ing, and we cover this reliableapproach in the next chapter. In fact, before we say anything further aboutstrategies, let’s talk about volatility . . .
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CHAPTER 3
Volatility
W
hen trading a security or a futures contract, you have one overriding concern: its price. However, options are more like a 3-Dchess game, with the three dimensions being price (of the underlying), time, and volatility. Of these, volatility is probably the most misunderstood and neglected dimension, and often the last thing a novice traderlearns about.An options trader needs to understand volatility and appreciate its effects to be successful. Option prices are highly sensitive to the perceivedvolatility of their underlying. The savvy options trader is aware of currentvolatility levels and adapts his trading accordingly, buying options whenthey are cheap, and ﬁnding ways to sell options when they are expensive.This gives him an advantage over traders who do not understand volatility. How much of an advantage? Sometimes an enormous one.For example, Figure 3.1 shows a six-year history of volatility for Eastman Kodak. The two lines represent two different measures of volatility.We’ll be discussing these soon, but for now, notice how high the dashedline is currently. It is at 48%—practically matching an all-time high for thesix-year period. This means options are more expensive now than theyhave been in the past.Just to give you an idea, the near-term, ATM (at-the-money) Kodakcall option is priced at 2.0 right now, compared with a more normal 1.25.You could say that option buyers are facing a stiff theoretical disadvantage here! So rather than buying options, you would prefer to use a strategy that involves selling these options.For instance, say you’re bullish on Kodak. Rather than buying calls,43
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VOLATILITY
FIGURE 3.1 Volatility History—Eastman Kodak
you might consider selling naked puts, or using a vertical credit spreadin puts. We’ll be discussing vertical spreads in the next chapter, butfor now, let’s just say that a vertical credit spread makes you a net seller.Or, if you’re conservatively bullish, you might consider a covered write.All of these approaches allow you to sell options as you construct a bullish position.Bottom line: Pay attention to what’s happening with volatility. Eachtime you analyze an asset, check whether today’s volatility reading ishigher or lower than usual. If it is higher than usual, you may sell optionswith greater conﬁdence. If it is lower than usual, you can feel free to buyoptions, knowing that you’re getting a bargain. Current volatility readingsare available in any good options analysis software. The options traderwho ignores volatility trades foolishly.
VOLATILITY TRADING—BUYING AND SELLING VOLATILITYMany sophisticated options traders go beyond just keeping an eye onvolatility, choosing to focus on volatility as the main aspect of their trading. How do they do this, and why?The essence of volatility-based trading, or V-trading for short, is buying options when they are cheap and selling options when they are dear.The reason it’s called volatility-based trading comes from the way we measure cheapness or dearness—using a parameter called implied volatility,
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or IV for short. Soon we’ll say exactly what IV is, but for the moment, itwill sufﬁce to say that high IV is synonymous with expensive options andlow IV is synonymous with cheap options.Actually, there are two ways of judging the cheapness or dearness ofoptions. The ﬁrst is simply by comparing current IV with past levels of IVon the same underlying asset. The second is by comparing current impliedvolatility with the volatility of the underlying itself. Both approaches areimportant and come into play in all V-trading decisions. The most attractive opportunities are when options are cheap or dear by both measures.The V-trader typically uses puts and calls in combination, selecting themost appropriate strikes, durations, and quantities to construct a positionthat is said to be delta-neutral. A delta-neutral position has nearly zero exposure to small price changes in the underlying. Sometimes the trader hasa directional opinion and deliberately biases his position in favor of the expected underlying trend. However, more often the V-trader is focused onmaking money just from volatility and is not interested in trying to makemoney from underlying price changes.Once a position is on, it may need adjusting at times to reestablish theappropriate delta. These adjustments can be costly in terms of transactioncosts and should be minimized, but not to the point where you exposeyourself to too much delta risk.Once volatility returns to a more normal, average level, the positioncan be closed. If not many adjustments were required in the meantime, thetrader should see a proﬁt.Since options are so sensitive to volatility, trading options on the basis ofvolatility can be lucrative. Occasionally, options become way too expensiveor way too cheap. In these situations the V-trader has a considerable edge.The options trader can always count on volatility returning to normallevels after going to an extreme. This principle is called the mean reversiontendency of volatility, and it is the foundation of volatility-based trading.That volatilities “mean revert” is well established in academic writings.1 Youcan also see it for yourself by looking at a few historical volatility charts. Youwill notice that when volatility goes to an extreme level, it always comesback to normal. Sometimes it doesn’t happen right away. It may take anywhere from days to months, but sooner or later it always comes back.
1
Michael Dueker, “Mean Reversion in Stock Market Volatility,” 1994; H. Schaller, “APanel Data Test for Mean Reversion Using Randomization,” 1993 (http://econpapers.hhs.se/paper/carcarecp/93-04.htm); T. Bollerslev, “Long-term Equity Anticipation Securities and Stock Market Volatility Dynamics,” 1996 (http://econpapers.hhs.se/paper/fthtinber/96-33.htm); Galen Burghardt and Morton Lane, “How to Tell if Options Are Cheap,” 1990.
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VOLATILITY
Implied volatilities seem to change from week to week, if not day today. V-traders ﬁnd proﬁt opportunities in this.
TOOLS OF THE V-TRADEAs was mentioned earlier, we measure how expensive or cheap optionsare using a parameter called implied volatility, or IV for short. The termimplied volatility comes from the fact that options imply the volatility oftheir underlying, just by their price. A computer model starts with the actual market price of an option, and measures IV by working the option fairvalue model backward, solving for volatility (normally an input) as if itwere the unknown. (Actually, the fair value model cannot be worked backward. It has to be worked forward repeatedly through a series of intelligent guesses until the volatility is found that makes fair value equal to theactual market price of the option.)Again, high IV is synonymous with expensive options; low IV is synonymous with cheap options. It can be useful to plot an asset’s IV over aperiod of years to see the extent of its highs and lows, as well as what constitutes a normal, or average, level.We measure how much the price of an asset bounces around using aparameter called statistical volatility, or SV for short. There are severaldifferent computer models for measuring SV. All of them seek to quantifythe extent, or magnitude, of the asset’s price swings on a percentage basis,and use varying periods of the asset’s recent price history (for example, 10,20, or 30 days). SV can also be plotted, so that the investor can see the periods of relative price activity and inactivity over time.Much of the options trading community refers to this as historicalvolatility, but we at OptionVue Systems prefer to call it statistical volatility,reserving the word historical for when we are referring to the history ofboth IV and SV.Regardless of the length of the sample period, when we compute SV,we always normalize the number to represent a one-year, single standarddeviation price move of the underlying asset. IV is normalized in the sameway. Thus IV and SV are directly comparable, and it is very useful to seethem plotted together.It is customary to state volatility levels as percentages. Don’t let thisconfuse you. Volatility is just a number. For example, if the number resulting from calculating SV or IV is 0.27, you would commonly see it expressedas 27%.What does this number relate to in the real world? Truthfully, volatility does not relate to anything tangible. It is just a number, and it only relates to other volatility numbers. However, I’ll give you something to hang
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Selling High Volatility
47
your hat on that is roughly correct. Note that volatility is the percentagestandard deviation of price changes. Therefore, as an example, when astock is 100 and its volatility is 27%, this would indicate that in the comingyear this stock’s price should be in a range from 73 (100 × (1 – 0.27)) to136 (100/(1 – 0.27)) roughly 68% of the time. (From statistics, a standarddeviation encompasses 68% of the data samples.)
SELLING HIGH VOLATILITYWhen the options of a particular asset are more expensive than usual, it issometimes justiﬁed by unusually high volatility in the underlying. While itmay be a decent opportunity to sell options in this case, it is even more advantageous to sell options when the extra IV is not accompanied by extraSV. One example of this kind of situation was the gold/silver index (XAU)in October 2002 (see Figure 3.2). IV (represented by the dashed line) wasat a relatively high level, but these high IV levels were not supported, orjustiﬁed, by a correspondingly high SV.Clearly, the advantage is with the trader who sells this high volatility, andthat means selling options. Generally, any position in which you are shortmore options than you are long is also short volatility. The purest way to sellvolatility is to sell a naked strangle, which involves selling out-of-the-moneycalls and out-of-the-money puts. Some traders also like to buy farther out-ofthe-money calls and puts at the same time for protection (thus creating credit
FIGURE 3.2 IV and SV Levels—Gold/Silver Index
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VOLATILITY
spreads), but this considerably weakens the position’s vega, or sensitivity tovolatility. We want a substantial vega, so that when IV eventually comesdown, our position makes money. See Figure 3.3 for the matrix of XAU options, including a naked strangle constructed by selling 5 calls and 7 puts. Foreach option, the ﬁgure shows the price, IV, and potential trade.We are using an unequal number of calls and puts because no putscould be found that were the same price as the calls. After locating someputs that were of a somewhat lower price than the calls, we determined,with the help of the software, that 7 of the puts would appropriately balance out the position in 5 calls, to give us a delta-neutral position to startwith. See Figure 3.4 for the graphic analysis of this short strangle position.We constructed this position using options expiring in 71 days. Youcan see from the three time lines that this position develops a proﬁt overtime. If held all the way to expiration, both options expire worthless (yourbest outcome) if the index is between 55 and 70. As you are receiving approximately 6 points of credit for selling the strangle, the two breakevenpoints for this strategy are at roughly 6 points below 55, or 49, and at 6points above 70, or 76. More precise breakeven values can be seen in thelower left area of the ﬁgure.
FIGURE 3.3 Matrix of Options—Gold/Silver Index
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Selling High Volatility
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FIGURE 3.4 Short Strangle Position—Graphic Analysis
The strangle need not be held all the way to expiration, however. Whilethe position beneﬁts from time decay, it beneﬁts even faster from a drop inIV levels, should that happen. If we projected a not-too-unreasonable 10percentage point drop in IV, from the current 57% down to 47% (this projection is made subjectively by the trader, as he views the historical volatilitychart), we see that this position may be closed out at the halfway point (36days from now) for a signiﬁcant proﬁt—as much as $2,100 on a $4,600 investment. (See Figure 3.5.)Whether held to expiration or closed early, this position has a signiﬁcant edge from inception because we are selling overvalued calls and puts.Out-of-the-money options are preferable in a strangle trade because itgives the underlying some room to wander and increases the likelihood ofrealizing a proﬁt. Generally, the farther out-of-the-money you go, the loweryour returns, but the greater the probability of achieving those returns. Bygiving the underlying room to move, the trader minimizes his chances ofhaving to make costly adjustments.One other strategy for selling volatility (but which cannot apply to index options, unfortunately) is covered writing, which involves buyingstock, or futures contracts, and selling calls. However, covered writing isnot delta-neutral and, since it usually involves the ownership of a portfolioof stocks, it is in a camp by itself. There are many mutual funds and indi-
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VOLATILITY
FIGURE 3.5 Effects of 10 Percent Drop in IV
vidually managed covered writing programs. Managers of these funds dowell to pay attention to IV levels in timing the sale of their calls.When selling volatility, it is best to use the longest-term options available, provided they have decent liquidity. Longer-term options have highervega and will respond best when IV comes down. Longer-term optionshave the additional advantage of having a lower gamma. As noted in Chapter 1, gamma measures how fast delta changes with price changes in theunderlying. By using lower gamma options, it takes a bigger price changein the underlying to imbalance your position.
BUYING LOW VOLATILITYLow volatility situations can be just as lucrative. I have heard argumentsagainst buying options because time decay is against you. Time decay is afunny concept. Do you remember using “imaginary numbers” in math classto deal with the square roots of negative numbers? Time decay (measuredas theta) is kind of like that. It’s an imaginary number. It says that if the underlying asset’s price holds perfectly still, the option will decay at a certainrate. But what underlying asset price holds still? None, obviously. In fact,time is what gives the asset its freedom to move!
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I may have a short volatility position, and let’s say it has a theta of 100.This means I’m making $100 dollars per day from time decay. Should I feelgratiﬁed to see this? Not really. It’s a false gratiﬁcation, because today’smovement in the underlying could easily take away $100 or more.There is nothing wrong with buying options. When an option is fairlyvalued, by deﬁnition there is no advantage to the buyer or the seller. If youbuy a fairly valued option, you have not taken on an implicitly disadvantaged position. Why? Because, despite the option’s time decay, the underlying is in constant motion.The situation in orange juice options in the spring of 2002 is a good example of extremely low volatility (see Figure 3.6). Current IV was approximately 15%, way below normal levels and the lowest it had been in ﬁveyears. Computer simulations showed that when orange juice’s IV returnedto a more normal 24 to 32%, the long-dated orange juice options would approximately double in price. In this situation the recommended strategywould be to buy calls and puts in a straddle or strangle purchase.A straddle, remember, is a popular strategy formed by buying bothcalls and puts on the same underlying, at the same strike and in the sameexpiration month. A strangle is like a straddle, except that it allows thecalls and puts to have different strike prices. In Figure 3.7, we have entered a prospective straddle in the long-dated orange juice options.Once again using an unequal number of puts and calls in order to con-
FIGURE 3.6 Low Volatility
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VOLATILITY
FIGURE 3.7 Example of Straddle
struct a delta-neutral position, the position costs $4,200 to put on. The average IV of the options we’re buying is 14.8%—making the options a veritable bargain by recent standards.Figure 3.8 shows the graphic analysis of this position, with themidterm line highlighted—the line representing the theoretical proﬁt/lossof the position halfway to expiration (94 days from now). Thus, the numbers along the bottom and in the lower left area reﬂect this midterm scenario. From looking at the historical volatility chart, we felt it reasonableto expect IV to go up 10 percentage points by this time frame. Thereforewe entered a +10 in the Volty Chg ﬁeld, and the analysis reﬂects this projected increase. While there is no guarantee that IV will go up 10 percentage points, if it does, the model shows that our investment has a 94%probability of proﬁt, making it truly an excellent trade!When buying options, it makes sense to buy near-the-money. That way,a sharp move in the underlying has a better chance of helping the position.When that happens, not only does IV normally receive a boost, driving upthe value of both sides, but the move may also drive one of the sides deepin-the-money and give you a gain just from price movement.
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FIGURE 3.8 Graphic Analysis of Straddle
Of course, this price movement might not happen right away, but useof the longer-term options should help allow plenty of time. When buyingvolatility, just as when selling volatility, my advice is to use the longestdated options you can ﬁnd that give you decent liquidity. The reason is thesame: high vega. The long-dated options, with their higher vega, will respond the best when IV increases.It is notable that long volatility positions have a completely differentfeel than short volatility positions. Short volatility positions usually gratifythe holder with steady, almost daily, gains, but can suddenly lose money ifthe underlying makes a sharp move. Long volatility positions can dribbleaway value day by day for many weeks, then suddenly gain very quickly.Despite their opposite psychological feels, a mix of both types of positionsbelongs in the V-trader’s portfolio.Deciding when to close a long volatility position can be a challenge. Ifa move in the underlying has caused your position to show a gain, it hasprobably imbalanced your position. One leg is now stronger than theother, and the dominant leg is more sensitive to changes in the underlying.The ﬁrst thing to consider is whether volatility has returned to normal levels. If it has, you should consider closing the position. If it has not, youmight consider continuing with an adjusted (rebalanced) position.There are many ways to adjust the position. A small adjustment can be
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VOLATILITY
made by simply buying or selling one or more contracts of the same options you already have in the existing position. A larger adjustment can bemade by closing one leg and reopening it at a new strike. Or sometimes it’sbetter to simply close your position and open a completely new one. If youdo this, you may want to consider changing expiration months as well, togive yourself more time.There is no science about deciding which kind of adjustment isbest in any particular circumstance. The correct adjustment to make isthe one that leaves you completely comfortable with the new positiongoing forward.
DELTA-NEUTRAL TRADING—IN A NUTSHELLThe type of V-trading we’ve been discussing so far is called delta-neutraltrading. It is the main type of V-trading. To recap, you begin by opening along straddle (or strangle) in an asset whose implied volatility is low (i.e.,cheap options), or a short straddle (or strangle) in an asset whose impliedvolatility is high (i.e., expensive options). (Please note that the latterwould be naked writing, and for this, the investor would need to thoroughly understand the risks.) In the absence of any directional bias withregard to the underlying, you would open this position “delta-neutral” byselecting the appropriate strikes and quantities of each leg in such a wayas to create a position that, theoretically, gains or loses nothing with asmall change in the price of the underlying.Note that options analysis software is needed for modeling and whatifﬁng positions this way. It would be next to impossible to do delta-neutraltrading without it.Over time, the underlying price naturally moves away from the starting place, throwing your original position out of balance. A small amountof delta should probably be tolerated, because the transaction costs associated with keeping the position perfectly delta-neutral would eat away atproﬁts. However, when delta moves an uncomfortable distance from zero,the trader needs to consider making an adjustment.Note that in the case of being long a straddle, technical traders mightwant to leave an imbalanced position alone if they feel that the strong legof the straddle (and therefore delta as well) favors a new trend in the underlying. On the other hand, pure volatility traders will want to adjust.Your position may be closed when implied volatility returns to normallevels, as judged by viewing a historical volatility chart. If not too many adjustments were necessary during the life of the position, you should normally be able to post a proﬁt.
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Seasonal Patterns in the Grains
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To ﬁnd good candidates for delta-neutral trading, you need some kindof system for screening and ﬁnding assets whose implied volatility is extremely low or high right now. Some options-oriented web sites providethis kind of service for a reasonable fee. It can also be found in the software and services that OptionVue Systems provides.
SEASONAL PATTERNS IN THE GRAINSIn general, V-traders buy cheap options and sell expensive options, as opportunities arise, hoping that IV soon returns to average levels and theycan realize a proﬁt. It’s an extra bonus when the cycles of nature come intoplay and lend an element of predictability to the timing.Not many assets exhibit a seasonal pattern. However, a strong and regular seasonal pattern exists in the grains that can be exploited. In the deadof winter, corn and soybean prices, for example, are usually stable andtheir options are cheap. With the onset of spring, IV begins to rise. It continues to rise throughout the spring, reaching a peak sometime during thesummer when uncertainty surrounding crop yields is at maximum, andwhen the slightest change in the weather forecast sends tremors throughthe markets. Then, beginning in late summer or early fall, IV comes tumbling back down again. The magnitude of the cycle is signiﬁcant, with summer IV levels often double those of winter. Figures 3.9 and 3.10 showsix-year historical volatility charts for corn and soybeans.The cycle can be played both ways. Let’s discuss buying low IV in thewintertime ﬁrst. From examining the charts, it would seem that IV usuallybegins ramping up in February, suggesting that February might be the besttime for buying a straddle. However, are we sure it should be a straddle?Note that rising IV has usually been accompanied by rising prices in recentyears, suggesting that we might consider just buying calls.Consider soybeans for a moment. From the charts, I notice that whenever the cycle begins with soybean prices being near their multiyear ﬂoorlevel of around 440, it turns out you would have been better off just buyingcalls. Otherwise, it was safer to buy both calls and puts, as soybean priceswere just as likely to fall as rise if their starting point was above, say, 480.Note that once, in the summer of 1999, soybeans’ IV spike coincided with aprice collapse. In corn, it would seem that the best approach is always tobuy a straddle, as a ﬂoor price is harder to discern in that commodity.Both corn and soybeans are amazingly regular, at least in recent years,in the level to which IV goes in the summer. When you see IV go above 30%(the same for both, remarkably), you can sell your long position and getready to play the downside of the cycle. Before we look at the downside of
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FIGURE 3.9 Seasonal Pattern of Volatility—Corn
FIGURE 3.10 Seasonal Pattern of Volatility—Soybeans
VOLATILITY
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Seasonal Patterns in the Grains
the cycle, however, why don’t we take a look at how well the upside strategy would have paid off recently?Table 3.1 shows what could have been achieved in the spring/summerof 2001 and 2002 using this strategy. All four trades were initiated in midFebruary. Since soybean prices were near 440 in mid-February both times,we simulated buying calls instead of straddles. In this study, the timing ofthe exits was admittedly optimized with the beneﬁt of hindsight, so actualresults may not be as good (unless you’re one of those people who cansense the perfect time to exit). The results nevertheless illustrate the potential of this strategy.Note the use of September options. This is recommended because itallows time in case the peak arrives late in the season. Also note that theoptions bought were at-the-money or very nearly at-the-money. That isconservative. You could just as well consider using out-of-the-money options (especially on the call side), shooting for better returns, becausewith the arrival of summer one usually sees a radical skew in grain options, giving the out-of-the-monies an amazing boost. (We haven’t discussed the concept of skew yet, but we will shortly.)Now let’s turn our attention to the downside of the cycle. Shortly afterclosing your long straddle (or just calls, if that’s all you bought), it is timeto consider selling the high IV. This is best done by selling naked strangles.I wouldn’t use credit spreads (in both calls and puts) because, although itlimits your risk, it also limits your potential. I prefer to manage risk bykeeping a close watch on the position and possibly rolling out one of thelegs if it goes in-the-money.Table 3.2 shows what could have been achieved in the summers of 2001and 2002 by selling naked strangles in corn and soybeans. The results areshown in dollar terms this time because, with naked options positions, it isimportant to consider margin requirements. Contrary to the principle espoused earlier of using long-term options, we felt compelled to use theTABLE 3.1 Upside StrategyDateCommodity Strategy Description Opened
Opening DatePriceClosed
ClosingPrice
PriceChange
Corn
BuySep 240straddle
2/16/01
37.5
6/25/01
49
+11.5
Corn
BuySep 230straddle
2/15/02
32
8/14/02
43.5
+11.5
Soybeans
Buy call
Sep 480
2/16/01
23.75
7/17/01
56.5
+32.75
Soybeans
Buy call
Sep 480
2/15/02
19
8/14/02
112
+93.0
58
Sell 10 Sep 250 CallsSell 10 Sep 210 Puts
Sell 10 Sep 260 CallsSell 10 Sep 230 Puts
Sell 10 Sep 280 CallsSell 10 Sep 260 Puts
Sell 10 Sep 520 CallsSell 10 Sep 470 Puts
Sell 10 Sep 590 CallsSell 10 Sep 530 Puts
Corn
Corn
Closedabove androlled into
Soybeans
Soybeans
TABLE 3.2 Downside Strategy
08/02/02
08/03/01
08/13/02
07/26/02
07/17/01
DateOpened
$9,250
$5,200
$1,500
$4,500
$5,875
Credit
$14,770
$11,900
$6,600
$7,950
$8,800
GrossReqmt.
$5,500
$6,700
$5,100
$3,450
$2,950
NetReqmt.
08/23/02
08/24/01
08/23/02
08/13/02
08/24/01
DateClosed
$9,250
$5,200
$1,500
$190
$5,875
Gain/Loss
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Other Commodities
59
nearby options because they were the only ones showing an IV of 30%+. Thefarther-out options had so much lower IVs—for example, 22% to 24%—thatthey weren’t worth selling. One of the corn strangles, and both of