maker several minutes to calculate the value of thespread. But regardless of the complexity of a spread, the market-maker will make aneffort to give his best two-sided (bid and ask} market.
Spread orders, like individual option orders, can be submitted with qualifyinginstructions. The most common types are market orders (orders to be filled at thecurrent market price) and limit orders (orders to be filled at a specified price}, Othercontingency orders may also include instructions specifying how the order is to beexecuted in the marketplace. The following contingency orders, all of which are definedin Appendix A, are often used in option markets:
All Or None
Fill Or Kill
Immediate Or CancelMarket If TouchedMarket On Close
Not Held
One Cancels The OtherStop Limit Order
Stop Loss Order
Two typical spread orders, submitted with their contingency instructions, areshown in Figures 8-23a and 8-23b.
A broker executing a spread order is responsible for adhering to any specialinstructions which accompany the order. Unless a trader knows exactly what currentmarket conditions are, or has a great deal of confidence in the broker who will behandling the order, it is always a good practice to submit specific instructions with theorder as to how it is to be filled. Additionally, when one considers all the informationthat must be communicated with a spread order (the expiration months, the exerciseprices, the type of options, whether the order is a buy or sell, the ratio), it is easy to seeVolatility Spreads 171
 
 
Figure 8-23a
FUTURES ORDERAccount Number Broker Memo.ee$ABCDEFGHIJKLMNOPQRSTUVWXYZ23456789%S
      
BUY SELL75 Crude O1} SantIAC 125 Crude Oil Feb. 1c
24 <— an indication of the —» u uy. prices the brokershould look at
[x | 20 Gedrt AM or None
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how incorrect information might inadvertently be transmitted with the order. For thisreason, it ts also a good practice to recheck all orders before submitting them for
execution. Option trading can be difficult enough without the additional problems ofmiscommunication.172 Chapter 8
Figure 8-23b
                       
(Py = I
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Risk Considerations
Consider the prices and theoretical values shown in Figure 9-1. What categories ofvolatility spreads might be profitable under these conditions? By comparing prices totheoretical values, or by comparing the implied volatilities of the various options to thevolatility input of 15%, we can see that all options are overpriced. Recalling the generalguidelines in the last chapter, under the given conditions a trader will want to considerspreads with a negative vega:
Call and Put Ratio Vertical SpreadsShort Straddles and Strangies
Long Butterflies
Short Time Spreads
Which of these categories is likely to represent the best spreading opportunity? Andwithin each category, which specific spread might be best?
CHOOSING THE BEST SPREAD
For the moment, let’s focus on May options only. Having eliminated the possibility oftime spreads, we will have to look for spreads in the ratio vertical category (negativegamma, negative vega}. With ten different May options (five calls and five puts), it ispossible to construct a wide variety of spreads which fall into this category. How canwe make an intelligent decision about which spread might be best?
Suppose we choose three possible strategies and try to analyze them. The threestrategies which have been chosen are spreads 1, 2, and 3, shown in Figure 9-2.
These are certainly not the only possible spreads, nor can we be certain that theyare the best possible spreads. But in theory each spread ought to be profitable under thegiven market conditions, since each fits into the ratio vertical spread category: spread 1is a short straddle, spread 2 is a call ratio vertical spread, and spread 3 is a long putbutterfly. How can we evaluate the relative merits of each spread?
Initially it may appear that spread 1 is best since it has the greatest theoretical edge.If the volatility estimate of 15% turns out to be correct, spread | will show a profit of2.86, while spread 2 will show a profit of 1.00, and spread 3 will show a profit of only40.
But is theoretical edge our only concern? If that were true we could simply do eachspread in bigger and bigger size to make the theoretical edge as large as we want. Insteadof doing spread 2 at 10 x 15, we might increase the size fivefold to 50 x 75. This will
173Chapter 9
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 Risk Considerations 175
 
Figure 9-2Delta Position Theoretical EdgeSpread 1: Short 10 May 50 calls @ 1.07 ~10 x +44 10x +15Short 8 May 50 puts @ 1.59 -8 x -55 8 x4+.170 +2.86Spread 2: Long 10 May 51 calls @ .77 +10 x +44 10x +15Short 15 May 52 calls @ 53 -15 x +21 15x .20- +1.00Spread 3: Long 10 May 48 puts @ 1.05 +10 x-42 10x—14Short 20 May 50 puts @ 1.59 20 x -65 20 x+.17Long 10 May §1 puts @ 2.22 +10 x-68 10 x-.160 +.40
increase the theoretical edge fivefold to 5.00, and ostensibly makes spread 2 a betterstrategy than spreads 1 and 3. Clearly, theoretical edge can’t be the only consideration.
Theoretical edge is only an indication of what we expect to earn if we are rightabout market conditions. Since there is no guarantee that we will be right, we must giveat least as much consideration to the question of risk. If we are wrong about marketconditions, how badly might we be hurt?
In order to focus on the risk considerations, let’s change the size of spreads 2 and3 so that their theoretical edge is approximately equal to that of spread 1. We canachieve this by tripling the size of spread 2 to 30 x 45, and increasing the size of spread3 sevenfold to 70 x 140 x 70. The spreads in their new sizes with their total theoreticaledge and risk sensitivities are shown in Figure 9-3.
With all three spreads having approximately the same theoretical edge, we can nowfocus on the risks associated with each spread,
As with all volatility spreads, one of the risk considerations is the possibility of anincorrect volatility estimate. Since each spread has a negative vega, there will be noproblem if volatility turns out to be lower than 15%. In that case, the value of eachspread will increase and we will show a greater profit than originally expected. On theother hand, if volatility turns out to be greater than 15%, this could present a problem.What will happen if volatility turns out to be 17%, or 20%, or some higher number?Each spread will be hurt due to the negative vega, but each spread may not be hurt tothe same degree.
One way to analyze the volatility risk associated with each spread is to use atheoretical pricing model to simulate the value of each spread at increasingly greatervolatilities. From these values we can construct graphs reflecting each spread’s theoreti-cal edge versus volatility. Such a graph is shown in Figure 9-4.
With our size adjustments each spread now has approximately the same initialtheoretical edge, enabling us to focus on the volatility risk associated with each spread.Looking at Figure 9-4 we can see that each spread, 1, 2, and 3, loses its theoretical edgeChapter 9
176
 
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 Risk Considerations 177
as volatility increases. But the slope of spread 1 is most severe. It loses its value veryquickly as volatility increases, much more quickly than spreads 2 and 3.
For each of our spreads we might logically ask how high volatility can rise beforewe begin to lose money. That is, we might want to determine the break-even volatility,or implied volatility, for each spread. This is simply an extension of the general definitionof implied volatility: the volatility which would have to occur over the life of an option,or options, such that a position would show neither a profit nor a loss. It is commonamong traders to determine the implied volatility of a spread position, just as theydetermine the implied volatility of individual options. We can see from Figure 9-3 thatthe implied (break-even) volatilities of spreads 1, 2, and 3 are approximately 17%, 20%,and 22%, respectively.
From a volatility perspective, spread 3 shows the best risk/reward characteristics.With each spread we are, in a sense, selling volatility, and we would like to do so at thehighest possible price. Would we rather sell something that’s worth 15% (our volatilityestimate) at 17% (the implied volatility of spread 1}, at 20% (the implied volatility ofspread 2), or at 22% (the implied volatility of spread 3}? The higher the implied volatilityof the spread, the greater the margin for error in our volatility estimate and, conse-quently, the greater the likelihood of showing a profit. Spread 1 has only a 2-percent-age-point margin for error, while spread 3 has a margin for error more than three timesgreater, at 7 percentage points. Spread 2 falls somewhere in between.
Why are we so concerned about our volatility estimate being too low? A tradermight take the view that he is just as likely to overestimate as underestimate volatility.If this happens, how will it affect the potential outcome of each spread? Suppose wedecide to do spread 1 and volatility turns out to be 18%, three percentage points higherthan our estimate of 15%. Looking at Figure 9-4 we can see that if this happens we willlose approximately 1.21. Suppose, however, that there is an equal chance that volatilitywill turn out to be 12%, three percentage points lower than our estimate. In Figure 9-5,where we have extended volatility down to 10%, we can see that in this case we willmake approximately 6.95. In a more extreme case, when volatility turns out to be 20%we will lose 3.95, But if volatility turns out to be 10% we will make 9.64, For each timewe underestimate volatility and show an unexpected loss, we might assume there willbe an equal number of times when we overestimate volatility and show an unexpectedprofit. The end result of all these outcomes will be an average profit of approximately2.86, the predicted profit of the spread at a volatility estimate of 15%.
Suppose that the average result of doing any one of our spreads, 1, 2, and 3, isaprofit of approximately 2.80. If the outcome in each case is identical, why should itmake any difference which spread we choose? While the end result is certainly animportant theoretical consideration, how the end result comes about may be an equallyimportant practical consideration.
Every trader knows that there are times when he shows a profit and times whenhe shows a loss. No one wins all the time. In the long run, however, a good trader’sprofits will more than offset his losses. For example, suppose a trader chooses a strategywhich will show a profit of $7,000 half of the time, and which will show a loss of $5,000the other half of the time. In the long run he will show an average profit of $1,000. But178
Chapter 9
 
Figure 9-4
 
Theoretical Profit & Loss
-105
 
 
spread 3(long butterfly)
        
spread 2
spread | (ratio vertical spread)
(short straddle)
 
 
18 20
Volatility (%)
Tr19
 
 
     
spread 3(long butterfly)
 
Theoretical Protit & Loss
 
         
spread 1(short straddle)
spread 2(ratio vertical spread)
 
 
1D =
16 18 20 22
Volatility (9%)
 
 
24Risk Considerations 179
suppose the first time the trader executes the strategy he loses $5,000 and the traderonly has $3,000? Now the trader will not be able to stay in business for all those timeswhen he is fortunate enough to show a profit of $7,000. Every trader knows that it isonly over long periods of time that good luck and bad luck even out. No experiencedtrader will initiate a strategy where short-term bad luck might terminate his tradingcareer. This is the reason an experienced option trader will tend to avoid spread 1.
Any financial officer knows that it is much easier to manage a steady cash flowrather than one that swings wildly. This is equally true for an option trader. He mustsensibly manage his finances so that he can avoid being ruined by the periods of badtuck which will inevitably occur, no matter how skillfully he trades.
An incorrect volatility estimate may not be the only risk with which an optiontrader must be concerned. Every input into a theoretical pricing model represents a riskto the trader since an incorrect input may alter an option’s theoretical value. These risksare reflected in the delta, gamma, theta, vega, and rho associated with a spread. We cansummarize these risks as follows:
Deita (Directional) Risk-—The risk that the underlying market will move in onedirection rather than another. When we create a position which is delta neutral, we aretrying to ensure that initially the position has no particular preference as to the directionin which the underlying instrument will move. A delta neutral position does notnecessarily eliminate all directional risk, but it usually leaves us immune to directionalrisks within a limited range.
Gamma (Curvature) Risk—The risk of a large move in the underlying contract,regardless of direction. The gamma position is a measure of how sensitive a position isto such large moves. A positive gamma position does not really have gamma risk sincesuch a position will, in theory, increase in value with movement in the underlyingcontract. A negative gamma position, however, can quickly lose its theoretical edge witha large move in the underlying contract. The consequences of such a move must alwaysbe a consideration when analyzing the relative merits of different positions.
Theta (Time Decay) Risk—The risk that time will pass with no movement in theunderlying contract. This is the opposite side of gamma risk. Positions with positivegamma become more valuable with large moves in the underlying. But if movementhelps, the passage of time hurts. A positive gamma always goes hand in hand with anegative theta. A trader with a negative theta will always have to consider the risk interms of how much time can pass before the spread’s theoretical edge disappears. Theposition wants movement, but if the movement fails to occur within the next day, ornext week, or next month, will the spread, in theory, still be profitable?
Vega (Volatility) Risk—The risk that the volatility which we input into the theoreticalpricing model will be incorrect. If we input an incorrect volatility, we will be assumingan incorrect distribution of underlying prices over time. Since some positions have apositive vega and are hurt by declining volatility, and some positions have a negativevega and are hurt by rising volatility, the vega represents a risk to every position. A trader180 Chapter 9
must always consider how much the volatility can move against him before the potentialprofit from a position disappears.
Rho (Interest Rate) Risk—The risk that interest rates will change over the life of theoption. A position with a positive rho will be helped (hurt) by an increase (decline) ininterest rates, while a position with a negative rho will show just the oppositecharacteristics.! Generally, the interest rate is the least important of the inputs into atheoretical pricing model, and it is unlikely, except for special situations, that a traderwill give extensive thought to the rho risk associated with a position.
So far we have compared only the volatility risk associated with spreads 1, 2, and3. Is there any other risk with which we ought to be concerned? All of our spreads havea negative gamma, so they will all be adversely affected by a large move in theunderlying contract. In order to compare the relative gamma risks, we can construct agraph showing the values of the spreads at varying prices of the underlying contract.This has been done in Figure 9-6. Again, we assume that each spread has approximatelythe same theoretical value under our theoretical assumptions, in this case at the currentunderlying price of 49.50.
Figure 9-64
 
 
       
spread 2{ratio vertical spread)
   
  
spread 3(long butterfly)
Theoretical Profit & Loss
spread 1(short straddle)
 
 
-10 t 1 T 1 T47 48 49 50 51 52 53
Underlying Price
 
1. Of course, we are only considering the interest rate risk as it applies to the evaluation of options.Changes in interest rates can also affect the evaluation of an underlying contract, such as a bond, oreven the shares in a company. But that is a separate matter.Risk Considerations 181
Looking at Figure 9-6 we can see that if the underlying contract makes a largeupward move, spread 3 will be the least affected. It can stand a move up to 52.75without losing its positive theoretical edge. Spreads 1 and 2 can stand upward movesto only 51.05 and 51.75, respectively. On the downside, spread 1 is still the riskiestsince it loses all its theoretical edge if the underlying market should make a swift movedown to 47.90. Spread 3 is less risky because it can stand a move down to 47.50. Butthe least risky on the downside is clearly spread 2, since it never loses all its theoreticaledge. In the most extreme downward move the theoretical edge of spread 2 willcollapse to approximately zero.
PRACTICAL CONSIDERATIONS
Considering the vega and gamma risk, spread 3 seems to have the best risk charac-teristics. It has a larger margin for error in terms of volatility than either spread 1 or 2.In terms of underlying price movement it can also stand a larger upward move than theother two spreads. Only when we consider the possibility of a large downward movedoes spread 3 not display the best risk characteristics. In this case spread 2 comes infirst. But spread 3 still looks better than spread 1. In theory, a trader ought to be morewilling to execute spread 3 than either spread 1 or 2. In the real world, however,practical trading considerations may play a role in the trader’s decision.
Even though spread 3, the butterfly, appears to be the best theoretical choice of thethree, it has some practical drawbacks which may make it an unrealistic choice. Spread3 is a three-sided spread, as opposed to spreads 1 and 2, which are two-sided. Athree-sided spread will probably be more difficult to execute in the marketplace, and islikely to cost more in terms of the total width of the bid/ask. Ifa trader wants to executethe complete spread at one time, as is most common, he may not be able to do so at histarget prices. If, on the other hand, he tries to execute one leg? at a time, he will be atrisk from adverse changes in the market until the other legs have been executed.
Additionally, there is the question of market liquidity. In order to obtain atheoretical edge commensurate with spreads 1 and 2, it was necessary to increase thesize of the butterfly sevenfold to 70 x 140 x 70, If there is insufficient liquidity in theMay 49, 50, and 51 puts to support this size, it may not be possible to execute thebutterfly in the size required to meet our profit expectations. Alternatively, we may beable to execute part of the spread at favorable prices, but as we increase the size, theprices may become less satisfactory. Moreover, for a retail customer the increased sizemay entail significantly greater transaction costs,
If trading considerations make spread 3 impractical, we may have to choosebetween spreads 1 (the straddle) and 2 (the ratio vertical spread). If that happens, spread2 is the clear winner. It allows fora much greater margin for error in both volatility (vegarisk) and underlying price change (gamma risk}. A trader who is given a choice betweenthese two spreads will strongly prefer spread 2.
The choice of spreads may not always be as clear as in this example. The superiorityof spread 3, at least from the theoretical standpoint, was relatively obvious. Sometimes,
 
2. The options which comprise a spread position are sometimes referred to as the /egs of the spread.182 Chapter 9
however, one spread may be superior with respect to one type of risk, while a differentspread may be superior with respect to a different risk.
Let’s consider three new spreads, 4 (a ratio vertical spread), 5 (a short time spread],and 6 (a diagonal spread). The total theoretical edge of each spread, as well as their risksensitivities (all taken from the theoretical evaluation table in Figure 9-1), are shown inFigure 9-7. In order to again focus on the risks associated with each spread, the size ofeach spread has been adjusted to yield approximately the same theoretical edge.
Since each spread has a negative vega, we will want to consider the volatility riskif volatility should turn out to be greater than our estimate of 15%. The sensitivity ofeach spread to increasing volatility is shown in Figure 9-8, We can see that spread 4 hasan implied volatility of approximately 18.1%, spread 5 approximately 17.0%, and spread6 approximately 17.2%. If an increase in volatility is our primary concern, then spread4 (the ratio vertical spread) seems to offer the best risk characteristics.
In addition to the volatility risk, we can see that spread 4 also has a negative gamma,so that it will be adversely affected by a sudden large move in the underlying contract.If we are concerned about the possibility of such a move we may want to determineexactly how a large move in the price of the underlying contract will affect the value ofthe spread. Figure 9-9 shows the sensitivity of each of our spreads, 4, 5, and 6, to achange in the price of the underlying contract.3
Note that spread 4 has the narrowest profit range of the three spreads, in theorylosing all its theoretical value if the market should immediately drop below 46.50 or riseabove 52.20. On the other hand, spread 6 has very little downside risk and can stillstand an immediate move upward to about 52.30. Ifa trader were worried about thepossibility of a swift fall in the market, he might be willing to give up the extra volatilitycushion offered by spread 4 over spread 6 (18.0% vs. 17.2%) for the additional downsideprotection offered by the latter spread. This is reflected in the smaller negative gammaassociated with spread 6 as compared with spread 4.
Finally, we can see that spread 5, while having the least desirable volatility risk,also has a positive gamma. This means that any large move in the underlying contractwill increase the value of the position. If a trader were worried about the possibility ofa sudden large move in the underlying contract, but were not overly concerned with anincrease in volatility, he might be willing to accept the less desirable volatility riskassociated with spread 5 for the more desirable positive gamma characteristics.
A trader who executes spread 5 will have a positive gamma, so he has no gammarisk. But he will have a theta risk if the underlying contract fails to move. How great isthe risk? Figure 9-10 shows the sensitivity of all three spreads to the passage of time.Since spreads 4 and 6 have negative gammas, they can only gain value with the passageof time. On the other hand, spread 5 loses value as each day passes. Looking at the graphassociated with this spread, we can see that if no movement occurs in the underlyingcontract, the spread loses all its theoretical edge after about 18 days. This is the priceone has to pay for the privilege of having a positive gamma.
 
3. We assume here that the May and July underlying contracts maintain the same approximaterelationship. That is, the July contract Is always 1.0123 times the May contract since 50.11/49.50 =1.0123. The x-axis in Figure 9-9 is the price of the May contract.183
Risk Considerations
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