be between $68 and $132 in one year’stime—that’s $100 ± ($100 × 0.32). The estimation for the market’sexpectation for the volatility of the stock for one day in terms of standard deviation as apercentage of the price of the underlying is computed as follows:
In one day’stime, based on an IV of 32 percent, there is a 68 percent chance of the stock’sbeing within 2 percent of the stock price—that’sbetween $98 and $102.
There may be times when it is helpful for traders to have avolatility estimation for aperiod of time longer than one day—aweek or amonth, 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 aone-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’sclosing between $90.62 and $109.38 based on an IV of 32 percent.
Expected Implied Volatility
Although there is agreat 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’sprice 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, atrader must forecast IV.
Conceptually, trading IV is much like trading anything else. Atrader who thinks astock is going to rise will buy the stock. Atrader 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 away that it better illustrates market activity. TA studies are usually represented graphically on achart.
Developing TA tools for IV is more of achallenge than it is for stocks. One reason is that there is simply alot 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 aclear 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 atrader to work with. It’sincomplete. For example, if acall 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 avolatility chart in conjunction with aconventional 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 avery small percentage of the stock’sprice. Because options are highly leveraged instruments, their bid-ask width can equal amuch higher percentage of the price.
If atrader uses the last trade to graph an option’sprice, it could look as if avery large percentage move has occurred when in fact it has not. For example, if the option trades asmall 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, t


lable. 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 acase-by-case basis. But there are afew observations to be made that can help atrader make better-educated decisions about IV.
Reversion to the Mean
The IVs of the options on many stocks and indexes tend to trade in arange 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 aperiod long enough to confirm that it is atypical IV for the security, not just atemporary 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 abreakout 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 away 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, anew mean volatility level may be established.
When considering the likelihood of whether IV will revert to recent levels after it has deviated or find anew 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 alater 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, anew, 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 astock. 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’srising before the last 15 earnings reports doesn’tmean it will this time.
CBOE Volatility Index
®
Often traders look to the implied volatility of the market as awhole 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 abroad-based index covering many stocks on many diverse industries. Usually, they are referring to the S&P 500. Just as the IV of astock may offer insight about investors’ feelings about that stock’sfuture volatility, the volatility of options on the S&P 500—SPX options—may tell something about the expected volatility of the market as awhole.
VIX is an index published by the Chicago Board Options Exchange that measures the IV of ahypothetical 30-day option on the SPX. A 30-day option on the SPX only truly exists once amonth—30 days before expiration. CBOE computes ahypothetical 30-day option by means of aweighted 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 aperception of higher risk in the market as awhole, there can consequently be aperception 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’safraid 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.
Exhi

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Direction
Who’safraid 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 aturnaround 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 astock 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 avalue that is easily calculated from publicly accessible past closing prices of astock. It’srather 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 acalculation with little subjectivity—the numbers add up how they add up. IV, however, can be abit 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, atrader will calculate IV for the bid, the ask, the last trade price, or, sometimes, another value altogether. There may be avalid reason for any of these different methods for calculating IV. For example, if atrader 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 avolatility 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 acurrent IV, and rarely are there any answers to support the number. Traders should trust only IV data they knowingly generated themselves using apricing 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’sestimate 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 acompany involved in amajor product-liability lawsuit is expecting averdict 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 abig 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 alower volatility than the back months, or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have ahigher IV than the back months.
Exhibi


mon for the month with the least amount of time until expiration, also known as the front month, to trade at alower volatility than the back months, or months with more time until expiration. Conversely, when volatility is rising, the front month tends to have ahigher 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 aperiod 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 ahigher IV than the previous month. Agraduated 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’svalue, 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 ageneral 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, aput can be synthetically created from acall, and acall can be synthetically created from aput 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 atypical 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’svolatility 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 agreater 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 astraight 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 atypical 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.


CHAPTER 4
Option-Specific Risk and Opportunity
New endeavors can be intimidating. The first day at anew job or new school is achallenge. 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 acall as asubstitute for buying astock is alogical progression. And for the most part, call buying is apretty straightforward way to take abullish position in astock. But it’snot
just
abullish position. The greeks come into play with the long call, providing both risk and opportunity.
Long ATM Call
Kim is atrader 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 aloss if the stock price declines. These expectations are related to the position’sdelta, 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’simmediate directional exposure is quantified by the delta, which is 0.57. Delta is immediate directional exposure because it’ssubject 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’sshare price remains unchanged. She also has positive vega exposure. Aone-percentage-point increase in implied volatility (IV) earns Kim just under $0.05. Aone-point decrease costs her about $0.05. With so few days until expiration, the 35-strike call has very little rho exposure. Afull one-percentage-point change in the interest rate changes her call’svalue by only $0.023.
Delta
Some of Kim’srisks 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 afaster rate as the stock rises and loses value at aslower 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 averitable 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

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he 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 averitable 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 aloss 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 abig 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’sconcerns if the stock makes abig move.
Vega
After delta and theta, vega is the next most influential contributor to Kim’sprofit 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’svalue 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’svega 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’seasy to see that as the time value of the option declines, so does Kim’sexposure 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 aconcern. 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—acommon occurrence—the adverse effect of vega will be minimal. Even if IV declines by 5 points, to ahistorically low IV for DIS, the call loses less than $0.10. That’sless than 5 percent of the new value of the option.
If dividend policy changes or the interest rate changes, the value of Kim’scall will be affected as well. Dividends are often fairly predictable. However, alarge unexpected dividend payment can have asignificant adverse impact on the value of the call. For example, if asurprise $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 ascenario that an experienced trader like Kim will realize is apossibility, although not aprobability. 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 abelief could be rumors or the company’shistorically 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 amajor 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 afew 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’sunlikely 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 awhole percentage point—which is four times the most common incremental change—the call value will change by alittle more than $0.02. In this case, this is an acceptable risk. With 23 days to expiration, the ATM 35 call has arho 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 adecline in IV? She may want to decrease her vega. Conversely, she may believe I


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 adecline 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 aspread. The simplest way to alter her exposure to option greeks is to choose adifferent call to buy. Instead of buying the ATM call, Kim can buy acall with adifferent 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 aviable 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 afew 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’sconcerns 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 afavorable difference. Her vega is lower with the 37.50 call, too. This may or may not be afavorable difference. That depends on Kim’sopinion of IV.
On the surface, the disparity in delta appears to be ahighly 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 agrain of salt. It is ultimately gamma that will make or break this delta play.
The price of the option is 0.20—arather 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’sforecast is correct and there is abig move upward, gamma will cause the delta to increase, and therefore also the premium to increase exponentially. The call’ssensitivity 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 ashare, 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’sthoughts, 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 agood pop in th


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 agood 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’sabout a 150 percent profit. At $38,
Exhibit 4.9
reveals the call value to be 1.04. That’sa 420 percent profit.
On one hand, it’shard for atrader like Kim not to get excited about the prospect of making 420 percent on an 8 percent move in astock. 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’sdefinition 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’sstarting 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’sabit more to it. They are really about gamma, time, and the magnitude of the stock’smove (volatility). Long OTM calls require abig 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 avery different trade from the two previous alternatives.
Exhibit 4.10
shows acomparison 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 alower gamma, theta, and vega than the ATM 35-strike call. Because the call is ITM, it has ahigher 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’thelp 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 amore 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 arelatively low gamma, the delta remains high even if Disney declines significantly. Gamma doesn’treally 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 abig loss, and the higher gamma is of little comfort.
Kim’smotivation 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 asecondary consideration.
If this were adeeper 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 acall, 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 arobust marketplace. Differing opinions are the oil that greases the machine that is price discovery. From amarket standpoint, it’swhat makes the world go round.
It is possible that there is anoth


spoken bullish analyst with an equally unreserved bearish analyst. But differing opinions also make for arobust marketplace. Differing opinions are the oil that greases the machine that is price discovery. From amarket standpoint, it’swhat 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’sposition and Kim’sposition share many similarities.
Exhibit 4.13
offers acomparison 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’snegative 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 abig enough delta to offer the directional exposure Mick desires. The delta can change, but gamma ensures that it always changes in Mick’sfavor.
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, adecline 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 astock, 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 along 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’splan. 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’tmove at all. At the time the position is established, the theta is 0.009, just under apenny. 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 aday 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’tchange much over the first three weeks, Mick can eyeball the theta rather easily. As expiration ap


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’tchange 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’sput 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’tmoved. Mick’saverage daily theta during that period is about 0.0129 (0.45 ÷ 35). The more time he holds the trade, the greater aconcern is theta. Mick must weigh his assessment of the likelihood of the option’sgaining 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 aput with agreater 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’scall alternatives, the OTM put would have less exposure to time decay, lower vega, lower gamma, and alower delta. It would have alower premium, too. It would require abigger 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 ahigher delta. It would take on more of the functionality of ashort stock position in much the same way that Kim’s ITM call alternative did for along stock position. In its very essence, however, an option trade, ITM or otherwise, is still fundamentally different than astock trade.
Stock has a 1.00 delta. The delta of astock 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’sstrike 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 acomponent of the option’sprice 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 afavorable 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 asimilar 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’sprice 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’sforecasted direction the better. Volatility in the form of an adverse directional move results in adecline 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 aparticular 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 abreakdown of common option strategies into categories of volatility-buying strategies and vol


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 abreakdown 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 arange—that is, neutral. Although some option-selling strategies—for example, anaked put—may have apositive or negative delta in the short term, profit potential is decidedly limited. This means that if traders are expecting abig 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 awinner.
Are You a Buyer or a Seller?
The question is: which is better, selling volatility or buying volatility? Ihave attended option seminars with instructors (many of whom Iregard with great respect) teaching that volatility-selling strategies, or income-generating strategies, are superior to buying options. Ialso know option gurus that tout the superiority of buying options. The answer to the question of which is better is simple: it’sall amatter of personal preference.
When Ibegan trading on the floor of Chicago Board Options Exchange (CBOE) in the 1990s, Iquickly became aware of adichotomy 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 adollar—ateenie
. 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 ateenie, 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’san inexpensive lottery ticket. At worst, the trader can only lose ateenie. Teenie buyers felt being short OTM options that could be closed by paying asixteenth 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 adollar per contract representing 100 shares) by selling their long OTMs at ateenie to close the position. They sometimes would even initiate short OTM contracts at one sixteenth.
These long-option or short-option biases hold for othe


e sellers would routinely save themselves $6.25 (one sixteenth of adollar per contract representing 100 shares) by selling their long OTMs at ateenie 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 afew months of profits is all part of the game.
Options and the Fair Game
There may be astatistical advantage to buying stock as opposed to shorting stock, because the market has historically had apositive annualized return over the long run. Astatistical 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 agame consisting of one six-sided die. Each time aone, two, or three is rolled, the house pays the player $1. Each time afour, five, or six is rolled, the house pays zero. What is the most aplayer would be willing to pay to play this game? If the player paid nothing, the house would be at atremendous disadvantage, paying $1 50 percent of the time and nothing the other 50 percent of the time. This would not be afair game from the house’sperspective, 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 afair game from the player’sperspective.
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 afair game with an entrance fee of $0.50.
Now imagine asimilar game in which asix-sided die is rolled. This time if aone is rolled, the house pays $1. If any other number is rolled, the house pays nothing. What is afair price to play this game? The same logic and the same math apply. There is apercent chance of aone coming up and the player receiving $1. And there is apercent chance of each of the other five numbers being rolled and the player receiving nothing. Mathematically, this translates to:
percent
percent). Fair value for achance 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’sexpectations of future volatility. If buying options offered asuperior payout based on the odds of success, the market would put upward pressure on prices until this arbitrage opportunity ceased to exist. It’sthe same for selling volatility. If selling were afundamentally better strategy, the market would depress option prices until selling options no longer produced away 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.


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 abusiness 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 away to profit from this fact, but it’snot 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 aroundabout 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 atrade-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 astock 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 adecision to make. Short-term speculative traders very often choose to cut their losses and exit the position early rather than risk alarger loss hoping for arecovery.
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 aposition can help traders make better decisions if they plan to close the position before expiration.
Naked Call
Anaked call is when atrader shorts acall without having stock or other options to cover or protect it. Since the call is uncovered, it is one of the riskier trades atrader 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 atrade. When astock has been trading in arange 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 acall.
For example, atrader, Brendan, has been studying achart of Johnson & Johnson (JNJ). Brendan notices that for afew months the stock has trading been in achannel between $60 and $65. As he observes Johnson & Johnson beginning to approach the resistance level of $65 again, he considers selling acall 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 afilter to determine the strength of atrend and whether the stock is overbought or oversold. In this case, the indicator shows no strong trend pre

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ng 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 afilter to determine the strength of atrend 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 atakeover 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’searnings report falls. Although recent earnings have seldom been amajor 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 arather 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’scalls 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 abig 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 aloss 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 agood-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—amental 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 anegative 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 adirectional trade per se, delta is acrucial element. It will have abig impact on Brendan’sexpectations 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 astock 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 aproduct of the bid-ask spread. It’sthe difference between theory and reality. If the bid-ask spread had atypical 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 afew 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 apart 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 arise 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 g


Initially, the delta is −0.34 and the gamma is −0.15. After arise 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’scalls to be offered at his stop-loss price of 1.10.
While having apredefined 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 asmall 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 auseful rule of thumb.
Would I Do It Now? Rule
To follow this rule, ask yourself, “If Idid not already have this position, would Ido it now? Would Iestablish 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 Iwere not already short the calls, would Ishort them now at the current price of 0.75, with the stock trading at $64.50?”
Brendan’sopinion 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’stheta 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 alittle closer to his goal—to have the 65 calls expire out-of-the-money (OTM) and reap aprofit 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 aday (1.80 × 10 contracts). Is the risk of loss in the short run worth earning $18 aday? With Johnson & Johnson at $64.50, would Brendan now short 10 calls at 0.75 to collect $18 aday, knowing that each day may bring acontinued move higher in the stock? The answer to this question depends on Brendan’sassessment 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: arisk factor.
Asmall 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’srising though the strike price for the trade to be aloser 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. Anaked put is ashort 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 ahigher delta. If her price rise comes sooner than expected, the high delta may allow her to take aprofit 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.


it 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’snaked put trade if she holds it until expiration.
EXHIBIT 5.4
Naked Johnson & Johnson put at expiration.
While harvesting the entire premium as aprofit 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 aprofit. Furthermore, she realizes that her outlook may be wrong: Johnson & Johnson may decline. She may have to close the position early—maybe for aprofit, maybe for aloss. 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 adirectional bias. This bias can work for or against her. With apositive 0.65 delta per contract, this position has adirectional sensitivity equivalent to being long around 650 shares of the stock. That’sthe delta × 100 shares × 10 contracts.
Stacie’strade is not just abullish version of Brendan’s. Partly because of the size of the delta, it’sdifferent—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 anet favorable effect on Stacie’sprofitability. Theta is small in comparison and won’thave too much of an effect. Delta/gamma will account for adecrease in the put’stheoretical value of about $0.73. That’sthe estimated average delta times the stock move, or [0.65 + (–0.15/2)] × 1.00.
Stacie’sactual 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 anickel 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 again 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’thave 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 abreakout 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 aloser. Her trade has ahigher delta. An adverse move in the underlying would affect Stacie’strade 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 astock 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 awinner 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’toccur. 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 astock price of about $63.28. Theta is somewhat relevant here. It helps Stacie’spotential 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’sexpectations.
The Double Whammy
With the stock around $64, there is anegative vega of abo


he 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’sexpectations.
The Double Whammy
With the stock around $64, there is anegative vega of about seven cents. As the stock moves lower, away from the strike, the vega gets abit smaller. However, the market conditions that would lead to adecline 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—adouble whammy. Stacie needs to watch her vega.
Exhibit 5.6
shows the vega of Stacie’sput 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 ashare, the vega will be 0.043 per contract. If IV subsequently rises 5 points as aresult of the stock falling, vega will make Stacie’sputs 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.
Agap 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’sassessment of future volatility. Is the market right? The other part is based on Stacie’srisk tolerance. Is she willing to endure the greater price swings associated with the potentially higher volatility? This can mean getting whipsawed, which is exiting aposition after reaching astop-loss point only to see the market reverse itself. The would-be profitable trade is closed for aloss. Higher volatility can also mean ahigher likelihood of getting assigned and acquiring an unwanted long stock position.
Cash-Secured Puts
There are some situations where higher implied volatility may be abeneficial trade-off. What if Stacie’smotivation 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 acash-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 adiscount 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’tget assigned and therefore can only profit amaximum of 1.75 per contract. If the stock is below $63.25 at expiration, the time premium no longer represents adiscount, in fact, the trade becomes aloser. In away, Stacie is still selling volatility.
Covered Call
The problem with selling anaked call is that it has unlimited exposure to upside risk. Because of this, many traders simply avoid trading naked calls. Amore common, and some would argue safer, method of selling calls is to sell them covered.
Acovered call is when calls are sold and stock is purchased on ashare-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 adifferent 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 cal


derlying security are bought. Because of the addition of stock to this strategy, covered calls are traded with adifferent 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 adelta of one, and all its other greeks are zero.
The pivotal point for both positions is the strike price. That’sthe 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 afew 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 Iwant 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, amain focus of acovered 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. Atrader, Bill, is neutral to slightly bullish on Harley-Davidson over the next three months.
Exhibit 5.7
shows aselection 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’san 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 adifferent 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 atheta advantage over the longer-term choices. The March 70 has atheta of 0.032, while the April 70’stheta is 0.026 and the May 70’sis 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 afavorable quality for ashort candidate. Bill must weigh his assessment of all relevant information and then decide which trade is best. With this type of astrategy, 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 anet delta of 0.588 per contract. That’sthe 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 ahigher strike. He would have to sell the April or May 75, since the March 75s are azero bid. This would give him ahigher 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 c


e him ahigher 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’drather 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’dprofit on both delta and theta. If the trade isn’texactly perfect, but still good, Harley-Davidson will be anywhere above $68.15 in 22 days. It’sthe prospect that the trade may not be so good at March expiration that occupies Bill’sthoughts, but atrader 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’strending to the upside are not quite so dire, although he might be somewhat frustrated with any lost opportunity above the indifference point. It’sthe 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. Arise in implied volatility will likely accompany adecline 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 anaked 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 atime. If he legs out of the trade, he’slikely to close the call first. The motivation for exiting atrade early is to reduce risk. Anaked call is hardly less risky than acovered 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 alot 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 anickel, adime, 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 asingle order, it is called acalendar spread or atime 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 acovered put, atrader sells both puts and stock on aone-to-one basis. The term
covered put
is abit of amisnomer, as the strategy changes from limited risk to unlimited risk when short stock is added to the short put. Anaked put can produce only losses until the stock goes to zero—still asubstantial 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 anaked call. In fact, they are synthetically equal. This concept will be addressed further in the next chapter.
Let’slooks at another trader, Libby. Libby is an active trader who trades several positions at once. Libby believes the overall market is in arange and will continue as such over the next few weeks. She currently holds ashort 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 acovered-put position. There is one caveat: Libby is leaving for acruise 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 t


ould consider buying in her short if the market dipped. She may consider entering into acovered-put position. There is one caveat: Libby is leaving for acruise 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. Amove 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 apremium-over-parity standpoint. Below the strike, the intrinsic value of the put doesn’tmatter 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’sa 73-cent profit, or $730 on her 10 contracts. This doesn’taccount for any changes in the time value that may occur as aresult 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 aprofit on aposition that worked out just about exactly as planned.
Her risk, though, is to the upside. Abig rally in the stock can cause big losses. From atheoretical standpoint, losses are potentially unlimited with this type of trade. If the stock is above the strike, she needs to have amental 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 astock will not rise above acertain price, the most straightforward way to trade the forecast is to sell acall. Likewise, if the trader believes the stock will not go below acertain price he can sell aput. 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.