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 126 Chapter 6
In our example we have:
elasticity = a x 25 = 5
One final observation for the prospective trader. All the numbers we have discussedin this chapter, the theoretical value, delta, gamma, theta, vega, and rho, are constantlychanging, so that the profitability and risks associated with different strategies are alsochanging. The importance of analyzing risk cannot be overemphasized. The greatmajority of traders who fail at option trading do so because they fail to fully understandrisk and how to manage it. But there is another type of trader, one who attempts toanalyze every possible risk. When this happens, the trader finds it difficult to make anytrading decisions at all; he is stricken with paralysis through analysis. A trader who isso concerned with risk that he is afraid to make a trade cannot profit, no matter howwell he understands options. When a trader goes into the marketplace he has chosen totake on some risk. The delta gamma, theta, and vega enable him to identify risk; theydo not eliminate risk. The intelligent trader uses these numbers to help him decidebeforehand which risks are acceptable and which risks are not.% 7 %
Introductionto Spreading
In option markets, as in all markets, there are many ways to trade profitably. One typeof trading strategy, common among floor traders, is scalping. A scalper attempts to buyat the bid price and sell at the offer price as often as possible, without regard to thecontract’s theoretical value. Although the profit from each trade may be small, ifa tradercan do this enough times each day he can expect to show a reasonable profit. Scalping,however, requires a highly liquid market, and option markets are rarely sufficientlyliquid to support this type of trading.
A different type of trading strategy involves speculating on the direction in whichthe underlying contract will move. If a speculator correctly anticipates the marketdirection, and takes an appropriate position, he can also expect to show a profit. Buteven when the market moves in the expected direction, taking a directional position inan option market will not necessarily be profitable. Many different forces beyonddirectional considerations can affect an option’s price. If a trader’s sole consideration isdirection, he will usually be better off taking a position in the underlying market. If hedoes, and he is right, he is assured of making a profit.
The majority of successful option traders engage in spread trading. Since optionevaluation is based on the laws of probability, and because the laws of probability canbe expected to even out only over long periods of time, option traders must often holdpositions for extended periods. Unfortunately, over short periods of time, while thetrader is waiting for the option price to move towards theoretical value, the trader maybe at risk from a wide variety of changes in market conditions which threaten hispotential profit. Indeed, over short periods of time there is no guarantee that an optionwill react in a manner consistent with a theoretical pricing model. Spreading is simplya way of enabling an option trader to take advantage of theoretically mispriced options,while at the same time reducing the effects of short-term changes in market conditionsso that he can safely hold an option position to maturity.
WHAT IS A SPREAD?
A spread is a strategy which involves taking simultaneous but opposing positions indifferent instruments. A spread trader makes the assumption that there is an identifiableprice relationship between different instruments and, although he may not know in
127128 Chapter 7
which direction the market will move, the price relationship between the instrumentsought to remain relatively constant. When the relationship appears to be temporarilymispriced, the spread trader will take a long position in the instrument which appearsto be underpriced and a short position in the instrument which appears to be overpriced,The trader hopes to profit when the prices of the instruments return to their expectedrelationship.
Among futures traders the most common type of spread involves taking opposingpositions in different delivery months for the same commodity. A trader might purchaseOctober crude oil and sell November crude oil on the New York Mercantile Exchange.Or he might buy December corn and sell July corn on the Chicago Board of Trade. Thevalue of this type of intra-market spread depends on a variety of factors, the mostimportant of which is usually the cost of carrying the physical commodity from onedelivery month to another.
Suppose that February gold on the COMEX is trading for $360 per ounce. Whatshould April gold be trading for? A trader who takes delivery of gold in February at $360per ounce and holds it until April will incur a debit of $360 per ounce for a two-monthperiod. If interest rates are 9 percent annually, the two-month financing cost will be:
9% x 2/12 x $360 = $5.40
Given the financing cost of $5.40 per ounce that can be saved by purchasing anApril futures contract rather than purchasing the physical commodity, the April contractought to be worth $5.40 more than the February contract, or $365.40 per ounce. If theFebruary contract is trading at $360 and the April contract is trading at $364, the traderknows that the spread is $1.40 too cheap. He can profit from this mispricing bypurchasing the spread for $4.00 (buy April for $364, sell February for $360). If thespread returns to its expected value of $5.40, the trader can buy back the Februarycontract and sell out the April contract, thereby realizing a profit of $1.40.
Note that the above spread will be profitable regardless of the general direction ofthe gold market, as long as the prices of the two delivery months return to their expected$5.40 spread. If February gold rises to $370, the trader will lose $6 on the February sideof his spread. If, however, the April contract rises to $375.40, the gain in the value ofthe April contract will more than offset the loss on the February contract and result inthe expected $1.40 per ounce profit.
Factors other than financing costs can also affect the price relationship betweendifferent futures months for the same commodity. The futures price of some commodi-ties must also include the cost of storing and insuring the commodity for the periodbetween delivery months. In theory, the cost of financing, storing, and insuring atraditional commodity (precious metals, agricultural products, livestock, energy prod-ucts, etc.) must be some positive number, so that the price of a more distant deliverymonth ought to be greater than the price of a nearby delivery month. This is known asa contango relationship. Any increase in these costs will increase the value of a futurescontract.
Supply and demand considerations can also affect the spread relationship ofdifferent delivery months. In theory, a November crude oil contract ought to alwaysIntroduction to Spreading 129
trade for more than an October crude oil contract. But if crude oil is currently in shortsupply, refiners may be willing to pay more for an October futures contract in order toensure an uninterrupted flow of crude oil to their refineries. Markets where the near-bydelivery month is trading at a premium to the more distant months are said to be inbackwardation. Supply and demand for raw materials can often cause traditionalcommodities markets to go into backwardation. Examples of contango and backwarda-tion markets are shown in Figure 7-1.
The cost of carrying a position in an underlying commodity is only one of manyfactors which can affect a futures spread relationship. A trader who purchases a stockindex futures contract will save the financing costs associated with owning the basketof stocks which make up the index. At the same time, he gives up the rights to anydividends he might receive if he actually owned the stocks. The savings in financingcosts add value to the futures contract, but the loss in dividends reduces the contract’svalue.
Matters can be further complicated if different interest rates play a role in theevaluation of a spread relationship. The value of a treasury bond futures contractdepends not only on the carrying costs saved by purchasing a futures contract insteadof the actual bond (the short-term rate}, but also on the interest lost by not owning thebond (the long-term rate]. Depending on the difference between short- and long-termrates, distant delivery months in the treasury bond futures market can be trading ateither a premium to the nearby months or at a discount to the nearby months. Similartypes of considerations affect relationships in foreign currency futures markets, but herethe determining factors are the difference between domestic and foreign interest rates.When foreign rates are low compared to domestic rates, the more distant months tradeat a premium; when foreign rates are high, the more distant months trade at a discount.
Calculating the spread relationship between different delivery months can be acomplex problem, and is covered more fully in texts focusing specifically on futurestrading. The point here is that, in theory, there ought to be a well defined priceTelationship between different delivery months. When this relationship is violated in themarketplace, a potential profit opportunity exists by selling the overpriced contract andbuying the underpriced.
Spreads need not be based solely on the relationship between different deliveryMonths for the same commodity. They can also be based on presumed price relation-ships between different, though usually related, instruments. The NOB (notes overbonds) spread traded on the Chicago Board of Trade is based on the assumption thatthere is an identifiable relationship between the price of Treasury Bonds and TreasuryNotes. When the spread between the prices of these two futures contracts is more orless than expected, traders will sell one instrument and buy the other. For example,with Treasury Notes at 99-162 and Treasury Bonds at 96-00, there is a 3-16 spreadbetween the two instruments. If a trader feels, based on his analysis of interest rates,
1, Because of their unique importance in financial markets, we will look at stock index futures and optionsin detail in Chapter 15.
2. U.S. Treasury Bonds and Notes are traded in points and 325. 90.16 Tepresents a price of 99 16/32.130 Chapter 7Figure 7-1Contango Markets-Lifetime-Month Open High Low Settie Change High LowFriday, October 22, 1993COCOA (CSCE); 10 metric tons; $ per gaiion (1 = $10.00)Dec 1163 1166 4125 1134 -21 1506 919Mar94 1200 1203 1161 4174 -20 1495 835May 1215 1215 4172 1183 +24 1518 841Jui 1226 1226 4190 1200 -23 1530 845Sep 1237 1237 1220 1220 -20 1536 878Mar95 1239 1239 1239 1239 -20 1346 980COTTON (CTN); 50,000 ibs.; ¢ per ib. (.04 = $5.00)Dec 87.74 57.94 57.20 57.55 19 64.25 $4.60Maro4 59.35 59.45 58.85 59.17 -.20 64.20 55.62May 60,10 60.30 59.75 59.95 -30 64.85 57.47Jui 60.68 60.80 60.30 60.55 25 65.00 58.30Oct 61.80 62.20 61.80 62.00 +.35 64.00 59.81Dec 61.50 62.20 61.35 62.10 +35 62.90 59.48SOYBEAN MEAL (CBT); 100tons.; $ perton. (.04 = $10.00)Dec 193.30 194.60 492.90 193.10 +30 235.50 183.40Jan 493.30 194.70 193.10 193.40 sone 231.50 176.90Mar 494.30 195.90 1494.30 194.40 10 231.00 175.60May 196.00 197.00 195.40 195.40 +.40 228.00 477.00Jui 497.50 198.70 197.20 197.40 +.10 245.00 479.00Aug 497.50 198.40 197.50 197.50 . 237.50 180.10Backwardation Markets-Lifetime-Month Open High Low Settie Change High LowMonday, December 10, 1990CATTLE (CME); 44,000 ibs.; ¢perib. (.01 = $4.40)Dec 79.97 80.75 79.97 80.70 +.78 79.77 71.00Feb91 76.35 77.00 76,25 76.87 +.70 77.80 72.50Apr 76.20 76.95 76.20 76,87 +65 78.05 74.00Jun 74.10 74.65 74.10 74.55 +.50 75.45 72.15Aug 72.70 73.12 72.70 72.92 +.35 73.85 70.35Oct 72.70 73.05 72.70 72.90 +.48 72.85 70.70COPPER (COMEX); 25,000 ibs.; ¢perib. (.04 = $2.50)Jan 110.00 110.85 109.60 110.80 +1.30 126.40 91.50Feb 109.00 109.80 108.90 109.80 +1.60 115.80 99.50Mar 106.40 108.40 106.30 108.00 +2.00 122.60 92.30Apr 106.00 108.00 106.00 107.20 +2.00 115.50 99.85May 105.15 106.70 105.00 106.40 +2.05 417.80 97.00Jui 103.80 105.30 103.80 104.80 +2.40 410.50 95.50HEATING OiL (NYMEX); 42,000 gaiions; ¢ per galion (.01 = $4.20)Jan 81.60 82.50 80.80 80.97 +1.80 107.25 52.95Feb 79.00 79.20 77.60 77.76 +1.52 102.00 52.60Mar 74.00 74.00 72.70 72.82 +.81 96.50 50.70Apr 69.50 69.50 68.10 68.12 +.48 92.00 49.30May 66.20 66.25 65.90 66.12 +11 88.50 48.40Jun 64.75 64.75 64.00 63.22 -.14 85.75 48.40
 Introduction to Spreading 131
that the spread between Notes and Bonds ought to be 3-00, he can sell the spread at3-16 (sell Notes at 99-16, buy Bonds at 96-00). If the spread returns to its expected valueof 3-00, the trader can buy in his Notes and sell out his Bonds, realizing a profit of1639,
Spreads can also be based on more complex relationships. Many traders on theCOMEX follow the price relationship between gold and silver. However, with gold at$300 to $400 per ounce and silver at $4 to $5 per ounce (as of this writing), therelationship is more commonly expressed as a ratio. Suppose a trader decides that thespread between the two metals ought to be 80 ounces of silver to one ounce of gold (an80:1 ratio). If silver is trading at $4.50, given the 80:1 price ratio, gold ought to betrading at $4.50 x 80 = $360. If, however, gold is at $375, the spread trader will sellone ounce of gold at $375, and buy 80 ounces of silver at $4.50. Regardless of thegeneral trend in prices of precious metals, he expects to make $15 when the spreadreturns to its 80:1 ratio. If the precious metals market drops, so that gold is at $336 andsilver is at $4.20 (the expected 80:1 ratio), the trader’s total profit will be:
80 x ($4.20 - $4.50) = -$24 (silver)$375 — $336 = +$39 (gold)
As expected, he has shown a profit of $15.
Spreads can also reflect a trader’s opinion that one contract will outperform adifferent contract. Futures on the New York Stock Exchange Composite Index tradedon the New York Futures Exchange represent the value of approximately 1500 activelytraded stocks. Futures on the Standard & Poor’s 500 Index traded on the ChicagoMercantile Exchange represent the value of 500 such stocks. If a trader believes therelationship between the two index values ought to be 9 to 5 (9 NYSE = 4 S&P 500),and the current prices are 220 and 396, the price relationship is, as expected, 9:5 (9 x220 = 5 x 396). There does not seem to he any reason to either buy or sell the spread.If, however, a trader believes that in percent terms the 500 stocks in the S&P willoutperform the 1500 stocks in the NYSE, he can buy five S&P contracts and sell nineNYSE contracts. If, in percent terms, the S&P rises more quickly, or declines less quickly,the trader will profit from the better performance of the contracts which he owns.
Spread relationships need not be restricted to two instruments. Sometimes three,or even more, different instruments may define a spread relationship. We calculated thatif February gold is at $360, and interest rates are 9%, the spread between February andApril gold ought to be $5.40. If interest rates rise, the carrying costs will also rise, andthe February/April spread will widen. If a trader is long February gold and short Aprilgold, and he feels that Eurodollar interest rates correlate closely to his cost of carry, hecan sell Eurodollar futures to protect himself against a rise in interest rates. If interestrates do rise, he will lose on his February/April spread, but this will be offset by theprofit on his Eurodollar position, He has made the assumption that there is a three-sidedspread relationship between the price of February gold, April gold, and Eurodollars.
Much of the most sophisticated trading in derivative markets involves identifyingand following spread relationships. When a trader decides that a spread relationship is132 Chapter 7
mispriced in the marketplace, it can be just as profitable to buy or sell the spread as totake an outright long or short position in a single instrument.
In the foregoing examples the price relationship between instruments was definedin point or currency terms. In some cases, however, it may be more practical to definethe relationship in other terms. In Chapter 4 we used a theoretical pricing model todetermine an option’s implied volatility, and we noted that for an option trader theimplied volatility might be a more accurate reflection of an option’s price than its dollarprice. An option trader might therefore express the spread value between two optionsin terms of the spread between their implied volatilities. An option with an impliedvolatility of 15% and a different option with an implied volatility of 17% have a two-pointvolatility spread, regardless of the difference in their dollar prices. If both options havethe same underlying instrument, a trader might purchase the option with an impliedvolatility of 15% and sell the option with an implied volatility of 17%, hoping to profitwhen the spread between the implied volatilities narrows.
As we shall see, the foregoing example is simplistic. An option trader cannot simplybuy options with low implied volatilities and sell options with high implied volatilities.Not only is the spread between implied volatilities important, but also the general levelof implied volatility. A two-percentage-point volatility spread may mean one thing if theimplied volatilities are 6% and 8%, and something else if the implied volatilities are 26%and 28%. Moreover, there are important considerations of risk arising from difficultiesin predicting volatility, as well as the possible inaccuracies in the models themselves. Inspite of these factors, volatility spreads form one of the most important classes of optiontrading strategies. Much of an option trader’s education is spent studying volatilityrelationships, and learning to create spreads based on mispriced volatility.
In the previous examples we assumed that a spreading strategy was static, that oncethe spread was initiated it was only necessary to wait for the spread to reach its expectedvalue. Spreads can also be dynamic, requiring action over the life of the spread in orderto profit from the mispricing. This was the method used in Chapter 5 to take advantageof a mispriced option. The option was spread against the underlying contract, and theposition was adjusted over the life of the option. At expiration, the resulting profit wasapproximately equal to the amount by which the option was originally mispriced.
WHY SPREAD?
We saw in Chapter 3 that most theoretical pricing models depend on the laws ofprobability to generate option values. Even if we have correctly estimated the prob-abilities, i.e., volatility, we know that probability theory is only valid over manyoccurrences or, in the case of options, over long periods of time. A trader will sometimeshave to hold an option position for an extended period in order to profit from theoption’s mispricing. Unfortunately, while he is holding the position, over short periodsof time he may have to put up with adverse fluctuations in the position’s value. Thefluctuations might be severe enough that the trader, because of capital requirements,will not be able to maintain the position. If he is forced to liquidate the position prior toIntroduction to Spreading 133
expiration, there is no guarantee that he will profit from the option’s mispricing, evenif he has accurately estimated all the inputs into the pricing model. By spreading, a traderis attempting to reduce the effect of short-term “bad luck” that goes with any investmentbased on the laws of probability.
Spreading strategies not only take advantage of the laws of probability by enablinga trader to hold option positions over long periods of time, but such strategies also havethe effect of protecting the trader against incorrectly estimated inputs into the theoreti-cal pricing model. Suppose a trader estimates that over the life of an option the volatilityof an underlying Deutschemark futures contract will be 13%. Based on this estimate hefinds that a certain call trading at the Chicago Mercantile Exchange has a theoreticalvalue of 1.75 but is actually trading for 2.00. If the call has a delta of 25, one strategyis to sell four calls for 2.00 each and buy one futures contract, yielding a theoretical edgeof 4 x .25 = 1.00, or $1,250. (Each point in currency contracts at the ChicagoMercantile Exchange is worth $1,250.) Of course, if the trader can make $1,250 witha 4x 1 spread, it may occur to him that he can make $12,500 if he increases the sizeof the spread to 40 x 10. Why stop now? He can make $125,000 if he increases thesize to 400 x 100.
Even if the market is sufficiently liquid to absorb unlimited size, is this a reasonableapproach to trading? Should a trader simply find a theoretically profitable strategy anddo it as many times as possible in order to maximize the profit potential? At some pointthe intelligent trader will have to consider not only the potential profit, but also the riskassociated with a strategy. After all, his volatility estimate of 13% is just that, an estimate.What will happen if volatility actually turns out to be some higher number, perhaps15%, ot 17%? If the calls which he sold at 2.00 are worth 2.25 at a volatility of 17%,and volatility actually turns out to be 17%, then his hoped-for profit of $125,000(assuming a size of 400 x 100) will turn into a loss of $125,000.
A trader must always consider the effects of an incorrect estimate, and then decidehow much risk he is willing to take. If the trader in this example decides that he cansurvive if volatility goes no higher than 15% (a two-percentage-point margin for error},he might only be willing to do the spread 40 x 10. But if there were some way toincrease his break-even volatility to 19% (a six-percentage-point margin for error), hetight indeed be willing to do the spread 400 x 100. Option spreading strategies enabletraders to profit over a wide variety of market conditions by giving them an increasedmargin for error in estimating the inputs into a theoretical pricing model. No trader willsurvive very long if his livelihood depends on estimating each input with 100%accuracy. Even when he incorrectly estimates the inputs, the experienced trader cansurvive if he has constructed intelligent spread strategies which allow fora wide marginof error.
SPREADING AS A RISK MANAGEMENT TOOL
Recall our example in Chapter 3 where a casino is selling a roulette bet with an expectedreturn of 95¢ (American conditions) for $1.00. The casino owner knows that based on134 Chapter 7
the laws of probability he has a 5% theoretical edge. Suppose that one day a bettor comesinto the casino and proposes to bet $2,000 on one number at the roulette table. Thecasino owner knows that the odds are on his side and that he will most likely get tokeep the $2,000 bet. But there is always a chance that the player will win, and that thecasino will lose $70,000 (the $72,000 payoff less the $2,000 cost of the bet) if theplayer’s number does come up.
Now suppose that two other bettors come into the casino, and each proposes toplace a $1,000 bet at the roulette table. They promise, however, to bet on differentnumbers. Whichever number one bettor chooses, the other bettor will choose someother number. As with the first bettor and his single bet of $2,000, the casino’s potentialreward in this new scenario is also $2,000, if neither of the two numbers come up. Butthe risk to the casino is now only $34,000 (the $36,000 payoff if one player wins, lessthe cost of the two $1,000 bets). Since only one player can win, the two bets aremutually exclusive: if one wins, the other must lose.