
Given our two scenarios, one bettor wagering $2,000 on one number, or twoplayers wagering $1,000 each on different numbers, what is the theoretical edge to thecasino? The edge to the casino in both cases is still the same 5%. Regardless of theamount wagered, or the number of individual bets, the laws of probability say that inthe long run the casino gets to keep 5% of everything that is bet at the roulette table. Inthe short run, however, the risk to the casino is greatly reduced with two $1,000 betsbecause the bets have been spread around the table.
A casino does not like to see a bettor wager a large amount of money on oneoutcome, whether at roulette or any other casino game. The odds are still in the casino’sfavor. But, if the bet is large enough, and the bettor is lucky, short-term bad luck canoverwhelm the casino. Indeed, if a bettor knows that the odds are against him, and hewaits the greatest chance of showing a profit, his best course is to wager the maximumamount on one outcome, and hope that in the short run he gets lucky. If he continuesto make bets over a long period of time, the laws of probability will eventually catch upwith him and the casino will end up with the bettor’s money. The ideal scenario fromthe casino’s point of view is for 38 players to place 38 bets of $1,000 each on all 38numbers at the roulette table. Now the casino has a perfect spread position. One playerwill collect $36,000, but with $38,000 on the table the casino has a sure profit of$2,000.
The option trader prefers to spread for the same reason that the casino prefers thebets to be spread around the table: spreading maintains profit potential but reducesshort-term risk. There is no perfect spread position for the option trader, as there is fora casino. But the intelligent option trader learns to spread off his risk in as many differentways as possible in order to minimize the effects of short-term bad luck.
New traders are sometimes astonished at the size of the trades an experiencedtrader is prepared to make. For example, an independent floor trader in Treasury Bondoptions at the Chicago Board of Trade who buys 100 calls at 2-00 ($2,000) each hastaken a position worth $200,000. How can he afford to do this? His capital resourcescertainly play a role in the risk he is willing to accept. But equally important is his abilityIntroduction to Spreading 135
to spread off risk. An experienced trader may know a wide variety of ways to spread offthe risk associated with the 100 calls he purchased, either using other options, futurescontracts, cash bonds, or some combination of these instruments. He may not be ableto completely eliminate his risk. But he may be able to reduce it to such an extent thathis risk is actually less than that of a much smaller trader who does not know how tospread, or knows only a limited number of spreading strategies.x 8 oO
Volatility Spreads
To take advantage of a theoretically mispriced option, it is necessary to hedge thepurchase or sale of the option by simultaneously taking an opposing market position. Inthe examples in Chapter 5, the opposing market position was always taken in theunderlying instrument. It is also possible to hedge an option position with other optionswhich are theoretically equivalent to the underlying instrument. For example, supposewe feel a certain call with a delta of 50 is underpriced in the marketplace. If we buy 10calls, giving us a total delta position of +500, we can hedge our position in any of thefollowing ways:
*% = Sell five underlying contracts
* Buy puts with a total delta of -500
“+ Sell calls, different than those which we purchased, with a total delta of +500“ Combine several of these strategies, such that we create a total delta of -500
With many different calls and puts available, as well as the underlying contract,there are many different ways of hedging our ten calls. Regardless of which method wechoose, each spread will have certain features in common:
“* Each spread will be approximately delta neutral.
+ Each spread will be sensitive to changes in the price of the underlyinginstrument.
“+ Each spread will be sensitive to changes in implied volatility.
“+ Each spread will be sensitive to the passage of time.
Spreads with the foregoing characteristics fall under the general heading of volatil-ity spreads. In this chapter we will define the basic types of volatility spreads and lookat their characteristics, initially by examining the expiration values of the spread, andthen by considering the delta, gamma, theta, vega, and rho associated with each spread.
Before defining the primary types of spreads, it should be noted that spreadingterminology is not uniform. Traders sometimes use different terms when referring to thesame spread; they sometimes use the same term when referring to different spreads. Anattempt has been made to use the most common terminology, but alternative spreaddefinitions are also given where appropriate.
137138 Chapter 8
BACKSPREAD(also referred to as a ratio backspread or long ratio spread)
A backspread is a delta neutral spread which consists of more long (purchased) optionsthan short (sold) options where all options expire at the same time. In order to achievethis, options with smaller deltas must be purchased and options with larger deltas mustbe sold. A call backspread consists of long calls at a higher exercise price and short callsat a lower exercise price. A put backspread consists of long puts at a lower exercise priceand short puts at a higher exercise price.
Typical backspreads and their values at expiration are shown in Figures 8-1 and8-2. (These, and the example spreads in the following sections, are taken from theoption evaluation table in Figure 8-20.) In each case, a move away from the longoption’s exercise price will increase the value of the spread. Depending on the type ofbackspread, movement in one direction may be preferable to movement in the otherdirection. In a call backspread the upside profit potential is unlimited; in a putbackspread the downside profit is unlimited. But the primary consideration is that somemovement will occur. If no movement occurs, a backspread is likely to be a losingstrategy.
Typically, a backspread is done for a credit. That is, the amount of premiumreceived for the sold options is greater than the premium paid for the purchased options.This ensures that the backspread will be profitable if the market makes a large move ineither direction. If the market collapses in the case of a call backspread, or the market
Figure 8-1: Call Backspread
 
 
sell the buy thelower higherexercise exerciseprice price= : i8 |oa ~t8 long 30 March 105 calls (24)g short 10 March 95 calls (78)
long 25 June 110 calls (23)short 10 June 100 calls (61)
 
 
 Volatility Spreads 139
Figure 8-2: Put Backspread
 
 
buy the sell thelower higherexercise exerciseprice priceSoO ~n6 long 80 March 90 puts (-6)a
 
short 10 March 100 puts (-48)
Jong 45 June 95 puts (-30)short 30 June 100 puts (-46)
 
 
 
explodes in the case of a put backspread, all options will expire worthless and the traderwill keep the credit from the initial transaction.
A trader will tend to choose the type of backspread which reflects his opinion aboutmarket direction. If he foresees a market with great upside potential, he will tend tochoose a call backspread; if he foresees a market with great downside potential he willtend to choose a put backspread. He will avoid backspreads in quiet markets since theunderlying contract is unlikely to move very far in either direction.
RATIO VERTICAL SPREAD{also referred to as a ratio spread, short ratio spread,vertical spread, or front spread)
A trader who takes the opposite side of a backspread also has a delta neutral spread, buthe ts short more contracts than long, with all options expiring at the same time. Such aspread is sometimes referred to as a ratio spread or a vertical spread. However, theseterms can also be applied to other types of spreads. In order to avoid later confusion, wewill designate the opposite of a backspread as a ratio vertical spread.
Typical ratio vertical spreads, and their expiration values, are shown in Figures 8-3and 8-4. From these graphs we can see that a ratio vertical spread will realize itsmaximum profit at expiration when the underlying contract finishes right at the short(sold) option’s exercise price. Since a ratio vertical spreader assumes the opposite risksof a backspreader, his risk is unlimited on the upside in a call ratio vertical spread, and140
Profit
Loss
Profit
Loss
 
 
 
 
 
 
 
 
 
Chapter 8Figure 8-3: Call Ratio Vertical Spreadlong 20 March 96 calls (78)short 30 March 100 calls (51)long 10 June 95 calls (67)short 30 June 110 calls (23)buy the sell thelower higherexercise exerciseprice priceFigure 8-4: Put Ratio Vertical Spreadlong 20 March 95 puts (-21)short 60 March 90 puts (-6)long 15 June 105 puts (-62): short 20 June 100 puts (-46)| >sell the buy thelower higherexercise exerciseprice price
 
 
 
 Volatility Spreads 141
unlimited on the downside in a put ratio vertical spread. While a ratio vertical spreaderexpects the market to remain relatively stable, he will tend to choose either a call or putratio vertical spread in order to limit his losses if he is wrong. If he is primarily worriedabout a swift rise in the market, he will choose a put ratio vertical spread; if he isprimarily worried about a swift fall in the market, he will choose a call ratio verticalspread. In both cases, if the market does make a big move, his loss will be limited sincethe calls can only collapse to zero if the market falls, and the puts can only collapse tozero if the market rises.
STRADDLE
A straddle consists of either a long call and a long put, or a short call and a short put,where both options have the same exercise price and expire at the same time. If boththe call and put are purchased, the trader is said to be long the straddle; if both optionsare sold, the trader is said to be short the straddle. Typical long and short straddles, withtheir expiration values, are shown in Figures 8-5 and 8-6,
While most straddles are executed with a one-to-one ratio (one call for each put),this is not a requirement. A straddle can also be ratfoed, so that it consists of unequalnumbers of calls and puts. Any spread where the number of long market contracts (longcalls or short puts) and short market contracts (short calls or long puts) are unequal fsconsidered a ratio spread. The most common types of ratio spreads are backspreads and
Figure 8-5: Long Straddle
 
 
bu= calls and puts© at the sameoa exercise priceon3a
long 10 March 100 calls (51) : long 10 June 95 calls (67)long 10 March 100 puts (-48) Y long 25 June 95 puts (-30)
 
 
 142 Chapter 8
Figure 8-6: Short Straddle
 
short 30 March 105 calls (24)short 10 March 105 puts (-75)
short 20 June 100 calls (51)short 20 June 100 puts (-46)
             
Profit
calls and putsat the sameexercise price
Loss
 
 
 
ratio vertical spreads. But other spreads, including straddles, can be ratioed. This isusually done to ensure that the spread is delta neutral.
A long straddle has many of the same characteristics as a backspread. Like abackspread it has limited risk and unlimited profit potential. With a long straddle,however, the trader’s potential profit is unlimited in either direction. If the marketmoves sharply up or down, the straddle wil! realize ever increasing profits as long as themarket continues to move in the same direction.
A short straddle has many of the same characteristics as a ratio vertical spread. Thespread will realize its maximum profit if the market stays close to the call and putexercise price. The spread has a limited profit potential, and unlimited risk should theMarket move violently in either direction.
The new option trader often finds long straddles attractive because strategies withlimited risk and unlimited profit potential offer great appeal, especially when the profitis unlimited in both directions. However, if the hoped for movement fails to materialize,he soon finds that losing money little by little, even a limited amount, can also be apainful experience. This is not an endorsement of either long or short straddles. Underthe right conditions either strategy may be sensible. But the intelligent trader’s primaryconcern ought to be the total expected return. If the strategy with the greatest expectedreturn also entails unlimited risk, a trader may have to accept that risk as part of doingbusiness.Volatility Spreads 143
STRANGLE
Like a straddle, a strangle consists of a long call and a long put, ora short call and a shortput, where both options expire at the same time. In a strangle, however, the optionshave different exercise prices. If both options are purchased, the trader is long thestrangle; if both options are sold, the trader is short the strangle. Typical long and shortstrangles are shown in Figures 8-7 and 8-8.
Strangles have characteristics similar to straddles, and are therefore similar tobackspreads and ratio vertical spreads. Like a long straddle, a long strangle needsmovement to be profitable, and has unlimited profit potential should such movementoccur. Like a short straddle, a short strangle has unlimited risk in either direction, butwill show a profit if the underlying market remains in a narrow trading range.
If a strangle is simply identified by its expiration month and exercise prices, theremay be some confusion as to the specific options involved. A June 95/105 stranglemight consist of a June 95 put and June 105 call. But it might also consist of a June 95call and a June 105 put. Both these combinations are consistent with the definition ofa strangle. To avoid confusion a strangle is commonly assumed to consist of out-of-the-money options. If the underlying market is currently at 100 and a trader wants topurchase the June 95/105 strangle, it is assumed that he wants to purchase a June 95put and a June 105 call. When both options are in-the-money, the position is sometimesreferred to as a guts.
Figure 8-7: Long Strangle
 
 
oe lt calls ‘euts)puts (calls)at a lower at a higher= exercise price exercise priceS i . i: ia : 1|\ |23
long 20 March 105 calls long 30 June 110 callslong 20 March 95 puts fong 1 June 100 puts
 
 
 144 Chapter 8
Figure 8-8: Short Strangle
 
 
 
 
short 30 March 110 calls short 10 June 95 callsshort 40 March 90 puts short 10 June 105 puts=Oo=oana§selputs (calls) calls (puts)at a lower at a higherexercise price exercise price
 
 
 
Tn the absence of other identifying information, strangles, like straddles, are usuallyexecuted with a one-to-one ratio (one call for each put). However, there is no lawagainst executing a strangle with some other ratio. If the call has a delta of 15 and theput has a delta of —30, and a trader wants to be delta neutral, it is perfectly acceptableto trade two calls for each put.
If we ignore the limited or unlimited risk/reward characteristics of backspreads,long straddles, and long strangles, these spreads essentially differ in the degree of desiredmovement. A backspread needs some market movement to show a profit, a long straddleneeds more movement, and a long strangle needs even greater movement. Indeed, astrangle is usually considered the most highly leveraged of all option positions becauseout-of-the-money options are cheap relative to other options. Several strangles can oftenbe purchased for the price of just one straddle. If significant movement occurs with sucha position, its value can increase dramatically. But there is a tradeoff. If movement failsto occur, the position will swiftly lose its value through the passage of time.
The same considerations of degree are also true for ratio vertical spreads, shortstraddles, and short strangles. A ratio vertical spread, a short straddle, and a shortstrangle all want the market to sit still. But again, the strangle is considered the mosthighly leveraged of these positions. If a trader sells several strangles and the market doessit still his profits will usually be greater than if he had sold one straddle or done amoderate sized ratio vertical spread. If, however, the market makes an unexpectedlylarge Move, short strangles also entail the greatest risk. All option positions are a tradeoffVolatility Spreads 148
between risk and reward. If the reward is great, so is the risk; if the risk is small, so isthe reward.
Based on their similar characteristics, it is sometimes convenient to classify longstraddles and long strangles as special types of backspreads. This follows logically fromthe definition of a backspread: long more contracts than short, with all options expiringin the same month. A long straddle or strangle consists only of long options {long callsand long puts), with all options expiring at the same time. Hence, these positions arebackspreads. (Even though the owner of a put has a short market position, he is said tobe long the put because he has purchased it.}
The same reasoning leads us to classify short straddles and strangles as special typesof ratio vertical spreads. Short straddles and strangles consist only of short options, withall options expiring at the same time. Hence, the positions conform to our definition ofa ratio vertical spread.
BUTTERFLY
Thus far we have looked at spreads which involve buying or selling two different optioncontracts. However, we need not restrict ourselves to two-sided spreads. We can alsoconstruct spreads consisting of three, four, or even more different options. A butterflyconsists of options at three equally spaced exercise prices, where all options are of thesame type (either all calls or all puts} and expire at the same time. In a long butterfly theoutside exercise prices are purchased and the inside exercise price is sold, and vice versafor a short butterfly.! Moreover, the ratio of a butterfly never varies. It is always 1 x 2x 1, with two of each inside exercise price traded for each one of the outside exerciseprices. ff the ratio is other than 1 x 2 x 1, the spread is no longer a butterfly. Typicalexamples of long and short butterflies are shown in Figures 8-9 and 8-10.
Since a butterfly consists of equal numbers of long and short options, it does not fitconveniently into the backspread or ratio vertical spread category. However, as com-monly traded, a long butterfly tends to act like a ratio vertical spread and a short butterflytends to act like a backspread. To understand why, consider a trader who buys a95/100/105 call butterfly (long a 95 call, short two 100 calls, long a 105 call). Whatwill be the value of this position at expiration? If the underlying contract is below 95 atexpiration all the calls will expire worthless, and the value of the position will be zero.If the underlying contract is above 105 at expiration, the value of the 95 and 105 callstogether will be identical to the value of the two 100 calls. Again, the value of thebutterfly will be zero. Now suppose the underlying contract is somewhere between 95and 105 at expiration, specifically, right at the inside exercise price of 100. The 95 callWill be worth 5 points, while the 100 and 105 calls will be worthless. The position willtherefore be worth 5 points. If the underlying moves away from 100 the value of thebutterfly will decline, but its value can never fall below zero.
 
1, The inside exercise price is sometimes referred to as the body of the butterfly, while the outsideexercise prices are referred to as the wings.146
Figure 8-9: Long Buiterfly
Chapter 8
 
 
 
 
7]long 10 March 95 calls (78) long 30 June 90 puts (-17)short 20 March 100 calls (51) short 60 June 95 puts (-30)long 10 March 105 calls (24} long 30 June 100 puts (-46)
=
e
2
oa
2
g j i
4 i : :
buy a sell two buy acall (put) calls (puts) call (put)at a lower at a middle at a higherexercise price exercise price exercise price+
 
 
 
Figure 8-10: Short Buiterfly
 
 
sella buy two sell acall (put) calls (puts) call (put)at a lower at a middle at a higherexercise price exercise price exercise price
- i=° : ia = : =”B }aa
short 20 March 100 puts {-48)long 40 March 105 puts (-75)short 20 March 1410 puts (-91)
 
short 25 June 95 calls (67)long 50 June 100 calls (51)short 25 June 105 calls (36)
 
 Volatility Spreads 147
At expiration a butterfly will always have a value somewhere between zero and theamount between exercise prices. It will be worth zero if the underlying contract isbelow the lowest exercise price or above the highest exercise price, and it will be worthits maximum if the underlying contract is right at the inside exercise price.
Since a butterfly has a value between zero and the amount between exercise prices(5 points in our example), a trader should be willing to pay some amount between zeroand 5 for the position. The exact amount depends on the likelihood of the underlyingcontract finishing right at or close to the inside price at expiration. If there is highprobability of this occurring, a trader might be willing to pay as much as 414 or 414 forthe butterfly, since it might very will expand to its full value of 5 points. If, however,there is a low probability of this occurring, and consequently a high probability that theunderlying contract will finish outside the extreme exercise prices, a trader may only bewilling to pay 14 or %, since he may very will lose his entire investment.
Now we can see why a long butterfly tends to act like a ratio vertical spread. Ifatrader feels that the underlying contract will remain within a narrow range untilexpiration, he can buy a butterfly where the inside exercise price is at-the-money. If heis right, and the market does stay close to the inside exercise price, the butterfly willexpand to its maximum value (Figure 8-9). A long butterfly tends to act like a ratiovertical spread since it increases in value as the underlying market sits still.
In contrast, the trader who sells a butterfly wants the underlying market to moveas far away from the inside exercise price as possible so that the position will expire withthe underlying contract either below the lowest exercise price or above the highestexercise price. In this case, the butterfly will expire worthless and he will be able tokeep the full amount he received when he sold the butterfly (Figure 8-10). A shortbutterfly tends to act like a backspread since it increases in value with movement in theunderlying market.
Why are the strategies in Figure 8-9 referred to as “long” butterflies, and thestrategies in Figure 8-10 referred to as “short” butterflies? It is common practice to referto a spread which requires an outlay of capital as a long, or purchased, spread. Ifa traderinitiates a butterfly by purchasing the outside exercise prices and selling the insideexercise price, he has a position which can never be worth less than zero at expiration.The trader can therefore expect to lay out some amount of capital for the position whenhe initiates it. When the trader does this, he has purchased, or is “long,” the butterfly.(If a trader can initiate a long butterfly for a credit, he should do it as many times as thelaw will allow; he can’t lose.) When the trader sells the outside exercise prices andpurchases the inside exercise price, he can expect to receive some amount of capital.He has sold, or is “short,” the butterfly.
Since all butterflies are worth their maximum amount when the underlyingcontract is right at the inside exercise price at expiration, both a call and put butterflywith the same exercise prices and the same expiration date desire exactly the sameoutcome, and therefore have identical characteristics. Both the March 95/100/105 callbutterfly and the March 95/100/105 put butterfly will be worth a maximum of 5 withthe underlying contract right at 100 at expiration, and a minimum value of zero withthe underlying contract below 95 or above 105. If both butterflies are not trading at the148 Chapter &
same price, there is a sure profit opportunity available by purchasing the cheaper andselling the more expensive.2
Ifa trader foresees a quiet market, why might he choose a long butterfly over someother type of strategy, for example a short straddle? An important characteristic of abutterfly is its limited risk. Ifa trader initiates a long butterfly in the belief that the marketis unlikely to move very far from the current price, the most he can lose if he is wrongis the amount he laid out to purchase the butterfly. On the other hand, if a trader sellsa straddle and the market makes a large move, his potential risk is unlimited. Regardlessof theoretical considerations, some traders are not comfortable with the possibility ofunlimited risk. If given the choice between purchasing butterflies and selling straddles,they will prefer the former strategy to the latter.
Of course the straddle, while riskier, also has greater profit potential. If a traderintends to purchase butterflies but wants a potential profit commensurate with that ofa short straddle, he will have to trade butterflies in much greater size. A trader who isconsidering the sale of 25 straddles might decide instead to buy 100 butterflies (100 x200 x 100). While trading 100 spreads may appear riskier than trading 2.5 spreads, 100butterflies may tn fact be much less risky than 25 straddles because of the riskcharacteristics associated with a butterfly. A trader should never confuse size and risk.Risk often depends on the characteristics of the strategy, not on the size in which theStrategy is executed.
TIME SPREAD{also referred to as a calendar spread or horizontal spread)
If all options in a spread expire at the same time, the value of the spread is simply afunction of the underlying price at expiration. If, however, the spread consists of optionswhich expire at different times, the value of the spread cannot be determined until bothoptions expire. The spread’s value depends not only on where the underlying market iswhen the short-term option expires, but also on what will happen between that timeand the time when the long-term option expires. Time spreads, sometimes referred toas calendar spreads or horizontal spreads,’ consist of opposing positions which expirein different months.
The most common type of time spread consists of opposing positions in two optionsof the same type (either both calls or both puts] where both options have the sameexercise price. When the long-term option is purchased and the short-term option tssold, a trader is long the time spread; when the short-term option is purchased and thelong-term option is sold, the trader is short the time spread. Since a long-term optionwill have more time value, and therefore a higher price than a short-term option, this isconsistent with the practice of referring to any spread which is executed at a debit(credit) as a long (short) spread position.
2. This is not necessarily the case if the spreads consist of American options, where there Is a possjbilityof early exercise. A sure profit would exist only if one were certain of carrying the position to expiration.
3. Expiration months were originally listed horizontally on exchange option displays. Hence the termhorizontal spread.Volatility Spreads 149
Although time spreads are most commonly executed one-to-one (one contractpurchased for each contract sold}, a trader may ratio a time spread to reflect a bullish,bearish, or neutral market sentiment. For the present we will assume that all timespreads will be ratioed delta neutral. Typical long and short time spreads are shown inFigures 8-11 and 8-12.
A time spread has different characteristics from the other spreads we have dis-cussed, because its value depends not only on movement in the underlying market, butalso on other traders’ expectations about future market movement as reflected in theimplied volatility. If we assume that the options making up a time spread are approxi-mately at-the-money, time spreads have two important characteristics.
A long time spread always wants the underlying market to sit still. An importantcharacteristic of an at-the-money option’s theta (time decay) is its tendency to becomeincreasingly large as expiration approaches. As time passes, a short-term at-the-moneyoption, having less time to expiration, will lose its value at a greater rate than a long-termat-the-money option. (Note the value of at-the-money options in Figures 6-13 and 6-14,and the theta values in Figure 6-15.) This principle has an important effect on the valueof a time spread,
For example, suppose two at-the-money calls, one with three months to expirationand one with six months to expiration, have values of 6 and 714, respectively. The valueof the spread is therefore 14%. If one month passes and the underlying market isunchanged, both options will lose value. But the short-term option, with its greatertheta, will lose a greater amount. If the long-term option loses '/, the short-term option
Figure 8-11: Long Time Spread (Value at Near Term Expiration)
 
     
tong 10 June 95 puts (-31)
long 20 June 100 calls (51) short 10 March 95 puts (21)
short 20 March 100 calls (61)
Profit
 
||||||
buy a long term optionat one exercise price
Loss
sell a short term optionof the same typeat the same exercise price
 
 
 
 150 Chapter 8
 
Figure 8-12: Short Time Spread (Value at Near Term Expiration)
 
buy a short term optionat one exercise price
 
= sell a long term option2 of the same typeo at the same exercise price|||o |8 *long 10 March 105 calls (24) | long 25 March 100 puts (-48)4 short 10 June 110 cails (23) short 25 June 100 puts (-47)|
“technically a diagonal spread, but with many of thesame characteristics as a time spread
 
 
 
may lose a full point. Now the options are worth 5 and 7%, and the spread is worth2%. If another month passes and the market is still unchanged, both options willcontinue to decay, But, again, the short-term option, with less time remaining toexpiration, will decay at a greater rate. If the long-term option loses %4, the short termoption may lose 2 points. Now the options are worth 3 and 6%, and the spread has