of option writers; certainly those optionwriters who were not employing very strict defensive strategies toprotect any puts they had written.
Huge stock market declines are bound to be accompanied bygreatly expanded option prices on stock index futures, simplybecause the uncertainty following such an event is so acute.Figures 8-7 and 8-8 show how S&P options and futures reactedin the days leading up to and following the days of the large pricedeclines. In the debacle of 1987, on the Friday preceding "CrashMonday," the implied volatility of the at-the-money S&P optionexpanded from 22.90 to 27.22, a steep rise, to be sure, but not asurprising increase in view of the larger than normal drop in theBorN AGAIN 147
futures market that day. The S&P options market has alwaysbeen very sensitive to even slightly larger than usual daily pricedeclines in stock futures, for there is a constant and justifiablefear among option writers of a sudden downside washout in stockprices. (Memories of 1929 still lingered in 1987.)
No one, of course — including the holders of put options whomay claim great after-the-fact wisdom-—-could have foreseenwhat would happen on Monday, October 20. Not even in 1929had a one-day decline of 25 percent--or anything like that—been experienced. The crash was of such unprecedented propor-tions that settlement prices on S&P options could not bepublished, the first and only time this has occurred. On the dayfollowing the crash, Tuesday, October 21, S&P futures closedhigher, and option settlement prices were available, but only onthe December series (November was still the front month).Option implied volatility had shot up from 27.23 to 83.51. Thenext day, futures rallied again, and implied volatility shrank to56.08.
What happened subsequently is rather curious. A couple ofdays later, on Friday, October 23, a quietish day in which futuresdeclined from 244 to 241, implied volatility shot up again to 85percent, and on the following day to 93 percent. It was as ifoption traders had all woken up to a new reality and decided col-lectively, overnight, that options were way too cheap. I find thisa curious reaction, because, in a high-priced environment, espe-cially an environment in which stability appears to be returning,option implied volatility usually drops quite sharply.
Within a few days, implied volatility had dropped back to the40 to 50 percent range. To a lesser extent, the same optionimplied volatility pattern emerged after in the plunge of 1997: arapid increase in implied volatility due to the decline in futures,a pullback in implied volatility as the market appeared to be sta-bilizing, then an increase in implied volatility to new heights forno apparent reason, followed by a rapid decline. Clearly, in ahighly unstable futures market, ideas of what constitutes fairoption value can shift substantially from day to day. In circum-stances such as these, the trader who can come up with an inde-pendent estimate of option fair value may want to bid or offer at148 OPTION REALITY
Futures(1) Volatility (3),(4)Date High Low Close aay piragalee) Days Implied MarketOct 1 332 326 «4331 Nw 18.90 36 19.03 20.93Oct 2 333 3300«331Ss«NNw 18.40 35 18.79 19.88Oct 5 332 328 «4330 «=0Nw 18.00 34 18.71 19.22Oct 6 330 «319 «319 NW 19.35 33 21.12 22.05Oct 7 322 317 320 No 17.35 32 19.17 21.29Oct 8 321. 313° 315 sNov 17.30 31 19.73 21.97Oct 9 317° 311 3120 «Nw 17.30 30 20.25 21.93Oct 12 314 308) «311. Nov 17.20 29 20.54 21.19Oct13 «317,312,315 sNNW 16.65 28 19.98 21.53Oct 14 313 304 «305 Nov 16.60 27 20.95 24.06Oct15 307 297 298 Nw 17.40 26 22.90 25.44Oct16 301 277° 282 = =Now 19.20 25 27.23 30.41Oct 19 269 #198 201 Nov Not available 73,22Oct 20 242 181 «216 = Dec 57.75 a1 83.51 77.19Oct 21 259 «239 «258 =~ Dec. 45.75 40 56.08 91.24Oct 22 250 195 244 Dec 47.25 39 62.02 92.99Oct 23 253° 2340241 Dec 63.50 38 85.49 = 89.71Oct 26 237° 218 «= 220—Ss«éCec 62.25 37 93.03 95.73Oct 27 242 223° «228 = Dec 47.40 36 69.30 94.80Oct 28 234-218 )=231—Ss Dec 43.25 35 63.30 91.49Oct29 249 2385 245—s«(ae 38.50 34 53.90 93.20Oct 30 260 252 «259 = «Dec 36.65 33 49.27 94.48Nov 2 258 49251 257 Dec 32.50 32 44.71 90.62Nov 3 254 240 250 Oec 34.35 31 49.36 89.17Nov 4 253 «246 «= 250—Ss«éCec 32.85 30 47.98 84.71Nov 5 258 4247 «255 = ec 30.60 29 44.57 82.63Nov 6 258 4242 249 8©Dec 30.10 28 45.69 81.15Nov 9 248 242 245 Dec 29.70 27 46.66 78.89Nov10 243. 237° «-239~Ss«(Dec 29.80 26 48.91 77.70Nov11 245 240 242)—Ss«éec 28.25 25 46.69 75.18Novi2 251 247 249 Dec 27.05 24 44.35 74.07
FIGURE 8-7. The December 1987 S&P futures contract, showing how option pre-miums and implied volatilities fluctuated before and after the "crash of '87." The finalcolumn shows market volatility derived by exponentially smoothing the mean absolutedeviation of daily price changes. In chaotic conditions, the relationship between impliedvolatility and market volatility is tenuous, to say the least. Notes (1) and (2) below, andnotes (3) and (4) under Figure 8-8 pertain to both Figure 8-7 and Figure 8-8.
1 Futures prices have been rounded to nearest whole number.2 Straddle premium is the combined value of the put and call premiums availableat the closest-to-the-money strike price.
a fixed price, especially if the quoted bid—asked spread is verywide or not quoted at all. The fixed price order may be filledagainst a market order on the other side—just because no oneelse is brave enough to declare.Born AGAIN 149
Futures(1) Option Straddle(2) Volatility(9).(4)Date High Tow Close Month Premium Days Implied MarketOct 1 967 954 963 Nov 57.40 37 19.60 17,80Oct 2 970 961 969 Nw 56.20 36 19.33 17.60Oct 5 986 961 975 Nov 54.95 35 19.05 17.39Oct 6 983 976 981 Nw 53.80 34 18.81 17.20Oct 7 992 979 989 Nw 51.40 33 18.09 17.23Oct 8 991 975 982 Nw 50.75 32 18.27 17.15,Oct 9 983 969 978 Nw 49,75 31 18,27 16.74Oct 12 980 965 976 Nov 48.85 30 18,28 16.13Oct 13 982 974 976 Nw 47,30 29 18.00 15.32Oct 14 981 968 978 Nov 46.70 28 18.05 14.78Oct 15 977 968 973 Nw 45.60 27 18.04 14.61Oct 16 981 956 960 Nov 45.80 26 18.71 15.37Oct 19 959 935 948 Nw 45,75 25 19.30 15.99Oct 20 963 947 962 Nw 43.50 24 18.46 16.79Oct 21 980 962 979 Nov 40.65 23 17.32 17.86Oct 22 980 970 86974 Nov 40.30 22 17.64 17,53Oct 23 976 948 955 Nov 43.70 21 19.97 18.85Oct 26 969 942 944 Nov 44.65 20 21.15 19.19Oct 27 944 874 874 Nov 59.40 19. 31.18 27.04
Oct 28 932 844 «(924 Nov 49.50 18 25.25 31.64Oct 29 941 917 924 Nov 49.75 17 26.412 30.06Oct 30 929 902 ©6903 Nov 57.90 16 32.06 31.11NwNwwNov
Nov 2 926 899-924 50.30 15 28.11 32.06Nov 3 946 921 945 43.90 14 24.83 32.90Nov 4 946 936 942 43.50 13 25.62 31.60Nov 5 955 938 86947 41.00 12 25.00 30.60Nov 6 947 937 942 Nov 40.40 1 25.86 29.66Nov 9 943 916 6931 Nov 44.90 10 30.50 29.47Nov10 9941 923° 926 Nw 42.20 9 30.38 28.59Nov 11 933. 922 926 Nov 37.00 8 28.25 = 27.16Nov 12 929 905 908 Nw 37.70 7 31.39 27.99
FIGURL 8-8. The December 1997 S&P futures contract, showing how option pre-miums and implied volatilities fluctuated around the time of the record one-day pointloss in the Dow Jones industrial average. Compared to 1987, the options marketreacted in a much more orderly fashion, Option-implied volatilities stayed pretty muchin line with calculated market volatility.
3 Implied volatilities may be obtained from the table entries of Figure 4-7 or fromthe equation: fv = 20 x pNt.
4 Market volatility on October 1] is calculated from the MAD of observed valuesduring September and updated thereafter by exponential smoothing, using a smooth-ing constant of 0.05,according to:
MAD, = 0.95 x MAD, + 0.05 x | price change, |and
mv, = 22.0x MAD,150 OPTION REALITY
From close observation of the way stock index futures trade,I have come to the belief that stock averages generate price pat-terns that are rather different from all other traded commodities.The most striking difference, in my view, is the speed with whichthe S&P (the one I watch most closely) moves between whattechnicians call support and resistance levels—with very littletrading in between. Either everybody seems to want it, or nobodyseems to want it. The usual middle ground appears to be miss-ing. What's more, this on-again off-again love-hate affair isoccurring on an ever-shortening time horizon. What are theimplications, apart from the obvious one that the whole thingmay suddenly implode in some bizarre unimaginable way?
My assessment of the current frenzy on Wall Street (August1998) is that short-term stock market volatility may be increas-ing, while long-term volatility may be staying the same. If true,this could present an opportunity in options. The volatility of atrue random variable does not depend on the time horizon overwhich it is observed, and that is why the option pricing structureon the carrying-charge commodities, such as currencies and met-als, follows the square-root-time equation almost exactly. Doesthe S&P option pricing structure also follow the square-root-timelaw? Yes, it does. And that means one of two things. Either mysuggestion that short-term volatility is greater than long-termvolatility is incorrect, or options on deferred S&P contracts areovervalued in relation to nearbys. If the latter is the case, a trad-ing opportunity may exist.
What psychology could account for a market becoming morevolatile only in the short-term? I think the answer may lie in thecomposition of the players playing the game and in the technol-ogy these players are using in their attempts to outsmart eachother. It is well known that, in the last few years, index funds,that is, mutual funds which try to mimic the performance of theS&P Index, have become major players in the S&P futures trad-ing pit. In other words, more big players can influence—if onlyin the short-term— the direction of the market. These large play-ers may also be able to create their own bandwagon effects. Ithink it would definitely be fair to conjecture that markets dom-inated by the actions of a few large players are going to be moreBORN AGAIN 151
volatile than markets dominated by a large number of small play-ers, even when the total trading volumes are the same. With thepossible exception of Alan Greenspan, however, no individual orconsortium is large enough to influence prices over the longerterm.
It is also fair to conjecture that the amount of computer andtelecommunications gadgetry employed at the present time—bytraders desperate to divine the next 10-minute trend—is alsodestabilizing to the market, since a "high-tech" psychology pro-motes decisionmaking based on observing price patterns ratherthan decisionmaking based on economics. It does not surpriseme in the least that the implied volatility of S&P options contin-ues on its long-term secular uptrend. In such a crap-shoot envi-ronment as Wall Street 1998, it may be hard to see how any kindof fundamental judgment on option valuations can be brought tobear. But, there are always hidden truths waiting to be discoveredby an astute and patient observer.
*
How much of an additional edge can an option writer hope toachieve through the exercise of fundamental judgment? Based onmy own trading experience, I would cautiously suggest that asound fundamental override can reduce the option writer's pay-out ratio from 0.88 (purely technical) to around 0.85, equivalentto a trading edge of 15 percent. It is now time to investigatewhether a gross trading edge of 15 percent can translate into arespectable return on the investment required to finance theappropriate transactions.CHAPTERNINE
THE ARMCHAIRBROKER
fter completing Chapter 5, the last of the theoretical chapters
of this book, I sent the manuscript to a friend, for his com-
ments. He pronounced it a "good read" but reminded me that my
stated goal was to explore the available empirical evidence, with
the objective of answering some questions that had long goneunanswered. He wrote down these questions, rather succinctly:
Being a pragmatic kind of a guy, I am looking forward to the second partof the book, to see the answer to my three-part question, which, to review,is:
1. Applying a purely systematic and objective approach to trading options,is it possible to obtain a long-term positive mathematical expectation?
2. Is the edge large enough to overcome a series of impediments that wemust cope with, the most important being transaction costs and "slip-page” associated with each trade?
3. Finally, will the edge provide a worthwhile return on the "true and nec-essary" trading capital?
Well, I do believe I have answered the first question; theother two still require a bit of work, but I will get to these beforethis final chapter is over.
From the hypothetical trading results detailed in previouschapters, and from personal experience writing option straddlesin many different markets, I feel confident in asserting that a 15percent trading edge can be attained by any disciplined option
153154 OpTioN REALITY
writer using a little bit of imagination. Iam not aware of any trad-ing technique that can produce a positive expectation throughthe systematic buying of options. Therefore, in these few remain-ing pages, I am going to concentrate exclusively on option-writ-ing strategy, expectations, and return on invested capital. In theprocess, I will be drawing on my own practical experience as anoption trader (nonspecialist) as well as on information gatheredfrom individuals with first-hand knowledge of what actually hap-pens on the option trading floor.
First, a 15 percent trading edge does not translate into a 15percent return on equity. To understand what an edge doesmean, let's review how the cash flows in an options-writing pro-gram. An option writer operating with a gross 15 percent tradingedge can expect to keep $150 out of every $1000 received in pre-miums; the other $850 will be paid back to the option buyers.These, however, are the cash flows that would prevail in a"Goldilocks" trading environment. In real trading, the writer isgoing to keep less than $150. The key question is how much less.
*
For all option traders, there are going to be significant costsassociated with executing trades. Commission costs are relativelystraightforward to estimate, and I'll deal with those shortly. Lessobvious, and sometimes hidden, are the costs incurred by thetrader who pays more to purchase an option and receives less forselling an option than the true equilibrium trading price.
In all the calculations leading up to the estimated 15 percenttrading edge, it was assumed that hypothetical trades were exe-cuted at the closing prices posted by the option exchanges. Theseare the numbers that appear in option tables in the financialpress, and are unbiased estimates of the true trading values ofoptions —as distinct from fair value, which is another conceptaltogether. Because of their low trading volumes compared tofutures, it will frequently be the case that with certain options noactual trades are made on the close—or at any time during a ses-sion for that matter. With illiquid and nontraded options, it is thejob of the exchanges to estimate closing prices and to maintainTHE ARMCHAIR BROKER 155
option values in logical proportions to each other. They have toestimate prices, because brokerage firms need to know, on a dailybasis, the market value of each and every listed option to prop-erly calculate clients' equities.
The setthement committees of the different optionsexchanges are made up of traders with extensive first-handknowledge of the trading pits and with a good understanding ofrelative values, and these committees do a pretty good job of set-tling prices at close to their true trading values. Far out-of-the-money options, for example, will be keyed mostly off theat-the-money option, according to recent historical proportions.So, whether actual trades are made on the close or not, it is safeto assume that posted prices are at least unbiased and that noinherent error should arise in using posted prices to test a hypo-thetical trading system. In practice, naturally, it is not likely thata trader will execute a trade right on the close, and it is also truethat option premiums are continuously declining, even as thetrading session progresses. These considerations, however, donot make the closing price any less relevant as a reference point.In hypothesis testing, one point in time is as valid as any other.
Yet, even with unbiased closing price estimates, the optiontrader is still going to be faced with execution costs. As all activetraders know, posted option closing prices represent the middlepoint between a hypothetical bid and a hypothetical asking price.As a buyer, you will, in reality, have to pay an asking price higherthan the true value, and as a seller you will have to take a bidprice lower than the true value —that is, if you want your orderto be executed right away, or, at the market, to use the technicalterm. The spread between the bid price and the asking price canhave serious long-run consequences for traders using marketorders, since an option writer is already working with a rathersmall edge to begin with. It is important, therefore, to have anidea of the size of this spread and the conditions under which theuse of market orders may be acceptable.
Many option traders would recoil at the thought of usingmarket orders in the somewhat illiquid option pits, fearing thatthe dearth of volume would all but guarantee lousy fills, therebynegating any hard-won edge achieved through the exercise of156 OPTION REALITY
good discipline and a little creative imagination. I had some ofthese concerns myself. So, to understand the trading process alittle better, I paid a visit to the New York Cotton Exchange,where Jurgens Bauer, an options floor trader of some consider-able experience and reputation, agreed, goodnaturedly, to answersome of my layman's questions.
*
"One of my real problems with options," I said, "is not beingable to act fast and get a reasonable price. I trade a lot of futures,often with market orders, and I don't feel I'm giving too muchaway. But here?
"That's a common fear," said Bauer. "But an exaggeratedone."
"Sometimes an option will not trade for hours," I said. "Whatif there is no one around to take the other side of my trade, at thetime I want it done?"
"There's always a bid and an asking price," he said. "The num-bers may not show up on your quotation monitor, but you canalways get them off the floor." Bauer pointed out some intense-looking individuals on the other side of the pit, who appeared. tobe checking the futures boards while punching data into pocketcalculators. "One of these guys will give me a price on any optionor combination I want," he added.
"But what if I give you, as my broker, say, a big sell order atthe market? Won't the other guy drop his bid, knowing that youhave a market order which you will have to keep offering loweruntil somebody bites?"
"T's not quite like that," said Bauer, smiling. "Watch, you saidselling a hundred of the December seventy-ones, didn't you?"
Before I could answer, he had boomed out a request.
"Tm talking hypothetically," I said, just slightly alarmed.
"Don't worry," he said. "So am I."
Seconds later, a shout came back from the other side of thepit: "One sixty-five bid, one seventy-two offered."
"That's fine," I said. "But he still doesn't know whether youwant to buy or sell, does he?"THE ARMCHAIR BROKER 157
"That's right," said Bauer.
"And he doesn't know how many contracts?
"Right again. Why should I tip my hand?"
"Okay, I'm getting the idea," I said. "But how is the tradefinally executed? Surely, somebody has to declare eventually?"
"He already has. He has to take what I give him now.
"Buy or sell?"
"Buy or sell."
"And the quantity?"
"Whatever I want."
"One contract or ten?"
"Or a thousand, for that matter."
"And what if the guy on the floor takes a thousand lot posi-tion and the market starts to move against him?
"Don't worry about him. There are plenty of ways he canhedge with futures. Now, are you still afraid to go with a big mar-ket order?"
"Not as much as I was," I had to concede.
"Just one thing, though," said Bauer. "Make sure you knowyour broker." At least, I think that's what I heard him say.
*
Since my visit to the Cotton Exchange, I have been less reluc-tant to use market orders in the options pit, especially when exit-ing from a position — which, as an option writer, is usually whenthe futures market is accelerating against me. I try to enter newpositions, particularly straddles, with limit orders, and try to esti-mate this limit, or fixed price, as the midpoint between what Ithink the bid and the asked ought to be. That way, I become theoffer, and an antsy buyer may be tempted to grab me. But, some-times, even with a straddle, I will go at the market—if Iabsolutely don't want to miss the trade or if the apparent pre-mium available even at the bid strikes me as unusually favorableand I don't expect it to stay there long.
An option trader should always be familiar with the "mood"of the futures market, before deciding on which way to have anorder executed. In volatile conditions — where futures are trading158 OPTION REALITY
at the daily price limit, say—-option asking prices may rise abovetheir true trading values, simply because writers choose to standback and give themselves time to assess the situation. These arenot the conditions in which to enter market orders. They are,however, exactly the conditions where a well-thought-out fixed-price order may find a taker. Where chaos reigns, it sometimespays to be bold.
Whether one uses market orders or not, there is no way ofavoiding execution costs, and these have to be viewed simply ascosts of doing business. With a market order, the executioncost— sometimes called slippage—-can be estimated from the typ-ical bid-asked spread associated with the option in question. If,for example, you are quoted a straddle price of 2.35 bid, 2.45offered, you are going to be giving away 0.05, either as a buyer oras a seller, because the true value is going to be 2.40. The 15 per-cent edge was calculated, remember, on true values. Of the 2.40premium received, you "expect" to keep 15 percent, or 0.36. Infact, because of the slippage of 0.05, you can expect to keep only0.31, which, in this case, would bring the trading edge down wellbelow 15 percent.
If you try to avoid slippage by splitting the bid and the asked,and offer 2.40, the true value, instead of taking the bid at 2.35,you may or may not get the transaction completed, and if youdon't, there will be a "hidden" execution cost, since the grosstrading edge is predicated upon getting all hypothetical positionstransacted.
In estimating potential returns from option writing, I preferto be conservative and assume that orders are filled at the mar-ket, in which case, from my own experience, the overall grosstrading edge will come down to a net of around 13 percent. Bearin mind, too, that in the systematic writing of straddles there aregoing to be exit as well as entry execution costs. I'm referring tothose cases where defensive follow-up action is necessary. If thelosing side of a straddle is to be covered either by direct offset orby the purchase of another option, there will be a further execu-tion cost incurred. Furthermore, even with a successfully writtenstraddle that is held till option expiry, it is axiomatic that one sideof the straddle will end up having residual value, and that optionTHE ARMCHAIR BROKER 159
will be exercised and will require a futures offset to cancel it out.Consequently, a further small slippage charge will be incurred.All things considered, I would suggest that execution costs, con-servatively, are going to knock 3 percentage points of the optionwriter's edge, bringing net expectation down from 15 percent toaround 1|2 percent.
*
In all the hypothetical trading results from the 1996 database, it was assumed that whenever it was necessary to "protect"the losing side of a straddle, this protection was accomplished viaan offsetting position in the futures market. Using futures wasthe simplest way (computationally) to evaluate the effects ofemploying a defensive strategy. In actual trading