.7+6.9–5.5+9.1+8.8+4.5+21.5+21.7+29.5–16.9*+26.4–5.5*–38.7–10.3*–1.9*
DrawdownIntraday
Close
0.0–2.40.0–0.7–0.7–1.8–7.5–1.20.0–0.8–1.70.0–2.2–17.7*–42.4–6.2*–40.9*–18.4–3.7*
0.00.00.00.00.0–0.3–5.50.00.00.00.00.00.0–16.9*–38.4–5.5*–38.7*–13.9–1.9*
438
TRADING SYSTEMS AND STRATEGIES
any more—four seems to be optimum, and even three days in somecases. Take 2004 as an example: the buy point was 1128.4 (SPXprice) on January 28, the close of the eighteenth trading day of January. Over the next four trading days, SPX rallied about 8 points,closing at 1136 on February 3, 2004, the fourth day. But then onthe fifth day, it fell nearly 10 points and caused the system to recordanother losing year (bottom line of Table 5.8). Also, the year 2000 isworth mentioning, in that a big profit was registered, but the drawdown was huge. Someone trading this with options might have doneokay, but anyone trading it with futures would probably have stoppedhimself out when the loss loomed large during the drawdown (which,by the way, occurred entirely on the first trading day of the system in2000).Here are the adjusted figures for 1999 through 2004, showingthat, in general, there was a market rally during the time frame, but itdidn’t last all five days.Year20032002200120001999
ObservationsProfit existed after day 1 and after day 4.A profit never existed; but loss was minimal after day 3, and SPXcollapsed 28 points on day 5.System +19 points after day 4; fell 24 points on day 5.Big drop on day 1, but recovered to a big profit by day 5.+14 on day 1; still had +7 after day 4; but day 5 was – 24.
So, you can see that in recent years, day 5 has often been a disaster. (In fact, is there are a corollary system that we short the marketon day 5 now?)Incorporating this recent data, the way to trade this system is (1)to use options and (2) to take most, if not all, of your money off thetable at by the end of day 4. The use of options will allow you toknow your maximum risk going into the trade and will allow youto wait out drawdowns (as in the year 2000) without panicking out ofyour position. Your results would be much better than those shownin Table 5.8 if you merely exited at the end of day 4 (true, you wouldhave missed that last 15 points profit in 2000, but you would havestill shown a profit). Table 5.9 shows what exiting at the end of day 4would have done since 1999. This is clearly an improvement, as five
SUMMARY
439
Table 5.9LATE-JANUARY SEASONAL TRADEWITH EXIT AT END OF DAY 4Year
Result at End of Day 4
Result at End of Day 5
199920002001200220032004
+6.7+10.6+18.1–10.8+1.8+7.6
–16.9+26.4–5.5–38.7–10.3–1.9
of six years now make money instead losing money. So, the preferred system is now to be adjusted to exit after four days. If youfeel that day 5 will be good also, you could retain a portion of theposition and see how that day develops, using some sort of tightintraday stop in case it’s another down day 5.
SUMMARYIn this chapter, we have presented a series of trading strategies thathave good track records. Some are very short-term oriented— daytrading—while others are longer-term in nature. You may not followall of them, but at least you can choose the ones that are amenableto your philosophy of trading. When the time is right, whether thatbe daily, or less frequently as with the momentum oscillator, or onlyonce a year as with some of the seasonal trades, analyze the futuresand the options before actually trading. Be aware of fair value of thefutures and of implied volatility on the options. With careful analysis,you should be able to turn profits with the strategies introducedherein.
6
Trading Volatilityand OtherTheoreticalApproaches
In this chapter, we look at another approach to trading, one basedon mathematical evaluations. It is sometimes called neutral tradingbecause the price movement of the underlying security doesn’t haveto be predicted in order to make money. That may be true, but youmust understand one thing: it is certain that you will have to predict something in order to profit, for only market makers andarbitrageurs can construct totally risk-free positions that exceedthe risk-free rate of return, after commissions. Moreover, even if aposition is neutral initially, it is likely that the passage of time or a significant change in the price of the underlying will introduce someprice risk into the position.In Chapters 3, 4, and 5, we have looked at various trading strategies that rely on pricing projections, many of them based on past history or technical analysis. These methods are successful and rational.What they all have in common is that in order for these strategies toprofit, the underlying security generally needs to move in a favorabledirection. There were some exceptions, such as using options inintermarket spreads in order to give yourself an extra chance tomake money if prices are merely volatile; but normally the precedingstrategies were price-dependent. Each strategy, whether it was basedon option volume or on the historical relationship of two markets,had its own particular “edge.” That edge will often be good enoughto generate superior returns.
441
442
TRADING VOLATILITY
However, some traders prefer an approach that relies less onpredicting prices, which many mathematicians claim cannot bedone, and more on the mathematics of options. This, in essence, isthe theoretical approach. With the theoretical approach, youattempt to construct strategies that will make money based on factorsother than price changes. Moreover, since options are a derivativesecurity, there are definite relationships between the option and theunderlying security—and between the properties of both of them—that can be exploited without predicting price movements.This chapter is divided into four broad segments: the introductory material; the basic strategies used for trading volatility within arange; more-advanced strategies for trading volatility within a range;and, finally, trading a volatility skew, a situation where individualoptions on the same underlying security have distinctly differentimplied volatilities.Before getting into the actual strategies, we define some moreterms and properties that are needed for these discussions.
VOLATILITYIn Chapter 1, it was stated that the value of an option is a function ofsix variables: stock price, strike price, time, interest rates, volatility,and dividends (for equity and index options). All of these are knownquantities, except for volatility. As also noted in Chapter 1, there aretwo types of volatility: historical volatility, which tells how fastprices have been changing; and implied volatility, which is theoption market’s perception of future volatility.In order to calculate implied volatility, all you need to do is todetermine what volatility it is necessary to use in your evaluationmodel, so that the model’s theoretical value agrees with the actualmarket price of the option. The model’s general equation can bewritten asOption value = f (stock price, strike, time, rate, volatility)We know the stock price, the strike price, the time remaining toexpiration, and the interest rate. We also know at what price the op-
VOLATILITY
443
tion is actually trading in the marketplace. Therefore, what volatilitymust we use in the model—along with these other four known values—in order for the model to yield the current option price as theoption value? That volatility is the implied volatility.Most option software will quickly give you the implied volatility ofan option or a list of options. The implied volatility is actually determined by an iterative process, which can require a rather large number of calculations; but today’s computers are so fast that you don’treally notice the amount of calculating that’s going on.When trying to evaluate whether an option is expensive orcheap, we usually state that quality in terms of implied volatility.For example, rather than saying, “That option is overvalued,” it ismore common to say, “That option is trading with a high impliedvolatility.” In this statement, the term “high” would presumably bewith reference to the levels of historical volatility or to past measures of implied volatility on this particular underlying security.Many theoretical traders feel that volatility is not only the mostcrucial element of understanding and profiting from option trading,but it is the easiest thing to predict. Therefore, if we could shift ouremphasis away from trying to predict the price movement of theunderlying security and toward trying to predict the volatility of theunderlying security, we could profit with more regularity and lessuncertainty.
In January 1994, the implied volatility of Standard & Poor's 100 Index(OEX) options dropped to its lowest level ever. A compilation of past readings of OEX volatility showed that it had rarely been measured at a levelbelow 10 percent. In fact, it had only dipped to that level two other times.Most of the time, OEX implied volatility had traded higher—normally in the11 percent to 14 percent range in the previous few years—and even athigher levels in the 1980s.Not only that, but historical volatility was low as well, as it stood atabout 7 percent. It had occasionally been as low as 6 percent briefly in its10-year history, and normally ranged in the 9 percent to 12 percent neighborhood, or higher.Meanwhile, the stock market was making all-time highs after a longround of interest-rate cuts by the Federal Reserve System (although therehadn’t been any cuts recently), and bond futures were trading near all-time
444
TRADING VOLATILITY
highs as well. Earnings projections seemed to be quite bullish, and economicactivity was positive, although not overheated. There were some troublingitems out there—utility stocks had made a peak and turned down about fourmonths earlier; and some fundamental valuations of stocks showed them tobe rather high priced, especially in light of the fact that there had not beensubstantial stock market correction for three years.Given these data, which would you feel more comfortable predicting:future volatility levels or the direction of the stock market? If you said volatility, then this chapter is for you. If you said the stock market, then youshould read this chapter also—and I’ll try to change your mind.The fact is that volatility was rarely this low, so you would have to suspect that it was going to increase to more normal levels. Sometimes, suchan increase doesn’t occur right away; although with a market as large as theU.S. stock market, you wouldn’t expect it to take too long. On the otherhand, which way the stock market was headed seemed to be anyone’sguess—as it often is—because there were arguments to justify both a bearish and a bullish scenario. Thus, to me, it seems as if a prediction thatvolatility would increase was much more certain to come true than a prediction of whether the stock market would rise or fall. A simple strategy to takeadvantage of this analysis would be the purchase of a straddle, which couldmake money if prices either rose or fell and would be benefited by anincrease in implied volatility.As it turned out, the Federal Reserve System (the Fed) raised interestrates in early February, touching off a nasty correction in the stock market.Implied volatility exploded to 22 percent by the end of March, and the priceof OEX fell over 9 percent. Straddle buyers profited handsomely.
This example may admittedly be an extreme one: OEX impliedand historical volatilities were at all-time lows, so it was a pretty safebet that they were going to rise. But, in more normal situations, youmight remain skeptical of anyone’s ability to predict future volatility.In the next few sections, we look at two ways of trading volatility andsome simple, as well as complex, ways in which to structure strategies for that purpose.So now the emphasis of our strategy will be on predicting volatility and trading its movements, if possible, rather than on predictingthe price of the underlying security. In fact, we would just as soon beneutral with respect to the price of the underlying, for we don’t care
DELTA NEUTRAL TRADING
445
if it rises or falls, as long as our prediction of volatility is correct.Thus, we need to discuss how to make a strategy price neutral.
DELTA NEUTRAL TRADINGWhen most people talk about trading neutral strategies, they meandelta neutral. Recall that delta is the measure of how much anoption moves when the underlying instrument moves one point. Ifwe calculate the deltas of all the options in a strategic position andadd them together, we can arrive at a position delta, which tells ushow much money we can expect to make or lose if the underlyinginstrument moves one point.Example: Suppose that a trader has a bull spread in place—long the Jan100 calls and short the Jan 110 calls. He can calculate his position delta byusing the deltas of the options in the spread. The pertinent statistics are:Stock Price: 98Option
Position
Price
Delta
Jan 100 callJan 110 call
Long 10Short 10
52
0.500.20
If the stock moves up one point, each of his long calls will increase invalue by a half point, since the delta is 0.50. Thus, since he owns 10 ofthem, the long side of his spread will appreciate by five points when theunderlying stock moves up one point.Meanwhile, the Jan 110 call that he is short will increase in value by 20cents if the stock moves up one point. So, the 10 of them that he is shortwill increase in value by a total of two points.Therefore, his position delta is long three points (the longs will increaseby a total of five points, while the shorts will increase in value by two points,hence the net of these is five minus two, or three). This means that his position will increase in value by $300 if the underlying moves up one point; italso means that his position will lose $300 if the stock falls by one point.
446
TRADING VOLATILITY
The position delta is also called the equivalent stock position(ESP), or if futures and futures options are being evaluated, the position delta can also be referred to as an equivalent futures position(EFP). The position delta can be calculated for any complex portfoliomerely by calculating each option’s equivalent stock position andsumming them all together. The simple formula for calculating anequivalent position in an individual option is:ESP or EFP = quantity × trading unit × delta of optionAgain, using the data from the preceding example, we can calculate the equivalent stock position of the two options in the spread. Inboth cases, the “trading unit” is 100 (for 100 shares per option).ESP of Jan 100 call = 10 × 100 × 0.50 = 500 sharesESP of Jan 110 call = –10 × 100 × 0.20 = –200 sharesTotal ESP = position delta = 500 – 200 = +300 sharesThus, owning this spread is “equivalent” to owning 300 shares ofthe underlying stock. Of course, as the underlying stock moves up ordown, the deltas of the options will change (they will also change astime passes). When the deltas change, the ESP will change as well.But for this moment, the position is equivalent to owning 300 sharesof the stock.So, it is a simple matter to compute the position delta on even acomplex option strategy and “reduce” the position to an equivalentnumber of shares of the underlying stock. If this position delta is verynear to zero, then we have a neutral position that won’t make or losemoney if the underlying stock moves one point. This is extremelyuseful information because, if you want to hedge the risk of yourposition, you merely have to use that information to take an equalbut opposite position in the underlying stock. In the preceding example, you would sell short 300 shares of the underlying stock in orderto neutralize your price risk (at least for the moment).Such a position is considered to be a delta neutral positionbecause it is neutral with respect to the variable, delta. The neutralposition has always held attraction to investors, especially those who
DELTA NEUTRAL TRADING
447
(1) are mathematically inclined, (2) believe prices move in a randommanner, or (3) are just tired of trying to predict the market and beingincorrect. In theory, if you were able to sell an “expensive” optionand hedge its sale with the purchase of a “fairly” priced option, youcould capture the differential in price by a neutral position. Mathematics bears out this philosophy, but the reality of trading such aposition is more difficult than you might expect. In reality, neutraltrading can be very dangerous if you aren’t careful.In a delta neutral position, the other variables that affect theprofitability of a position are not necessarily neutral, but at leastdelta is. When you have a delta neutral position, you have no risk ofloss or potential for gain for small, short-term moves by the underlying instrument. However, if the stock rises or falls too much, or iftime passes, or even if the implied volatility changes, the delta ofeach option will change. Once these deltas change, the position willgenerally no longer be delta neutral. In fact, it might acquire quite abit of risk.In July 1993, soybeans had rallied quite a bit because of heavy rains andflood conditions in the Midwest. Options had gotten quite expensive, and astrategist might have considered a ratio spread as a way of establishing adelta neutral position. The following statistics describe the position on July2, 1993:August Soybeans: 665Quantity/Option
Price
Delta
Position Delta (EFP)
Long 50 Aug 650 callsShort 100 Aug 700 calls
301⁄212
0.630.31
Long 31.5 contractsShort 31.0 contracts
Total:
Long 0.5 contracts
This position is very nearly delta neutral, since the EFP of the longoptions is just about completely offset by the EFP of the short options.Since these options were due to expire on July 24, 1993, they were quiteshort-term options. This led to the appeal of a neutral position.A three-day weekend including the Fourth of July followed, so the nexttrading day was July 6. The floods had worsened, so beans opened up thelimit and remained there. The following prices existed at that point:
448
TRADING VOLATILITYAugust Soybeans: 695Quantity/Option
Price
Delta
Position Delta (EFP)
Long 50 Aug 650 callsShort 100 Aug 700 calls
59321⁄2
0.740.50
Long 37 contractsShort 50 contracts
Total:
Short 13 contracts
At this time, the position had become seriously delta short. Not onlythat, the position was losing significant money. The 50 longs had appreciated by 281⁄2 points, or $71,250. However, the 100 short options had lost201⁄2 points, or $102,500. The overall unrealized loss was $31,250.Even though the position was delta neutral initially, it had destabilizedsignificantly in just one trading day, quickly becoming delta short and losingconsiderable money.
This example demonstrates just how deceiving a delta neutralposition can be; such a position is only delta neutral for small movesby the underlying security (soybean futures, in this case). Notice thatthe losses could be significant even for the smaller trader. Using thesame example, if you were long 5 of the Aug 650 calls and short 10of the Aug 700 calls, you would still be losing $3,125 on that smallposition in just one trading day.The preceding example demonstrates the importance of therelationship between price and delta. However, delta can also besignificantly affected by volatility, or, more appropriately, impliedvolatility—that is, if the options get more expensive or become muchcheaper in terms of implied volatility, the deltas of the options canchange. Any such change would distort the neutrality of a delta neutral position.Federal Paperboard (FBO) was trading just under $40 a share in late October 1995 when a vague takeover rumor surfaced. Initially, the rumor wasmore evident in the price of the options than it was in the price of thestock—that is, the options gained considerable implied volatility, but thestock only rose slightly. The following statistics show how such an eventaffected a delta neutral position. On October 30, 1995, the following pricesexisted, and a trader might have established a delta neutral spread, notknowing that there was a takeover rumor:
DELTA NEUTRAL TRADING
449
FBO: 395⁄8; Implied Volatility of the Options: 54%Quantity/OptionLong 10 Jan 40 callsShort 30 Jan 45 calls
Price
Delta
Position Delta (ESP)
3⁄2
0.520.16
Long 520 sharesShort 480 shares
Total ESP:
Long 40 shares
1
This initial position has an ESP very nearly zero, so it is considered tobe delta neutral. Within three days, the stock had edged up to 41—not alarge move. However, option buyers obviously had some informationregarding the takeover rumors and were bidding up the options, which hadincreased to an 89 percent implied volatility just three days later. This is asignificant increase in implied volatility, and the position had thus acquiredthe following look:FBO: 41; Implied Volatility of the Options: 89%Quantity/Option
Price
Delta
Position Delta (ESP)
Long 10 Jan 40 callsShort 30 Jan 45 calls
51⁄221⁄4
0.600.32
Long 600 sharesShort 960 shares
Total ESP:
Short 360 shares
So this position had now acquired the look of a short position, equivalent to being short 360 shares of FBO. Part of that change in the delta wasdue to the stock’s increase in price from 395⁄8 to 41, but the majority of itwas due to the explosion in implied volatility. Also notice that this relativelysmall position was showing an unrealized loss of $2,750 after this change inimplied volatility.
The general relationships between delta and time and betweendelta and volatility are discussed in more detail later in this chapter.The previous two examples involved selling naked options. Neutral positions don’t always require you to have naked options inthem. In fact, you can construct delta neutral positions with longoptions in them (backspreads, for example). However, that doesn’tmitigate the fact that a price change or a change in implied volatilitycan severely alter the neutrality of the position.
450
TRADING VOLATILITY
Keeping a Position NeutralSometimes, when the neutrality changes, losses result. Even if lossesdon’t accrue, the position acquires market risk as it becomes eitherdelta long or delta short. The position might eventually becomeprofitable, but it is important to understand that merely establishing adelta neutral position doesn’t mean that you can just walk away fromit and make a profit. Since price changes by the underlying securityaffect the neutrality of the position, it is necessary to readjust thedelta to keep the position neutral.The easiest way to adjust a position back into a delta neutral status is to use the underlying security. In the most recent example, theposition had become delta short 360 shares of FBO after the impliedvolatility increased. Obviously, that delta could easily be neutralizedby buying 360 (or, more likely, 400) shares of FBO. Then the position would once again be delta neutral. Of course, it would still besusceptible to further swings in position delta, each of which wouldrequire another adjustment.Another way to adjust the FBO spread back to neutrality would be to buysome more of the Jan 40 calls, which were already long in the position.After the stock rose to 41 and implied volatility ballooned to 89 percent, theposition was delta short 360 shares of FBO. Moreover, the delta of the Jan40 calls was 0.60 (see the preceding example for these details).Notice that the ESP of one Jan 40 call is 60 shares:ESP = 1 × 100 × 0.60 = 60 sharesSo, if you were to buy six more of these Jan 40 calls, you would beadding 6 × 60, or 360, delta long into the position. This would completelyand exactly neutralize the existing delta short position. Thus the new position would be:Quantity/Option
Delta
Position Delta (ESP)
Long 16 Jan 40 callsShort 30 Jan 45 calls
0.600.32
Long 960 sharesShort 960 sharesTotal ESP:
0 shares
DELTA NEUTRAL TRADING
451
So, you could either buy stock or buy more of the calls that youare already long in order to adjust. These are the most common tactics used, although you may also buy in some of your short calls. Infact, you could buy any calls in the proper amount in order to neutralize the position. Usually, small traders will buy one or the other ofthe calls that are already in the position. However, a market makeror a trader with a large position may be forced to buy whatever isbeing offered. Thus, he might wind up with a rather complex position. It is no problem to evaluate the neutrality of the larger, morecomplex positions, though, since the same ESP formula can beapplied to each option in the position, no matter how many of themthere are, and the result totaled.Market makers attempt to keep their positions neutral. They prefer to make their money by buying on the bid and selling on the offer.If they have to carry a position, they would just as soon that it nothave any price risk. Market makers of listed options can usually extricate themselves from their positions fairly quickly, especially if theoptions are liquid. However, over-the-counter option market makers(which include several of the largest banks and brokerage houses) andmarket makers in illiquid options may be forced to carry their positions for quite a while before they can hedge them off completely orbefore the options expire. These are the market makers who keeptheir positions neutral and make adjustments as time goes by.
The necessity of these market makers to adjust positions raises the specterof something similar to what caused the crash. Recall from the example inChapter 3 that practitioners of portfolio insurance had to sell futures inhuge quantities in order to protect their stock positions. That practice is nolonger being followed. However, what is being done by some of these sameinstitutions for protection is that they are buying puts as insurance against alarge market decline. Many of these puts are of the over-the-counter variety,being transacted directly between buyer and seller and tailored in specificways as to expiration dates, striking prices, and underlying “security.” Infact, the underlying security may be a very specific basket of stocks thatresemble the stocks in the institution’s portfolio.Someone, of course, is selling these puts to the institutions that are buying them. That “someone” is the over-the-counter market makers—largefirms such as Salomon Brothers, Goldman Sachs, Morgan Stanley, Swiss-
452
TRADING VOLATILITY
bank, or Banker’s Trust. The puts are generally overpriced when the institution buys them—that’s why the trading houses are willing and eager to sellthem. So all the market maker has to do is hedge his portfolio properly, andhe will profit to the tune of the “overpriced” portion of these puts. If he isshort puts, that makes him delta long. Since most of these puts are on baskets of stock or on broad-based stock indices, the market maker is thus deltalong “the market.” He can easily hedge this long by selling S&P 500 futures.What worries some regulators is that if the market were to head downin earnest, as it did in 1987, these market makers might have to sell a lot offutures in order to hedge their short put positions. Since these puts werecreated in over-the-counter transactions, no one really knows how many ofthem are in existence, in total. Moreover, no one knows the extent of thehedges at any time. So there is some chance that what happened in 1987to worsen the market decline on the day of the crash could happen again.
These over-the-counter market makers are smart traders. So theyunderstand the ramifications of a portfolio that is too delta long or thathas the potential to become too delta long if the market declines.Thus, they have attempted to balance out their portfolios whereverpossible by encouraging institutions or other traders to sell puts. This,of course, would transfer the potential of downside liability from themarket makers to other traders. Overall, however, it seems to me thatmost institutions are overall net buyers of puts for their insurancevalue. Thus, whoever sold those puts, be it market makers or otherinstitutions, have potential downside liability. Perhaps the marketwon’t ever decline so severely or so far that it would force those whoare delta long to take drastic measures, but you can’t be sure.
Other Forms of NeutralityWe have already shown that delta neutral trading is only neutral for ashort period of time and within a fairly short price range of theunderlying. As long as you understand this fact, you can devisestrategies that will compensate and adjust for the changing delta.However, if there is too great a change in price or in implied volatility, there may not be any adjustments that can “save” the position.Throughout history, we have seen such gaps and they have been
DELTA NEUTRAL TRADING
453
costly to delta neutral traders. Earlier in this book, we gave severalexamples of this: the crash of 1987, the large rally in April 1978, orthe Barings Bank problem that began with straddle selling.When neutral trading first became possible shortly after the introduction of listed options in 1973, there were only a few practitioners. Option premiums were extremely expensive in those times, andthe neutral strategies worked fairly well, although even at that timethere were problems caused for ratio writers by large rallies in October 1974, January 1975, and January 1976. Then listed puts became available, and straddle selling seemed extremely profitable; soeven more “delta neutral” adherents began to surface.Note that straddle selling is less “neutral” than is the type of callratio spread that we used in the earlier examples in this chapter.True, you may be able to initialize a position that has no delta tobegin with. However, almost any movement at all by the underlyingwill cause a straddle position to lose its neutrality.Example: XYZ is 50.Quantity/Option
Delta
ESP
Short 9 XYZ Jan 50 callsShort 11 XYZ Jan 50 puts
0.55–0.45
Short 495 shares of XYZLong 495 shares of XYZTotal ESP:
0 shares
This is a typical, delta neutral, short straddle position, established whenthe underlying is near the striking price of the short straddle. You sell a fewmore puts than calls in order to make the position delta neutral. Now, if thestock moves a little higher, the delta of the call might increase