tly what the maximum profit can be.
Exhibit 11.10
provides an alternative picture of the position that is useful in managing the trade on a day-to-day basis.
EXHIBIT 11.10
10-lot Minnesota Mining & Manufacturing Aug–Oct 85–90 double call calendar.
These numbers are a good representation of the position’s risk. Knowing that long calendars and long double calendars have maximum losses at the expiration of the short-term option equal to the net premiums paid, the max loss in this example is 3.20. Break-even prices are not relevant to this position because they cannot be determined with any certainty. What is important is to get a feel for how much movement can hurt the position.
To make $19 a day in theta, a −0.468 gamma must be accepted. In the long run, $1 of movement is irrelevant. In fact, some movement is favorable because the ideal point for MMM to be at, at August expiration is either $85 or $90. So while small moves are acceptable, big moves are of concern. The negative gamma is an illustration of this warning.
The other risk besides direction is vega. A positive 1.471 vega means the calendar makes or loses about $147 with each one-point across-the-board change in implied volatility. Implied volatility is a risk in all calendar trades. Volatility was one of the criteria studied when considering this trade. Recall that the August IV was one point higher than the October and that the October IV was in line with the 30-day historical volatility at inception of the trade.
Considering the volatility data is part of the due diligence when considering a calendar or a double calendar. First, the (slightly) more expensive options (August) are being sold, and the cheaper ones are being bought (October). A study of the company reveals no news to lead one to believe that Minnesota Mining & Manufacturing should move at a higher realized volatility than it currently is in this example. Therefore, the front month’s higher IV is not a red flag. Because the volatility of the October option (the month being purchased) is in line with the historical volatility, the trader could feel that he is paying a reasonable price for this volatility.
In the end, the trade is evaluated on the underlying stock, realized volatility, and IV. The trade should be executed only after weighing all the available data. Trading is both cerebral and statistical in nature. It’s about gaining a statistically better chance of success by making rational decisions.
Diagonals
Definition
: A diagonal spread is an option strategy that involves buying one option and selling another option with a different strike price and with a different expiration date. Diagonals are another strategy in the time spread family.
Diagonals enable a trader to exploit opportunities similar to those exploited by a calendar spread, but because the options in a diagonal spread have two different strike prices, the trade is more focused on delta. The name
diagonal
comes from the fact that the spread is a combination of a horizontal spread (two different months) and a vertical spread (two different strikes).
Say it’s 22 days until January expiration and 50 days until February expiration. Apple Inc. (AAPL) is trading at $405.10. Apple has been in an uptrend heading toward the peak of its six-month range, which is around $420. A trader, John, believes that it will continue to rise and hit $420 again by February expiration. Historical volatility is 28 percent. The February 400 calls are offered at a 32 implied volatility and the January 420 calls are bid on a 29 implied volatility. John executes the following diagonal:
Exhibit 11.11
shows the analytics for this trade.
EXHIBIT 11.11
Apple January–February 400–420 call diagonal.
From the presented data, is this a good trade? The answer to this question is contingent on whether the position John is taking is congruent with his view of direction and volatility and what the market tells him about these elements.
John is bullish up to August expiration, and the stock in this example is in an uptrend. Any rationale for bullishness may come from technical or fundamental analysis, but techniques for picking direction, for the most part, are beyond the scope of this book. Buying the lower strike in the February option gives this trade a more positive delta than a straight calendar spread would have. The trader’s delta is 0.255, or the equivalent of about 25.5 shares of Apple. This reflects the trader’s directional view.
The volatility is not as easy to decipher. A specific volatility forecast was not stated above, but there are a few relevant bits of information that should be considered, whether or not the trader has a specific view on future volatility. First, the historical volatility is 28 percent. That’s lower than either the January or the February calls. That’s not ideal. In a perfect world, it’s better to buy below historical and sell above. To that point, the February option that John is buying has a higher volatility than the Jan


olatility. First, the historical volatility is 28 percent. That’s lower than either the January or the February calls. That’s not ideal. In a perfect world, it’s better to buy below historical and sell above. To that point, the February option that John is buying has a higher volatility than the January he is selling. Not so good either. Are these volatility observations deal breakers?
A Good Ex-Skews
It’s important to take skew into consideration. Because the January calls have a higher strike price than the February calls, it’s logical for them to trade at a lower implied volatility. Is this enough to justify the possibility of selling the lower volatility? Consider first that there is some margin for error. The bid-ask spreads of each of the options has a volatility disparity. In this case, both the January and February calls are 10 cents wide. That means with a January vega of 0.34 the bid-ask is about 0.29 vol points wide. The Februarys have a 0.57 vega. They are about 0.18 vol points wide. That accounts for some of the disparity. Natural vertical skew accounts for the rest of the difference, which is acceptable as long as the skew is not abnormally pronounced.
As for other volatility considerations, this diagonal has the rather unorthodox juxtaposition of positive vega and negative gamma seen with other time spreads. The trader is looking for a move upward, but not a big one. As the stock rises and Apple moves closer to the 420 strike, the positive delta will shrink and the negative gamma will increase. In order to continue to enjoy profits as the stock rises, John may have to buy shares of Apple to keep his positive delta. The risk here is that if he buys stock and Apple retraces, he may end up negative scalping stock. In other words, he may sell it back at a lower price than he bought it. Using stock to adjust the delta in a negative-gamma play can be risky business. Gamma scalping is addressed further in Chapter 13.
Making the Most of Your Options
The trader from the previous example had a time-spread alternative to the diagonal: John could have simply bought a traditional time spread at the 420 strike. Recall that calendars reap the maximum reward when they are at the shared strike price at expiration of the short-term option. Why would he choose one over the other?
The diagonal in that example uses a lower-strike call in the February than a straight 420 calendar spread and therefore has a higher delta, but it costs more. Gamma, theta, and vega may be slightly lower with the in-the-money call, depending on how far from the strike price the ITM call is and how much time until expiration it has. These, however, are less relevant differences.
The delta of the February 400 call is about 0.57. The February 420 call, however, has only a 0.39 delta. The 0.18 delta difference between the calls means the position delta of the time spread will be only about 0.07 instead of about 0.25 of the diagonal—a big difference. But the trade-off for lower delta is that the February 420 call can be bought for 12.15. That means a lower debit paid—that means less at risk. Conversely, though there is greater risk with the diagonal, the bigger delta provides a bigger payoff if the trader is right.
Double Diagonals
A double diagonal spread is the simultaneous trading of two diagonal spreads: one call spread and one put spread. The distance between the strikes is the same in both diagonals, and both have the same two expiration months. Usually, the two long-term options are more out-of-the-money than the two shorter-term options. For example
Buy 1 XYZ May 70 put
Sell 1 XYZ March 75 put
Sell 1 XYZ March 85 call
Buy 1 XYZ May 90 call
Like many option strategies, the double diagonal can be looked at from a number of angles. Certainly, this is a trade composed of two diagonal spreads—the March–May 70–75 put and the March–May 85–90 call. It is also two strangles—buying the May 70–90 strangle and selling the March 75–85 strangle. One insightful way to look at this spread is as an iron condor in which the guts are March options and the wings are May options.
Trading a double diagonal like this one, rather than a typically positioned iron condor, can offer a few advantages. The first advantage, of course, is theta. Selling short-term options and buying long-term options helps the trader reap higher rates of decay. Theta is the raison d’être of the iron condor. A second advantage is rolling. If the underlying asset stays in a range for a long period of time, the short strangle can be rolled month after month. There may, in some cases, also be volatility-term-structure discrepancies on which to capitalize.
A trader, Paul, is studying JPMorgan (JPM). The current stock price is $49.85. In this example, JPMorgan has been trading in a pretty tight range over the past few months. Paul believes it will continue to do so over the next month. Paul considers the following trade:
Paul considers volatility. In this example, the JPMorgan ATM call

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an (JPM). The current stock price is $49.85. In this example, JPMorgan has been trading in a pretty tight range over the past few months. Paul believes it will continue to do so over the next month. Paul considers the following trade:
Paul considers volatility. In this example, the JPMorgan ATM call, the August 50 (which is not shown here), is trading at 22.9 percent implied volatility. This is in line with the 20-day historical volatility, which is 23 percent. The August IV appears to be reasonably in line with the September volatility, after accounting for vertical skew. The IV of the August 52.50 calls is 1.5 points above that of the September 55 calls and the August 47.50 put IV is 1.6 points below the September 45 put IV. It appears that neither month’s volatility is cheap or expensive.
Exhibit 11.12
shows the trade’s greeks.
EXHIBIT 11.12
10-lot JPMorgan August–September 45–47.50–52.50–55 double diagonal.
The analytics of this trade are similar to those of an iron condor. Immediate directional risk is almost nonexistent, as indicated by the delta. But gamma and theta are high, even higher than they would be if this were a straight September iron condor, although not as high as if this were an August iron condor.
Vega is positive. Surely, if this were an August or a September iron condor, vega would be negative. In this example, Paul is indifferent as to whether vega is positive or negative because IV is fairly priced in terms of historical volatility and term structure. In fact, to play it close to the vest, Paul probably wants the smallest vega possible, in case of an IV move. Why take on the risk?
The motivation for Paul’s double diagonal was purely theta. The volatilities were all in line. And this one-month spread can’t be rolled. If Paul were interested in rolling, he could have purchased longer-term options. But if he is anticipating a sideways market for only the next month and feels that volatility could pick up after that, the one-month play is the way to go. After August expiration, Paul will have three choices: sell his Septembers, hold them, or turn them into a traditional iron condor by selling the September 47.50s and 52.50s. This depends on whether he is indifferent, expects high volatility, or expects low volatility.
The Strength of the Calendar
Spreads in the calendar-spread family allow traders to take their trading to a higher level of sophistication. More basic strategies, like vertical spreads and wing spreads, provide a practical means for taking positions in direction, realized volatility, and to some extent implied volatility. But because calendar-family spreads involve two expiration months, traders can take positions in the same market variables as with these more basic strategies and also in the volatility spread between different expiration months. Calendar-family spreads are veritable volatility spreads. This is a powerful tool for option traders to have at their disposal.
Note
1
. Advanced hedging techniques are discussed in subsequent chapters.


CHAPTER 12
Delta-Neutral Trading
Trading Implied Volatility
Many of the strategies covered so far have been option-selling strategies. Some had a directional bias; some did not. Most of the strategies did have a primary focus on realized volatility—especially selling it. These short volatility strategies require time. The reward of low stock volatility is theta. In general, most of the strategies previously covered were theta trades in which negative gamma was an unpleasant inconvenience to be dealt with.
Moving forward, much of the remainder of this book will involve more in-depth discussions of trading both realized and implied volatility (IV), with a focus on the harmonious, and sometimes disharmonious, relationship between the two types. Much attention will be given to how IV trades in the option market, describing situations in which volatility moves are likely to occur and how to trade them.
Direction Neutral versus Direction Indifferent
In the world of nonlinear trading, there are two possible nondirectional views of the underlying asset: direction neutral and direction indifferent. Direction neutral means the trader believes the stock will not trend either higher or lower. The trader is neutral in his or her assessment of the future direction of the asset. Short iron condors, long time spreads, and out-of-the-money (OTM) credit spreads are examples of direction-neutral strategies. These strategies generally have deltas close to zero. Because of negative gamma, movement is the bane of the direction-neutral trade.
Direction indifferent means the trader may desire movement in the underlying but is indifferent as to whether that movement is up or down. Some direction-indifferent trades are almost completely insulated from directional movement, with a focus on interest or dividends instead. Examples of these types of trades are conversions, reversals, and boxes, which are described in Chapter 6, as well as dividend plays, which are described in Chapter 8.
Other direction-indifferent strategies are long option strategies that have positive gamma. In these trades, the focus is on movement, but the direction of that movement is irrelevant. These are plays that are bullish on realized volatility. Yet other direction-indifferent strategies are volatility plays from the perspective of IV. These are trades in which the trader’s intent is to take a bullish or bearish position in IV.
Delta Neutral
To be truly direction neutral or direction indifferent means to have a delta equal to zero. In other words, there are no immediate gains if the underlying moves incrementally higher or lower. This zero-delta method of trading is called
delta-neutral trading
.
A delta-neutral position can be created from any option position simply by trading stock to flatten out the delta. A very basic example of a delta-neutral trade is a long at-the-money (ATM) call with short stock.
Consider a trade in which we buy 20 ATM calls that have a 50 delta and sell stock on a delta-neutral ratio.
Buy 20 50-delta calls (long 1,000 deltas)
Short 1,000 shares (short 1,000 deltas)
In this position, we are long 1,000 deltas from the calls (20 × 50) and short 1,000 deltas from the short sale of stock. The net delta of the position is zero. Therefore, the immediate directional exposure has been eliminated from the trade. But intuitively, there are other opportunities for profit or loss with this trade.
The addition of short stock to the calls will affect only the delta, not the other greeks. The long calls have positive gamma, negative theta, and positive vega.
Exhibit 12.1
is a simplified representation of the greeks for this trade.
EXHIBIT 12.1
20-lot delta-neutral long call.
With delta not an immediate concern, the focus here is on gamma, theta, and vega. The +1.15 vega indicates that each one-point change in IV makes or loses $115 for this trade. Yet there is more to the volatility story. Each day that passes costs the trader $50 in time decay. Holding the position for an extended period of time can produce a loser even if IV rises. Gamma is potentially connected to the success of this trade, too. If the underlying moves in either direction, profit from deltas created by positive gamma may offset the losses from theta. In fact, a big enough move in either direction can produce a profitable trade, regardless of what happens to IV.
Imagine, for a moment, that this trade is held until expiration. If the stock is below the strike price at this point, the calls expire. The resulting position is short 1,000 shares of stock. If the stock is above the strike price at expiration, the calls can be exercised, creating 2,000 shares of long stock. Because the trade is already short 1,000 shares, the resulting net position is long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock moves in either direction the greater the profit potential. The underlying has to move far enough above or below the strike price to allow the beneficial gains fro

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e is already short 1,000 shares, the resulting net position is long 1,000 shares (2,000 − 1,000). Clearly, the more the underlying stock moves in either direction the greater the profit potential. The underlying has to move far enough above or below the strike price to allow the beneficial gains from buying or selling stock to cover the option premium lost from time decay. If the trade is held until expiration, the underlying needs to move far enough to cover the entire premium spent on the calls.
The solid lines forming a V in
Exhibit 12.2
conceptually illustrate the profit or loss for this delta-neutral long call at expiration.
EXHIBIT 12.2
Profit-and-loss diagram for delta-neutral long-call trade.
Because of gamma, some deltas will be created by movement of the underlying before expiration. Gamma may lead to this being a profitable trade in the short term, depending on time and what happens with IV. The dotted line illustrates the profit or loss of this trade at the point in time when the trade is established. Because the options may still have time value at this point—depending on how far from the strike price the stock is trading—the value of the position, as a whole, is higher than it will be if the calls are trading at parity at expiration. Regardless, the plan is for the stock to make a move in either direction. The bigger the move and the faster it happens, the better.
Why Trade Delta Neutral?
A few years ago, I was teaching a class on option trading. Before the seminar began, I was talking with one of the students in attendance. I asked him what he hoped to learn in the class. He said that he was really interested in learning how to trade delta neutral. When I asked him why he was interested in that specific area of trading, he replied, “I hear that’s where all the big money is made!”
This observation, right or wrong, probably stems from the fact that in the past most of the trading in this esoteric discipline has been executed by professional traders. There are two primary reasons why the pros have dominated this strategy: high commissions and high margin requirements for retail traders. Recently, these two reasons have all but evaporated.
First, the ultracompetitive world of online brokers has driven commissions for retail traders down to, in some cases, what some market makers pay. Second, the oppressive margin requirements that retail option traders were subjected to until 2007 have given way to portfolio margining.
Portfolio Margining
Customer portfolio margining is a method of calculating customer margin in which the margin requirement is based on the “up and down risk” of the portfolio. Before the advent of portfolio margining, retail traders were subject to strategy-based margining, also called Reg. T margining, which in many cases required a significantly higher amount of capital to carry a position than portfolio margining does.
With portfolio margining, highly correlated securities can be offset against each other for purposes of calculating margin. For example, SPX options and SPY options—both option classes based on the Standard & Poor’s 500 Index—can be considered together in the margin calculation. A bearish position in one and a bullish position in the other may partially offset the overall risk of the portfolio and therefore can help to reduce the overall margin requirement.
With portfolio margining, many strategies are margined in such a way that, from the point of view of this author, they are subject to a much more logical means of risk assessment. Strategy-based margining required traders of some strategies, like a protective put, to deposit significantly more capital than one could possibly lose by holding the position. The old rules require a minimum margin of 50 percent of the stock’s value and up to 100 percent of the put premium. A portfolio-margined protective put may require only a fraction of what it would with strategy-based margining.
Even though Reg. T margining is antiquated and sometimes unreasonable, many traders must still abide by these constraints. Not all traders meet the eligibility requirements to qualify for portfolio-based margining. There is a minimum account balance for retail traders to be eligible for this treatment. A broker may also require other criteria to be met for the trader to benefit from this special margining. Ultimately, portfolio margining allows retail traders to be margined similarly to professional traders.
There are some traders, both professional and otherwise, who indeed have made “big money,” as the student in my class said, trading delta neutral. But, to be sure, there are successful and unsuccessful traders in many areas of trading. The real motivation for trading delta neutral is to take a position in volatility, both implied and realized.
Trading Implied Volatility
With a typical option, the sensitivity of delta overshadows that of vega. To try and profit from a rise or fall in IV, one has to trade delta neutral to eliminate im


e real motivation for trading delta neutral is to take a position in volatility, both implied and realized.
Trading Implied Volatility
With a typical option, the sensitivity of delta overshadows that of vega. To try and profit from a rise or fall in IV, one has to trade delta neutral to eliminate immediate directional sensitivity. There are many strategies that can be traded as delta-neutral IV strategies simply by adding stock. Throughout this chapter, I will continue using a single option leg with stock, since it provides a simple yet practical example. It’s important to note that delta-neutral trading does not refer to a specific strategy; it refers to the fact that the trader is indifferent to direction. Direction isn’t being traded, volatility is.
Volatility trading is fundamentally different from other types of trading. While stocks can rise to infinity or decline to zero, volatility can’t. Implied volatility, in some situations, can rise to lofty levels of 100, 200, or even higher. But in the long-run, these high levels are not sustainable for most stocks. Furthermore, an IV of zero means that the options have no extrinsic value at all. Now that we have established that the thresholds of volatility are not as high as infinity and not as low as zero, where exactly are they? The limits to how high or low IV can go are not lines in the sand. They are more like tides that ebb and flow, but normally come up only so far onto the beach.
The volatility of an individual stock tends to trade within a range that can be unique to that particular stock. This can be observed by studying a chart of recent volatility. When IV deviates from the range, it is typical for it to return to the range. This is called
reversion to the mean
, which was discussed in Chapter 3. IV can get stretched in either direction like a rubber band but then tends to snap back to its original shape.
There are many examples of situations where reversion to the mean enters into trading. In some, volatility temporarily dips below the typical range, and in some, it rises beyond the recent range. One of the most common examples is the rush and the crush.
The Rush and the Crush
In this situation, volatility rises before and falls after a widely anticipated news announcement, of earnings, for instance, or of a Food and Drug Administration (FDA) approval. In this situation, option buyers rush in and bid up IV. The more uncertainty—the more demand for insurance—the higher vol rises. When the event finally occurs and the move takes place or doesn’t, volatility gets crushed. The crush occurs when volatility falls very sharply—sometimes 10 points, 20 points, or more—in minutes. Traders with large vega positions appreciate the appropriateness of the term crush all too well. Volatility traders also affectionately refer to this sudden drop in IV by saying that volatility has gotten “whacked.”
In order to have a feel for whether implied volatility is high or low for a particular stock, you need to know where it’s been. It’s helpful to have an idea of where realized volatility is and has been, too. To be sure, one analysis cannot be entirely separate from the other. Studying both implied and realized volatility and how they relate is essential to seeing the big picture.
The Inertia of Volatility
Sir Isaac Newton said that an object in motion tends to stay in motion unless acted upon by another force. Volatility acts much the same way. Most stocks tend to trade with a certain measurable amount of daily price fluctuations. This can be observed by looking at the stock’s realized volatility. If there is no outside force—some pivotal event that fundamentally changes how the stock is likely to behave—one would expect the stock to continue trading with the same level of daily price movement. This means IV (the market’s expectation of future stock volatility) should be the same as realized volatility (the calculated past stock volatility).
But just as in physics, it seems there is always some friction affecting the course of what is in motion. Corporate earnings, Federal Reserve Board reports, apathy, lulls in the market, armed conflicts, holidays, rumors, and takeovers, among other market happenings all provide a catalyst for volatility changes. Divergences of realized and implied volatility, then, are commonplace. These divergences can create tradable conditions, some of which are more easily exploited than others.
To find these opportunities, a trader must conduct a study of volatility. Volatility charts can help a trader visualize the big picture. This historical information offers a comparison of what is happening now in volatility with what has happened in the past. The following examples use a volatility chart to show how two different traders might have traded the rush and crush of an earnings report.
Volatility Selling
Susie Seller, a volatility trader, studies semiconductor stocks.
Exhibit 12.3
shows the volatilities of a $50 chip stock. The circled area


. The following examples use a volatility chart to show how two different traders might have traded the rush and crush of an earnings report.
Volatility Selling
Susie Seller, a volatility trader, studies semiconductor stocks.
Exhibit 12.3
shows the volatilities of a $50 chip stock. The circled area shows what happened before and after second-quarter earnings were reported in July. The black line is the IV, and the gray is the 30-day historical.
EXHIBIT 12.3
Chip stock volatility before and after earnings reports.
Source
: Chart courtesy of
iVolatility.com
In mid-July, Susie did some digging to learn that earnings were to be announced on July 24, after the close. She was careful to observe the classic rush and crush that occurred to varying degrees around the last three earnings announcements, in October, January, and April. In each case, IV firmed up before earnings only to get crushed after the report. In mid-to-late July, she watched as IV climbed to the mid-30s (the rush) just before earnings. As the stock lay in wait for the report, trading came to a proverbial screeching halt, sending realized volatility lower, to about 13 percent. Susie waited for the end of the day just before the report to make her move. Before the closing bell, the stock was at $50. Susie sold 20 one-month 50-strike calls at 2.10 (a 35 volatility) and bought 1,100 shares of the underlying stock at $50 to become delta neutral.
Exhibit 12.4
shows Susie’s position.
EXHIBIT 12.4
Delta-neutral short ATM call, long stock position.
Her delta was just about flat. The delta for the 50 calls was 0.54 per contract. Selling a 20-lot creates 10.80 short deltas for her overall position. After buying 1,100 shares, she was left long 0.20 deltas, about the equivalence of being long 20 shares. Where did her risk lie? Her biggest concern was negative gamma. Without even seeing a chart of the stock’s price, we can see from the volatility chart that this stock can have big moves on earnings. In October, earnings caused a more than 10-point jump in realized volatility, to its highest level during the year shown. Whether the stock rose or fell is irrelevant. Either event means risk for a premium seller.
The positive theta looks good on the surface, but in fact, theta provided Susie with no significant benefit. Her plan was “in and out and nobody gets hurt.” She got into the trade right before the earnings announcement and out as soon as implied volatility dropped off. Ideally, she’d like to hold these types of trades for less than a day. The true prize is vega.
Susie was looking for about a 10-point drop in IV, which this option class had following the October and January earnings reports. April had a big drop in IV, as well, of about eight or nine points. Ultimately, what Susie is looking for is reversion to the mean.
She gauges the normal level of volatility by observing where it is before and after the surges caused by earnings. From early November to mid- to late- December, the stock’s IV bounced around the 25 percent level. In the month of February, the IV was around 25. After the drop-off following April earnings and through much of May, the IV was closer to 20 percent. In June, IV was just above 25. Susie surmised from this chart that when no earnings event is pending, this stock’s options typically trade at about a 25 percent IV. Therefore, anticipating a 10-point decline from 35 was reasonable, given the information available. If Susie gets it right, she stands to make $1,150 from vega (10 points × 1.15 vegas × 100).
As we can see from the right side of the volatility chart in
Exhibit 12.3
, Susie did get it right. IV collapsed the next morning by just more than ten points. But she didn’t make $1,150; she made less. Why? Realized volatility (gamma). The jump in realized volatility shown on the graph is a function of the fact that the stock rallied $2 the day after earnings. Negative gamma contributed to negative deltas in the face of a rallying market. This negative delta affected some of Susie’s potential vega profits.
So what was Susie’s profit? On this trade she made $800. The next morning at the open, she bought back the 50-strike calls at 2.80 (25 IV) and sold the stock at $52. To compute her actual profit, she compared the prices of the spread when entering the trade with the prices of the spread when exiting.
Exhibit 12.5
shows the breakdown of the trade.
EXHIBIT 12.5
Profit breakdown of delta-neutral trade.
After closing the trade, Susie knew for sure what she made or lost. But there are many times when a trader will hold a delta-neutral position for an extended period of time. If Susie hadn’t closed her trade, she would have looked at her marks to see her P&(L) at that point in time. Marks are the prices at which the securities are trading in the actual market, either in real time or at end of day. With most online brokers’ trading platforms or options-trading software, real-time prices are updated dynamically and always at their finger


ks to see her P&(L) at that point in time. Marks are the prices at which the securities are trading in the actual market, either in real time or at end of day. With most online brokers’ trading platforms or options-trading software, real-time prices are updated dynamically and always at their fingertips. The profit or loss is, then, calculated automatically by comparing the actual prices of the opening transaction with the current marks.
What Susie will want to know is why she made $800. Why not more? Why not less, for that matter? When trading delta neutral, especially with more complex trades involving multiple legs, a manual computation of each leg of the spread can be tedious. And to be sure, just looking at the profit or loss on each leg doesn’t provide an explanation.
Susie can see where her profits or losses came from by considering the profit or loss for each influence contributing to the option’s value.
Exhibit 12.6
shows the breakdown.
EXHIBIT 12.6
Profit breakdown by greek.
Delta
Susie started out long 0.20 deltas. A $2 rise in the stock price yielded a $40 profit attributable to that initial delta.
Gamma
As the stock rose, the negative delta of the position increased as a result of negative gamma. The delta of the stock remained the same, but the negative delta of the 50 call grew by the amount of the gamma. Deriving an exact P&(L) attributable to gamma is difficult because gamma is a dynamic metric: as the stock price changes, so can the gamma. This calculation assumes that gamma remains constant. Therefore, the gamma calculation here provides only an estimate.
The initial position gamma of −1.6 means the delta decreases by 3.2 with a $2 rise in the stock (–1.60 times the $2 rise in the stock price). Susie, then, would multiply −3.2 by $2 to find the loss on −3.2 deltas over a $2 rise. But she wasn’t short 3.2 deltas for the whole $2. She started out with zero deltas attributable to gamma and ended up being 3.2 shorter from gamma over that $2 move. Therefore, if she assumes her negative delta from gamma grew steadily from 0 to −3.2, she can estimate her average delta loss over that move by dividing by 2.
Theta
Susie held this trade one day. Her total theta contributed 0.75 or $75 to her position.
Vega
Vega is where Susie made her money on this trade. She was able to buy her call back 10 IV points lower. The initial position vega was −1.15. Multiplying −1.15 by the negative 10-point crush of volatility yields a vega profit of $1,150.
Conclusions
Studying her position’s P&(L) by observing what happened in her greeks provides Susie with an alternate—and in some ways, better—method to evaluate her trade. The focus of this delta-neutral trade is less on the price at which Susie can buy the calls back to close the position than on the volatility level at which she can buy them back, weighed against the P&(L) from her other risks. Analyzing her position this way gives her much more information than just comparing opening and closing prices. Not only does she get a good estimate of how much she made or lost, but she can understand why as well.
The Imprecision of Estimation
It is important to notice that the P&(L) found by adding up the P&(L)’s from the greeks is slightly different from the actual P&(L). There are a couple of reasons for this. First, the change in delta resulting from gamma is only an estimate, because gamma changes as the stock price changes. For small moves in the underlying, the gamma change is less significant, but for larger moves, the rate of change of the gamma can be bigger, and it can be nonlinear. For example, as an option moves from being at-the-money (ATM) to being out-of-the-money (OTM), its gamma decreases. But as the option becomes more OTM, its gamma decreases at a slower rate.
Another reason that the P&(L) from the greeks is different from the actual P&(L) is that the greeks are derived from the option-pricing model and are therefore theoretical values and do not include slippage.
Furthermore, the volatility input in this example is rounded a bit for simplicity. For example, a volatility of 25 actually yielded a theoretical value of 2.796, while the call was bought at 2.80. Because some options trade at minimum price increments of a nickel, and none trade in fractions of a penny, IV is often rounded.
Caveat Venditor
Reversion to the mean holds the promise of profit in this trade, but Susie also knows that this strategy does not come without risks of loss. The mean to which volatility is expected to revert is not a constant. This benchmark can and does change. In this example, if the company had an unexpectedly terrible quarter, the stock could plunge sharply. In some cases, this would cause IV to find a new, higher level at which to reside. If that had happened here, the trade could have been a big loser. Gamma and vega could both have wreaked havoc. In trading, there is no sure thing, no matter what the chart looks like. Remember, every ship on the bottom of the ocean


his would cause IV to find a new, higher level at which to reside. If that had happened here, the trade could have been a big loser. Gamma and vega could both have wreaked havoc. In trading, there is no sure thing, no matter what the chart looks like. Remember, every ship on the bottom of the ocean has a chart!
Volatility Buying
This same earnings event could have been played entirely differently. A different trader, Bobby Buyer, studied the same volatility chart as Susie. It is shown again here as
Exhibit 12.7
. Bobby also thought there would be a rush and crush of IV, but he decided to take a different approach.
EXHIBIT 12.7
Chip stock volatility before and after earnings reports.
Source
: Chart courtesy of
iVolatility.com
About an hour before the close of business on July 21, just three days before earnings announcements, Bobby saw that he could buy volatility at 30 percent. In Bobby’s opinion, volatility seemed cheap with earnings so close. He believed that IV could rise at least five points over the next three days. Note that we have the benefit of 20/20 hindsight in the example.
Near the end of the trading day, the stock was at $49.70. Bobby bought 20 33-day 50-strike calls at 1.75 (30 volatility) and sold short 1,000 shares of the underlying stock at $49.70 to become delta neutral.
Exhibit 12.8
shows Bobby’s position.
EXHIBIT 12.8
Delta-neutral long call, short stock position.
With the stock at $49.70, the calls had +0.51 delta per contract, or +10.2 for the 20-lot. The short sale of 1,000 shares got Bobby as close to delta-neutral as possible without trading an odd lot in the stock. The net position delta was +0.20, or about the equivalent of being long 20 shares of stock. Bobby’s objective in this case is to profit from an increase in implied volatility leading up to earnings.
While Susie was looking for reversion to the mean, Bobby hoped for a further divergence. For Bobby, positive gamma looked like a good thing on the surface. However, his plan was to close the position just before earnings were released—before the vol crush and before the potential stock-price move. With realized volatility already starting to drop off at the time the trade was put on, gamma offered little promise of gain.
As fate would have it, IV did indeed increase. At the end of the day before the July earnings report, IV was trading at 35 percent. Bobby closed his trade by selling his 20-lot of the 50 calls at 2.10 and buying his 1,000 shares of stock back at $50.
Exhibit 12.9
shows the P&(L) for each leg of the spread.
EXHIBIT 12.9
Profit breakdown.
The calls earned Bobby a total of $700, while the stock lost $300. Of course, with this type of trade, it is not relevant which leg was a winner and which a loser. All that matters is the bottom line. The net P&(L) on the trade was a gain of $400. The gain in this case was mostly a product of IV’s rising.
Exhibit 12.10
shows the P&(L) per greek.
EXHIBIT 12.10
Profit breakdown by greek.
Delta
The position began long 0.20 deltas. The 0.30-point rise earned Bobby a 0.06 point gain in delta per contract.
Gamma
Bobby had an initial gamma of +1.8. We will use 1.8 for estimating the P&(L) in this example, assuming gamma remained constant. A 0.30 rise in the stock price multiplied by the 1.8 gamma means that with the stock at $50, Bobby was long an additional 0.54 deltas. We can estimate that over the course of the 0.30 rise in the stock price, Bobby was long an average of 0.27 (0.54 ÷ 2). His P&(L) due to gamma, therefore, is a gain of about 0.08 (0.27 × 0.30).
Theta
Bobby held this trade for three days. His total theta cost him 1.92 or $192.
Vega
The biggest contribution to Bobby’s profit on this trade was made by the spike in IV. He bought 30 volatility and sold 35 volatility. His 1.20 position vega earned him 6.00, or $600.
Conclusions
The $422 profit is not exact, but the greeks provide a good estimate of the hows and the whys behind it. Whether they are used for forecasting profits or for doing a postmortem evaluation of a trade, consulting the greeks offers information unavailable by just looking at the transaction prices.
By thinking about all these individual pricing components, a trader can make better decisions. For example, about two weeks earlier, Bobby could have bought an IV level closer to 26 percent. Being conscious of his theta, however, he decided to wait. The $64-a-day theta would have cost him $896 over 14 days. That’s much more that the $480 he could have made by buying volatility four points lower with his 1.20 vega.
Risks of the Trade
Like Susie’s trade, Bobby’s play was not without risk. Certainly theta was a concern, but in addition to that was the possibility that IV might not have played out as he planned. First, IV might not have risen enough to cover three days’ worth of theta. It needed to rise, in this case, about 1.6 volatility points for the 1.20 vega to cover the 1.92 theta loss. It might even have dropped. An earlier-than-expected announcement that


CHAPTER 13
Delta-Neutral Trading
Trading Realized Volatility
So far, we’ve discussed many option strategies in which realized volatility is an important component of the trade. And while the management of these positions has been the focus of much of the discussion, the ultimate gain or loss for many of these strategies has been from movement in a single direction. For example, with a long call, the higher the stock rallies the better.
But increases or decreases in realized volatility do not necessarily have an exclusive relationship with direction. Recall that realized volatility is the annualized standard deviation of daily price movements. Take two similarly priced stocks that have had a net price change of zero over a one-month period. Stock A had small daily price changes during that period, rising $0.10 one day and falling $0.10 the next. Stock B went up or down by $5 each day for a month. In this rather extreme example, Stock B was much more volatile than Stock A, regardless of the fact that the net price change for the period for both stocks was zero.
A stock’s volatility—either high or low volatility—can be capitalized on by trading options delta neutral. Simply put, traders buy options delta neutral when they believe a stock will have more movement and sell options delta neutral when they believe a stock will move less.
Delta-neutral option sellers profit from low volatility through theta. Every day that passes in which the loss from delta/gamma movement is less than the gain from theta is a winning day. Traders can adjust their deltas by hedging. Delta-neutral option buyers exploit volatility opportunities through a trading technique called gamma scalping.
Gamma Scalping
Intraday trading is seldom entirely in one direction. A stock may close higher or lower, even sharply higher or lower, on the day, but during the day there is usually not a steady incremental rise or fall in the stock price. A typical intraday stock chart has peaks and troughs all day long. Delta-neutral traders who have gamma don’t remain delta neutral as the underlying price changes, which inevitably it will. Delta-neutral trading is kind of a misnomer.
In fact, it is gamma trading in which delta-neutral traders engage. For long-gamma traders, the position delta gets more positive as the underlying moves higher and more negative as the underlying moves lower. An upward move in the underlying increases positive deltas, resulting in exponentially increasing profits. But if the underlying price begins to retrace downward, the gain from deltas can be erased as quickly as it was racked up.
To lock in delta gains, a trader can adjust the position to delta neutral again by selling short stock to cover long deltas. If the stock price declines after this adjustment, losses are curtailed thanks to the short stock. In fact, the delta will become negative as the underlying price falls, leading to growing profits. To lock in profits again, the trader buys stock to cover short deltas to once again become delta neutral.
The net effect is a stock scalp. Positive gamma causes the delta-neutral trader to sell stock when the price rises and buy when the stock falls. This adds up to a true, realized profit. So positive gamma is a money-making machine, right? Not so fast. As in any business, the profits must be great enough to cover expenses. Theta is the daily cost of running this gamma-scalping business.
For example, a trader, Harry, notices that the intraday price swings in a particular stock have been increasing. He takes a bullish position in realized volatility by buying 20 off the 40-strike calls, which have a 50 delta, and selling stock on a delta-neutral ratio.
Buy 20 40-strike calls (50 delta) (long 1,000 deltas)
Short 1,000 shares at $40 (short 1,000 deltas)
The immediate delta of this trade is flat, but as the stock moves up or down, that will change, presenting gamma-scalping opportunities. Gamma scalping is the objective here. The position greeks in
Exhibit 13.1
show the relationship of the two forces involved in this trade: gamma and theta.
EXHIBIT 13.1
Greeks for 20-lot delta-neutral long call.
The relationship of gamma to theta in this sort of trade is paramount to its success. Gamma-scalping plays are not buy-and-hold strategies. This is active trading. These spreads need to be monitored intraday to take advantage of small moves in the underlying security. Harry will sell stock when the underlying rises and buy it when the underlying falls, taking a profit with each stock trade. The goal for each day that passes is to profit enough from positive gamma to cover the day’s theta. But that’s not always as easy as it sounds. Let’s study what happens the first seven days after this hypothetical trade is executed. For the purposes of this example, we assume that gamma remains constant and that the trader is content trading odd lots of stock.
Day One
The first day proves to be fairly volatile. The stock rallies from $40 to $42 early in th

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happens the first seven days after this hypothetical trade is executed. For the purposes of this example, we assume that gamma remains constant and that the trader is content trading odd lots of stock.
Day One
The first day proves to be fairly volatile. The stock rallies from $40 to $42 early in the day. This creates a positive position delta of 5.60, or the equivalent of being long about 560 shares. At $42, Harry covers the position delta by selling 560 shares of the underlying stock to become delta neutral again.
Later in the day, the market reverses, and the stock drops back down to $40 a share. At this point, the position is short 5.60 deltas. Harry again adjusts the position, buying 560 shares to get flat. The stock then closes right at $40.
The net result of these two stock transactions is a gain of $1,070. How? The gamma scalp minus the theta, as shown below.
The volatility of day one led to it being a profitable day. Harry scalped 560 shares for a $2 profit, resulting from volatility in the stock. If the stock hadn’t moved as much, the delta would have been smaller, and the dollar amount scalped would have been smaller, leading to an exponentially smaller profit. If there had been more volatility, profits would have been exponentially larger. It would have led to a bigger bite being taken out of the market.
Day Two
The next day, the market is a bit quieter. There is a $0.40 drop in the price of the stock, at which point the position delta is short 1.12. Harry buys 112 shares at $39.60 to get delta neutral.
Following Harry’s purchase, the stock slowly drifts back up and is trading at $40 near the close. Harry decides to cover his deltas and sell 112 shares at $40. It is common to cover all deltas at the end of the day to get back to being delta neutral. Remember, the goal of gamma scalping is to trade volatility, not direction. Starting the next trading day with a delta, either positive or negative, means an often unwanted directional bias and unwanted directional risk. Tidying up deltas at the end of the day to get neutral is called going home flat.
Today was not a banner day. Harry did not quite have the opportunity to cover the decay.
Day Three
On this day, the market trends. First, the stock rises $0.50, at which point Harry sells 140 shares of stock at $40.50 to lock in gains from his delta and to get flat. However, the market continues to rally. At $41 a share, Harry is long another 1.40 deltas and so sells another 140 shares. The rally continues, and at $41.50 he sells another 140 shares to cover the delta. Finally, at the end of the day, the stock closes at $42 a share. Harry sells a final 140 shares to get flat.
There was not any literal scalping of stock today. It was all selling. Nonetheless, gamma trading led to a profitable day.
As the stock rose from $40 to $40.50, 140 deltas were created from positive gamma. Because the delta was zero at $40 and 140 at $40.50, the estimated average delta is found by dividing 140 in half. This estimated average delta multiplied by the $0.50 gain on the stock equals a $35 profit. The delta was zero after the adjustment made at $40.50, when 140 shares were sold. When the stock reached $41, another $35 was reaped from the average delta of 70 over the $0.50 move. This process was repeated every time the stock rose $0.50 and the delta was covered.
Day Four
Day four offers a pleasant surprise for Harry. That morning, the stock opens $4 lower. He promptly covers his short delta of 11.2 by buying 1,120 shares of the stock at $38 a share. The stock barely moves the rest of the day and closes at $38.
An exponentially larger profit was made because there was $4 worth of gains on the growing delta when the stock gapped open. The whole position delta was covered $4 lower, so both the delta and the dollar amount gained on that delta had a chance to grow. Again, Harry can estimate the average delta over the $4 move to be half of 11.20. Multiplying that by the $4 stock advance gives him his gamma profit of $2,240. After accounting for theta, the net profit is $2,190.
Days Five and Six
Days five and six are the weekend; the market is closed.
Day Seven
This is a quiet day after the volatility of the past week. Today, the stock slowly drifts up $0.25 by the end of the day. Harry sells 70 shares of stock at $38.25 to cover long deltas.
This day was a loser for Harry, as profits from gamma were not enough to cover his theta.
Art and Science
Although this was a very simplified example, it was typical of how a profitable week of gamma scalping plays out. This stock had a pretty volatile week, and overall the week was a winner: there were four losing days and three winners. The number of losing days includes the weekends. Weekends and holidays are big hurdles for long-gamma traders because of the theta loss. The biggest contribution to this being a winning week was made by the gap open on day four. Part of the reason was the sheer magnitude of the move, and part was the fact


ber of losing days includes the weekends. Weekends and holidays are big hurdles for long-gamma traders because of the theta loss. The biggest contribution to this being a winning week was made by the gap open on day four. Part of the reason was the sheer magnitude of the move, and part was the fact that the deltas weren’t covered too soon, as they had been on day three.
In a perfect world, a long-gamma trader will always buy the low of the day and sell the high of the day when covering deltas. This, unfortunately, seldom happens. Long-gamma traders are very often wrong when trading stock to cover deltas.
Being wrong can be okay on occasion. In fact, it can even be rewarding. Day three was profitable despite the fact that 140 shares were sold at $40.50, $41, and $41.50. The stock closed at $42; the first three stock trades were losers. Harry sold stock at a lower price than the close. But the position still made money because of his positive gamma. To be sure, Harry would like to have sold all 560 shares at $42 at the end of the day. The day’s profits would have been significantly higher.
The problem is that no one knows where the stock will move next. On day three, if the stock had topped out at $40.50 and Harry did not sell stock because he thought it would continue higher, he would have missed an opportunity. Gamma scalping is not an exact science. The art is to pick spots that capture the biggest moves possible without missing opportunities.
There are many methods traders have used to decide where to cover deltas when gamma scalping: the daily standard deviation, a fixed percentage of the stock price, a fixed nominal value, covering at a certain time of day, “market feel.” No system appears to be absolutely better than another. This is where it gets personal. Finding what works for you, and what works for the individual stocks you trade, is the art of this science.
Gamma, Theta, and Volatility
Clearly, more volatile stocks are more profitable for gamma scalping, right? Well . . . maybe. Recall that the higher the implied volatility, the lower the gamma and the higher the theta of at-the-money (ATM) options. In many cases, the more volatile a stock, the higher the implied volatility (IV). That means that a volatile stock might have to move more for a trader to scalp enough stock to cover the higher theta.
Let’s look at the gamma-theta relationship from another perspective. In this example, for 0.50 of theta, Harry could buy 2.80 gamma. This relationship is based on an assumed 25 percent implied volatility. If IV were 50 percent, theta for this 20 lot would be higher, and the gamma would be lower. At a volatility of 50, Harry could buy 1.40 gammas for 0.90 of theta. The gamma is more expensive from a theta perspective, but if the stock’s statistical volatility is significantly higher, it may be worth it.
Gamma Hedging
Knowing that the gamma and theta figures of
Exhibit 13.1
are derived from a 25 percent volatility assumption offers a benchmark with which to gauge the potential profitability of gamma trading the options. If the stock’s standard deviation is below 25 percent, it will be difficult to make money being long gamma. If it is above 25 percent, the play becomes easier to trade. There is more scalping opportunity, there are more opportunities for big moves, and there are more likely to be gaps in either direction. The 25 percent volatility input not only determines the option’s theoretical value but also helps determine the ratio of gamma to theta.
A 25 percent or higher realized volatility in this case does not guarantee the trade’s success or failure, however. Much of the success of the trade has to do with how well the trader scalps stock. Covering deltas too soon leads to reduced profitability. Covering too late can lead to missed opportunities.
Trading stock well is also important to gamma sellers with the opposite trade: sell calls and buy stock delta neutral. In this example, a trader will sell 20 ATM calls and buy stock on a delta-neutral ratio.
This is a bearish position in realized volatility. It is the opposite of the trade in the last example. Consider again that 25 percent IV is the benchmark by which to gauge potential profitability. Here, if the stock’s volatility is below 25, the chances of having a profitable trade are increased. Above 25 is a bit more challenging.
In this simplified example, a different trader, Mary, plays the role of gamma seller. Over the same seven-day period as before, instead of buying calls, Mary sold a 20 lot.
Exhibit 13.2
shows the analytics for the trade. For the purposes of this example, we assume that gamma remains constant and the trader is content trading odd lots of stock.
EXHIBIT 13.2
Greeks for 20-lot delta-neutral short call.
Day One
This was one of the volatile days. The stock rallied from $40 to $42 early in the day and had fallen back down to $40 by the end of the day. Big moves like this are hard to trade as a short-gamma trader. As the stock r


d lots of stock.
EXHIBIT 13.2
Greeks for 20-lot delta-neutral short call.
Day One
This was one of the volatile days. The stock rallied from $40 to $42 early in the day and had fallen back down to $40 by the end of the day. Big moves like this are hard to trade as a short-gamma trader. As the stock rose to $42, the negative delta would have been increasing. That means losses were adding up at an increasing rate. The only way to have stopped the hemorrhaging of money as the stock continued to rise would have been to buy stock. Of course, if Mary buys stock and the stock then declines, she has a loser.
Let’s assume the best-case scenario. When the stock reached $42 and she had a −560 delta, Mary correctly felt the market was overbought and would retrace. Sometimes, the best trades are the ones you don’t make. On this day, Mary traded no stock. When the stock reached $40 a share at the end of the day, she was back to being delta neutral. Theta makes her a winner today.
Because of the way Mary handled her trade, the volatility of day one was not necessarily an impediment to it being profitable. Again, the assumption is that Mary made the right call not to negative scalp the stock. Mary could have decided to hedge her negative gamma when the stock reach $42 and the position delta was at −$560 by buying stock and then selling it at $40.
There are a number of techniques for hedging deltas resulting from negative gamma. The objective of hedging deltas is to avoid losses from the stock trending in one direction and creating increasingly adverse deltas but not to overtrade stock and negative scalp.
Day Two
Recall that this day had a small dip and then recovered to close again at $40. It is more reasonable to assume that on this day there was no negative scalping. A $0.40 decline is a more typical move in a stock and nothing to be afraid of. The 112 delta created by negative gamma when the stock fell wouldn’t be perceived as a major concern by most traders in most situations. It is reasonable to assume Mary would take no action. Today, again, was a winner thanks to theta.
Day Three
Day three saw the stock price trending. It slowly drifted up $2. There would have been some judgment calls throughout this day. Again, delta-neutral trades are for active traders. Prepare to watch the market much of the day if implementing this kind of strategy.
When the stock was at $41 a share, Mary decided to guard against further advances in stock price and hedged her delta. At that point, the position would have had a −2.80 delta. She bought 280 shares at $41.
As the day progressed, the market proved Mary to be right. The stock rose to $42 giving the position a delta of −2.80 again. She covered her deltas at the end of the day by buying another 280 shares.
Covering the negative deltas to get flat at $41 proved to be a smart move today. It curtailed an exponentially growing delta and let Mary take a smaller loss at $41 and get a fresh start. While the day was a loser, it would have been $280 worse if she had not purchased stock at $41 before the run-up to $42. This is evidenced by the fact that she made a $280 profit on the 280 shares of stock bought at $41, since the stock closed at $42.
Day Four
Day four offered a rather unpleasant surprise. This was the day that the stock gapped open $4 lower. This is the kind of day short-gamma traders dread. There is, of course, no right way to react to this situation. The stock can recover, heading higher; it can continue lower; or it can have a dead-cat bounce, remaining where it is after the fall.
Staring at a quite contrary delta of 11.20, Mary was forced to take action by selling stock. But how much stock was the responsible amount to sell for a pure short-gamma trader not interested in trading direction? Selling 1,120 shares would bring the position back to being delta neutral, but the only way the trade would stay delta neutral would be if the stock stayed right where it was.
Hedging is always a difficult call for short-gamma traders. Long-gamma traders are taking a profit on deltas with every stock trade that covers their deltas. Short-gamma traders are always taking a loss on delta. In this case, Mary decided to cover half her deltas by selling 560 shares. The other 560 deltas represent a loss, too; it’s just not locked in.
Here, Mary made the conscious decision not to go home flat. On the one hand, she was accepting the risk of the stock continuing its decline. On the other hand, if she had covered the whole delta, she would have been accepting the risk of the stock moving in either direction. Mary felt the stock would regain some of its losses. She decided to lead the stock a little, going into the weekend with a positive delta bias.
Days Five and Six
Days five and six are the weekend.
Day Seven
This was the quiet day of the week, and a welcome respite. On this day, the stock rose just $0.25. The rise in price helped a bit. Mary was still long 560 deltas from Friday. Negative gamma took o


the weekend with a positive delta bias.
Days Five and Six
Days five and six are the weekend.
Day Seven
This was the quiet day of the week, and a welcome respite. On this day, the stock rose just $0.25. The rise in price helped a bit. Mary was still long 560 deltas from Friday. Negative gamma took only a small bite out of her profit.
The P&(L) can be broken down into the profit attributable to the starting delta of the trade, the estimated loss from gamma, and the gain from theta.
Mary ends these seven days of trading worse off than she started. What went wrong? The bottom line is that she sold volatility on an asset that proved to be volatile. A $4 drop in price of a $42 dollar stock was a big move. This stock certainly moved at more than 25 percent volatility. Day four alone made this trade a losing proposition.
Could Mary have done anything better? Yes. In a perfect world, she would not have covered her negative deltas on day 3 by buying 280 shares at $41 and another 280 at $42. Had she not, this wouldn’t have been such a bad week. With the stock ending at $38.25, she lost $1,050 on the 280 shares she bought at $42 ($3.75 times 280) and lost $770 on the 280 shares bought at $41 ($2.75 times 280). Then again, if the stock had continued higher, rising beyond $42, those would have been good buys.
Mary can’t beat herself up too much for protecting herself in a way that made sense at the time. The stock’s $2 rally is more to blame than the fact that she hedged her deltas. That’s the risk of selling volatility: the stock may prove to be volatile. If the stock had not made such a move, she wouldn’t have faced the dilemma of whether or not to hedge.
Conclusions
The same stock during the same week was used in both examples. These two traders started out with equal and opposite positions. They might as well have made the trade with each other. And although in this case the vol buyer (Harry) had a pretty good week and the vol seller (Mary) had a not-so-good week, it’s important to notice that the dollar value of the vol buyer’s profit was not the same as the dollar value of the vol seller’s loss. Why? Because each trader hedged his or her position differently. Option trading is not a zero-sum game.
Option-selling delta-neutral strategies work well in low-volatility environments. Small moves are acceptable. It’s the big moves that can blow you out of the water.
Like long-gamma traders, short-gamma traders have many techniques for covering deltas when the stock moves. It is common to cover partial deltas, as Mary did on day four of the last example. Conversely, if a stock is expected to continue along its trajectory up or down, traders will sometimes overhedge by buying more deltas (stock) than they are short or selling more than they are long, in anticipation of continued price rises. Daily standard deviation derived from implied volatility is a common measure used by short-gamma players to calculate price points at which to enter hedges. Market feel and other indicators are also used by experienced traders when deciding when and how to hedge. Each trader must find what works best for him or her.
Smileys and Frowns
The trade examples in this chapter have all involved just two components: calls and stock. We will explore delta-neutral strategies in other chapters that involve more moving parts. Regardless of the specific makeup of the position, the P&(L) of each individual leg is not of concern. It is the profitability of the position as a whole that matters. For example, after a volatile move in a stock occurs, a positive-gamma trader like Harry doesn’t care whether the calls or the stock made the profit on the move. The trader would monitor the net delta that was produced—positive or negative—and cover accordingly. The process is the same for a negative-gamma trader. In either case, it is gamma and delta that need to be monitored closely.
Gamma can make or break a trade. P&(L) diagrams are helpful tools that offer a visual representation of the effect of gamma on a position. Many option-trading software applications offer P&(L) graphing applications to study the payoff of a position with the days to expiration as an adjustable variable to study the same trade over time.
P&(L) diagrams for these delta-neutral positions before the options’ expiration generally take one of two shapes: a smiley or a frown. The shape of the graph depends on whether the position gamma is positive or negative.
Exhibit 13.3
shows a typical positive-gamma trade.
EXHIBIT 13.3
P&(L) diagram for a positive-gamma delta-neutral position/l.
This diagram is representative of the P&L of a delta-neutral positive-gamma trade calculated using the prices at which the trade was executed. With this type of trade, it is intuitive that when the stock price rises or falls, profits increase because of favorably changing deltas. This is represented by the graph’s smiley-face shape. The corners of the graph rise higher as the underlying moves away from the cen


which the trade was executed. With this type of trade, it is intuitive that when the stock price rises or falls, profits increase because of favorably changing deltas. This is represented by the graph’s smiley-face shape. The corners of the graph rise higher as the underlying moves away from the center of the graph.
The graph is a two-dimensional snapshot showing that the higher or lower the underlying moves, the greater the profit. But there are other dimensions that are not shown here, such as time and IV.
Exhibit 13.4
shows the effects of time on a typical long-gamma trade.
EXHIBIT 13.4
The effect of time on P&(L).
As time passes, the reduction in profit is reflected by the center point of the graph dipping farther into negative territory. That is the effect of time decay. The long options will have lost value at that future date with the stock still at the same price (all other factors held constant). Still, a move in either direction can lead to a profitable position. Ultimately, at expiration, the payoff takes on a rigid kinked shape.
In the delta-neutral long call examples used in this chapter the position becomes net long stock if the calls are in-the-money at expiration or net short stock if they are out-of-the-money and only the short stock remains. Volatility, as well, would move the payoff line vertically. As IV increases, the options become worth more at each stock price, and as IV falls, they are worth less, assuming all other factors are held constant.
A delta-neutral short-gamma play would have a P&(L) diagram quite the opposite of the smiley-faced long-gamma graph.
Exhibit 13.5
shows what is called the short-gamma frown.
EXHIBIT 13.5
Short-gamma frown.
At first glance, this doesn’t look like a very good proposition. The highest point on the graph coincides with a profit of zero, and it only gets worse as the price of the underlying rises or falls. This is enough to make any trader frown. But again, this snapshot does not show time or volatility.
Exhibit 13.6
shows the payout diagram as time passes.
EXHIBIT 13.6
The effect of time on the short-gamma frown.
A decrease in value of the options from time decay causes an increase in profitability. This profit potential pinnacles at the center (strike) price at expiration. Rising IV will cause a decline in profitability at each stock price point. Declining IV will raise the payout on the Y axis as profitability increases at each price point.
Smileys and frowns are a mere graphical representation of the technique discussed in this chapter: buying and selling realized volatility. These P&(L) diagrams are limited, because they show the payout only of stock-price movement. The profitability of direction-indifferent and direction-neutral trading is also influenced by time and implied volatility. These actively traded strategies are best evaluated on a gamma-theta basis. Long-gamma traders strive each day to scalp enough to cover the day’s theta, while short-gamma traders hope to keep the loss due to adverse movement in the underlying lower than the daily profit from theta.
The strategies in this chapter are the same ones traded in Chapter 12. The only difference is the philosophy. Ultimately, both types of volatility are being traded using these and other option strategies. Implied and realized volatility go hand in hand.


CHAPTER 14
Studying Volatility Charts
Implied and realized volatility are both important to option traders. But equally important is to understand how the two interact. This relationship is best studied by means of a volatility chart. Volatility charts are invaluable tools for volatility traders (and all option traders for that matter) in many ways.
First, volatility charts show where implied volatility (IV) is now compared with where it’s been in the past. This helps a trader gauge whether IV is relatively high or relatively low. Vol charts do the same for realized volatility. The realized volatility line on the chart answers three questions:
Have the past 30 days been more or less volatile for the stock than usual?
What is a typical range for the stock’s volatility?
How much volatility did the underlying historically experience in the past around specific recurring events?
When IV lines and realized volatility lines are plotted on the same chart, the divergences and convergences of the two spell out the whole volatility story for those who know how to read it.
Nine Volatility Chart Patterns
Each individual stock and the options listed on it have their own unique realized and implied volatility characteristics. If we studied the vol charts of 1,000 stocks, we’d likely see around 1,000 different volatility patterns. The number of permutations of the relationship of realized to implied volatility is nearly infinite, but for the sake of discussion, we will categorize volatility charts into nine general patterns.
1
1. Realized Volatility Rises, Implied Volatility Rises
The first volatility chart pattern is that in which both IV and realized volatility rise. In general, this kind of volatility chart can line up three ways: implied can rise more than realized volatility; realized can rise more than implied; or they can both rise by about the same amount. The chart below shows implied volatility rising at a faster rate than realized vol. The general theme in this case is that the stock’s price movement has been getting more volatile, and the option prices imply even higher volatility in the future.
This specific type of volatility chart pattern is commonly seen in active stocks with a lot of news. Stocks du jour, like some Internet stocks during the tech bubble of the late 1990s, story stocks like Apple (AAPL) around the release of the iPhone in 2007, have rising volatilities, with the IV outpacing the realized volatility. Sometimes individual stocks and even broad market indexes and exchange-traded funds (ETFs) see this pattern, when the market is declining rapidly, like in the summer of 2011.
A delta-neutral long-volatility position bought at the beginning of May, according to
Exhibit 14.1
, would likely have produced a winner. IV took off, and there were sure to be plenty of opportunities to profit from gamma with realized volatility gaining strength through June and July.
EXHIBIT 14.1
Realized volatility rises, implied volatility rises.
Source
: Chart courtesy of
iVolatility.com
Looking at the right side of the chart, in late July, with IV at around 50 percent and realized vol at around 35 percent, and without the benefit of knowing what the future will bring, it’s harder to make a call on how to trade the volatility. The IV signals that the market is pricing a higher future level of stock volatility into the options. If the market is right, gamma will be good to have. But is the price right? If realized volatility does indeed catch up to implied volatility—that is, if the lines converge at 50 or realized volatility rises above IV—a trader will have a good shot at covering theta. If it doesn’t, gamma will be very expensive in terms of theta, meaning it will be hard to cover the daily theta by scalping gamma intraday.
The question is: why is IV so much higher than realized? If important news is expected to be released in the near future, it may be perfectly reasonable for the IV to be higher, even significantly higher, than the stock’s realized volatility. One big move in the stock can produce a nice profit, as long as theta doesn’t have time to work its mischief. But if there is no news in the pipeline, there may be some irrational exuberance—in the words of ex-Fed chairman Alan Greenspan—of option buyers rushing to acquire gamma that is overvalued in terms of theta.
In fact, a lack of expectation of news could indicate a potential bearish volatility play: sell volatility with the intent of profiting from daily theta and a decline in IV. This type of play, however, is not for the fainthearted. No one can predict the future. But one thing you can be sure of with this trade: you’re in for a wild ride. The lines on this chart scream volatility. This means that negative-gamma traders had better be good and had better be right!
In this situation, hedgers and speculators in the market are buying option volatility of 50 percent, while the stock is moving at 35 percent volatility. Traders putting on a delta-neutral v

eBooks\Trading Options Greeks\Trading Options Greeks_ How Time, Volatility, and Other Pricing Factors Drive Profits (Bloomberg Financial).epub#section:text00025.html


is chart scream volatility. This means that negative-gamma traders had better be good and had better be right!
In this situation, hedgers and speculators in the market are buying option volatility of 50 percent, while the stock is moving at 35 percent volatility. Traders putting on a delta-neutral volatility-selling strategy are taking the stance that this stock will not continue increasing in volatility as indicated by option prices; specifically, it will move at less than 50 percent volatility—hopefully a lot less. They are taking the stance that the market’s expectations are wrong.
Instead of realized and implied volatility both trending higher, sometimes there is a sharp jump in one or the other. When this happens, it could be an indication of a specific event that has occurred (realized volatility) or news suddenly released of an expected event yet to come (implied volatility). A sharp temporary increase in IV is called a spike, because of its pointy shape on the chart. A one-day surge in realized volatility, on the other hand, is not so much a volatility spike as it is a realized volatility mesa. Realized volatility mesas are shown in
Exhibit 14.2
.
EXHIBIT 14.2
Volatility mesas.
Source
: Chart courtesy of
iVolatility.com
The patterns formed by the gray line in the circled areas of the chart shown below are the result of typical one-day surges in realized volatility. Here, the 30-day realized volatility rose by nearly 20 percentage points, from about 20 percent to about 40 percent, in one day. It remained around the 40 percent level for 30 days and then declined 20 points just as fast as it rose.
Was this entire 30-day period unusually volatile? Not necessarily. Realized volatility is calculated by looking at price movements within a certain time frame, in this case, thirty business days. That means that a really big move on one day will remain in the calculation for the entire time. Thirty days after the unusually big move, the calculation for realized volatility will no longer contain that one-day price jump. Realized volatility can then drop significantly.
2. Realized Volatility Rises, Implied Volatility Remains Constant
This chart pattern can develop from a few different market conditions. One scenario is a one-time unanticipated move in the underlying that is not expected to affect future volatility. Once the news is priced into the stock, there is no point in hedgers’ buying options for protection or speculators’ buying options for a leveraged bet. What has happened has happened.
There are other conditions that can cause this type of pattern to materialize. In
Exhibit 14.3
, the IV was trading around 25 for several months, while the realized volatility was lagging. With hindsight, it makes perfect sense that something had to give—either IV needed to fall to meet realized, or realized would rise to meet market expectations. Here, indeed, the latter materialized as realized volatility had a steady rise to and through the 25 level in May. Implied, however remained constant.
EXHIBIT 14.3
Realized volatility rises, implied volatility remains constant.
Source
: Chart courtesy of
iVolatility.com
Traders who were long volatility going into the May realized-vol rise probably reaped some gamma benefits. But those who got in “too early,” buying in January or February, would have suffered too great of theta losses before gaining any significant profits from gamma. Time decay (theta) can inflict a slow, painful death on an option buyer. By studying this chart in hindsight, it is clear that options were priced too high for a gamma scalper to have a fighting chance of covering the daily theta before the rise in May.
This wasn’t necessarily an easy vol-selling trade before the May realized-vol rise, either, depending on the trader’s timing. In early February, realized did in fact rise above implied, making the short volatility trade much less attractive.
Traders who sold volatility just before the increase in realized volatility in May likely ended up losing on gamma and not enough theta profits to make up for it. There was no volatility crush like what is often seen following a one-day move leading to sharply higher realized volatility. IV simply remained pretty steady throughout the month of May and well into June.
3. Realized Volatility Rises, Implied Volatility Falls
This chart pattern can manifest itself in different ways. In this scenario, the stock is becoming more volatile, and options are becoming cheaper. This may seem an unusual occurrence, but as we can see in
Exhibit 14.4
, volatility sometimes plays out this way. This chart shows two different examples of realized vol rising while IV falls.
EXHIBIT 14.4
Realized volatility rises, implied volatility falls.
Source
: Chart courtesy of
iVolatility.com
The first example, toward the left-hand side of the chart, shows realized volatility trending higher while IV is trending lower. Although fundamentals can often provide logical reasons for these volatili


Realized volatility rises, implied volatility falls.
Source
: Chart courtesy of
iVolatility.com
The first example, toward the left-hand side of the chart, shows realized volatility trending higher while IV is trending lower. Although fundamentals can often provide logical reasons for these volatility changes, sometimes they just can’t. Both implied and realized volatility are ultimately a function of the market. There is a normal oscillation to both of these figures. When there is no reason to be found for a volatility change, it might be an opportunity. The potential inefficiency of volatility pricing in the options market sometimes creates divergences such as this one that vol traders scour the market in search of.
In this first example, after at least three months of IV’s trading marginally higher than realized volatility, the two lines converge and then cross. The point at which these lines meet is an indication that IV may be beginning to get cheap.
First, it’s a potentially beneficial opportunity to buy a lower volatility than that at which the stock is actually moving. The gamma/theta ratio would be favorable to gamma scalpers in this case, because the lower cost of options compared with stock fluctuations could lead to gamma profits. Second, with IV at 35 at the first crossover on this chart, IV is dipping down into the lower part of its four-month range. One can make the case that it is getting cheaper from a historical IV standpoint. There is arguably an edge from the perspective of IV to realized volatility and IV to historical IV. This is an example of buying value in the context of volatility.
Furthermore, if the actual stock volatility is rising, it’s reasonable to believe that IV may rise, too. In hindsight we see that this did indeed occur in
Exhibit 14.4
, despite the fact that realized volatility declined.
The example circled on the right-hand side of the chart shows IV declining sharply while realized volatility rises sharply. This is an example of the typical volatility crush as a result of an earnings report. This would probably have been a good trade for long volatility traders—even those buying at the top. A trader buying options delta neutral the day before earnings are announced in this example would likely lose about 10 points of vega but would have a good chance to more than make up for that loss on positive gamma. Realized volatility nearly doubled, from around 28 percent to about 53 percent, in a single day.
4. Realized Volatility Remains Constant, Implied Volatility Rises
Exhibit 14.5
shows that the stock is moving at about the same volatility from the beginning of June to the end of July. But during that time, option premiums are rising to higher levels. This is an atypical chart pattern. If this was a period leading up to an anticipated event, like earnings, one would anticipate realized volatility falling as the market entered a wait-and-see mode. But, instead, statistical volatility stays the same. This chart pattern may indicate a potential volatility-selling opportunity. If there is no news or reason for IV to have risen, it may simply be high tide in the normal ebb and flow of volatility.
EXHIBIT 14.5
Realized volatility remains constant, implied volatility rises.
Source
: Chart courtesy of
iVolatility.com
In this example, the historical volatility oscillates between 20 and 24 for nearly two months (the beginning of June through the end of July) as IV rises from 24 to over 30. The stock price is less volatile than option prices indicate. If there is no news to be dug up on the stock to lead one to believe there is a valid reason for the IV’s trading at such a level, this could be an opportunity to sell IV 5 to 10 points higher than the stock volatility. The goal here is to profit from theta or falling vega or both while not losing much on negative gamma. As time passes, if the stock continues to move at 20 to 23 vol, one would expect IV to fall and converge with realized volatility.
5. Realized Volatility Remains Constant, Implied Volatility Remains Constant
This volatility chart pattern shown in
Exhibit 14.6
is typical of a boring, run-of-the-mill stock with nothing happening in the news. But in this case, no news might be good news.
EXHIBIT 14.6
Realized volatility remains constant, implied volatility remains constant.
Source
: Chart courtesy of
iVolatility.com
Again, the gray is realized volatility and the black line is IV.
It’s common for IV to trade slightly above or below realized volatility for extended periods of time in certain assets. In this example, the IV has traded in the high teens from late January to late July. During that same time, realized volatility has been in the low teens.
This is a prime environment for option sellers. From a gamma/theta standpoint, the odds favor short-volatility traders. The gamma/theta ratio provides an edge, setting the stage for theta profits to outweigh negative-gamma scalping. Selling calls and buying stock delta neutral


een in the low teens.
This is a prime environment for option sellers. From a gamma/theta standpoint, the odds favor short-volatility traders. The gamma/theta ratio provides an edge, setting the stage for theta profits to outweigh negative-gamma scalping. Selling calls and buying stock delta neutral would be a trade to look at in this situation. But even more basic strategies, such as time spreads and iron condors, are appropriate to consider.
This vol-chart pattern, however, is no guarantee of success. When the stock oscillates, delta-neutral traders can negative scalp stock if they are not careful by buying high to cover short deltas and then selling low to cover long deltas. Time-spread and iron condor trades can fail if volatility increases and the increase results from the stock trending in one direction. The advantage of buying IV lower than realized, or selling it above, is statistical in nature. Traders should use a chart of the stock price in conjunction with the volatility chart to get a more complete picture of the stock’s price action. This also helps traders make more informed decisions about when to hedge.
6. Realized Volatility Remains Constant, Implied Volatility Falls
Exhibit 14.7
shows two classic implied-realized convergences. From mid-September to early November, realized volatility stayed between 22 and 25. In mid-October the implied was around 33. Within the span of a few days, the implied vol collapsed to converge with the realized at about 22.
EXHIBIT 14.7
Realized volatility remains constant, implied volatility falls.
Source
: Chart courtesy of
iVolatility.com
There can be many catalysts for such a drop in IV, but there is truly only one reason: arbitrage. Although it is common for a small difference between implied and realized volatility—1 to 3 points—to exist even for extended periods, bigger disparities, like the 7- to 10-point difference here cannot exist for that long without good reason.
If, for example, IV always trades significantly above the realized volatility of a particular underlying, all rational market participants will sell options because they have a gamma/theta edge. This, in turn, forces options prices lower until volatility prices come into line and the arbitrage opportunity no longer exists.
In
Exhibit 14.7
, from mid-March to mid-May a similar convergence took place but over a longer period of time. These situations are often the result of a slow capitulation of market makers who are long volatility. The traders give up on the idea that they will be able to scalp enough gamma to cover theta and consequently lower their offers to advertise their lower prices.
7. Realized Volatility Falls, Implied Volatility Rises
This setup shown in
Exhibit 14.8
should now be etched into the souls of anyone who has been reading up to this point. It is, of course, the picture of the classic IV rush that is often seen in stocks around earnings time. The more uncertain the earnings, the more pronounced this divergence can be.
EXHIBIT 14.8
Realized volatility falls, implied volatility rises.
Source
: Chart courtesy of
iVolatility.com
Another classic vol divergence in which IV rises and realized vol falls occurs in a drug or biotech company when a Food and Drug Administration (FDA) decision on one of the company’s new drugs is imminent. This is especially true of smaller firms without big portfolios of drugs. These divergences can produce a huge implied–realized disparity of, in some cases, literally hundreds of volatility points leading up to the announcement.
Although rising IV accompanied by falling realized volatility can be one of the most predictable patterns in trading, it is ironically one of the most difficult to trade. When the anticipated news breaks, the stock can and often will make a big directional move, and in that case, IV can and likely will get crushed. Vega and gamma work against each other in these situations, as IV and realized volatility converge. Vol traders will likely gain on one vol and lose on the other, but it’s very difficult to predict which will have a more profound effect. Many traders simply avoid trading earnings events altogether in favor of less erratic opportunities. For most traders, there are easier ways to make money.
8. Realized Volatility Falls, Implied Volatility Remains Constant
This volatility shift can be marked by a volatility convergence, divergence, or crossover.
Exhibit 14.9
shows the realized volatility falling from around 30 percent to about 23 percent while IV hovers around 25. The crossover here occurs around the middle of February.
EXHIBIT 14.9
Realized volatility falls, implied volatility remains constant.
Source
: Chart courtesy of
iVolatility.com
The relative size of this volatility change makes the interpretation of the chart difficult. The last half of September saw around a 15 percent decline in realized volatility. The middle of October saw a one-day jump in realized of about 15 points. Historical volatility has had sever


iVolatility.com
The relative size of this volatility change makes the interpretation of the chart difficult. The last half of September saw around a 15 percent decline in realized volatility. The middle of October saw a one-day jump in realized of about 15 points. Historical volatility has had several dynamic moves that were larger and more abrupt than the seven-point decline over this six-week period. This smaller move in realized volatility is not necessarily an indication of a volatility event. It could reflect some complacency in the market. It could indicate a slow period with less trading, or it could simply be a natural contraction in the ebb and flow of volatility causing the calculation of recent stock-price fluctuations to wane.
What is important in this interpretation is how the options market is reacting to the change in the volatility of the stock—where the rubber hits the road. The market’s apparent assessment of future volatility is unchanged during this period. When IV rises or falls, vol traders must look to the underlying stock for a reason. The options market reacts to stock volatility, not the other way around.
Finding fundamental or technical reasons for surges in volatility is easier than finding specific reasons for a decline in volatility. When volatility falls, it is usually the result of a lack of news, leading to less price action. In this example, probably nothing happened in the market. Consequently, the stock volatility drifted lower. But it fell below the lowest IV level seen for the six-month period leading up to the crossover. It was probably hard to take a confident stance in volatility immediately following the crossover. It is difficult to justify selling volatility when the implied is so cheap compared with its historic levels. And it can be hard to justify buying volatility when the options are priced above the stock volatility.
The two-week period before the realized line moved beneath the implied line deserves closer study. With the IV four or five points lower than the realized volatility in late January, traders may have been tempted to buy volatility. In hindsight, this trade might have been profitable, but there was surely no guarantee of this. Success would have been greatly contingent on how the traders managed their deltas, and how well they adapted as realized volatility fell.
During the first half of this period, the stock volatility remained above implied. For an experienced delta-neutral trader, scalping gamma was likely easy money. With the oscillations in stock price, the biggest gamma-scalping risk would have been to cover too soon and miss out on opportunities to take bigger profits.
Using the one-day standard deviation based on IV (described in Chapter 3) might have produced early covering for long-gamma traders. Why? Because in late January, the standard deviation derived from IV was lower than the actual standard deviation of the stock being traded. In the latter half of the period being studied, the end of February on this chart, using the one-day standard deviation based on IV would have produced scalping that was too late. This would have led to many missed opportunities.
Traders entering hedges at regular nominal intervals—every $0.50, for example—would probably have needed to decrease the interval as volatility ebbed. For instance, if in late January they were entering orders every $0.50, by late February they might have had to trade every $0.40.
9. Realized Volatility Falls, Implied Volatility Falls
This final volatility-chart permutation incorporates a fall of both realized and IV. The chart in
Exhibit 14.10
clearly represents the slow culmination of a highly volatile period. This setup often coincides with news of some scary event’s being resolved—a law suit settled, unpopular upper management leaving, rumors found to be false, a happy ending to political issues domestically or abroad, for example. After a sharp sell-off in IV, from 75 to 55, in late October, marking the end of a period of great uncertainty, the stock volatility began a steady decline, from the low 50s to below 25. IV fell as well, although it remained a bit higher for several months.
EXHIBIT 14.10
Realized volatility falls, implied volatility falls.
Source
: Chart courtesy of
iVolatility.com
In some situations where an extended period of extreme volatility appears to be coming to an end, there can be some predictability in how IV will react. To be sure, no one knows what the future holds, but when volatility starts to wane because a specific issue that was causing gyrations in the stock price is resolved, it is common, and intuitive, for IV to fall with the stock volatility. This is another type of example of reversion to the mean.
There is a potential problem if the high-volatility period lasted for an extended period of time. Sometimes, it’s hard to get a feel for what the mean volatility should be. Or sometimes, because of the event, the stock is fundamentally different—i


is another type of example of reversion to the mean.
There is a potential problem if the high-volatility period lasted for an extended period of time. Sometimes, it’s hard to get a feel for what the mean volatility should be. Or sometimes, because of the event, the stock is fundamentally different—in the case of a spin-off, merger, or other corporate action, for example. When it is difficult or impossible to look back at a stock’s performance over the previous 6 to 12 months and appraise what the normal volatility should be, one can look to the volatility of other stocks in the same industry for some guidance.
Stocks that are substitutable for one another typically trade at similar volatilities. From a realized volatility perspective, this is rather intuitive. When one stock within an industry rises or falls, others within the same industry tend to follow. They trade similarly and therefore experience similar volatility patterns. If the stock volatility among names within one industry tends to be similar, it follows that the IV should be, too.
Regardless which of the nine patterns discussed here show up, or how the volatilities line up, there is one overriding observation that’s representative of all volatility charts: vol charts are simply graphical representations of realized and implied volatility that help traders better understand the two volatilities’ interaction. But the divergences and convergences in the examples in this chapter have profound meaning to the volatility trader. Combined with a comparison of current and past volatility (both realized and implied), they give traders insight into how cheap or expensive options are.
Note
1
. The following examples use charts supplied by
iVolatility.com
. The gray line is the 30-day realized volatility, and the black line is the implied volatility.