to –0.65, andthat of the put would fall to –0.35. This slight movement exacts a ratherlarge toll on the neutrality of the position; the position delta now becomesshort 200 shares.What has happened is that when the stock moves, the deltas of bothoptions in the straddle are changing in the same direction—that is, if thestock moves up, the calls are being more delta short, while the puts aresimultaneously becoming less delta long.At least with the call ratio spread, this is not the case; there, when thestock moves up, the short calls become more delta short, but that is miti-
454
TRADING VOLATILITY
gated somewhat by the fact that the long calls in that spread become moredelta long.
The Gamma. The more serious disciples of neutral trading realized that merely being delta neutral was not enough. There was stilltoo much risk to price movements by the underlying security. Whatwas needed was something that helped them reduce their exposureto price risk by the underlying security. If they could have somethingthat would allow them to keep the delta constant—presumably, neutral—then they could have a more truly neutral position. It turns outthat there is indeed just such a measure. It is called the gamma, andit is a measure of how fast delta changes. Thus, if you were to construct a gamma neutral position, delta wouldn’t change at all! And,if delta didn’t change, then the position would remain delta neutral.Voila! We discuss gamma neutral trading later in this chapter, afterwe have laid some more groundwork.Mathematicians quickly determined that they could, in fact, quantify any position’s or portfolio’s exposure to any of the variables thatgo into making up the option price. We already know that exposureto price change is called delta. But you can also calculate, if youdesire, the exposure of a position with respect to time, volatility, andeven interest rates (there is no need to calculate the change withrespect to the striking price, since the striking price cannot changeover the life of the option). The names given to these measures areas follows:Variable AffectingOption PriceUnderlying priceStriking priceTime to expirationShort-term interest ratesVolatility
Measure ofExposureDeltaNot applicableThetaRhoVega
As you can see, the mathematicians gave these “measures ofexposure” the names of Greek letters or names that sound like
PREDICTING VOLATILITY
455
they’re Greek letters (vega is not in the Greek alphabet, but it soundslike it might be).Moreover, as we saw in the description of gamma, you could getreally carried away with this and determine how much exposure eachmeasure of exposure has. This information is useful to neutraltraders because they can then establish positions that are indeedquite neutral with respect to many of the things that can go wrong—specifically, sudden price changes by the underlying and suddenswings in implied volatility.It should be understood that any of these measures of exposurewill change as market conditions change. We know that the deltachanges when the stock moves, or when implied volatility changes,or when time passes. In a similar manner, these other measureschange under those conditions as well. However, the profitability ofan option position or portfolio will be much more stable when it isneutral with respect to several of these measures of exposure.It is sufficient to understand that we can use these other measures of neutrality. We return to them, in more specific terms, later inthe chapter. For now, we return to the concept of attempting to predict volatility, as opposed to predicting price, the latter being whatmost of us are accustomed to.
PREDICTING VOLATILITYIf you are able to predict volatility, then you can construct a positionthat is neutral with respect to price movements and just concentrateon making money from your volatility prediction. While this is theoretically possible, it’s not easy. So, over the bulk of the remainder ofthis chapter, we address how this can be accomplished. Initially, weuse delta neutral examples to illustrate our points. However, you, thereader, know from the preceding sections that delta neutral has itsown set of problems. Eventually, we will resolve all of these problems, when we get to the sections on advanced concepts.Imagine, if you will, that you have found a stock that routinelytraded in a fixed range. It would then be a fairly simple matter to buyit when it was near the low end of that range and to then sell it when
456
TRADING VOLATILITY
it was at the top of the range. In fact, you might even decide to sell itshort near the top of the range, figuring you could cover it when itgot back to the bottom of the range. Occasionally, you are able tofind a stock like this, although they are rather few and far between.However, in many, many instances, volatility exhibits this exacttype of behavior. If you look at the history of volatility in many issues,you will find that it trades in a range. This is true for futures contracts,indices, and stocks. Even something as seemingly volatile asMicrosoft, whose stock rose from about 12 to 106 during the 1990s,fits this pattern. Its implied volatility never deviated outside of rangebetween 26 percent and 50 percent, and most of the time it was in amuch tighter range: 30 percent to 45 percent.Of course, there are times when the volatility of anything canbreak out to previously unheard-of levels. The stock market in 1987was a classic example. Also, volatility can go into a slumber as well,trading below historic norms. Gold in 1994 and 1995 was an example of this, as historic volatility fell to the 6 percent level, when it normally traded above 12 percent.Despite these occasional anomalies, volatility seems to havemore predictability than prices do. Mathematical and statistical measures bear this out as well—the deviation of volatilities is muchsmaller than the deviation of prices, in general.You should recall that there are two types of volatility: impliedand historical. Historical is a strict statistical measure of how fastprices have been changing. The historical volatility can be looked atover any set of past data that you desire, with 10-day, 20-day, 50day, and 100-day being very common measures. Implied volatility,on the other hand, is the volatility that the options are displaying.Implied volatility is an attempt by traders and market makers toassess the future volatility of the underlying instrument. Thus,implied volatility and historical volatility may differ at times. Whichone should you use if you are going to trade volatility?My answer to that question is this: use a comparison of historicaland implied volatility, but only if implied volatility is not predicting anusual occurrence for future volatility. Thus, if implied volatility is lowwith respect to historical volatility, then we would expect impliedvolatility to increase. In that case, option buying strategies, such asstraddle purchases, would be appropriate. However, if implied volatil-
COMPARING HISTORICAL AND IMPLIED VOLATILITY
457
ity is high with respect to historical volatility, then we would normallyexpect implied volatility to decrease and move back in line with historical volatility, so option selling strategies would be appropriate.However, if you have reason to suspect that implied volatility is out ofline for a specific reason, then you should avoid trading volatility inthat issue. That reason could be impending corporate news.In Chapter 4, when we discussed the predictive power of options,we noted that it is sometimes the case that expensive options are aharbinger of corporate news. In particular, if the options get veryexpensive, and particularly if they get active at the same time, then anevent may be just around the corner that indicates that a large changein price by the underlying security is about to take place—a takeover,a lawsuit verdict, a ruling by a government agency, or an unexpectedearnings report might fall into this category. You would want to avoidselling this type of high implied volatility.
COMPARING HISTORICAL ANDIMPLIED VOLATILITYThe situations that are often attractive for trading volatility are whenthere is a differential between implied and historical volatility. Thesesituations occur with relative frequency. However, it is not enoughthat there is a big discrepancy between them. We also need to knowwhere both implied and historical volatilities have been over the pastmonths or maybe even a year; that is, we want to know what rangethey have been trading in. Even if implied volatility is much higherthan historical volatility, we should not automatically sell the volatilityunless the trading range of implied volatility confirms that it is high.If you were to notice that the implied volatility of OEX was 11 percent andthe historical volatility was 6 percent, you might think that you should selloptions because of the differential between historical and implied volatilities.From this limited bit of information, that does seem like a logical conclusion. However, when you investigate more, you will see that it is an incorrect conclusion.OEX options traditionally trade with a higher implied volatility than theactual (historical) volatility of the OEX Index. There is probably not a logical
458
TRADING VOLATILITY
explanation for this fact, but it is a fact. Thus, it is not sufficient for you tobase your analysis on the fact that OEX implied volatility is currently 11 percent and historical volatility is 6 percent. Rather, you should look at past levels of both implied and historical volatility.In fact, over the past year or even several years, OEX implied volatilityhas ranged from a low of 10 percent to a high of 22 percent. So you can seethat the current reading of 11 percent is actually quite low. In a similar fashion, historical volatility has ranged from a low of 6 percent to a high of about15 percent over that same period. Hence, the current reading of 6 percent isat the absolute low end of the range. Given this information, it seems thatstrategies oriented toward buying options would be more prudent becausevolatility is currently low by both measures, historical and implied.These were actual readings of OEX volatility, taken from February1995, just before the market embarked on an upside explosion of historicproportions. Clearly, it was a good time to be buying volatility, not selling it.
This example demonstrates that knowing the previous range ofvolatility is much more important than merely comparing current values of implied and historical volatility. Using only the latter can leadto incorrect conclusions and losing trades. Moreover, since strategiesin which you are selling volatility often involve the use of nakedoptions, you should be extremely careful in your analyses beforeestablishing positions.An approach that works well is to represent the implied volatilitydata in percentiles. It is, thus, easy to speak about cheap or expensive options in this manner. To make it easier to scan a spectrum ofimplied volatility history, though, we use deciles. To break a set ofdata into deciles, if the current implied volatility is in the first or second decile, then option buying strategies may be appropriate, forimplied volatility is near the low end of its range. Conversely, ifimplied volatility is currently in decile 9 or 10, then option sellingstrategies should be considered. Alternatively stated, if implied volatility is in the twentieth percentile or lower, then favor buying strategies; if it's in the eightieth percentile or higher, then selling strategiesshould be favored.In addition, you would want some confirmation from historicalvolatility, using the same decile method. Historical volatility should bein the same decile or in a more favorable one: if implied volatility is in
COMPARING HISTORICAL AND IMPLIED VOLATILITY
459
decile 2 and you are considering option buying strategies, then youwould want historical volatility to be in decile 2 or higher. On theother hand, if implied volatility is high (in decile 9 or 10), then youwould want historical volatility to be in the same or in a lower decilein order for it to confirm the location of the implied volatility. Moreover, you should use several measures of historical volatility in thesecomparisons.The following is an OEX example where volatility was low:Decile1
2
3
4
5
6
7
8
9
10
Implied
10.3> 11.4
11.8
12.3
13.0
13.7
14.5
15.3
16.0
16.7
17.7
10-day20-day50-day100-day
4.35.46.37.4>
6.26.27.2>7.8
6.66.67.58.0
7.06.87.78.5
7.77.9>8.08.9
8.6>8.68.68.9
9.49.19.18.9
10.19.89.99.0
10.811.110.39.1
16.512.911.19.1
5.25.86.67.7
The implied volatility numbers are the 20-day moving average ofimplieds. These go back one year, and there are about 250 trading days ina year. So there would be 231 20-day observations in that time period. The“>” character indicates that the current reading is in that decile (the firstdecile for implied, the seventh decile for the 10-day, and so forth).The other four lines refer to historical volatility. There are four separatemeasures of historical. You can see that the 10-, 20-, and 50-day historicalaverages are all in higher deciles than the implied volatility is. The 100-dayis in the same first decile as implied volatility.Overall, this is an attractive picture of volatility for option buying strategies: implied volatility is at its lowest point, and historical volatility is more“normal” with the 10- and 20-day actually being in deciles slightly aboveaverage (the sixth and seventh deciles, respectively). Thus, if implied volatility were to return to the middle deciles as well, it would increase, and optionbuying strategies would benefit.
A similar situation holds for determining when implied volatility istoo high. You would compare its percentile with the historical volatil-
460
TRADING VOLATILITY
ity’s percentile. There is one exception about high implied volatilitythat should always be taken into consideration: very expensiveoptions on a moderately volatile stock may signal an impending corporate news event such as a takeover or earnings surprise. A goodrule of thumb is to only sell implied volatility if it is at the high end ofa previously determined range. But should the volatility break out ofthat range and rise to new highs, you should probably be very cautious about selling it and should even consider removing existingpositions.We previously mentioned Federal Paperboard (FBO) as an example. It is aclassic for demonstrating our point in this case. Traditionally, FBO optionstraded with implied volatilities ranging from the low 20 percents to about 40percent. Not only that, but the price of the stock had behaved in such amanner as to make trading the volatility quite profitable.Then, in October 1995, the stock ended a small correction at a price ofabout 35 and began to trade higher. Implied volatility rose above 40 to 41percent on one day and 44 percent on another, before exploding to readings of 48, 54, 60, 81, and 89 percent over the next five days! This kind ofincrease in implied volatility above the normal trading range is a warningsign for sellers of volatility to stay away. By this time, the stock hadincreased in price to 421⁄2—not much of a rise—so volatility sellers couldhave gotten out or adjusted at a small loss.As it turned out, FBO was taken over the next week, and it jumped toabout 53.
Thus, you should generally not engage in volatility selling strategies when the implied volatility exceeds the previous range, especially if the stock is on the rise. The one exception would be if a stockwere dropping rapidly in price, and you felt that that was the reasonfor the increase in implied volatility. In this situation—as we saw inChapter 4 with IBM and Telefonos de Mexico—covered writes ornaked put sales can often be very effective.As mentioned previously, free weekly volatility snapshots are presented on our web site, www.optionstrategist.com; and for a modestfee, subscribers of The Strategy Zone on our web site have access todaily volatility updates and implied volatility charts as well.
TRADING IMPLIED VOLATILITY
461
TRADING IMPLIED VOLATILITYSo, now that we have outlined the scenarios under which we wouldbuy or sell volatility, let’s take a look at what strategies might beappropriate. In this section, we use elementary strategies. Later, wesee how more advanced strategies can be used. Recall that as avolatility trader, we don’t really want to have to predict where theprice of the underlying is going to be. We merely want to predictwhere the volatility will be. In light of these facts, we normally establish a neutral position to begin with.With simple strategies, we usually begin with a delta neutral position. We explore those in this section. Remember, though, that adelta neutral position can quickly turn into a position with price risk;so these strategies, while useful, may not be enough to keep us fromhaving to get “involved” with the price movements by the underlying.
Selling VolatilityWhen the implied volatility is “too high,” the strategist wants to sellvolatility, intending to capitalize when it returns to more normal levels. When I want to sell volatility, I favor one of two strategies: (1)the sale of a naked strangle or (2) a ratio spread. Since bothstrategies involve the sale of naked options, some traders prefer topurchase deeply out-of-the-money options as disaster protection.That may or may not be a good idea. On the one hand, it allowsthem to be worry-free about large gap openings; but on the otherhand, it costs money. And if these traders have done their analysiscorrectly, they should be selling inflated volatility, not buying it. Ialso tend to keep the options relatively short-term in nature whenselling volatility.Before getting into the strategy of volatility trading, which is mainfocus of this chapter, let’s spend just a minute on mechanics. Youmust have approval from your broker in order to sell naked options.Your broker will want a larger minimum equity in your account ifyou’re going to sell naked options—$20,000 at some firms and asmuch as $100,000 at others. If you have that plus some trading
462
TRADING VOLATILITY
experience, you will probably be granted the broker’s approval.However, you should also ascertain whether your personality is capable of handling a naked option strategy. The following are my threesuitability criteria for naked option writing:1. Do you have the personality to handle the risk?2. Can you margin the position as it should properly be margined?3. Do you have the trading experience to adhere to stops andthe time to constantly monitor your positions?Let’s expand on these criteria. If you are going to lie awake atnight worrying about what might happen to your naked options,then you cannot honestly answer yes to the first question. If you onlyhave the margin available for the exchange minimum, then you can’tanswer yes to the second question (since margin requirementsincrease when the underlying makes an adverse move, you reallyhave to have enough margin to handle a move all the way to yourbreak-even point— where you would make an adjustment or closeout your position). Finally, you don’t have to have option tradingexperience, but you must be prepared to handle stops and monitorpositions as if this were a full-time job. If you can’t, then you can’tanswer yes to the third question. However, if you can answer yes toall three of these questions, then you are prepared to sell nakedoptions.In a naked strangle sale, an out-of-the-money call is sold, as wellas an out-of-the-money put. I favor this over a straddle sale becauseof the wider price range of profitability that is attained.Figure 6.1 compares the profit potential of a naked straddle salewith the sale of a naked strangle at expiration. Note that the straddlesale can make more money if the underlying is near the striking priceat expiration, but that the strangle sale makes money over a widerrange. Since you are often forced to make adjustments to nakedpositions when the underlying makes adverse price movements, theuse of the strangle sale lessens the odds of having to adjust so often.Before getting into an actual example, there is one other important concept that can be presented visually—the statistical advantagethat the position presents. When you are selling high volatility, you
TRADING IMPLIED VOLATILITY
463
Figure 6.1NAKED STRADDLE SALE VERSUS NAKED STRANGLE
expect that volatility will return to more normal levels. In most cases,when this happens, you will make money, and you can then exit theposition. This return to “normal” volatility may occur quickly, or itmay take a while (or may never happen at all). The trader’s statistical“edge” is that he is selling inflated volatility; and his profit potential,as represented by that edge, is the amount of money that he couldmake if volatility returned to normal levels.Figure 6.2 shows the general shape of a strangle sale, with twocurved lines inside of it. The straight lines are where the profits orlosses would lie if the position were carried all the way to expiration.The curved lines are profit projections if the position were held onlyhalfway to expiration. The reason that there are two curved lines isthat one represents the results with volatility remaining at high levels(the lower curved line), while the other depicts the results if volatilitywere to return to normal levels (the higher curved line).You can see that there are profits under both curved lines if theunderlying is near the center of the graph. Likewise, there can be
464
TRADING VOLATILITYFigure 6.2STRANGLE SALE
losses as well, as both curved lines penetrate below the zero profitline if the underlying rises or falls too far. What is most important,however, is that there is a definite space between the two curvedlines—the shaded area on the graph. This shaded area is a picture ofthe statistical advantage that the seller of high implied volatility has;for if volatility returns to its normal level, he will profit by the amountof the shaded area.A similar picture regarding the ratio spread strategy can beobserved in Figure 6.3. It is the graph of a call ratio spread. Simplistically, a call ratio spread involves buying one call at a lower strikeand selling more calls at a higher strike. Notice that the maximumprofit area of all three scenarios—expiration, halfway to expirationwith the same volatility, and halfway to expiration with decreasedvolatility—is at the higher striking price (i.e., the striking price of theshort options in the spread). It is at that point where the statisticaledge is the largest; the area between the two curved lines is widest atthat point.
TRADING IMPLIED VOLATILITY
465
Figure 6.3CALL RATIO SPREAD
Now, having established the general theory of trading highimplied volatility, some actual examples may prove to be beneficial.Admittedly, this first one is a favorable example; but it is one takenfrom real-life trading, and the decisions made at the time reflectedthe philosophies that we have discussed thus far.The American Stock Exchange (AMEX) listed options on the Hong KongOption Index (symbol: HKO) in 1993. The index was designed to performsimilarly to the Hang Seng Index, the main market measure of the HongKong Stock Exchange.The HKO is computed just once a day, before the opening of trading inthe United States, as the actual Hong Kong market is closed at that time.Closing prices of the stocks used to compute the HKO are taken from actualclosing prices in Hong Kong, converted to dollars. Thus, the HKO gaps everytrading day. Think of it as akin to being able to trade the Dow Jones IndustrialAverages only at night, where the only price you had to go from was eachday’s Dow closing price. This feature raises the implied volatility somewhat.
466
TRADING VOLATILITY
In late June 1994, the following situation existed with respect to thevarious implied and historical volatilities of the Hong Kong Option Index:
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
3416181921
10th7th7th7th8th
The previous range of the implied volatility of the HKO had been fromabout 21 percent to 38 percent. Thus, this situation fit both of the statedcriteria: (1) implied volatility was significantly higher than historical volatility,and (2) the implied volatility was in the 10th decile, while historical volatilities were high, but not quite as high. What’s more, an index is unlikely toacquire a sudden burst of volatility, as a stock might from an impendingtakeover offer.The HKO itself was trading at about 180 at the time, and the Julyoptions, which were due to expire in three weeks, were trading at the following prices:Date: June 23, 1994HKO: 180.79HKO July 190 call: 13⁄4HKO July 170 put: 2The fact that short-term (three-week) options were available at reasonably large prices was another added benefit. The combination—an equalamount of July 190 calls and July 170 puts—was sold; and as it turned out,implied volatilities remained high throughout the fairly short life of theoptions, so there was never a return to “normal” volatility. However, theHKO never moved much in price, trading in a range between about 170and 182 during the next three weeks. The combo expired worthless, andthe maximum profit was attained.
Some additional commentary may be beneficial here. First, thenaked combo was chosen as the vehicle of choice, because the HKO
TRADING IMPLIED VOLATILITY
467
had been trading in a range around 180 for several weeks prior toestablishing this position. Therefore, a position with break-evenpoints centered about the current price (180.79) seemed to be thebest choice of a neutral position.Second, when the HKO dropped to 170, the position had obviously become delta long. Should an adjustment have been made?That is a matter of conjecture, and I always feel it has to do with thesize of the position itself. When using an elementary neutral strategysuch as a short strangle, you are obviously going to have to assumesome delta risk eventually (or else you will be making numerousadjustments, and commissions and bid–asked spreads will eat youalive). With these short-term strangles, I generally feel that I will leavethem room to move and will remove them if (1) volatility drops and Ihave a profit equal to the statistical edge, as shown in the precedingchart, (2) they expire, or (3) they violate their break-even points.Obviously, no one wants to take large losses—especially in anaked writing situation—so the third criterion is mandatory. Therefore, when the position was established, I was prepared to close outthe strangle if HKO traded at 167 on the downside or at 193 on theupside. In either case, only a small loss would have resulted.The preceding example can be continued because, in a way, noconvergence had been reached between historical and impliedvolatilities. Notice that we said that implied volatility never returnedto normal by the time expiration arrived. Therefore, the same situation essentially was available for the next expiration.
At July expiration, the situation had not changed much as far as the HongKong Option Index volatilities were concerned:
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
3324222021
10th10th9th9th8th
468
TRADING VOLATILITY
This was still an attractive situation, although perhaps not quite asattractive as in the previous example. Implied volatility was still at the topend of the range, which was good; but it wasn’t that much higher than historical volatility when measured by the deciles. This could indicate that allthe volatilities were embarking on a higher move. Still, it seemed attractiveenough to repeat the strategy, using the following prices:Date: July 15, 1994HKO: 176.20Aug 190 call: 31⁄4Aug 165 put: 2You can see from these prices that the calls were more expensive thanthe puts, so a neutral position required the sale of five puts and three calls.Such a position took in a credit of (5 × 2) + (3 × 31⁄4) = 193⁄4 points. Thismakes the break-even points 196.58 (190 + 19.75/3) on the upside and161.05 (165 – 19.75/5) on the downside.During the ensuing four weeks to expiration, the implied volatility onceagain failed to move below the ninth percentile, and HKO traded in a rangefrom 176 up to about 194, before finishing at 188 at expiration. Since thebreak-even points weren’t violated, no defensive action was taken, and thecombo expired worthless once again.
At this point, I was admittedly feeling fairly fortunate to have hadtwo consecutive strangles expire worthless. Even more so, considering the fact that the first one had seen the HKO mostly trade lower,even threatening the downside break-even point; then the secondone had the opposite action—the HKO traded up and almost wentthrough the upside break-even point. However, the fact that impliedvolatility was high when these positions were established made thebreak-even points sufficiently far away from the initial index pricethat it contributed to the eventual inability of the index to exceedthose break-even points.It surely seemed that this situation couldn’t go on forever; butsince the implied volatility was still high after even the second strangle expired worthless, it seemed worthwhile to attempt a third one.After the second HKO combo expired worthless, the following situationexisted at August 1994 expiration:
TRADING IMPLIED VOLATILITY
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
3122212021
10th9th9th9th8th
469
The following prices existed at the time:Date: August 12, 1994HKO: 189.85Sep 205 call: 13⁄4Sep 175 put: 21⁄4The deltas of these two options were about the same, so this time thecombo consisted of selling an equal amount of Sep 205 calls and Sep 175puts. Over the next two weeks, HKO traded in a very tight range, between188 and 193. This had the effect, finally, of causing the implied volatility tocontract to 23 percent. At this time, the statistical advantage had finallybeen realized, and the strangles were covered.
Thus ended the profitable saga of the Hong Kong Index inflatedvolatility. Ironically, the volatility of the index did not return to the10th decile for over a year and a half after the summer of 1994. Perhaps the market makers and other traders decided that the somewhat disconcerting gap-every-night feature of the HKO did not meritsuch a large implied volatility on