a routine basis.Selling volatility in this manner is somewhat nerve-rackingbecause naked options are involved. There are always the disastersfrom naked option writing that you routinely read about and that wehave recounted as well—takeovers, crashes, and so on—but with theguidelines that we have set forth, you should be able to avoid those.For example, implied volatility was actually very low just before thecrash; thus, by our “rule” of requiring it to be in the 9th or 10thdecile, you wouldn’t have sold it. Also, as was described earlier,implied volatility usually skyrockets before a takeover; so if impliedvolatility suddenly blasts much higher than the previous 10th decilereadings, you shouldn’t sell that volatility either. Rather, with these
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guidelines, losses would generally be more modest, but that doesn’tmean that they don’t occur. Lest you think that selling naked optionswhen implied volatility reaches the 10th decile is a lock, the followingexample is provided.Also in the summer of 1994, UAL Corp’s (UAL) options had reachedexpensive levels, by all measurements.
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
3628262825
10th8th7th7th6th
Thus, implied volatility was not only higher than historical volatility inabsolute terms, but it was in a higher decile as well. Note that the absolutedifferential in volatilities is not as large here as it was in the HKO examples,but a 36 percent implied versus historicals in the 25–28 percent range isstill a significant difference.The pertinent prices at the time were:Date: June 10, 1994UAL: 116UAL July 125 call: 13⁄4UAL July 110 put: 21⁄2The deltas of these two options were about equal, so an equal numberof puts and calls were sold naked. The break-even points were 1291⁄4 on theupside and 1053⁄4 on the downside. In line with the philosophy stated earlier, the position was to be given room to “roam” until it hit the break-evenpoints. With about five weeks until expiration, this seemed like a reasonableamount of room—about 14 points on the upside and 11 points on thedownside.This position didn’t have the good fortune of the Hong Kong Indexputs. UAL immediately started to move higher and closed at 130 on July 1.At that time, July 125 calls were offered at 53⁄4 and were covered. The putswere trading at a small fraction and were covered as well.
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Moreover, implied volatility had fallen to 23 percent, so it was nolonger expensive. Thus, no other position was established in UAL.
The preceding example shows how using the simple neutral position was insufficient to capture the intended volatility decline. In fact,volatility did decline—from 34 percent to 23 percent—and that waswhat we were trying to predict. Unfortunately, with such a simpleneutral position, we were left too exposed to price movement byUAL. That price movement overrode the benefits of declining volatility, and the overall position became a loss. It is for reasons such as thisthat a more sophisticated approach is generally necessary in order toisolate volatility as the important variable. However, for the timebeing, we want to continue with the simpler strategies so that we canfurther lay the groundwork for the more complex material later.
Buying VolatilityThe strategist who is attempting to trade volatility will buy it when itis “too low.” In such cases, there are three applicable strategies: (1)long straddles, (2) backspreads, or (3) calendar spreads. Note that thefirst two simple strategies are merely the opposites of the ones usedfor selling volatility. The introduction of this third strategy, the calendar spread, into the mix gives us a slightly wider range of alternatives.The simple strategy for selling volatility discussed earlier wassomewhat heavily dependent on price movement of the underlying,which was a negative, and time decay, which was a positive. Asmight be expected, the first two strategies for buying volatility—longstraddles and backspreads—are affected in the opposite way:extreme price movement by the underlying is beneficial to thesestrategies, while time decay is an enemy. The ability to use calendarspreads for buying volatility gives the strategist an important alternative: time decay once again becomes a positive factor. The followinggraphs show these strategies’ profitability, both at expiration and atthe perhaps more important earlier times.Figure 6.4 is a graph of owning a straddle. If I am going to usethis strategy for buying volatility, I prefer to buy the straddle (both the
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TRADING VOLATILITYFigure 6.4STRADDLE BUY
put and the call have the same strike, which is initially quite near theprice of the underlying) rather than buying a strangle (out-of-themoney put and out-of-the-money call). The curved lines on the graphdepict the same sort of things that we saw in the last section: they arethe profits or losses halfway to expiration. If volatility remains low,then the profitability will fall on the lower curved line; however, ifvolatility increases, then profits will be on the higher curved line. Thespace between the two of them is the amount of profit that can beattributed to volatility returning to “normal” levels.Trading long straddles can be a somewhat depressing occupationbecause of the constant drag of time decay on the position. However, if volatility does explode or if the price explodes, profits comequickly and can be quite large. The position needs to be handled in away that is significantly different from the short strangle strategy thatwas previously discussed. For one thing, when you are long thestraddle, if the stock reaches your break-even point, you are mostlikely only just beginning to make money. Therefore, you must hold
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onto the position— even though it is in no way delta neutral anylonger—if you expect to maximize profits. Another thing that isimportant is to decide when to take losses. The following examples,again from actual trades, address these points.In late September 1995, retail stocks were beginning to come under somepressure. They had had a strong run in the bull market of that year but hadpeaked out in late July. There is a sector index that is composed of the retailstocks, and it trades with the symbol $RLX. The index had peaked out at342 that summer and had pulled back slightly to 330 by September. At thetime, the pertinent volatilities were:
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
121091013
1st2nd1st1st4th
It is fairly obvious from this data that the Retail Index was at a low ebb,both in implied and in historical volatility. The fact that the 100-day historical volatility was somewhat higher was evidence that the index had beenmore volatile in the past.With the index near 330, the December 330 straddle was purchasedfor 15 points.
There are two ways that a straddle owner can make money: (1) ifthe implied volatility increases or (2) if the underlying rises or falls farenough in price. The first condition will boost the price of any straddle, whether it be a short-term one or a longer-term one. However, ifvolatility remains at low levels, the straddle purchase relies on pricemovement by the underlying in order to make money. You will findthat at low-volatility conditions the underlying needs to move nearlyall the way to the break-even point in order for the straddle tobecome profitable.I usually attempt to buy straddles with about three or four monthsof time remaining when I am buying volatility. This length of time is
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selected for two reasons. First, the time decay isn’t too rapid for athree-month straddle, although time will definitely be working againstthe straddle owner to a certain extent. Second, the straddle has agood chance to respond if the underlying rises or falls by a reasonable distance. If you go too far out in time, you will be paying toomuch time value and may find that it is too difficult to make moneyfrom price movement by the underlying; you will be overly relying ona volatility increase.Continuing with the previous example, the retail stocks began to announcepoor earnings and earnings forecasts shortly after the straddle was purchased, and the Retail Index fell to 319 in just about two weeks. However,the straddle was still selling for about 15 because implied volatility had onlypicked up modestly—to 13 percent—and with the put being the in-themoney option, there wasn’t much time value premium in the straddle’s price.
Options lose time value premium as they become in-the-moneyoptions, and in-the-money puts lose their time value faster than inthe-money calls do. This is a fairly typical occurrence, and not a totallyunpleasant one: the underlying moves toward the break-even point,but the straddle price doesn’t really respond much because volatilityremains at low levels. With the underlying near one of the break-evenpoints, a long straddle position is by no means delta neutral.When that occurs, the straddle owner, who, it must be remembered, is really a volatility buyer, must make a decision. He could (1)close out the straddle, (2) readjust it so it becomes delta neutral oncemore, or (3) go with the flow and try to ride the existing trend. This isnot an easy choice, but some guidelines can be given. If volatility hasincreased, the first choice—to close the straddle—is probably appropriate. The second choice—readjusting—would be more appropriateif the implied and historical volatilities are still in the first or secondpercentile; that is not normally the case after the underlying hasmoved far enough to reach a break-even point. In essence, I onlyfavor the adjustment choice if the position is one that I would initializeif I had no position at all. The third choice—riding the trend—mightbe appropriate if volatility is still at low levels and if there is a goodtechnical reason to expect that the trend in prices will continue.
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In this same example, after the drop to 319, this Retail Index straddle wasquite delta short, as the Dec 330 put had a large negative delta, being 11points in-the-money, while the Dec 330 call didn’t have much of a delta atall, since it was out-of-the-money by an equal amount. Implied volatility hadrisen only slightly to 13 percent, so the first choice— closing the position—wasn’t overwhelmingly the best choice.In order to assess the second choice—readjusting—it was necessary tocompare the implied and historical volatilities once again. The overallvolatility picture at this time had become the following:
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
1313111112
2nd4th3rd2nd3rd
This is a picture of low volatilities, but not extremely low ones. I wouldnot normally initiate a position with this volatility picture, so readjusting wastherefore not attractive.The third choice—riding the trend—is sometimes the most risky choice,but it can produce the best profits as well. Figure 6.5 shows the Retail Indexat the time it had reached the 319 level in early October. There was previous support there from the bottom that had been made on September 1.However, should that support give way, it appeared that a much larger dropwas possible.Therefore, I decided to ride the trend, figuring that if I was wrong andRLX rallied instead, I could remove the straddle without too much harm,since volatilities might still increase. As it turned out, the support did giveway, and the index collapsed to 297. By this time, I was using a trailing stopand closed the position out on a reflex rally to 304. Thus, the straddle thatwas purchased for 15 was sold for 271⁄2 (the calls were sold for 11⁄2 on theday the index broke the 319 support level, and the puts were sold via thetrailing stop). This entire scenario occurred by November 2, so it did nottake long to unfold.
Once you have decided on the “go with the flow” choice, youshould sell out the unprofitable half of the straddle as soon as the
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TRADING VOLATILITYFigure 6.5RETAIL INDEX (RLX)
trend is technically confirmed. In the preceding example, that camewith the breaking of support at the 319 level, when the calls weresold for 11⁄2. Ironically, the Retail Index rallied all the way back to328 in late November, so the calls could probably have been sold formore. However, in most cases, when a technical level is broken andyou have decided to ride the trend, you should sell out the losing side,for it is probably headed toward zero.Handling losing straddle positions is actually a much easierproposition. All you have to do is set a mental stop in terms of thestraddle price and adhere to it. If the straddle declines in price to yourstop, you take your loss. After that, you may want to reestablish anew, longer-term straddle on the same underlying security, althoughin many cases, it may not be as attractive as the initial straddle was.
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We mentioned earlier that the volatility of gold declined to previouslyunheard of levels in 1994 and 1995. The decline in volatility began in late1993, from levels around 20 percent, and had reached low levels by June1994. At the time, the following statistics regarding volatility were observed:
Implied volatility10-day historical20-day historical50-day historical100-day historical
Actual (%)
Decile
10.76.06.410.011.3
1st1st1st1st2nd
With deciles like that, the straddles seemed like a very attractive purchase. So the Dec 390 straddles were purchased (Dec gold was trading at391 at the time) at a price of 18. These straddles had about 41⁄2 months oflife at the time, so that is why they were chosen.I usually use a stop loss of about 40 percent to 50 percent of the value ofthe straddle, so I set a mental stop at a price of 10 for this long straddle. If thestraddle settled at 10 or less on any trading day, the straddle would be sold.As it turned out, gold remained in a tight range and volatilities fell evenfarther. Gold traded between 380 and 400, never enough price movementto even approach the break-even points of 372 on the downside and 408on the upside. To make matters worse, implied volatility continued to fall aswell. Finally, by early October, the straddle had fallen to 10, and it was soldand the loss was taken.
When you take a loss on a long straddle position, you are usuallyfeeling somewhat frustrated, especially if you did your homeworkcorrectly and bought the straddle when volatility was extremely low.Your initial reaction is usually to delve into another straddle on thesame underlying security, figuring that this time, the volatility willhave to increase. This may be an emotional decision. To remove theemotion, you should analyze the volatility comparison and demandthe same or better volatility picture before repeating the position.Shortly after taking the loss on the preceding gold straddle, with April goldnear the 390 level and volatilities all in the 1st deciles (albeit at lower actual
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levels than shown in the previous example), the April 390 straddle wasbought for a price of 11. This one had just over four months of life remaining. Note the lower absolute price of the straddle, reflecting the diminishedimplied volatility.Without getting overly involved in the details, this time things workedbetter, as gold immediately fell below 380, the technical support level thathad been established earlier that summer.
Even if the second straddle purchase had been a loser as well, itwas still well-founded on the basis of low implied volatility. I don’tthink you can repeat such purchases over and over if losses continueto occur and implied volatility continues to decline. For example, theimplied volatility of gold continued to drift lower into 1995 and thenremained at very low levels before finally beginning to climb in early1996. Our philosophy of trading volatility was based on identifyingthe range of past volatilities; implicit in that philosophy is that volatility is going to remain within that range. When it breaks outside ofthe previous range, you should probably avoid positions in that security until you are confident that a new and relatively stable range hasbeen identified. As a result, no further gold straddles were boughtduring the subsequent decline in volatility.The second strategy that we described for buying volatility is thebackspread. Figure 6.6 is that of a call backspread—selling one inthe-money call and buying two at-the-money calls, for example. Youcan see by the straight lines on the graph that the call backspread isvery similar to the long straddle, except that the profit potential istruncated on the downside. The curved lines show the profit potential halfway to expiration. The higher curved line is the projectedprofit if implied volatility increases—returning to normal levels. Thelower one is the profit if implied volatility remains where it was initially. The space between the two lines graphically represents the statistical advantage that can be had by capturing the volatility if itshould increase to previously normal levels.As you can see from the graph, the call backpsread has unlimitedprofit potential to the upside. A put backspread, however, has unlimited downside profit potential. In either case, the maximum loss ofthe backspread is less than that of a corresponding long straddle
TRADING IMPLIED VOLATILITY
479
Figure 6.6CALL BACKSPREAD
because of the profit potential that is forsaken on one side of thebackspread.You might utilize a backspread instead of a long straddle if youthink the particular market is more likely to move in one direction orthe other. But the neutral strategist is not normally interested in priceprojection initially. Rather, the strategist would use the backspreadwhen the implied volatilities of the individual options in the spreaddiffer. This situation is called volatility skewing and is addressed laterin this chapter, so examples of backspread positions will be deferreduntil that time.The calendar spread is a strategy that benefits from increasedimplied volatility, but not from volatility of actual prices. A calendarspread involves buying a midterm option and selling a shorter-termoption, both with the same striking price. A strategist will normallytreat the calendar spread as just that—a spread—and remove it whenthe near-term option expires. Holding onto the longer-term option
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after the shorter-term one expires makes you a speculator instead ofa spreader.Figure 6.7 shows the profitability of a calendar spread at expiration of the near-term option. Notice that the maximum profit potential is realized if the underlying’s price is right at the striking price. Ifthe underlying moves too far away from the strike in either direction, then losses will occur. However, losses are limited to the initialdebit spent for the spread. There are two curves on the graph—thehigher one shows what would happen if volatility increased, whilethe lower one shows profits if volatility remains low. The spacebetween the two is, once again, the statistical edge attributable to anincrease in volatility.Most option traders are familiar with calendar spreads, but theydon’t often think of them as being so affected by volatility. As aresult, novice traders often establish calendar spreads when volatilityis high because the spread seems attractive, when, in fact, it is not.Ordinarily, we use examples to show how to use a strategy, but theFigure 6.7CALL CALENDAR SPREAD
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following is an example of how not to use one. The reason that weare including it is because of the propensity of people to use calendarspreads when they shouldn’t, that is, when implied volatility is high.This is a theoretical example using actual prices.Example: In the late summer and fall of 1994, Quaker Oats (OAT) was arumored takeover for several months. The stock’s price had risen from 60 tothe 75-to-80 area, and the implied volatility had risen even more: from 20percent to extremely high levels, ranging up to and even above 60 percent.When implied volatility increases by this much, it distorts the optionprices so that the near-term option seems ridiculously expensive in comparison to the longer-term options. In the first week of October, the followingprices existed:OAT Common: 75
Nov 75 callDec 75 call
Price
ImpliedVolatility (%)
61⁄281⁄8
6057
A calendar spread—buying the Dec 75 call and selling the Nov 75call— could be established for a seemingly low debit of 15⁄8. This calendarspread looks extremely attractive. The near-term November option is sellingfor a whopping 80 percent of the price of the December option, when bothare at-the-money. You don’t see that situation too often. Moreover, theNovember call has a slightly higher implied volatility than does the December call, so a calendar spread would have a slight theoretical edge in termsof the implied volatility, also.Furthermore, using a pricing model, you are able to determine that ifthe December option holds its 57 percent implied volatility, then the spreadwill make a profit if OAT is anywhere between 67 and 85 at Novemberexpiration (about six weeks away)—a very wide range.All of those things are true, as far as they go. What has not been investigated is what a contraction in volatility would do to the spread. In fact, itwould have a devastating effect. Nothing could prove this more conclusively than what actually happened in real life: on November 9, QuakerOats indicated that it would buy Snapple, thereby quashing takeoverrumors (most rumored suitors would not be interested in a money-losingventure like Snapple). The stock only dropped about 10 percent—to 67
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percent—but the implied volatility collapsed to 37 percent. The pricesthen looked like this:OAT Common: 67PriceNov 75 callDec 75 call
1
⁄16⁄8
7
ImpliedVolatility (%)n/a37
By expiration day itself (November 18), the common had fallen to 65,and the Dec 75 call was trading at a mere half point.Thus, the calendar spread, which was purchased for 15⁄8, was a largepercentage loser after volatility collapsed.
This example shows the importance of factoring volatility intoyour decision when trading calendar spreads. When volatility isalready pumped up, as in the Quaker Oats example, it is a potentialroadblock to profits for the calendar spread. At the end of this chapter, we present an aggressive strategy for using calendar spreads ininflated volatility situations; but statistically speaking, you shouldavoid the strategy when implied volatility is too high. It is moreadvantageous to use the calendar spread strategy when impliedvolatility is low, thereby reducing the possibility for decreasing volatility to harm the spread and enhancing the probability that increasingvolatility will help the spread.Overall, when trading volatility, the five delta neutral strategiesjust discussed are generally the preferred ones that you would wantto use. To summarize, if you are selling volatility, the two appropriatestrategies are the ratio spread (which could be established with eitherputs or calls) and the naked short combo. If you are buying volatility,backspreads (with either puts or calls), long straddles, or calendarspreads are germane. In addition, the spread strategies—ratiospread, backspread, and calendar spread—may be best utilized whenthere is a skew in the options implied volatilities. For example, if thenear-term options are trading with clearly higher implied volatility
THE “GREEKS”
483
than the intermediate-term or longer-term options, then a calendarspread may be preferable (again assuming that the percentile ofimplied volatility is not too high). Also, it is sometimes the case thatoptions with lower striking prices have higher implied volatilities thanoptions with higher striking prices. In that case, a put ratio spread (ifimplied volatility is high, in general) or a call backspread (if impliedvolatility is low) might be attractive.
THE “GREEKS”The preceding strategies and examples show the attractiveness ofattempting to trade volatility, as opposed to predicting prices. However, since they are such simple strategies, you are often forced toform opinions on prices as the strategies evolve. It is now time to discuss ways in which you can more easily isolate volatility and rely lessheavily on price in your strategies.In order to do that, we must approach things in a more theoretical manner. Thus, this section may seem a little complicated. However, the concepts are not all that difficult. I’ve often said thatstatistics on Wall Street is treated like rocket science—math that anundergraduate college math major would routinely understand isimbued with Einstein-like qualities by many traders. Moreover, manytraders feel that if the computer says it’s so, then it must be theabsolute truth. You must not be so awed by what we are about topresent. It’s not the Holy Grail, nor is it the absolute secret to success. If it were, everybody would be using it. However, it is a stepabove what you normally see in terms of option strategies and couldlead you to more consistent, less risky, investments.In order to isolate volatility, we need to understand how to isolateeach of the variables that affect an option’s price. Earlier in thischapter, we defined the names of the terms that describe the measure of exposure of an option or a portfolio for each variable thataffects the option price. Since these exposure measures have Greek(or Greek-sounding) names, we refer to them collectively as “theGreeks.”
484
TRADING VOLATILITYVariable AffectingOption PriceUnderlying priceTime to expirationShort-term interest ratesVolatility
Measure of ExposureDeltaThetaRhoVega
In addition, we also stated that “gamma,” which is the measureof exposure of “delta,” is also observed by sophisticated traders whouse this approach to neutral trading.
The ModelThe basis for calculating all of the preceding measures, as well as forcalculating implied volatility and also the theoretical value of anoption, is the option model. There are several models that are available to the general public: their formulas have been published andare in the public domain. The earliest and simplest of these was theBlack–Scholes model, derived in 1973 by two professors. Sincethen, many others have attempted to make adjustments andimprovements, and many of them purport to give more accurateanswers to the question of theoretical value.One of the more popular alternatives is the Binomial model (theformula for the model and some examples are given in Appendix C).It involves a lot more calculations than the Black–Scholes model; butin today’s world of very fast computers, those calculations can bedone rather quickly, although not nearly as quickly as the few calculations required for the Black–Scholes model. What’s ironic is thatafter all these “improvements” over the years, the newer modelsrarely give “answers”—that is, option values—that differ from theresults of the Black–Scholes model by more than a few pennies. Inessence, the difference between the results of the Black–Scholesmodel and the Binomial model is less than the bid–asked spreadbetween the option in the marketplace. Consequently, we see noreason to get more complicated than the Black–Scholes model, especially for a commission-paying, non–market maker.
THE “GREEKS”
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It is necessary to have a model, because “the Greeks” cannot becomputed without one. Recall that the model is a function that isbased on the five variables that control the price of an option (stockprice, striking price, time remaining, volatility, and interest rates). Ofthese five, only the striking price never changes for an individualoption. The others all change as the market trades, day after day.The Greeks measure the effect of one variable if all the others remainconstant. To conceptualize what the Greeks actually are, a simpleexample may suffice.Example: Suppose that we are attempting to evaluate an option where thefollowing data apply:Stock price: 50Strike price: 55Time remaining: 3 monthsVolatility: 25%Interest rate: 6%Under these assumptions, the Black–Scholes model returns a theoretical value of 1.02. Now suppose that we keep all the data the same, exceptthat we recompute the theoretical value with the stock price set to 51.These, then, are the new assumptions:Stock price: 51Strike price: 55Time remaining: 3 monthsVolatility: 25%Interest rate: 6%With this set of variables, the Black–Scholes model yields a theoreticalvalue of 1.33.What we have just done here is calculate the delta of this option. Thetheoretical value of this option increased by 31 cents when the stock priceincreased by one point, with all other variables remaining the same. Thus,the delta is 0.31.In reality, there is a mathematical equation for computing delta. Thatequation specifies that the delta of this option is 0.28 when the stock is 50
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and is 0.34 when the stock is 51. Thus, the first (less theoretical) methodyielded a result that was the average of the two mathematically computeddeltas. This example also points out that the delta changes all the time, evenas the stock is moving only one point. In any case, you can see that the twoways of computing delta yield very similar results.
You can extrapolate from the preceding example that a Greekis computed by changing one of the four variables that are subjectto fluctuation during any trading day, while leaving the othersunchanged. In this manner, you can measure the isolated effect ofthe change in any one variable on the price of an option. Almost alloption software programs give you all of the Greeks for any option.Mathematically, each of the Greeks is the partial derivative of themodel with respect to one of the four variables. Don’t worry if youdon’t know what a partial derivative is. As a strategist, you only needto know how to interpret the results of the mathematics, not how tocompute the math itself. This is important information, for we canuse it to establish positions that are neutral with respect to any orseveral of the variables. However, before getting into position analysis, let’s describe the Greek terms themselves.
DeltaAs you should know by now, the delta of an option is a measure ofhow much the option changes in price when the underlying changesin price by one point. The delta of a call is a positive number, ranging between 0 and 1; the delta of a put is a negative number, rangingbetween –1 and 0.The delta of an option has been discussed somwhat already, bothearlier in this chapter and in Chapter 1. In the context of the previous example, suppose that in addition to allowing the stock price toincrease by one point, we allowed the other three variables—timeremaining, volatility, and interest rate—to change as well. The theoretical value of the option will certainly change, but how much of it isattributable to the change in stock price? It’s difficult to say, but it isobvious that these other variables affect the delta, too.
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Figure 6.8 shows the relationship of delta and time. Note that theoption with a lot of time