General Motors Corp. stock and Ford Motor Co. stock. Clearly, some instru-ments are more closely related than others. The closer the relationship, the more suchinstruments lend themselves to intermarket spreading.
AN INTERMARKET HEDGE
Because intermarket spreading is most common in markets with close relationships, itis not surprising that among the most common markets for intermarket spreading arethose where one or more products are derived from some other product. For example,since both heating oil and gasoline are derived from crude oil one would expect pricemovements in these three markets to be closely correlated. If demand rises for heatingoil or gasoline, forcing up the price of these products, then the price of crude oil is alsolikely to rise. Similarly, if the supply of crude oil is disrupted and prices consequentlyrise, then the price of gasoline and heating oil is also likely to rise.
Refiners who purchase crude oil and refine it into gasoline and heating oil are oftensensitive to the value of crack spreads, the spread between the price of crude oil and itsderivative products. For example, a refiner who purchases crude oil and refines it intogasoline is concerned that the price of crude oil will rise and that the price of gasolinewill fall. If crude oil is at $19.00 per barrel and gasoline at $.5400 per gallon, the priceof a simple crude oil/gasoline crack spread is:!
($.54 x 42} - $19.00 = $3.68 per barrel
If the refiner is satisfied with the $3.68 profit margin, he might protect his position bypurchasing crude oil futures at $19.00 and selling an equal number of gasoline futuresat $.5400.2 If, however, he has an opinion on the volatility of either crude oil or gasoline,and this opinion differs from the implied volatility in the option market, he can takeeither position in options. If he feels that implied volatility in crude oil is unusually low(high), he can take his long position by purchasing calls (selling puts). If he feels thatimplied volatility in gasoline is unusually low (high), he can take his short position bypurchasing puts (selling calls).
While most intermarket spreads consist of opposing positions in two differentMarkets, there is no reason why an intermarket spread cannot be extended to multipleinstruments. For example, some refining operations produce a combination of bothgasoline and heating oil. In a typical combination 3:2:1 crack spread, from each threebarrels of crude oil which the refiner purchases he expects to produce two barrels ofgasoline and one barrel of heating oil. With crude oil at $19.00 per barrel, gasoline at$.5400 per gallon, and heating oil at $.5800 per gallon, the value of a3:2:1 crack spreadis;
((2 x 42 x $.5400) + (1 x 42 x $.5800) — (3 x $19.00)] / 3 = $4.24 per barrel
 
1. Since gasoline and heating oil are quoted in cents per gallon, and a barrel contains 42 gallons, thegasoline or heating oil price must be multiplied by 42 in order to calculate its price per barrel.
2. Although this is not a $delta neutral position, since the dollars at risk in crude oil are not equal to the
dollars at risk in gasoline, it is still an intermarket spread since one market is being spread off againstanother market.336 Chapter 16
Again, if the refiner is satisfied with the $4.24 profit margin, he can simply buy crudeoil futures and sell gasoline and heating oil futures in a 3:2:1 ratio. For each three crudeoil futures which he purchases, he can sell two gasoline futures and one heating oilfuture, If, however, the refiner has an opinion on the volatility of any of these products,he may find it advantageous to take his long or short position in the option market ratherthan in the futures market.
VOLATILITY RELATIONSHIPS
A close price relationship between markets may also mean that the markets have similarvolatility characteristics. This may enable the trader to identify mispriced optionswithout the necessity of picking the right volatility for either market. Returning to ourABC and XYZ contracts, suppose that a trader thinks ABC will be stronger than XYZ,and wants to take a long position in ABC and a short position in XYZ. If the impliedvolatility of ABC is 20% and the implied volatility of XYZ is 24%, the trader might nowhave reason to take his position in options rather than in the underlying instruments. Ifthe market were to rise, the trader expects ABC to go up faster than XYZ since ABC isexpected to be stronger than XYZ. In the trader’s estimation, ABC ought to have agreater volatility. But the implied volatilities reflect the opposite view. The marketplaceseems to believe that if both ABC and XYZ rise in price, XYZ (with its implied volatilityof 24%) will rise more quickly than ABC (with its implied volatility of 20%). Clearly, theprices in the marketplace do not reflect the trader’s opinion of market conditions. Thetrader can take advantage of this situation by purchasing ABC calls and selling XYZ calls.
Note that the trader has not made any attempt to predict the right volatility foreither ABC or XYZ. He has simply made the assumption that the implied volatilities donot reflect his view of market conditions.
If the trader wants to construct a $delta neutral spread he must still determine thedelta of the options involved. Since the $delta, like all deltas, is sensitive to changes involatility, it may seem that the trader will need a specific volatility to calculate the$delta. He can avoid this problem if he decides to use at-the-money options. No matterwhat the volatility, he knows that an at-the-money option will have a delta of approxi-mately 50. If ABC is trading at 50 and XYZ is trading at 100, he can buy ABC 50 callswith an implied volatility of 20%, and sell XYZ 100 calls with an implied volatility of24%. If there are 70 days remaining to expiration, with interest rates at 6%, the price ofthe ABC 50 call would be 1.73 (a dollar price of $692) and the price of the XYZ 100call would be 4.14 (a dollar price of $414). Since the $delta of ABC is $200 and the$delta of XYZ is $100, a typical $delta neutral spread might consist of purchasing 10ABC 50 calls and selling 20 XYZ 50 calls. The value of such a spread at expiration isshown in Figure 16-1.
In Figure {6-1 we can see that if ABC is stronger than XYZ, as the trader believes,the spread will show an ever increasing profit as ABC continues to outperform XYZ.Note that the trader will also show a profit if the market falls in both ABC and XYZ, orif ABC and XYZ move up at the same rate. This is because the trader received more forthe XYZ options which he sold than he paid for the ABC options which he bought. IfIntermarket Spreading 337
Figure 16-1: Long 10 ABC 50 Calls/Short 20 XYZ 100 Calls
ABC moves up twiceas fast as XYZ
ABC moves up 33% \ ae °
faster than XYZ
 
 
 
 
 
 
oO83 ola& aa& ao2 oea ABC moves up at thesame rate as XYZwe yoo+-4 T “T T T T T T T T T T48 49 50 51 52 53 54 55 56 57 58 59 60
ABC Price
the market falls and the entire position ends up worthless, or if ABC and XYZ move upat the same rate, the trader is left with a profit equal to the excess price of XYZ options.The only market conditions which would hurt this spread would be an upward movein both ABC and XYZ, with XYZ outperforming ABC.
What action could the trader take if the implied volatilities were reversed, withABC having an implied volatility of 24% and XYZ having an implied volatility of 20%?Now if ABC and XYZ both rise, the marketplace expects ABC to outperform XYZ. Sincethis is also what the trader believes, there does not seem to be any opportunity. ButSuppose, instead of buying calls in ABC and selling calls in XYZ, the trader decides totake his long position in ABC by selling puts, and his short position in XYZ by purchasingPuts. Assuming, again, that he uses at-the-money puts which he knows to have a deltaof approximately -50, he might create a $delta neutral position by selling 10 ABC 50puts and buying 20 XYZ 100 puts. If the market moves up, and ABC is stronger thanXYZ, all the options will collapse to zero. He will be left with a profit equal to the excesscredit when he sold ABC 50 puts at an implied volatility of 24% and bought XYZ 100Puts at an implied volatility of 20%. And if the market moves down, based on hisassumption that ABC will be stronger than XYZ, the trader expects XYZ to move downMore quickly than ABC. Hence, the XYZ puts will appreciate more rapidly than the ABCputs, leaving the trader with an ever-increasing profit. The results of this strategy isShown in Figure 16-2.Profit & Loss
338 Chapter 16
Figure 16-2: Short 10 ABC 50 Puts/Long 20 XYZ 100 Puts
 
 
 
 
 
 
XYZ moves down~~ twice as fast as ABCXYZ moves down sy33% faster than ABC ma° ~[ a ~ oe ~XYZ moves Joma me .the same rate as ABC ae Meae * sema0 _ aL = |T T T T T T T T T T T40 4 42 43 44 45 46 47 48 49 50 51 52ABC Price
In the foregoing examples we used at-the-money options which we knew to havea delta of 50. What about using either in-the-money or out-ofthe-money options? Nowthe situation becomes more complex. If we use at-the-money options we are onlyrequired to determine that ABC and XYZ implied volatilities are mispriced with respectto each other. If, however, we start to vary the options’ exercise prices, we need todetermine not only whether ABC and XYZ options are mispriced with respect to eachother, but also whether the individual implied volatilities are too high or too low.Whenever options appear cheap because implied volatility is lower than a trader’svolatility forecast, the trader will try to buy out-of-the-money options (options withlower deltas). Whenever options appear expensive because implied volatility is higherthan a trader’s volatility forecast, the trader will try to sell out-of-the-money options.
For example, if ABC options not only appear too cheap with respect to XYZ options,but also appear too cheap compared to a trader’s volatility forecast for ABC, the traderwill try to buy ABC options with smailer deltas and sell XYZ options with larger deltas.Assuming the trader wants to be long ABC and short XYZ, he might buy ABC 55 callsand sell XYZ 100 calls. Or he might buy ABC 50 calls and sell XYZ 95 calls. He is tryingto create an intermarket call backspread, by purchasing options with smaller deltas, andselling options with larger deltas. In the same way, if ABC options appear too expensivewith respect to XYZ, and also appear too expensive compared to a trader’s volatilityforecast, he might take his long position in ABC by selling puts with lower deltas, andtake his short position in XYZ options by purchasing puts with higher deltas. This willIntermarket Spreading 339
create an intermarket put ratio vertical spread. Examples of an intermarket callbackspread and an intermarket put ratio vertical spread are shown in Figures 16-3 and16-4. Note that such spreads are sensitive not only to the volatility relationship betweenABC and XYZ, but also to the general level of volatility. A backspread wants the marketto become more volatile; a ratio vertical spread wants the market to become less volatile.
INTERMARKET VOLATILITY SPREADS
Suppose a trader has decided that ABC and XYZ ought to have very similar volatilities,put he finds that the implied volatility of ABC options, at 20%, is markedly different thanthe implied volatility of XYZ options, at 25%. If the trader also believes that one marketwill outperform the other, he might take a position by purchasing calls (puts) in onemarket and selling calls (puts) in the other market. But suppose the trader has no opinionon the relative strengths of the two markets. His only opinion is that options in onemarket are too cheap or expensive in relation to options in the other market. He simplywants to be long volatility in one market and short volatility in the other. What can hedo?
Suppose the trader purchases ABC calls and sells XYZ calls. If he is right aboutvolatility and both markets move in the same direction, he will always show some profit(Figure 16-1}. But his profit will be greatest when ABC and XYZ rise in price. In thesame way, if the trader purchases ABC puts and sells XYZ puts, he will always show
Figure 16-3: Long 21 ABC 55 Calls/Short 12 XYZ 95 Calls
 
ABC moves up 33% 2faster than XYZ, or moves ifdown 33% slower than XYZ pf
ABC moves up twice as ryfast as XYZ, or moves afdown half as fast as XYZ if
Profit & Loss
o+
      
ABC and XYZ move up anddown at the same rate a
 
 
 
TTT T T T TT T T T T T T oto40 41 42 43 #44 #45 #46 #47 #48 #<49 «50 «#«51 52 5&3 54 55 56 57 58 59 60ABC Price340 Chapter 16
Figure 16-4: Short 21 ABC 45 Puts/Long 12 XYZ 105 Puts
 
ABC moves up twice asfast as XYZ, or movesdown half as tast as XYZ
 
Profit & Loss~
       
ABC and XYZ move up anddown at the same rate
ABC moves up 33%faster than XYZ, or movesdown 33% slower than XYZ
 
 
 
+4 T T T T T T T T T TT T T T T T T T T40 41 42 43 44 45 #46 47 #48 #49 SO 51 S62 53 54 5S 56 57 SB SB 60ABC Price
some profit (Figure 16-2). But now his profit will be greatest when ABC and XYZ fall inprice. A trader who has only a volatility opinion can combine these strategies to createan intermarket spread which is based solely on the assumption of a mispriced volatilityrelationship between the two markets. That is, the trader can buy straddles or stranglesin one market and sell straddles or strangles in the other market.
Since the trader is not taking a position on what the correct volatility is for ABC orfor XYZ, but rather on the relative volatility between the two markets, he can’tdetermine the exact delta for the options. The easiest way to solve this problem is tofocus on at-the-money straddles. Regardless of the correct volatility, he knows thatat-the-money options have deltas of approximately 50.
Suppose the trader decides to buy 20 ABC SO straddles. How many XYZ 100straddles should he sell if he wants the value of the total position to be dependent onlyon the volatility relationship between the two markets? The trader can think of hisposition as an ABC/XYZ call spread, combined with an ABC/XYZ put spread. SinceABC has a $delta of $200, the trader’s total $delta position in ABC 50 calls is:
20 x $200 x .50 = $2000
The $delta of XYZ is $100, so each XYZ call has a $delta of $100 x .SO = $50. Thecorrect number of XYZ calls to sell is therefore:
$2,000 / $50 = 40Intermarket Spreading 34]
The arithmetic is essentially the same for ABC and XYZ puts, each having a delta of -50.If the trader buys 10 ABC 50 puts, his $delta position is:
10 x $200 x -.50 = -$2000
With the $delta for the XYZ 100 put of -$50 we need to sell 40 XYZ 100 puts to balancethe 20 ABC 50 puts which we purchased. The complete position is:
long 20 ABC 50 calls short 40 XYZ 100 callslong 20 ABC 50 puts short 40 XYZ 100 puts
The value of this position at expiration is shown in Figure 16-5.
Note in Figure 16-5 that if ABC and XYZ move at the same rate, the position willalways show a profit equal to the excess premium received for XYZ options (impliedvolatility = 25%) over the premium paid for ABC options (implied volatility = 20%).Suppose the implied volatilities of 20% for ABC and 25% for XYZ turn out to be correct.This means that XYZ will move 25% faster than ABC since 25/20 = 1.25. If this happenswe can see from Figure 16-5 that the spread will now act like a short straddle, showingits maximum value if the market sits still and showing a loss if the market makes a bigmove.
If the trader believes that XYZ will move faster than ABC, as indicated by theimplied volatilities, he might alter the ratio. If XYZ does have a volatility 25% greaterthan ABC, the trader can rebalance the spread by purchasing 25% more ABC straddlesthan he originally intended. Instead of purchasing 20 ABC straddles he can purchase 25ABC straddles. The effect of doing the spread in this new ratio is shown in Figure 16-6.
We can see from Figure 16-6 that in the new size of 25 x 40 the spread breaks evenif XYZ does move 25% faster than ABC. But the position acts like a long straddle if ABCand XYZ move at the same rate. In the new size of 25 x 40 the volatility differencebetween the two contracts has become a factor in determining the correct ratio.Originally, the trader balanced his spread based on the following relationship:
ABC contracts x $delta of ABC x ABC option deltamust equalXYZ contracts x $delta of XYZ x XYZ option delta
But taking into consideration the different volatilities of the two contracts, the spread fsnow balanced if:
ABC contracts x $delta of ABC x ABC option delta x ABC volatilityequalsXYZ contracts x $delta of XYZ x XYZ option delta x XYZ volatility
Our XYZ call position is:40 x $100 x .50 x .25 = $500Taking into consideration the volatility, each ABC call has a $delta of$200 x .50 x .20 = $20342 Chapter 16
Figure 16-5: Long 20 ABC 50 Calls/Long 20 ABC 50 PutsShort 40 XYZ 100 Calls/Short 40 XYZ 100 Puts
 
ABC and XYZ move up anddown at the same rate
 
 
Profit & Losscd
XYZ moves up and down .25% faster than ABC . me
 
 
 
T T T T T T T T T T T T T T T T 7 T T40 41 42 43 44 45 46 47 #48 #49 50 51 52 53 54 55 66 57 58 59 60ABC Price
Therefore, the proper number of ABC contracts required to balance the spread is500/20, or 25 contracts. The spread is now completely balanced since:
25 x $200 x .50 x .20 = 40 x $100 x .50 x .25
We can see that the volatility relationship between the two contracts can be animportant factor in determining the proper ratio in an intermarket volatility spread.Since predicting the correct volatility of even one underlying contract can be such adifficult task, what chance does the trader have of being correct about the volatility oftwo different contracts? The important consideration in an intermarket spread is notnecessarily the volatility of each individual contract, but the volatility relationshipbetween the contracts. If a trader can determine the relationship, the actual volatilitymight not affect the spread value. For example, if we determine that XYZ is always 25%more volatile than ABC, the actual volitilities of ABC and XYZ don’t really matter. Theratio is the same whether the volatility of ABC is 20% and XYZ is 25%, or ABC is 12%and XYZ is 15%, or ABC is 28% and XYZ is 35%. In each case XYZ is 25% more volatilethan ABC, so the ratio of XYZ to ABC is the same.
Is it possible to identify markets with well defined volatility relationships? Whilethere can be no absolute answer, some markets do seem to be so closely related thattheir volatilities take on a well defined relationship,Intermarket Spreading 343
Profit & Loss
Figure 16-6: Long 25 ABC 50 Calls/Long 25 ABC 50 PutsShort 40 XYZ 100 Calls/Short 40 XYZ 100 Calis
 
  
ABC and XYZ move up anddown at the same rate
    
 
 
 
 
 
 
XYZ moves up and down25% faster than ABC
 
 
 
“T “T T T ~“T “TT TT T T T —~T T TT T T T T T T40 41 42 43 44 #45 #46 47 #48 #49 #50 51 52 53 54 55 56 57 58 59 60ABC Price
For example, several indexes exist which track the performance of the U.S. stockmarket. Not only might we expect these indexes to move up or down together, at leastover longer periods of time, but we might also expect them to have similar volatilitycharacteristics. As an example, the 50-day historical volatilities of two of these indexes,the S&P 100 (OEX) and the New York Stock Exchange Composite Index (NYA), areshown in Figure 16-7. There is clearly some relationship between the volatility of thesetwo indexes, but how close is the relationship? To help answer the question, NYAvolatility has been plotted as a percent of OEX volatility in Figure 16-8. We can see thatNYA volatility is typically somewhere between 80% and 95% of OEX volatility. As arough estimate we might decide that on average NYA volatility is approximately 87%of OEX volatility.
Suppose we find that OEX options, traded on the Chicago Board Options Exchange,and NYA options, traded on the New York Stock Exchange, are trading at approximatelythe same implied volatility. Since we expect the NYA to be approximately 13% lessvolatile than the OEX, how can we construct a strategy which exploits this apparentmispricing between OEX and NYA options? If we decide to buy at-themoney OEXstraddles and sell at-the-money NYA straddles, and also take into consideration therelative volatilities of the two markets, we know that in a balanced spread:Chapter 16
344
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 346 Chapter 16
number of OEX straddles x OEX $delta x .87must equalnumber of NYA straddles x NYA $delta
Suppose the OEX is at 440 and the NYA is at 260. Since both contracts have the samepoint value of $100, the $deltas for the two indexes are:
OEX $delta = 440 x $100 / 100 = $440NYA $delta = 260 x $100 / 100 = $260
For each NYA straddle which we sell, we must purchase .87 x 260/440, or approxi-mately .51 OEX straddles. If we were to purchase 20 OEX 440 straddies, a balancedintermarket volatility spread would require us to sell approximately 39 NYA 260straddles, since 39 x .51 = 20. Our spread might consist of:
long 20 OEX 440 calls / long 20 OEX 440 putsshort 39 NYA 260 calls / short 39 NYA 260 calls
If the OEX straddles are purchased and the NYA straddles sold at the same impliedvolatility, the value of the position at expiration is shown in Figure 16-9.
Note that if both contracts move in the same direction and, as we expect, NYAvolatility is 87% of OEX volatility, the position shows a constant profit equal to theexpected 13% difference in the volatilities. Even if we double or triple volatility, theprofit to the position will be identical, as jong as NYA volatility is 87% of OEX volatility.
We can see from Figure 16-8 that NYA volatility need not be exactly 87% of OEXvolatility. What will our position look like if NYA volatility turns out to be near the upperrange of OEX volatility, perhaps 95%, or near the lower range of OEX volatility, perhaps80%. These two possibilities have also been plotted in Figure 16-9. In the former caseour position will begin to act like a short straddle, and any increase in volatility willreduce the value of the position. In the latter case our position will begin to act like along straddle, and any increase in volatility will increase the value of the position.Obviously, if we were to focus on a risk to our position, the risk would be that NYAvolatility would increase relative to OEX volatility. Even with this risk the spread stilllooks very attractive since we have considerable margin for error.
In a typical volatility spread a trader often focuses on the delta, gamma, theta, andvega characteristics of the spread. We might also want to consider these sensitivitieswith respect to an intermarket spread. Just as we found it convenient to calculate a$delta to compare contracts in different markets, we will also find it convenient tocalculate the $gamma, $theta, and $vega. The definitions and interpretations are:
$gamma = underlying $delta x option’s gamma x underlying point value / 100
(the change in an option’s $delta for a one-percent change in the price of the underlyingcontract}
$theta = underlying point value x option’s theta(the doliar change in an option’s theoretical value with the passage of one day)Profit & Loss
Intermarket Spreading
347
Figure 16-9: Long 20 OEX 440 Calls/Long 20 OEX 440 Puts
Short 39 NYA 260 Calls/Short 39 NYA 260 Puts
 
 
 
 
 
 
Se
oN NYA volatility is 80%
are of OEX volatility ao~~ ~ ~ “ N ‘A volatil ‘%~ YA volatility is 87~ a of OEX volatilityaea NYA volatility is 95%“ “ of OEX volatility me
0 = a
a “ os,
T T 7 T T T TT T T T T T T T “T400 405 410 415 420 426 430 435 440 445 450 455 460 465 470 475 480OEX Price
$vega = underlying point value x option’s vega
(the dollar change in an option’s theoretical value for a one-percentage-point change in
volatility)
If we use implied volatilities of 11%, an interest rate of 5%, and assume 70 daysTemaining to expiration, the dollar sensitivities for several OEX and NYA options might
be approximately the
OEX = 440.00;volatility = 11%;
NYA = 260.00;volatility = 11%;
Option
OEX 425 callOEX 440 callOEX 455 call
following:
time to expiration = 70 days;interest rate = 5%
time to expiration = 70 days;interest rate = 5%
$delta $gamma364 23259 36140 33
$theta $vega8.57 499,29 756.87 69
3. These figures are approximations only. While early exercise was taken into cons{deration through theuse of the Cox-Ross-Rubenstein model, no dividends were used. In addition, the numbers have beenrounded for convenience.348 Chapter 16
Option ‘ $delta § $gamma _—‘$theta $