he payout at option expiry.
will be unclear, and the results of serial straddle writing or buy-ing will be very much a mixed bag (Figure 7-3).THE PROMISED LAND 107
$&P 500 INDEX January 1997 option and April 1997 future
January Change *Futureat ATMSe ATMSr ATMSt Days ImpliedDate future (no sign)(as%) expiry expiry rec'd -ATMSr left volatility
 
 
Novs 74080 78075 3995 3533 462 «49 13.63Nov 11 74065 15 0.02 78075 4010 3510 500 48 13.68Nov 12 73855 210 0.28 78075 4220 3468 -752 47 13.70Nov 13 74075 220 0.30 78075 4000 3349 -651 46 13.33Nov 14 74585 510 0.68 78075 3490 3287 -203 45 13.14Nov 15 74750 165 0.22 78075 3325 3218 10700 44 12.98Nov 18 74705 45 0.06 78075 3370 3255 115 43 13.29Nov 19 75315 610 0.81 78075 2760 3283 523 42 13.45Nov 20 75305 10 0.01 78075 2770 3464 694 4 14.37Nov 21 75245 60 0.08 78075 2830 3334 504 40 14.01Nov 22 75820 575 0.76 78075 2255 3288 1033.39 13.89Nov 25 76700 880 1.16 78075 1375 3383 2008 =. 38 14.31Nov 26 76445 255 0.33 78075 1630 3571 1941 37 15.36Nov 27 76305 140 0.18 78075 1770 3528 1758 = 36 15.41Nov 29 76530 225 0.29 78075 1545 3518 1973-34 15.77Dec 2 76510 20 0.03 78075 1565 3479 1914 33 15.83Dec3 75255 1255 1.67 78075 2820 3607 787) = 32 16.94Dec4 75475 220 0.29 78075 2600 3343 74300¢«O31 15.91Dec 5 75245 230 0.31 78075 2830 3378 548 8=30 16.39Decé 74755 490 0.66 78075 3320 3404 84 29 16.91Deco 75855 1100 1.45 78075 2220 3178 958 28 15.84Dec 10 75510 345 0.46 78075 2565 3089 $24 27 15.75Dec 11 74655 855 1.16 78075 3420 3202 -218 «26 16.82Dec 12 73450 1205 1.64 78075 4625 3386 = -1239. 25 18.44Dec 13 73640 190 0.26 78075 4435 3378 = -1057 24 18.73Dec 16 72775 865 1.19 78075 5300 3263-2037 23 18.70Dec 17 73325 550 0.75 78075 4750 3000 «-1750 22 17.45Dec 18 73815 490 0.66 78075 4260 2809 =-1451 21 16.61Dec 19 75350 1535 2.04 78075 2725 2727 2 20 16.19Dec 20 75725 375 0.50 78075 2350 2668 318 19 16.17Dec 23 75410 315 0.42 78075 2665 2593 72 18 16.21Dec 24 75905 495 0.65 78075 2170 2437 267 17 15.57Jac 26 76460 585 0.73 78075 1615 2377 762 15 16.05Dec 27 76460 oO 0.00 78075 1615 2377 762 14 16.62Dec 30 75910 550 0.72 78075 2165 2283 118 13 16.68Dec 31 74450 1460 | 1.96 78075 3625 2356-1269 12 18.27Averages ——~B> 486 0.65 2972 3148 176
* On January 17, the Jan 97 option expired at 78075
FIGURE 7-3. In contrast to the previous examples of crude oil and silver, theS&P500 Index, over the period November 8 to December 31, generated mixed tradingresults slightly favoring the straddle writer.
To make any sound conclusion about the buyer or the writer'sexpectation in general, it will be necessary to look at the outcomesof hypothetical straddle positions taken in many different com-modity markets and over a much longer period of time.
*108 OPTION REALITY
Option premiums begin to shrink rapidly as the optionexpiry date approaches, so, in order to keep the size of thehypothetical straddle premiums over an entire year roughlycomparable, it is appropriate to switch to a new futures con-tract approximately every 2 months. (The final hypotheticalstraddles listed in Figures 7-1, 7-2, and 7-3 occur with at least10 trading days remaining till option expiry.) There is no loss ofcontinuity in switching months, since each hypothetical strad-dle is independent of all others, regardless of the future onwhich it is based.
It would be impractical to document here all the individualresults from all the observations in the data base, though theentire data base is available for inspection— and possible inde-pendent testing by the reader—at the end of the book. Thecumulative results of taking one hypothetical straddle position in15 diverse commodity markets, every trading day of calendar year1996— and holding that position till option expiry —are summa-rized in Figure 7-4. On average, there are 252 trading days peryear per commodity, and the total number of observations turnsout to be 3781. The precise number of trading days in a calendaryear varies according to the holiday policies of differentexchanges and can also vary due to occasional emergency shut-downs, as happened during severe weather in January of 1996.(And more extensively in a previous year when the World TradeCenter in New York was bombed—an unexpected bonus foroption writers.)
In order to make results directly comparable and compensatefor vastly different contract sizes, equal weightings are given tothe results from each of the 15 commodities, in the followingway. The average payout received for buying a straddle and hold-ing it till expiry is divided by the average premium collected forwriting that straddle. A ratio of exactly 1 indicates that the mar-ket neither favors the writer nor the buyer. The payout ratio mea-sured for the 15 commodities under study ranges from a low 0.50in sugar (most favorable to the writer) to a high of 1.42 in wheat(most favorable to the buyer).THE PROMISED LAND 109
* Tradin Average Average Payoutdavs 1 Premium Payout Premium
FINANCIALSS&P 500 254 2459 2160 0.878T-Bonds 252 298 283 0.950Swiss franc 254 219 251 1.146Yen 254 228 222 0.974
RESOURCEGold 252 107 134 1.252Silver 252 369 261 0.707Crude oil 251 167 232 1.389Cotton 249 466 328 0.704
FOOD
Soybeans 254 452 521 1.153Wheat 254 364 517 1.420Com 254 281 379 4.349Cattle 254 272 151 0.555Cocoa 249 88 87 0.779Coffee 249 1348 1871 1.240Sugar 249 78 39 0.500Total —— 3781 Average —- 1.000
* Different exchanges operate on slightlydifferent business schedules
FIGURE 7-4, Average premiums received and average payouts made during calen-dar year 1996 have been calculated for straddle positions on 15 actively traded com-modities —from a total of 3781 independent observations.
To make the results directly comparable and to accord the same weighting to eachcommodity in the overall result, the ratio of average payout to average premium hasbeen calculated for each commodity, with a ratio of 1.0 indicating the break-even con-dition. Surprisingly, the overall average of this ratio turns out to be almost exactly 1.0(a statistical fluke), indicating a fairly priced overall market.
These two extreme values of the payout ratio do not provide anyinformation on the relative pricing of options on sugar and wheat.It just so happened that during the course of calendar year 1996wheat experienced a major bull market followed by a major bearmarket, while sugar basically did nothing. Even if wheat optionshad been greatly overpriced in relation to wheat's average dailytrading range, buyers of wheat options would probably still havecome out winners; and even if sugar options had been underpriced,sugar option writers would probably still have come out on top.110 OPTION REALITY
The payout ratio that is truly meaningful is the overall payoutratio, and rather surprisingly, this turns out to be almost exactlyequal to one. Of course, it is something of a fluke that the aver-age ratio should be this close to unity. Nevertheless, it is the bestestimate of the true ratio, and, if all 3781 independent straddleshad, in fact, been written or purchased, the net result — ignoringtransaction costs—would have balanced out very close to zero.No clear winner.
I have to rank this finding as something of a major surprise,because, if truly representative, it means that in general there isno intrinsic writer's edge in the options market, and I certainlywas expecting to find some kind of edge. I believe most optiontraders would have expected the same thing. This rather surpris-ing conclusion can be summarized as follows: The conventionalwisdom that indiscriminate option buying is a losing play is incor-rect. At the most general level, the option market is remarkablyefficient, neither favoring the buyer nor the writer, and equalizingtheir expectations at zero.
I was sufficiently surprised by this finding to suspect somesort of computational error. There is none that I can see. Onepossibility which must be acknowledged is that even a samplesize approaching 4000 may not be large enough to be truly rep-resentative of the universe of all option trades. Is there anyprecedent for nonrepresentative conditions prevailing over sucha length of time and averaged over such a diverse group of com-modities? The answer is yes, but it is a rather muted yes.
Suppose 1972 had been chosen instead of 1996. Almost everyresource and food commodity was caught up that year in a gen-eral inflationary spiral precipitated by a sudden quadrupling ofoil prices. (Not that a general bull or bear market guarantees askewed result, for much depends on how option writers react, asa group, to a period of sustained option writing losses.)Regardless of which side a generally trending market finallyfavors, any deductions from a price data base derived from sucha year would have to be interpreted with some caution—simplybecause it is an aberration. (The year 1972 has always been afavorite one for testing historical price data to back up a claimfor a commodity trading system, since it always generates,retrospectively of course, such amazing returns.)THE PROMISED LAND 111
Ultimately, the reader must judge whether 1996 is typical oratypical of general commodity price behavior. To assist, detailedweekly price charts for all commodities are included in Chapter10, under "Volatility Profiles." Generally, grains experienced bothmajor bull and bear trends, gold drifted steadily lower as did thecurrencies and treasury bonds. The S&P 500 worked irregularlyhigher. Coffee, sugar, cocoa, silver, cattle, and crude oil experi-enced no major moves. In broad terms, an unexceptional year.
In the absence of any compelling reason to doubt the findingof equality of expectations for the buyer and the writer, I mean totake the result as valid until proven otherwise. One way to proveit otherwise would be to repeat the whole exercise for 1997, orany other year. But that is a task for someone else.
It is worth noting that equality of expectations in option trad-ing does not imply that commodity prices are random in the longterm. What equality of options expectations does say is that theoptions market, as a whole, manages to price itself fairly after tak-ing into consideration whatever trend component exists in com-modity futures prices. And doubtless, this balancing act occursthrough that most elemental of self-correcting mechanisms, thereactions of the players to their experiences as winners andlovers.
*
What does equality of expectations tell option buyers thatthey may not have known before? Most palpably this: The strat-egy of buying options to establish a fundamental position in afutures market now compares rather more favorably with thestrategy of taking an outright futures position. Not that theexpectations of the two strategies are necessarily any different—both are still 50-50 propositions. The option position does how-ever have the feature of built-in stop-loss protection, or stayingpower, that the futures position lacks—a feature that now looksconsiderably more attractive.
What does equality of expectations tell option writers thatthey may not have known before? Most palpably this: Thestraightforward strategy of indiscriminate option writing is not112 OPTION REALITY
automatically going to be a winning play. Even if a writer coversevery option in every market, he or she will still wind up havingno positive expectation-—certainly no significant expectation. Andthis, too, before any transaction costs are considered.
*
Before exploring, in the next chapter, the implications of this"unexpected" finding of equality of expectations, it is worthreviewing, perhaps, how the most fundamental equations dealingwith option option valuation tie together. None of these equa-tions is difficult to apply, but it is not always immediately obviouswhich one is appropriate in a particular circumstance. A numer-ical example will be helpful at this point.
Consider the silver market, say, where the following informa-tion is known at a particular time.
At-the-money option price = 21.6centsCorresponding futures price = $6.00Trading days till expiry = 36Average daily price change
(measured over 30 days) = 5.4cents
A trader wishes to know if this option is overvalued or under-valued in relation to the current market volatility. The time inter-val over which market volatility is measured is at the discretionof the trader, of course. (In this case, let us assume that pricechanges have been measured over 30 trading days.) The meanabsolute deviation is the average daily price change taking all val-ues as positive, and this deviation may be expressed either as anabsolute price unit or as a percentage of the futures pricedepending on the equation in which it is used.
Overvaluation or undervaluation can be assessed by compar-ing volatilities (implied versus market). This exercise, naturally,only works for at-the-money options.THE PROMISED LAND 113
Observed market volatility = 20 x MAD (by Eq. 5-2)
20 x 5.4 x 100600
18.0 percent
7 40 x ATMOImplied volatility = e (by Eq. 3-8)t
40 x 21.6 x 100600 x 136
24 percent
By this comparison, the silver option would appear to beovervalued.
The limitations of the usefulness of valuation judgmentsusing these equations should be well understood. First, the num-ber of trading days used in the calculation of the mean absolutedeviation is always arbitrary. Second, an option may appear to besubstantially overvalued or undervalued relative to current mar-ket volatility, yet still be fairly priced in relation to other marketimponderables weighing on the market—a crop forecast about tobe released, or a major political uncertainty on the point of beingresolved, say—forces whose potential impact on option pricesmay not be reflected in recent futures price action. The “unre-flected uncertainty" component of an option pricing structurewill be explored in detail in the next chapter.CHAPTEREIGHT
BORN AGAIN
an a finding of quality of expectations for option buyersC and option writers be reconciled with common sense? Itdoes seem only fair that option writers be awarded something fortaking on risks with unlimited liability and that option buyersshould have to pay something for the privilege of enjoying limitedliability. Could this be happening, even under equivalence ofbasic expectations? I believe the answer is yes, for I was forget-ting two things.
One is rather obvious: The writer gets to invest the proceedsreceived for writing the option, whereas the buyer has capital tiedup in the options transaction until the option is exercised, therebymissing Out on interest that could be earned elsewhere. If short-term interest is at 5 percent, the option writer has a built-in 10percent advantage over the option buyer. In general, with$100,000 in equity, a well-diversified option writing account cangarner an equivalent amount in option premium — funds that canbe invested in short-term fixed interest securities and still be usedto margin positions. At 5 percent nominal interest, then, a diver-sified option writer can expect a risk-free return of something like10 percent on his invested capital. The option buyer is immedi-ately behind to the extent that he receives no interest at all.
The second advantage accruing to the writer is not quite soobvious: It lies in his ability to take dynamic action after theoption has been written. Let's consider, first, the option buyer's"options" after the option is bought. The buyer really has no fol-low-up strategy that makes sense; it is very much a case of buy,hold, and wait. Certainly, an option buyer may resell an option inthe open market at any time, but under what rationale? If the
115116 OPTION REALITY
option is appreciating in value, he will want to hold on to it, forto sell out an option whose price is going up is tantamount toselling into a trending market in the underlying future, a strategyknown to be unsuccessful in the long run. If the option is declin-ing in value, the loss may be due either to time decay or to anunfavorable move in the futures price. Regardless, the option willstill reflect fair value (on average), and will certainly not be pos-ing any immediate threat to the trader's equity, since the optionwill have already been paid for.
An option writer, on the other hand, faces starker choiceswhen contemplating an option that is going against him. The rea-son is that when an option is going against an option writer, it isalways due to a sustained trend developing in the underlyingfutures market. An option position which is allowed to appreciateunchecked will eventually become equivalent to a full-blownfutures position and pose an unacceptably large risk to the trader'soption-writing account. At the very least, a deep in-the-moneyoption will mean large daily swings in account equity—a rollercoaster effect that an astute option writer will strive to avoid.
It is prudent, therefore, for an option writer to have somekind of defensive plan drawn up in advance to handle an optiongoing against him in a big way. The ability to take defensiveaction, the freedom to act dynamically, is an asset the optionwriter must be prepared to exploit. He is in much the same situ-ation as the backgammon player who has been doubled by hisopponent--down but not out.
Figure 8-1 shows the distribution of wins and losses associ-ated with the hypothetical writing of the 3781 at-the-moneystraddles described in the previous chapter, where the overallresult is known to be very close to break even. With individualstraddles, the most favorable result for the option writer is a pay-out ratio of zero, while the most unfavorable result (theoreticallyunbounded) comes in at a payout ratio of around 6.0. A goodnumber of payout ratios fall in the 2.0 to 3.0 range, and if awriter by some preemptive defensive action could bring downthese large payouts, the overall payout ratio would drop sub-stantially. The crucial question, of course, is this: Can theoption writer take defensive action which will cut into losingtransactions without reducing, proportionally, the payouts fromBORN AGAIN 117
500Retums from indiscriminate buying orwaiting d at-the-money option straddles400g Mf Writer Wins@ Buyer Wins2= 300333°°@ 2002£3z100
 
Oo 05 1 15 2 25 3 35 4 45 5 55 6Ratio of payout to premium received
FIGURE 8-1. The frequency distribution above is compiled from 3781 independentobservations of the outcome of buying or writing at-the-money straddles during calen-dar year 1996. The most a writer can gain on any one transaction is 100 percent of thepremium (equivalent to zero on the ratio scale of the x axis). The buyer's gain on anyone straddle is theoretically unlimited.
In the distribution above, the writer prevails in most of the transactions (about2200 times out of 3781). The writer's overall expectation, however, is close to zero,since the higher percentage of winners is balanced by a lower average amount won.
winning transactions? If the answer to this question is yes, thenthe option edge can shift in favor of the writer.
*
An option writer who is going to employ a defensive strategymust be prepared to abide by some discipline that announceswhen action is necessary. Defensive action is necessary only inthe event that the value of the straddle is increasing; the writerhopes, naturally, not to have to cover the straddle at all. To avoidexcessive transaction costs, the writer must limit the number ofstraddles to be defended to those cases where there is a substan-tial adverse price move. If this rule is to be consistent in differ-ent commodity markets at different times, then the amount118 OPTION REALITY
risked on a position ought, logically, to be related to premiumreceived.
There are several ways to deal with a potentially troublesomeoption. Most obviously, the writer can simply close out the posi-tion by purchasing the previously written option in the free mar-ket. In the case of a straddle, the writer can buy both sides or justthe side that is causing the loss. The advantage of the "close-out"solution is that the transaction becomes history, any funds previ-ously tied up in margin are immediately available to financeother transactions, and the writer can look for writing opportu-nities elsewhere. The disadvantage of the close-out solution isthat by the time an at-the-money option has moved far enoughagainst the writer to be creating a problem, it is going to be wellinto the money, and therefore likely to be rather thinly traded.Since the writer at this juncture will be looking to exit the mar-ket rather smartly, he or she may have to enter a market order inan illiquid trading environment and may have an order filled wellaway from fair value. The writer may not even know what fairvalue is, since the option will no longer be close to the money,and the million dollar formula won't help. Whatever fair value is,the writer can be pretty sure of getting less. A writer who doesnot close out with a market order, or near market order, and triesto finesse for a predetermined price, could be stuck, unhedged,in a market that is running away.
An alternative to closing out a problem option is to "freeze"the loss by purchasing a more liquid option on the same future.This solution probably gets the seller a fairer price, but, althoughit does limit the loss, the complex options combination must beheld until option expiry and the ultimate loss will not be knownuntil option expiry. Trading capital will also be tied up to someextent.
A third way to temporarily neutralize a problem option is toinitiate a position in the underlying futures contract. The appealof this strategy is that market orders can be used, since thefutures markets is going to be much more liquid than the optionsmarket. The downside of defending an option with a future isthat the strategy may require additional defense if the futuresprice should whipsaw after the position is taken. This strategyalso ties up capital.BoRN AGAIN 119
If an option writer can set the levels at which to take protec-tive action far enough from the market to ensure that relativelyfew options need be defended—and transaction costs therebyminimized, any of the defensive strategies described above willhave the same long-run expectation, just as all logical trend-fol-lowing "systems" for trading commodity futures have the samelong-run expectation. There may be no hard evidence to back upthis assertion, but it is one of the few assertions that I am happyto take on intuition alone.
It is virtually impossible to track, historically, the day-to-dayprice of any particular straddle after it has been written. Testingof defensive strategies based on option close-outs is therefore nota feasible proposition. The futures defensive strategy can, how-ever, with some considerable difficulty, be put to the test. A sys-tem based on action at closing prices will give unbiased estimatesof the prices at which transactions would have been made. In theexceptional instances where a market closes at a limit price, theopening price on the following day can be used instead of theclosing price.
Historical opening, high, low, and closing prices are readilyavailable for all actively traded future contracts. This informationallows for the testing of hypothetical futures trades using good-till-cancelled stop-loss orders, which may be activated during atrading session. A problem with testing using stop-loss orders,however, is that under certain very volatile market conditions theopening, high, low, and closing prices do not unambiguouslyreveal whether the high or the low came first, and thus a hypo-thetical stop order might be hypothetically "missed" when, inhypothetical reality, it would have been elected!
Numbers in the financial press, too, have become less trust-worthy because of the emergence of subsidiary futures markets(to satisfy the cravings of insomniacs) called Globex—wherefinancial instruments such as stock index, interest rate, and cur-rency futures can be traded almost round the clock. A Globexsession on the S&P, for example, commences shortly after themain Chicago Mercantile Exchange trading pit finishes businessfor the day, and continues overnight, closing just 15 minutesbefore Chicago reopens on the following day. Opening, high, low,120 OPTION REALITY
and closing prices quoted in the financial press reflect Globexvalues as well as Chicago values, and the former can be all overthe map because of the thinness of trading. It is therefore impos-sible to trust results from hypothetical stop loss trading usingthese numbers. No such problem exists with using closing prices,however, as these always reflect the official exchange closings.
It goes almost without saying that any defensive system anoption writer uses to limit losses on straddles that are going souris bound to have some negative impact on transactions that wouldhave been ultimately profitable at option expiry without interven-tion. You can't have your cake and eat it too.
*
Figure 8-2, which consists of a series of hypothetical strad-dles on crude oil—excerpted from the data base described inChapter 6—shows how an option writer might employ a defen-sive strategy using a futures position to offset the losing optionside of a straddle which has increased in value by a certainamount—a quantity to be determined ahead of time under someconsistent rule equally valid in all commodities.
In testing the entire data base (Figure 8-2 contains just 43hypothetical transactions out of a total of 3781), the size of anadverse price move at which an unrealized loss on a straddle wasdeemed sufficient to trigger an offsetting futures transaction wasdefined in this arbitrary, though consistent, way:
If a commodity future closes at a price higher than the strike price ofan at-the-money straddle plus the value of the straddle premiumreceived, a hypothetical ong futures will be initiated at that