fit the forecast. If this trader were a more bullish than indicated by the profit and loss diagram, a more-balanced bull call spread would be a better strategy, eliminating the unlimited upside risk. If upside risk were acceptable, this trader could get more aggressive by trading the spread one-by-three. That would result in a credit of 0.05 per spread. There would then be no ultimate risk below $70 but rather a 0.05 gain. With double the naked calls, however, there would be double punishment if the stock rallied strongly beyond the upside breakeven. Ultimately, mastering options is not about mastering specific strategies. It’s about having a thorough enough understanding of the instrument to be ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:467 SCORE: 48.00 ================================================================================ flexible enough to tailor a position around a forecast. It’s about minimizing the unwanted risks and optimizing exposure to the intended risks. Still, there always exists a trade-off in that where there is the potential for profit, there is the possibility of loss—you can always be wrong. Recalling the at-expiration diagram and examining the greeks, the best- case scenario is intuitive: the stock at $75 at expiration. The biggest theta would be right at that strike. But that strike price is also the center of the biggest negative gamma. It is important to guard against upward movement into negative delta territory, as well as movement lower where the position has a slightly positive delta. Exhibit 16.6 shows what happens to the greeks of this trade as the stock price moves. EXHIBIT 16.6 Ratio vertical spread at various prices for the underlying. As the stock begins to rise from $71 a share, negative deltas grow fast in the short term. Careful trend monitoring is necessary to guard against a rally. The key, however, is not in knowing what will happen but in skillfully hedging against the unknown. The talented option trader is a disciplined risk manager, not a clairvoyant. One of the risks that the trader willingly accepted when placing this trade was short gamma. But when the stock moves and deltas are created, decisions have to be made. Did the catalyst(s)—if any—that contributed to the rise in stock price change the outlook for volatility? If not, the decision is simply whether or not to hedge by buying stock. However, if it appears that volatility is on the rise, it is not just a delta decision. A trader may consider buying some of the short options back to reduce volatility exposure. In this example, if the stock rises and it’s feared that volatility may increase, a good choice may be to buy back some of the short 75-strike calls. This has the advantage of reducing delta (buy enough deltas to flatten ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:469 SCORE: 17.00 ================================================================================ How Market Makers Manage Delta-Neutral Positions While market makers are not position traders per se, they are expert position managers. For the most part, market makers make their living by buying the bid and selling the offer. In general, they don’t act; they react. Most of their trades are initiated by taking the other side of what other people want to do and then managing the risk of the positions they accumulate. The business of a market maker is much like that of a casino. A casino takes the other side of people’s bets and, in the long run, has a statistical (theoretical) edge. For market makers, because theoretical value resides in the middle of the bid and the ask, these accommodating trades lead to a theoretical profit—that is, the market maker buys below theoretical value and sells above. Actual profit—cold, hard cash you can take to the bank— is, however, dependent on sound management of the positions that are accumulated. My career as a market maker was on the floor of the Chicago Board Options Exchange (CBOE) from 1998 to 2005. Because, over all, the trades I made had a theoretical edge, I hoped to trade as many contracts as possible on my markets without getting too long or too short in any option series or any of my greeks. As a result of reacting to order flow, market makers can accumulate a large number of open option series for each class they trade, resulting in a single position. For example, Exhibit 16.7 shows a position I had in Ford Motor Co. (F) options as a market maker. EXHIBIT 16.7 Market-maker position in Ford Motor Co. options. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:472 SCORE: 91.00 ================================================================================ options to me at prices I wanted to buy them—my bid—and buying options from me at prices I wanted to sell them—my offer. Upon making an option trade, I needed to hedge directional risk immediately. I usually did so by offsetting my option trades by taking the opposite delta position in the stock —especially on big-delta trades. Through this process of providing liquidity to the market, I built up option-centric risk. To manage this risk I needed to watch my other greeks. To be sure, trying to draw a P&L diagram of this position would be a fruitless endeavor. Exhibit 16.8 shows the risk of this trade in its most distilled form. EXHIBIT 16.8 Analytics for market-maker position in Ford Motor Co. (stock at $15.72). Delta +1,075 Gamma−10,191 Theta +1,708 Vega +7,171 Rho −33,137 The +1,075 delta shows comparatively small directional risk relative to the −10,191 gamma. Much of the daily task of position management would be to carefully guard against movement by delta hedging when necessary to earn the $1,708 per day theta. Much of the negative gamma/positive theta comes from the combined 1,006 short January 15 calls and puts. (Note that because this position is traded delta neutral, the net long or short options at each strike is what matters, not whether the options are calls or puts. Remember that in delta- neutral trading, a put is a call, and a call is a put.) The positive vega stems from the fact that the position is long 1,927 January 2003 20-strike options. Although this position has a lot going on, it can be broken down many ways. Having long LEAPS options and short front-month options gives this position the feel of a time spread. One way to think of where most of the gamma risk is coming from is to bear in mind that the 15 strike is synthetically short 503 straddles (1,006 options ÷ two). But this position overall is not like a straddle. There are more strikes involved—a lot more. There is more short gamma to the downside if the price of Ford falls toward $12.50. To the upside, the 17.50 strike is long a combined total of 439 options. Looking at just the 15 and 17.50 strikes, we can see something that ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:475 SCORE: 56.00 ================================================================================ Trading Flat Most market makers like to trade flat—that is, profit from the bid-ask spread and strive to lower exposure to direction, time, volatility, and interest as much as possible. But market makers are at the mercy of customer orders, or paper, as it’s known in the industry. If someone sells, say, the March 75 calls to a market maker at the bid, the best-case scenario is that moments later someone else buys the same number of the same calls—the March 75s, in this case—from that same market maker at the offer. This is locking in a profit. Unfortunately, this scenario seldom plays out this way. In my seven years as a market maker, I can count on one hand the number of times the option gods smiled upon me in such a way as to allow me to immediately scalp an option. Sometimes, the same option will not trade again for a week or longer. Very low-volume options trade “by appointment only.” A market maker trading illiquid options may hold the position until it expires, having no chance to get out at a reasonable price, often taking a loss on the trade. More typically, if a market maker buys an option, he must sell a different option to lessen the overall position risk. The skills these traders master are to lower bids and offers on options when they are long gamma and/or vega and to raise bids and offers on options when they are short gamma and/or vega. This raising and lowering of markets is done to manage risk. Effectively, this is your standard high school economics supply-and- demand curves in living color. When the market demands (buys) all the options that are supplied (offered) at a certain price, the price rises. When the market supplies (sells) all the options demanded (bid) at a price level, the price falls. The catalyst of supply and demand is the market maker and his risk tolerance. But instead of the supply and demand for individual options, it is supply and demand for gamma, theta, and vega. This is trading option greeks. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:476 SCORE: 44.00 ================================================================================ Hedging the Risk Delta is the easiest risk for floor traders to eliminate quickly. It becomes second nature for veteran floor traders to immediately hedge nearly every trade with the underlying. Remember, these liquidity providers are in the business of buying option bids and selling option offers, not speculating on direction. The next hurdle is to trade out of the option-centric risk. This means that if the market maker is long gamma, he needs to sell options; if he’s short gamma, he needs to buy some. Same with theta and vega. Market makers move their bids and offers to avoid being saddled with too much gamma, theta, and vega risk. Experienced floor traders are good at managing option risk by not biting off more than they can chew. They strive to never buy or sell more options than they can spread off by selling or buying other options. This breed of trader specializes in trading the spread and managing risk, not in predicting the future. They’re market makers, not market takers. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:477 SCORE: 52.50 ================================================================================ Trading Skew There are some trading strategies for which market makers have a natural propensity that stems from their daily activity of maintaining their positions. While money managers who manage equity funds get to know the fundamentals of the stocks they trade very well, options market makers know the volatility of the option classes they trade. When they adjust their markets in reacting to order flow, it’s, mechanically, implied volatility that they are raising or lowering to change theoretical values. They watch this figure very carefully and trade its subtle changes. A characteristic of options that many market makers and some other active professional traders observe and trade is the volatility skew. Savvy traders watch the implied volatility of the strikes above the at-the-money (ATM)—referred to as calls , for simplicity—compared with the strikes below the ATM, referred to as puts . In most stocks, there typically exists a “normal” volatility skew inherent to options on that stock. When this skew gets out of line, there may be an opportunity. Say for a particular option class, the call that is 10 percent OTM typically trades about four volatility points lower than the put that is 10 percent OTM. For example, for a $50 stock, the 55 calls are trading at a 21 IV and the 45 puts are trading at a 25 volatility. If the 45 puts become bid higher, say, nine points above where the calls are offered—for instance, the puts are bid at 32 volatility bid while the calls are offered at 23 vol—a trader can speculate on the skew reverting back to its normal relationship by selling the puts, buying the calls, and hedging the delta by selling the right amount of stock. This position—long a call, short a put with a different strike, and short stock on a delta-neutral ratio—is called a risk reversal. The motive for risk reversals is to capture vega as the skew realigns itself. But there are many risk factors that require careful attention. First, as in other positions consisting of both long and short strikes, the gamma, theta, and vega of the position will vary from positive to negative depending on the price of the underlying. Risk-reversal traders must be ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:479 SCORE: 62.50 ================================================================================ When Delta Neutral Isn’t Direction Indifferent Many dynamic-volatility option positions, such as the risk reversal, have vega risk from potential IV changes resulting from the stock’s moving. This is indirectly a directional risk. While having a delta-neutral position hedges against the rather straightforward directional risk of the position delta, this hidden risk of stock movement is left unhedged. In some circumstances, a delta-lean can help abate some of the vega risk of stock-price movement. Say an option position has fairly flat greeks at the current stock price. Say that given the way this particular position is set up, if the stock rises, the position is still fairly flat, but if the stock falls, short lower-strike options will lead to negative gamma and vega. One way to partially hedge this position is to lean short deltas—that is, instead of maintaining a totally flat delta, have a slightly short delta. That way, if the stock falls, the trade profits some on the short stock to partially offset some of the anticipated vega losses. The trade-off of this hedge is that if the stock rises, the trade loses on the short delta. Delta leans are more of an art than a science and should be used as a hedge only by experienced vol traders. They should be one part of a well- orchestrated plan to trade the delta, gamma, theta, and vega of a position. And, to be sure, a delta lean should be entered into a model for simulation purposes before executing the trade to study the up-and-down risk of the position. If the lean reduces the overall risk of the position, it should be implemented. But if it creates a situation where there is an anticipated loss if the stock moves in either direction and there is little hope of profiting from the other greeks, the lean is not the answer—closing the position is. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:480 SCORE: 48.00 ================================================================================ Managing Multiple-Class Risk Most traders hold option positions in more than one option class. As an aside, I recommend doing so, capital and experience permitting. In my experience, having positions in multiple classes psychologically allows for a certain level of detachment from each individual position. Most traders can make better decisions if they don’t have all their eggs in one basket. But holding a portfolio of option positions requires one more layer of risk management. The trader is concerned about the delta, gamma, theta, vega, and rho not only of each individual option class but also of the portfolio as a whole. The trader’s portfolio is actually one big position with a lot of moving parts. To keep it running like a well-oiled machine requires monitoring and maintaining each part to make sure they are working together. To have the individual trades work in harmony with one another, it is important to keep a well-balanced series of strategies. Option trading requires diversification, just like conventional linear stock trading or investing. Diversification of the option portfolio is easily measured by studying the portfolio greeks. By looking at the net greeks of the portfolio, the trader can get some idea of exposure to overall risk in terms of delta, gamma, theta, vega, and rho. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:481 SCORE: 20.00 ================================================================================ CHAPTER 17 Putting the Greeks into Action This book was intended to arm the reader with the knowledge of the greeks needed to make better trading decisions. As the preface stated, this book is not so much a how-to guide as a how-come tutorial. It is step one in a three- step learning process: Step One: Study . First, aspiring option traders must learn as much as possible from books such as this one and from other sources, such as articles, both in print and online, and from classes both in person and online. After completing this book, the reader should have a solid base of knowledge of the greeks. Step Two: Paper Trade . A truly deep understanding requires practice, practice, and more practice! Fortunately, much of this practice can be done without having real money on the line. Paper trading—or simulated trading—in which one trades real markets but with fake money is step two in the learning process. I highly recommend paper trading to kick the tires on various types of strategies and to see how they might work differently in reality than you thought they would in theory. Step Three: Showtime ! Even the most comprehensive academic study or windfall success with paper profits doesn’t give one a true feel for how options work in the real world. There are some lessons that must be learned from the black and the blue. When there’s real money on the line, you will trade differently—at least in the beginning. It’s human nature to be cautious with wealth. This is not a bad thing. But emotions should not override sound judgment. Start small—one or two lots per trade—until you can make rational decisions based on what you have learned, keeping emotions in check. This simple three-step process can take years of diligent work to get it right. But relax. Getting rich quick is truly a poor motivation for trading options. Option trading is a beautiful thing! It’s about winning. It’s about ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:485 SCORE: 57.00 ================================================================================ Example 1 Imagine a trader, Arlo, is studying the following chart of Agilent Technologies Inc. (A). See Exhibit 17.1 . EXHIBIT 17.1 Agilent Technologies Inc. daily candles. Source : Chart courtesy of Livevol® Pro ( www.livevol.com ) The stock has been in an uptrend for six weeks or so. Close-to-close volatility hasn’t increased much. But intraday volatility has increased greatly as indicated by the larger candles over the past 10 or so trading sessions. Earnings is coming up in a week in this example, however implied volatility has not risen much. It is still “cheap” relative to historical volatility and past implied volatility. Arlo is bullish. But how does he play it? He needs to use what he knows about the greeks to guide his decision. Arlo doesn’t want to hold the trade through earnings, so it will be a short- term trade. Thus, theta is not much of a concern. The low-priced volatility guides his strategy selection in terms of vega. Arlo certainly wouldn’t want a short-vega trade. Not with the prospect of implied volatility potential rising going into earnings. In fact, he’d actually want a big positive vega position. That rules out a naked/cash-secured put, put credit spread and the likes. He can probably rule out vertical spreads all together. He doesn’t need to spread off theta. He doesn’t want to spread off vega. Positive gamma is attractive for this sort of trade. He wouldn’t want to spread that off either. Plus, the inherent time component of spreads won’t work well here. As discussed in Chapter 9, the bulk of vertical spreads profits (or losses) take time to come to fruition. The deltas of a call spread are smaller than an outright call. Profits would come from both delta and theta, if the stock rises to the short strike and positive theta kicks in. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:487 SCORE: 54.00 ================================================================================ Example 2 A trader, Luke, is studying the following chart for United States Steel Corp. (X). See Exhibit 17.2 . EXHIBIT 17.2 United States Steel Corp. daily candles. Source : Chart courtesy of Livevol® Pro ( www.livevol.com ) This stock is in a steady uptrend, which Luke thinks will continue. Earnings are out and there are no other expected volatility events on the horizon. Luke thinks that over the next few weeks, United States Steel can go from its current price of around $31 a share to about $34. Volatility is midpriced in this example—not cheap, not expensive. This scenario is different than the previous one. Luke plans to potentially hold this trade for a few weeks. So, for Luke, theta is an important concern. He cares somewhat about volatility, too. He doesn’t necessarily want to be long it in case it falls; he doesn’t want to be short it in case it rises. He’d like to spread it off; the lower the vega, the better (positive or negative). Luke really just wants delta play that he can hold for a few weeks without all the other greeks getting in the way. For this trade, Luke would likely want to trade a debit call spread with the long call somewhat ITM and the short call at the $34 strike. This way, Luke can start off with nearly no theta or vega. He’ll retain some delta, which will enable the spread to profit if United States Steel rises and as it approaches the 34 strike, positive theta will kick in. This spread is superior to a pure long call because of its optimized greeks. It’s superior to an OTM bull put spread in its vega position and will likely produce a higher profit with the strikes structured as such too, as it would have a bigger delta. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:489 SCORE: 40.00 ================================================================================ Managing Trades Once the trade is on, the greeks come in handy for trade management. The most important rule of trading is Know Thy Risk . Knowing your risk means knowing the influences that expose your position to profit or peril in both absolute and incremental terms. At-expiration diagrams reveal, in no uncertain terms, what the bottom-line risk points are when the option expires. These tools are especially helpful with simple short-option strategies and some long-option strategies. Then traders need the greeks. After all, that’s what greeks are: measurements of option risk. The greeks give insight into a trade’s exposure to the other pricing factors. Traders must know the greeks of every trade they make. And they must always know the net-portfolio greeks at all times. These pricing factors ultimately determine the success or failure of each trade, each portfolio, and eventually each trader. Furthermore, always—and I do mean always—traders must know their up and down risk, that is, the directional risk of the market moving up or down certain benchmark intervals. By definition, moves of three standard deviations or more are very infrequent. But they happen. In this business anything can happen. Take the “flash crash of 2010 in which the Dow Jones Industrial Average plunged more than 1,000 points in “a flash.” In my trading career, I’ve seen some surprises. Traders have to plan for the worst. It’s not too hard to tell your significant other, “Sorry I’m late, but I hit unexpected traffic. I just couldn’t plan for it.” But to say, “Sorry, I lost our life savings, and the kids’ college fund, and our house because the market made an unexpected move. I couldn’t plan for it,” won’t go over so well. The fact is, you can plan for it. And as an option trader, you have to. The bottom line is, expect the unexpected because the unexpected will sometimes happen. Traders must use the greeks and up and down risk, instead of relying on other common indicators, such as the HAPI. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:490 SCORE: 14.00 ================================================================================ The HAPI: The Hope and Pray Index So you bought a call spread. At the opening bell the next morning, you find that the market for the underlying has moved lower—a lot lower. You have a loss on your hands. What do you do? Keep a positive attitude? Wear your lucky shirt? Pray to the options gods? When traders finds themselves hoping and praying—I swear I’ll never do that again if I can just get out of this position!—it is probably time for them to take their losses and move on to the next trade. The Hope and Pray Index is a contraindicator. Typically, the higher it is, the worse the trade. There are two numbers a trader can control: the entry price and the exit price. All of the other flashing green and red numbers on the screen are out of the trader’s control. Savvy traders observe what the market does and make decisions on whether and when to enter a position and when to exit. Traders who think about their positions in terms of probability make better decisions at both of these critical moments. In entering a trade, traders must consider their forecast, their assessment of the statistical likelihood of success, the potential payout and loss, and their own tolerance for risk. Having considered these criteria helps the traders stay the course and avoid knee-jerk reactions when the market moves in the wrong direction. Trading is easy when positions make money. It is how traders deal with adverse positions that separates good traders from bad. Good traders are good at losing money. They take losses quickly and let profits run. Accepting, before entering the trade, the statistical nature of trading can help traders trade their positions with less emotion. It then becomes a matter of competent management of those positions based on their knowledge of the factors affecting option values: the greeks. Learning to think in terms of probability is among the most difficult challenges for a new options trader. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:492 SCORE: 70.00 ================================================================================ Adjusting Sometimes the position a trader starts off with is not the position he or she should have at present. Sometimes positions need to be changed, or adjusted, to reflect current market conditions. Adjusting is very important to option traders. To be good at adjusting, traders need to use the greeks. Imagine a trader makes the following trade in Halliburton Company (HAL) when the stock is trading $36.85. Sell 10 February 35–36–38–39 iron condors at 0.45 February has 10 days until expiration in this example. The greeks for this trade are as follows: Delta: −6.80 Gamma: −119.20 Theta: +21.90 Vega: −12.82 The trader has a neutral outlook, which can be inferred by the near-flat delta. But what if the underlying stock begins to rise? Gamma starts kicking in. The trader can end up with a short-biased delta that loses exponentially if the stock continues to climb. If Halliburton rises (or falls for that matter) the trader needs to recalibrate his outlook. Surely, if the trader becomes bullish based on recent market activity, he’d want to close the trade. If the trader is bearish, he’d probably let the negative delta go in hopes of making back what was lost from negative gamma. But what if the trader is still neutral? A neutral trader needs a position that has greeks which reflect that outlook. The trader would want to get delta back towards zero. Further, depending on how much the stock rises, theta could start to lose its benefit. If Halliburton approaches one of the long strikes, theta could move toward zero, negating the benefit of this sort of trade all together. If after the stock rises, the trader is still neutral at the new underlying price level, he’d likely adjust to get delta and theta back to desired territory. A common adjustment in this scenario is to roll the call-credit-spread legs of the iron condor up to higher strikes. The trader would buy ten 38 calls ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:493 SCORE: 57.00 ================================================================================ and sell ten 39 calls to close the credit spread. Then the trader would buy 10 of the 39 calls as sell 10 of the 40 calls to establish an adjusted position that is short a 10 lot of the February 35–36–39–40 iron condor. This, of course, is just one possible adjustment a trader can make. But the common theme among all adjustments is that the trader’s greeks must reflect the trader’s outlook. The position greeks best describe what the position is—that is, how it profits or loses. When the market changes it affects the dynamic greeks of a position. If the market changes enough to make a trader’s position greeks no longer represent his outlook, the trader must adjust the position (adjust the greeks) to put it back in line with expectations. In option trading there are an infinite number of uses for the greeks. From finding trades, to planning execution, to managing and adjusting them, to planning exits; the greeks are truly a trader’s best resource. They help traders see potential and actual position risk. They help traders project potential and actual trade profitability too. Without the greeks, a trader is at a disadvantage in every aspect of option trading. Use the greeks on each and every trade, and exploit trades to their greatest potential. I wish you good luck ! For me, trading option greeks has been a labor of love through the good trades and the bad. To succeed in the long run at greeks trading—or any endeavor, for that matter—requires enjoying the process. Trading option greeks can be both challenging and rewarding. And remember, although option trading is highly statistical and intellectual in nature, a little luck never hurt! That said, good luck trading! ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:494 SCORE: 26.00 ================================================================================ About the Author Dan Passarelli is an author, trader, and former member of the Chicago Board Options Exchange (CBOE) and CME Group. Dan has written two books on options trading—Trading Option Greeks and The Market Taker’s Edge . He is also the founder and CEO of Market Taker Mentoring, a leading options education firm that provides personalized, one-on-one mentoring for option traders and online classes. The company web site is www.markettaker.com . Dan began his trading career on the floor of the CBOE as an equity options market maker. He also traded agricultural options and futures on the floor of the Chicago Board of Trade (now part of CME Group). In 2005, Dan joined CBOE’s Options Institute and began teaching both basic and advanced trading concepts to retail traders, brokers, institutional traders, financial planners and advisers, money managers, and market makers. In addition to his work with the CBOE, he has taught options strategies at the Options Industry Council (OIC), the International Securities Exchange (ISE), CME Group, the Philadelphia Stock Exchange, and many leading options-based brokerage firms. Dan has been seen on FOX Business News and other business television programs. Dan also contributes to financial publications such as TheStreet.com , SFO.com , and the CBOE blog. ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:497 SCORE: 51.00 ================================================================================ long OTM selling Cash settlement Chicago Board Options Exchange (CBOE) Volatility Index® Condors iron long short long short strikes safe landing selectiveness too close too far with high probability of success Contractual rights and obligations open interest and volume opening and closing Options Clearing Corporation (OCC) standardized contracts exercise style expiration month option series, option class, and contract size option type premium quantity strike price Credit call spread Debit call spread Delta dynamic inputs effect of stock price on effect of time on effect of volatility on moneyness and Delta-neutral trading art and science direction neutral vs. direction indifferent gamma, theta, and volatility gamma scalping implied volatility, trading selling portfolio margining realized volatility, trading reasons for smileys and frowns Diagonal spreads double Dividends basics and early exercise dividend plays strange deltas and option pricing pricing model, inputting data into dates, good and bad dividend size ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:498 SCORE: 62.00 ================================================================================ Estimation, imprecision of European-exercise options Exchange-traded fund (ETF) options Exercise style Expected volatility CBOE Volatility Index® implied stock Expiration month Ford Motor Company Fundamental analysis Gamma dynamic scalping Greeks adjusting defined delta dynamic inputs effect of stock price on effect of time on effect of volatility on moneyness and gamma dynamic HAPI: Hope and Pray Index managing trades online, caveats with regard to price vs. value rho counterintuitive results effect of time on put-call parity strategies, choosing between theta effect of moneyness and stock price on effects of volatility and time on positive or negative taking the day out trading vega effect of implied volatility on effect of moneyness on effect of time on implied volatility (IV) and where to find Greenspan, Alan HOLDR options Implied volatility (IV) trading selling and vega In-the-money (ITM) Index options Interest, open Interest rate moves, pricing in Intrinsic value Jelly rolls Long-Term Equity AnticiPation Securities® (LEAPS®) Open interest Option, definition of Option class ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:499 SCORE: 39.00 ================================================================================ Option prices, measuring incremental changes in factors affecting Option series Options Clearing Corporation (OCC) Out-of-the-money (OTM) Parity, definition of Pin risk borrowing and lending money boxes jelly rolls Premium Price discovery Price vs. value Pricing model, inputting data into dates, good and bad dividend size “The Pricing of Options and Corporate Liabilities” (Black & Scholes) Put-call parity American exercise options essentials dividends synthetic calls and puts, comparing synthetic stock strategies theoretical value and interest rate Puts buying cash-secured long ATM married selling Ratio spreads and complex spreads delta-neutral positions, management by market makers through longs to shorts risk, hedging trading flat multiple-class risk ratio spreads backspreads vertical skew, trading Realized volatility trading Reversion to the mean Rho counterintuitive results effect of time on and interest rates in planning trades interest rate moves, pricing in LEAPS put-call parity and time trading Risk and opportunity, option-specific finding the right risk long ATM call delta gamma rho theta ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:500 SCORE: 31.00 ================================================================================ tweaking greeks vega long ATM put long ITM call long OTM call options and the fair game volatility buying and selling direction neutral, direction biased, and direction indifferent Scholes, Myron Sell-to-open transaction Skew term structure trading vertical Spreads calendar buying “free” call, rolling and earning income-generating, managing strength of trading volatility term structure diagonal double ratio and complex delta-neutral positions, management by market makers multiple-class risk ratio skew, trading vertical bear call bear put box, building bull call bull put credit and debit, interrelations of credit and debit, similarities in and volatility wing butterflies condors greeks and keys to success retail trader vs. pro trades, constructing to maximize profit Standard deviation and historical volatility Standard & Poor’s Depositary Receipts (SPDRs or Spiders) Straddles long ================================================================================ SOURCE: eBooks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).pdf#page:502 SCORE: 48.50 ================================================================================ and volatility Volatility buying and selling teenie buyers teenie sellers calculating data direction neutral, direction biased, and direction indifferent expected CBOE Volatility Index® implied stock historical (HV) standard deviation implied (IV) and direction HV-IV divergence inertia relationship of HV and IV selling supply and demand realized trading skew term structure vertical vertical spreads and Volatility charts, studying patterns implied and realized volatility rise realized volatility falls, implied volatility falls realized volatility falls, implied volatility remains constant realized volatility falls, implied volatility rises realized volatility remains constant, implied volatility falls realized volatility remains constant, implied volatility remains constant realized volatility remains constant, implied volatility rises realized volatility rises, implied volatility falls realized volatility rises, implied volatility remains constant Volatility-selling strategies profit potential covered call covered put gamma-theta relationship greeks and income generation naked call short naked puts similarities Would I Do It Now? Rule