, two problemsare associated with the defensive futures strategy. First, thefutures position requires continuous monitoring to see if furtherdefensive action will be necessary. And second, a futures positionis going to tie up additional trading capital in margin.
An equally effective defensive strategy is accomplished withthe purchase of an at-the-money put or call, instead of a future.It should be clear that, since the purchase of an offsettingoption will only be necessary where one side of the originalstraddle is already incurring a large loss, the at-the-money strikeprice of a partially offsetting option will now be some consider-able distance away from the strike price of the original straddle.Whil- essentially locking in a loss, the at-the-money offset stillaffords protection and is still an effective way of neutralizing thestraddle.
Now, it is true that the "neatest" way out of the losing leg ofa straddle is to buy back the original straddle, or at least theoption component that is incurring the loss. The problem here isthat the losing option will be so deep in the money that it will beextremely illiquid, and it will therefore be difficult to get a rea-sonable execution price. On balance, it seems to me that the pur-chase of the current at-the-money or closest-to-the-money optionis the best way out of a problem straddle. The covering trade isgoing to be made in the most liquid option, and, once completed,160 OPTION REALITY
the straddle is basically shut down, allowing the writer to explorenew writing opportunities in that same commodity.
If a straddle is to be offset by the purchase of a put or a call,the writer has the choice of either going at the market or goingwith a limit order. Whenever a trader wishes to offset a losingposition via a relatively liquid (at-the-money) option, it is safer togo at the market. A lot of money can be given away fast, when anattempt to finesse a covering option fails and the futures marketroars away. In option writing, there's a lot to be said for getting inslow and getting out fast.
Execution-wise, there is a subtle difference between goingwith a limit order on a straddle and going with a limit order on aput or a call—if the order is to be left resting in the pit. Becausethe straddle curve is very flat, close to the money, even a suddenlarge move in the futures price is not going to change the truevalue of the straddle very much. So, there is a wide range offutures prices where a resting straddle may be fairly filled on aresting limit order. However, with a limit order on a put or a call,a sharp move in the futures price may cause this order to be filledat the limit price, even though the true value may now be quitedifferent — another good reason for using market orders on exit.The floor trader who is looking after a resting limit order may ormay not get a better price than the limit specified, but he is notobliged to get a better price just because the futures have moved.With a resting option limit order, the trader would do well to keepan eye on the futures price and be prepared to cancel quickly ifan unwelcome fill looms as a distinct possibility.
*
The other cost associated with trading is, of course, commis-sion. For floor traders, commission is negligible, but for armchairbookmakers commission is a major cost. Commission costs areusually the same regardless of the commodity or the size of con-tract. For the retail customer, I reckon that the commission costof executing a straddle to completion will average out at around$130, broken down as follows: $30 for the put, $30 for thecall, $50 for the offsetting futures trade, and an additional $20THE ARMCHAIR BROKER 161
(averaged) to cover situations where one or both sides of a strad-dle have to offset. (On occasions, a massive whipsaw move in afutures price may call for offsetting both sides of a straddle. It isa rare occurrence, but it does happen.) Large traders may be ableto negotiate lower commission rates for doing multiple contracts.For now, I want to consider the small trader doing one or twocontracts, who will definitely be looking at commission of around$130.
Since the commission for trading a straddle position is basi-cally fixed, its effect upon the profitability of the overall tradechanges dramatically with the dollar amount of premiumreceived, which in turn varies with the size of the contract, thevolatility of the contract, and the time till expiry of the options.Typical dollar amounts of premium available for writing straddleson different commodities, and for options with different expirytimes, are shown in Figure 9-1.
First, let's consider the extreme cases. The sale of a 7-weekS&P straddle will net the option writer over $30,000, from whichthe writer can "expect" to keep 12 percent, say, or $1200. Here,a commission charge of $130 will reduce the writer's edge by alittle over | percentage point (Figure 9-2). At the other extreme,consider sugar options, where a 6-month straddle will generate apremium of about $1200, from which the writer can "expect" tokeep $144. Here, the commission charge of $130 will reduce thewriter's edge to almost nothing, so that the only winners will bethe brokerage houses and the exchanges.
Clearly, commission cost has to be a major consideration forthe nonfloor trader who is trying to decide whether a low-pricedoption is worth trading in the first place. At some level of pre-mium received, a straddle cannot possibly be worth trading—even with a net positive expectation of 12 percent. I would putthe lower limit at around $2500, which would still leave thewriter a positive expectation of 6.5 percent.
With that restriction, it is obvious from Figure 9-1 that somecommodities will only rarely be candidates for writing, specifi-cally, sugar, cocoa, cattle, corn, and gold. When wheat, silver,and crude oil are active, it will usually be possible to net $2500by writing a straddle with a longish time till expiry. For the162 OpTION REALITY
S&P IndexT-BondsSwiss FranceJapanese YenGold
Silver
Crude Oil
Coffee
May10,5001,8002,600
2,800
4.100
June13,5002,9003,5003,8001,1001,600
1,600
1,2001,000
600
OPTION MATURITYJuly Aug.3,7001,5002,2002,1002.3004,600 5,7002,3001,7001,5001,50011,000
Sept. oO
2,700
2,500
FIGURE 9-1. Straddle premiums, expressed in dollars, available on «1muodities, as of March 27, 1997. At one extreme, $10,500 is available on ,straddle. At the other extreme, a sugar straddle with 6 months till 1 \pu.
$1200.
remaining commodities of Figure 9-1, it will almost ais,possible to net at least $3000. In cotton, this will re quiwriting of an option with as much as a 6-month teri |S&P, $3000 can be had from a straddle with as little a. *
till expiry.THE ARMCHAIR BROKER 163
10,000 5,000 4,000 3,000 2,000 1,000
130 130 130 130 130 1301,070 470 350 =. 230 110 —1010.7 9.4 8.7 7.7 5.5 <0
 
FHF 9-2. The expected profitability from writing options is highly sensitive towe dollar amount of premium received. Low-priced options, where the straddle pre-woes ta leas than $2500, say, are simply not worth writing—at least, for the generalet Lor large traders able to negotiate lower commission rates, the cut-off point athos 1s pruititiability will be compromised is lower.
(tae very good reason for writing straddles (at-the-money strikes) as opposed toseeegley (out-of-the-money strikes) is that the straddle yields the maximum premium
pomtble
Since the amount of premium received per option is so criti-eal to the profitability of option writing, it is especially importantto receive the maximum premium possible. For this reason, it isheater for the writer to concentrate on writing straddles (puts andsall, with the same strike price) rather than strangles (options#tth the call price higher than the put price). Although a stran-g* has us winning zone where the writer can, with a bit of luck,eefati all the premium, the lower total premium received in thefeat place makes the strangle an inferior choice to the straddle.iM should be noted in passing that the commission charge prob-fev allects option writers much more than option buyers, who#0 usually going after profits many times larger than their initial@seatments, and not buying options in any systematic way.
tours it make any sense to have a fixed commission charge forteding an option? That it should cost the same to trade an S&P@ption as a sugar option? I can't see it. At current price andtalatility levels, the daily price range of an S&P future, in dollarferns, 18 approaching $5000.In sugar, $300 would be a big day.‘Were 1s no reason why an option on a low-priced low-volatilitysmttact like sugar, cocoa, gold, and cattle—could not beteaieed to cover five contracts, say, with the same commission162 OpTION REALITY
tS&P Index
Wiailsseh
Swiss Franc
Japeneer Yen
pedeg
Soybeans
PEPeag
FIGURE 9-1. Straddle premiums, expressed in dollars, available on sclected com-modities,as of March 27, 1997. At one extreme, $10,500 is available on a 7-week S&Pstraddle. At the other extreme, a sugar straddle with 6 months till expiry yields only
$1200.
remaining commodities of Figure 9-1, it will almost always bepossible to net at least $3000. In cotton, this will require thewriting of an option with as much as a 6-month term. In theS&P, $3000 can be had from a straddle with as little as 2 weeks
till expiry.
OPTION MATURITY |May June © July Aug. Sept. Oct.10,500 13,5001,800 © 2,990 3,700 °
 
2.600 3,500£44900 es 4,5001,600 “2200ne 4,600 is 231002.300 3,800_ 8,000 800°" 8,700; muh a 2,700“1700 01,200 1,500 >1000, 4500,4.100 44,000THE ARMCHAIR BROKER 163
With ($) receipts of: 10,000 5,000 -4,000 3,000 2,000 1,000Retained before commission 1,200 600 480 86360 240 120Commission per straddle 190 «©1390 . 130130. 130130Retained after commission 1,070 470 350 230 110 -10Net expectation (%) 10.7 94 87 77 55
FIGURE 9-2. The expected profitability from writing options is highly sensitive tothe dollar amount of premium received. Low-priced options, where the straddle pre-mium is less than $2500, say, are simply not worth writing—at least, for the generalpublic. For large traders able to negotiate lower commission rates, the cut-off point atwhich profitability will be compromised is lower.
One very good reason for writing straddles (at-the-money strikes) as opposed tostrangles (out-of-the-money strikes) is that the straddle yields the maximum premiumpossible.
Since the amount of premium received per option is so criti-cal to the profitability of option writing, it is especially importantto receive the maximum premium possible. For this reason, it isbetter for the writer to concentrate on writing straddles (puts andcalls with the same strike price) rather than strangles (optionswith the call price higher than the put price). Although a stran-gle has a winning zone where the writer can, with a bit of luck,retain all the premium, the lower total premium received in thefirst place makes the strangle an inferior choice to the straddle.(it should be noted in passing that the commission charge prob-lem affects option writers much more than option buyers, whoare usually going after profits many times larger than their initialinvestments, and not buying options in any systematic way.
Does it make any sense to have a fixed commission charge fortrading an option? That it should cost the same to trade an S&Poption as a sugar option? I can't see it. At current price andvolatility levels, the daily price range of an S&P future, in dollarterms, is approaching $5000. In sugar, $300 would be a big day.There is no reason why an option on a low-priced low-volatilitycontract—like sugar, cocoa, gold, and cattle—could not beresized to cover five contracts, say, with the same commission164 OPTION REALITY
charge. If this were done, a great many more players would enterthe game, because at least they would have a shot at beating thehouse edge. As things stand, the option-writing public is essen-tially excluded from writing options on certain exchanges. Couldit be that these exchanges only want the public as buyers, thatoption writing is to be the preserve of floor traders who pay littleor no commission? It sure looks that way, but one has to wonderwhy
*
Many commodity-related trading systems have been devisedwith convincingly demonstrated high expectations — sometimeswith returns of over 100 percent per annum. These systems allsuffer from one rather unfortunate drawback. With convincinglydemonstrable regularity, they get wiped out.
Brokerage firms will not margin on "positive expectations"alone. They are only interested in positive equity balances, and itis a simple fact of life that trying to force more than 20 percentreturn per annum out of a futures trading system will run toohigh a risk of incurring an eventual equity drawdown that willcripple the account for good.
In Chapter 8, I showed that the single most important stepthat an option writer can take to ensure long-run profitability isto systematically employ defensive action in cases where one sideof a straddle position starts to go sour in a big way. I showed thatdefensive action alone shifts the payout ratio from 1.00 (breakeven) to 0.90 (a 10 percent writer's edge). The difference betweendefended option writing and undefended option writing wasaccomplished by trading futures — nothing else. A skeptic mightargue that since profitability was achieved purely on the strengthof futures positions, why not forget the whole option rigmaroleand just trade the futures. Since "defensive" futures positionswere always initiated with the trend and liquidated also with thetrend, omission of the straddles would leave a pure trend-follow-ing futures portfolio, which, as I demonstrated in Winner TakesAll, has a substantial positive expectation.
True enough. But one crucial detail is missing: In futures trad-THE ARMCHAIR BROKER 165
ing, even diversified futures trading, capital requirements willbe large, and equity variations will be large. The extraordinaryfeature about diversified straddle writing is that extraordinarilylarge positions can be financed with rather small amounts ofmoney, because variations in account equity can be kept atalmost incredibly low levels. Let's see how this is accomplished.
The key to low equity variability is diversification. At the indi-vidual commodity level, a straddle-writing portfolio is going toachieve diversification through the trading of options that areindependently variable in the first place. On a second level,diversification comes from the very nature of the straddle itself.Because the value of a straddle—a liability to the writer oncewritten--can only increase with a relatively large movement in itscorresponding future, the odds of a straddle going against thewriter in a very short time are not great. And the odds against 10independent straddles all going sour at the same time is corre-spondingly that much less. Option writers should be aware thatthis powerful brake against sudden large equity drawdowns doesnot exist to the same extent when options are written on only oneside of a market.
*
Returning now to the second of the three questions posed atthe beginning of the chapter: Is the edge large enough to overcomea series of impediments that we must cope with, the most impor-tant being transaction costs and "slippage” associated with eachtrade? The answer has to be, yes, with the proviso that a straddleyields a premium of at least $2500. From the numbers of Figure9-2, the writer's edge, net of all charges, should average, conser-vatively, about 8 percent. And how does a trading edge of 8 per-cent translate into return on investment? In other words, what isthe answer to my friend from Missouri's third and most impor-tant question: Js the whole exercise worthwhile when the return on"true and necessary” capital is considered?
To get the level of dollar premium necessary to overcome exe-cution and commission costs—that is, to maintain an averageedge of 8 percent— the average time to expiry of the straddles is166 OPTION REALITY
going to vary between 6 weeks and 6 months, with a conservativeestimate of the average being about 4 months. If $100,000, say,is the total amount of premium collected from writing straddleswith an average of 4 months to expiry, an 8 percent trading edgeshould net the writer $8000 three times per year, for a totalreturn of $24,000 per annum.
The crucial question now becomes: How much equity doesone need to finance a short option position of $100,000? And theanswer, which is defined by margin requirements, is approxi-mately $100,000. A well-diversified short option portfolio is ableto margin a surprisingly large number of option positions.Brokerage firms use a sophisticated program (SPAN) to calculatethe margin requirements of an account, based on the true degreeof risk to the equity of that account. In the case of an accountwhich concentrates exclusively on the writing of option straddles,the true degree of risk is very much diminished through diversi-fication and symmetry.
An initial equity of $100,000 deposited in a brokerageaccount will allow the writing of sufficient straddles to pull in$100,000 cash from option buyers, and most of this cash—atleast 60 percent—may safely be deposited, as margin collateral,in short-term treasury bills. So, too, can the entire originalinvestment. Taking 5 percent as a typical short-term yield ontreasury bills (it used to be considerably higher), the interestreturn on an investment of $100,000 will therefore be in theregion of $8000. Adding this amount to the annualized returnfrom the trader's edge, you wind up with a total annual cashreturn of $32,000.
Admittedly, an annual rate of return of 32 percent may notlook so spectacular to investors who have had their money parkedin an S&P-indexed mutual fund for the past several years. Atsome point though, double-digit stock market returns will be thestuff of fond memories —a refrain I seem to have been singing forlonger than I care to remember. Five years ago, in Winner TakesAll, I made a singularly unprophetic forecast:
At this time of writing (summer 1993) stock market "bears" rightly point outthat earnings and dividends in relation to stock prices are at historically lowlevels. Stock prices reflect public attitudes towards money and investments,even though, logically, stock prices ought to be related to company assetTHE ARMCHAIR BROKER 167
values. Even if the economy does recover with some vigor, there is no guar-antee that stock prices will go up from here.
Well, did I ever get a wrong number! The Dow JonesIndustrial Index was under 4000 at the time. (To be fair, I didalso point out that if you religiously enter a stop-loss order aftera trade is made, you can dial a lot of wrong numbers, and stilleventually get through.)
In the great post—bull market era which will come to passsooner or later, a rate of return from option writing of 32 percent,let's say, a rate of return certainly between 20 percent and 40 per-cent, is going to look very attractive, especially if it can be achievedwith minimum equity variability as I am suggesting is possiblefrom systematic straddle writing. Human nature and human frailtybeing what they are, I am not suggesting that very many peoplewould be able to achieve anything like this level of performance,because even the best-intentioned and hardest-headed of traderswould have many obstacles to surmount along the way.
Consider the evidence. It is generally understood andaccepted as truth that the key to long-run success in trading —beit in soybeans, spiders, or seashells —is to cut losses and let prof-its run. Yet, were you to look at the open positions in 95 percentof all futures accounts you would see that unrealized losses farexceed unrealized profits. Why? Why do people persist in behav-iors they know to be detrimental to their interests? Who knows?But fact is, they do, and in a remarkably consistent way.
I have a long-suffering friend who trades a lot of stocks,siumetimes on the recommendations of "insiders." He keeps pricehistories on every stock he follows for "technical signals," so hehas an objective system for cutting losses when the market tellshim he is wrong. He bought a stock recently at $4— because itwas "going to $10"—and he was risking a recently establishedlow on the price chart.
"Look, it was so obvious,” he said, showing me one of hismeticulously maintained charts. "There was huge support at$3.75. I knew when it took out this low there was somethingseriously wrong."
"Where did you get out?" I asked him.168 OPTION REALITY
“T didn't," he said.
"And what's it at now?"
"A buck forty.”
"What are you going to do?"
"Sell half of it. If it goes up to eight dollars, I'll break even."
I've been down that road before and so have most of the peo-ple reading this book.
The somewhat paradoxical truth-about option writing is thatdespite its extraordinary attractions as an investment— thepromise of exceptional returns combined with low risk, anddespite the powerful empirical evidence in support of thispromise, it will remain for most people a difficult feat to accom-plish—and I include myself in this group of potential under-achievers. In learning option writing by doing, I have to confessto numerous false starts already, and I have not been involvedwith the problem long enough to have generated conclusiveproof from actual trading results that option writing is as prof-itable as I am suggesting it should be. Yet, the evidence is there.It is not a question of being lucky or unlucky, and not a questionof having tremendous insight; it is truly a question of masteringone's own psychological weakness.
It can be done. The numbers say so.
*
For the last several chapters, it seems I have been talkingalmost exclusively about the merits of option writing as opposedto option buying. That is the way the wind has blown, because allthe empirical evidence points to the conclusion that, althoughsystematic option writing may be a winning play, systematicoption buying (that is routine buying without fundamentalinsight) can never be a winning play. But, I would not care toleave the reader with the impression that I am promoting just oneidea. People may trade options for any number of reasons that Icannot imagine, and I would like to think that the results of myresearch may be generally useful, whether the interests of theTHE ARMCHAIR BROKER 169
reader lie in the area of armchair bookmaking or in simply gettinga better understanding of option valuation. There is a great dealof data in the reference section of this book, data which should beuseful to anyone pursuing his or her own independent line ofinvestigation.
Perhaps, I have shown scant respect for the works ofacclaimed theoreticians on this topic, but as Truman Capoteobserved: If you're afraid of going too far, you may not go farenough. And doubtless, I shall be slammed in academic circlesfor lack of rigor, for rounding out numbers, for simplifying for-mulae by omitting unnecessary terms, and for generally cuttingto the chase where the trail seemed hot. However, I stand by thispragmatic approach.
Better this, surely, than to be skewered on a rigid mathemat-ical model divorced from all reality, as appears to have been thefate of one of the world's largest hedge funds, Long Term CapitalGrowth, which bet heavily on the validity of the million dollarformula and found itself victim of the billion-dollar blowout. Asthe Wall Street Journal (September 24, 1998, p.1) reported:
Much of Long Term Capital's success in previous years was the resultof its sophisticated models, devised by its Nobel laureates (Scholesand Merton) to predict how various markets would react in essentiallynormal times. While Long Term Capital won't comment, banks whowere present at the meeting (organized by the Federal Reserve) tocraft the bailout say that the firm's models failed to take into accountwhat might happen in the event of a world-wide financial crisis thatcaused reactions in the market.
So, the normal distribution of price charges turned out to benot so normal after all. Big surprise, and doubtless this blunderwill be rationalized as a once-in-a-lifetime ‘unforseeable' event,beyond the scope of conventional mathematical analysis.
But the money's gone, all the same.
Many financial commentators expressed shock that a giantfund managed by such a concentration of brain power could pro-duce such brainless results. They shouldn't have been so sur-prised. Had they probed behind the numbers a little, they wouldhave seen that the Black-Scholes option pricing model has, foryears, been an accident looking for a place to happen.170 OPTION REALITY
 
 
: Te cake inp wait of an ahem put orc aig‘price p (expressed as a percentage ¢ of futures price) and having ttrading daystH expiry read from the tables of Figure 4-7 or use: :
To calculate a futures market volatility mv from a mean absolute deviationMAD (exprecsed as 8 percentage of flee price) that wil be directly com-parable with jv above, use: —
mv = 22 x MAD~ , . . a
To calculate mean absolute deviation of a series of N price changes Ap; (ailrene) doer an OS Postive and expressed 88 & Percontage of of the’ futuresPrice) use:
MAD < cae
To mahinn an exonentiy soothed mean abso devin, updateMAD dally with a new lApl, using:
= 0.95 MAD pm + 0.05 141
To convert the nearest at-the-rhoney straddle price to a true at-the-moneystraddle price, calculate the oofraction multitier-CM from the straddle ratioFusing: a
CM = 1.04-0.04xR (see Figure 6-3)
FIGURE 9-3. A summary of some important formulae an option trader might wishto have at hand.*
What, then, does the aspiring trader really need? At the veryleast, an active trader needs a straightforward method of calcu-lating option volatilities, both implied and market, and of com-paring these numbers with historical patterns and averages. All ofthis information is contained in the equation summary of Figure9-3 or in the statistical reference section of Chapter 10.THE ARMCHAIR BROKER 171
My best advice to the aspiring option trader is to clear his orher thinking of all the superfluous complications which obfus-cate this fascinating subject and to focus only on those thingsthat are truly relevant to trading. Let's pack up all the betas,thetas, gammas, and deltas and send them back on a slow boatto Greece.
It's about time somebody called it.PARTFOUR
REFERENCECHAPTERTEN
VOLATILITYPROFILES
he data base which follows covers 15 diverse futures marketson which options are actively traded:
The S&P500 stock index Silver Corn
Treasury bonds Crude oil CattleSwiss franc Cotton CocoaJapanese yen Soybeans CoffeeGold Wheat Sugar
For each commodity is listed:
A five-year history of implied volatilities, sampled monthly
A weekly high/low/close chart for 1996 based on a nearbyfuture
Detailed daily statistics for calendar year 1996
FIVE-YEAR HISTORIES
Over a time period as long as 5 years, it is only practical to sam-ple implied volatilities periodically. Here, the implied volatilitiesfor 15 commodities are measured at the beginning of eachmonth based on a nearby option and future.
Because implied volatility is option specific, its value canjump suddenly when switching between options. This primarily
175176 REFERENCE
seasonal effect is found in crop commodities —in particular,grains, cotton, and coffee.
Over a 5-year period, each commodity is going to experiencea wide range of supply-demand configurations, and a corre-spondingly wide range of implied volatilities. The tables whichfollow show, historically, how volatility has varied with absoluteprice, giving some indication of what can reasonably be expectedin the future.
WEEKLY CHARTS
These charts have been developed from daily statistics. Impliedvolatilities, which were calculated weekly, may disagree slightlywith the volatilities in the 5-year summaries, as the latter weresampled at the beginning of each calendar month.
DAILY STATISTICS
For each trading day of calendar year 1996, the following dataare available:
Futures price of a nearby contract. Value of the put and call at the nearest strike price. Corrected value of the at-the-money straddle.. The number of trading days till expiryThe implied volatility of the at-the-money straddle
AWN
Regarding items 1 and 2, to maintain continuity as optionsapproach expiry it is necessary to switch to a new future every 2months or so. Note that all readings of implied volatility arerelated to a specific option on a specific future.
Historical daily futures prices are readily available from com-mercial data banks. Option prices in general must be extractedfrom the pages of the financial press.VOLATILITY PROFILES 177
The data contained in the following tables come from sourcesthe author considers reliable. In certain instances — where theauthor had good reason to believe published data to be inaccu-rate