N» aag spread 63 44 (diagonal spread)soa 24a een3° vee “B® o1-goco spread 4e -24 (ratio vertical spread)-4--6 T Tt T 1 T 146 47 48 49 50 34 52 53
Underlying Price (May Futures Contrac)
  
 
 
 
 
 
Risk Considerations 185Figure 9-108”2 _a 2‘ ical Spread 6
% (ratio vertical spread) (diagonal spread) ao% 0 =a -§ 2 —oga aF NS a spread 5
6) Ne (short time spread)
-8-
-10 T T T + 1 1 17 14 21 28 35 42 49 56
Time to Expiration (days)
If one has to choose from among spreads 4, 5, or 6, which spread is best? Thesituation is not clear-cut, and the answer will probably depend on a trader’s experiencein the market. [f he feels that an increase in implied volatility represents the greatestrisk, he will probably choose spread 4. If he feels that a large move in the underlyingcontract represents the greatest risk, he will probably choose spread 5. And if he iswilling to settle for partial protection against both volatility and market movement, hewill probably choose spread 6.
As must by now be obvious, the choice of spreads is never a simple matter of rightand wrong. Like all trading decisions, it is a question of risk and reward. While thereare many risks with which an option trader must deal, he will often have to ask himselfwhich risk represents the greatest threat. Sometimes, in order avoid one type of risk, hewill be forced to accept a different risk. Even if the trader is willing to accept some riskin a certain area, he may decide that he will only do so to a limited degree. Then he mayhave to accept increased risks in other areas.
If given the choice between several different spreads a trader can use a Computer,as was done in the foregoing examples, to study the risk characteristics of the differentspreads. Unfortunately, it may not always be possible to analyze the choices in suchdetail. A trader may not have the necessary computer support at his disposal, or marketconditions may be changing so rapidly that if he fails to make an immediate decisionopportunity may quickly pass him by. Is there any way to make a quick comparison ofspreads without doing a detailed graphic analysis?186 Chapter 9
One method that traders sometimes use is to think of every spread as a tradeoffbetween risk and reward. We might express this tradeoff as a fraction, risk/reward. Ifa trader goes into the marketplace, he would like to have the greatest possible reward.At the same time he would like to have the least possible risk. Indeed, the idealtisk/reward fraction would be 0 + o (zero risk, infinite reward}. But 0 + o = 0, so thatif we express the risk/reward characteristics of each spread as a fraction, risk/reward,then in theory the spread whose fraction is closest to zero has the best tradeoff betweenrisk and reward.
What numbers should we use to express the risk and reward for a spread? Thereward is what we expect to make when we are right about market conditions. This issimply the theoretical edge, and we can therefore make the theoretical edge thedenominator of our fraction. What about the numerator, or risk component? Here wemay have to deal with several different numbers since option positions are subject tomany different risks. These risks are represented by the various option sensitivities. Thepractical approach is to express the numerator of our fraction with the sensitivity withwhich we are most concerned. For example, if a change in volatility is our greatestconcern, we can use the vega of the spread as our numerator. If choosing from amongseveral different spreads, the spread whose vega/theoretical edge is closest to zero willhave the most desirable risk/reward characteristics. In the same way, if a large pricemove is our greatest concern, the spread whose gamma/theoretical edge is closest tozero will have the most desirable risk/reward characteristics.
Let's try to analyze spreads 4, 5, and 6 using this method. One risk with which wewill certainly have to be concerned is the possibility of a change in volatility. Calculatingthe vega/theoretical edge, we have:
Spread 4: -.840/2.70 = -311Spread 5: —-1.850/3.00 = -.617Spread 6: ~1.340/2.90 = -.462
From the above calculations we can see that spread 4 has the best volatilitycharacteristics since its vega/theoretical edge is closest to zero. This is the sameconclusion we reached from Figure 9-8, but without the necessity of doing a detailedstudy of each spread.
Note that when we divide the sensitivity of a spread by its theoretical value, theresult is independent of the size of the spread. If we had done spread 4 twice as large(40 x 60 instead of 20 x 30} this would have doubled the size of both the vega and thetheoretical edge. The resulting fraction would still have been -.311.
What about the risk of a large move in the price of the underlying contract? We donot need to worry about large price moves in spread 5 since its positive gamma meansthat a large move can only enhance the value of the position. However, we might stillwant to compare spreads 4 and 6 for gamma risk. Dividing the gamma by the theoreticaledge we have:
Spread 4: -72.0/2.70 = -26.7Spread 6: -56.0/2.90 = -19.3Risk Considerations 187
We can see that spread 6 is at less risk from a large move in the price of theunderlying contract because -19.3 is closer to zero than -26.7. This confirms theconclusion from Figure 9-9.
Aword of warning about this method of estimating the relative riskiness ofa spread.Because an option’s sensitivities are only well defined within a narrow range, dividingthe risk sensitivity by the theoretical edge offers only an estimate of the relative riskinessof a position. Consider, for example, the relative volatility risks of spreads 1, 2, and 3.Dividing the vega by the theoretical value for each spread we have:
Spread 1:  -1.368/2.86 = -478Spread 2: -435/3.00 = 145Spread 3: -630/2.80 =  -225
From these numbers it appears that spread 2 is the least risky with respect to volatilitysince —.145 is closer to zero than -.478 or —.225. But going back to Figure 9-4 we findthat spread 3 actually has the highest implied volatility, and therefore the least volatilitytisk. Even so, this method would have at least warned us away from spread 1, whichclearly has the greatest volatility risk.
Sometimes, if a trader is under great pressure to make a quick decision, he may nothave the time to make even a cursory analysis of relative riskiness of various spreads. Insuch cases, he will often have to rely on his instincts in choosing a strategy. While thereis no substitute for experience, most traders quickly learn an important rule: straddlesand strangles are the riskiest of all spreads. This is true whether one buys or sells thesestrategies. New traders sometimes assume that the purchase of straddles and stranglesis not especially risky because such strategies have limited risk. But it can be just aspainful to lose money day after day when one buys a straddle or strangle and the marketfails to move, as it is to lose the same amount of money all at once when one sells astraddle and the market makes a violent move. Of course, a trader who is right aboutvolatility can reap large rewards from straddles and strangles. But an experienced traderknows that such strategies offer the least margin for error, and he will usually preferother strategies with more desirable risk characteristics.
HOW MUCH MARGIN FOR ERROR?
New traders sometimes ask what is a reasonable margin for error in assessing the inputsinto a theoretical pricing model, particularly when it comes to the volatility input. As isoften the case, it will depend on the trader’s experience in the market in which he istrading. In some cases, 5 percentage points may be an extremely large margin for error,and the trader will feel very confident with any strategy passing such a test. In othercases, five percentage points may be almost no margin for error at all, and the traderwill find that the strategy is a constant source of worry.
Perhaps a better way to approach the question is to ask not what is a reasonablemargin for error, but rather to ask what is the correct size in which to do a spread givena known margin for error. Practical trading considerations aside, a trader should alwayschoose the spread with the best risk/reward characteristics. But sometimes even the188 Chapter 9
best spread will have only a small margin for error, and consequently entail significantrisk. In such cases a trader, if he wants to make a trade, ought to do so in small size. If,however, a trader can execute a spread with a very large margin for error, he ought tobe willing to do the spread in much larger size.
As an example, considet a trader whose best estimate of volatility in a certainmarket is 15%. If implied volatility is higher than 15% he will look for positions with anegative vega. If the best negative vega strategy the trader can find isa 1 x 2 ratio verticalspread with an implied volatility of 1614% (only a 1%4-percentage-point margin forerror), he will almost certainly keep the size of his strategy small, perhaps executing thespread only five times (5 x 10). If, however, the same spread has an implied volatilityof 25% (a 10-percentage-point margin for error), and the trader has never seen volatilitygo that high, he may have the confidence to execute the spread in much larger size,perhaps 50 x 100.4 The size of a trader’s positions should depend on the riskiness ofthe positions, and this in turn depends on how much can go wrong without the strategyturning against the trader.
DIVIDENDS AND INTEREST
In addition to the delta, gamma, theta, and vega risks which all traders must consider,stock option traders might also have to consider the risk of changes in dividends andinterest rates.> This is especially true of time spreads, since options with differentexpirations react differently to changes in these inputs.
Consider the evaluation table for stock options shown in Figure 9-11. With impliedvolatilities well below the forecast of 27%, it makes sense to look for spreads withpositive vegas, Suppose we focus on four possible spreads shown in Figure 9-12. Spreads7 and 8 are long time spreads, while spreads 9 and 10 are diagonal spreads. What arethe relative merits of each spread?
As with all option spreads, we have to consider a variety of risks. Note that in theevaluation table in Figure 9-11 we used an interest rate of 8%. Suppose we believe thatinterest rates are likely to rise sharply in the near future. How might these spreads reactto rising interest rates? We can see from Figure 9-13 that spreads 7 and 9 will be hurtby rising interest rates, while spreads 8 and 10 will be helped. If a rise in interest ratesis our primary concern, we might focus on spreads 8 and 10, regardless of any desirablevega or gamma characteristics associated with spreads 7 and 9.
If we focus on spreads 8 and 10, we will still want to consider the volatility risk.We can do a cursory comparison of this risk by dividing the vega by the theoretical edge.From this we find:
Spread 8: 1.380/6,45 | = 214Spread 10: 2.774/6.14 x 452
4. — Size, of course, is relative. To a well capitalized, experienced trader even 50 x 100 may be a small trade.
5. Futures options can also be affected by changes in interest rates since a change in interest rates willaffect the forward price of the underlying futures contract. Unlike stocks, factors other than interestrates, such as short term supply and demand, can also affect these contracts.189
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If volatility risk is our second concern, then spread 8 is probably best because its vegadivided by theoretical edge is much smaller than that of spread 10. Suppose, however,that we are more concerned with a large move in the underlying stock than with adecline in volatility. Now we can see that spread 10 is best because its positive gammameans that a large move in the price of the underlying stock can only work to ouradvantage. As always, the choice of strategies will require us to make some judgementsas to what risks we are willing to accept, and to what degree.
Finally, let’s look at our spreads with respect to a change in dividends. In ourevaluation table we assumed a quarterly dividend of 1.25. Suppose we believe that thedividend is likely to be increased. How will this affect our four spreads? From Figure9-14 we can see that now spreads 7 and 9 look the best since they are helped by anincrease in the dividend.
What about volatility and curvature risk? Estimating the relative risks by dividingthe sensitivity by theoretical edge, we have:
Vega Risk Gamma RiskSpread 7: 2.275/6.75 = .337 -32.5/6.75 = ~4.8Spread 9: 1.985/6.50= 305 -3.5/6.50= -.5
Since there is not much difference in the spreads in terms of vega risk, we mightchoose spread 9 since it has much less gamma risk. At the same time, if we believe an192 Chapter 9
 
 
         
 
 
 
 
 
 
 
Figure 9-1425spread 8 spread 7
20+ (long call time spread) (long put time spread)o fk = ifg 15 S _ow -5 1 .a J 7a spread 102 51 (diagonal call spread) Se spread 9D “(diagonal put spread)° Lo wa£ ae= O-e— coo pe - a
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WHAT IS A GOOD SPREAD?
Option traders, being human, would rather talk about their successes than theirdisasters. If one were to eavesdrop on conversations among traders, it would probablyseem that no one ever made a losing trade. Disasters, when they do occur, only happento other traders. The fact is every successful option trader has had his share of disasters.What separates the successful trader from the unsuccessful one is the ability to survivesuch occurrences.
Consider the trader who initiates a spread with a good theoretical edge and a largemargin for error in almost every risk category. If the trader still ends up losing moneyon the spread, does this mean that the trader has made a poor choice of spreads? Maybea similar spread, but one with less margin for error, would have resulted in an evengreater loss, perhaps a loss from which the trader could not recover.
It is impossible to take into consideration every possible risk. A spread which passedevery risk test would probably have so little theoretical edge that it wouldn’t be worthdoing. But the trader who allows himself a reasonable margin for error will find thateven his losses will not lead to financial ruin. A good spread is not necessarily the oneRisk Considerations 193
that shows the greatest profit when things go well; it may be the one which shows theleast loss when things go badly. Winning trades always take care of themselves. Losingtrades, which don’t give back all the profits from the winning ones, are just as important.
ADJUSTMENTS
In the last chapter we considered the question of when a trader should adjust a positionto remain delta neutral. The trader must also consider how best to adjust, for there aremany different ways to adjust the total delta position. An adjustment to a trader’s deltaposition may reduce his directional risk, but if he simultaneously increases his gamma,theta, or vega risk, he may inadvertently be exchanging one type of risk for another.
A delta adjustment made with the underlying contract is essentially a risk neutraladjustment. By this we mean that an adjustment made with the underlying contractwill not change any of the other risks we have discussed because the gamma, theta, andvega associated with an underlying contract are zero. Therefore, if a trader wants toadjust his delta position, but wants to leave the other characteristics of the positionunaffected, he can do so by purchasing or selling an appropriate number of underlyingcontracts.
An adjustment made with options may reduce the delta risk, but will also changethe other risk characteristics associated with the position. Every option, in addition tohaving a delta, also has a gamma, theta, and vega. When an option is added to orsubtracted from a position, it necessarily changes the total delta, gamma, theta, and vegaof the position. This is something which new traders sometimes forget.
Consider an option market where the underlying contract is trading at 99.25. If alloptions appear to be overpriced, a trader might decide to sell the 95/105 strangle (sellthe 95 put, sell the 105 call). Suppose the deltas of the put and call are, respectively,—36 and +36, and the trader decides to sell 20 strangles. He is initially delta neutralsince
(+20 x -36) + (-20 x +36) = 0
Suppose several days pass and the underlying market has fallen to 97.00, with newdelta values for the 95 put and 105 call of —41 and +30. Assuming that no adjustmentshave been made, the trader’s delta position is now
(-20 x—41) + (-20 x +30) = +220If the trader now decides to make an adjustment he has three basic choices:
1. sell underlying contracts
2. sell calls3. buy putsWhich method is best?
All other considerations being equal, whenever a trader makes an adjustment heshould do so with the intention of improving the risk/reward characteristics of the194 Chapter 9
position. If the trader decides to adjust his delta position by purchasing puts, he alsoreduces his other risks since the gamma, theta, and vega associated with the putpurchase are opposite in sign to the gamma, theta, and vega associated with his existingshort strangle position.
Unfortunately, all other considerations may not be equal. Since implied volatilitycan remain high or low for long periods of time, it is quite likely that if all options wereoverpriced when the trader Initiated his position, they will still be overpriced when hegoes back into the market to make his adjustment. Even though the purchase of puts tobecome delta neutral will reduce his other risks, such an adjustment will also have theeffect of reducing the theoretical edge. On the other hand, if all options are overpricedand the trader decides to sell additional calls to reduce the delta, the sale of theoverpriced calls will have the effect of increasing the theoretical edge. If the traderdecides that adding to his theoretical edge is of primary importance he may decide tosell seven more 105 calls, leaving him approximately delta neutral since
(-20 x41) + (-27 x +30) = +10
Now suppose several more days pass and the market has rebounded to 101.50,with new delta values for the 95 put and 105 cali of -26 and +40. The position deltais now
{-20 x -26} + (~27 x +40) = -560
Again, if the trader wants to adjust he is faced with three choices: buy underlyingcontracts, buy calls, or sell puts. Assuming that all options are still overpriced and thatthe trader wants to continue to increase his theoretical edge, he may decide to sell anadditional 22 of the 95 puts. The total delta position is
(-42 x -26) + (-27 x +40) = +12
It should be clear what will result from these adjustments. If all options remainoverpriced and the trader is always intent on increasing his theoretical edge, he willcontinue to make whatever adjustments are necessary by continuously selling over-priced options. This method of adjusting may indeed result in the greatest profit to thetrader. But notice what is happening. The strangle, which the trader was initiallyprepared to sell 20 times, has now increased in size to 42 x 27, If the market now makesa violent move in either direction, the negative consequences will be greatly magnified.Unfortunately, the new trader, overly concerned with always increasing his theoreticaledge, often finds himself in just such a position. If the market makes a very swift move,the trader may not survive, For this reason, a new trader who is unfamiliar with all thesubtleties of an option market should avoid making adjustments which increase the sizeof his position.
No trader can afford to ignore the effect his adjustments will have on the total riskto his position. If he has a positive (negative) gamma position, buying (selling) anyadditional options will increase his gammia risk. Likewise, if he has a positive (negative)vega position, buying (selling) any additional options will increase his vega risk. A tradercannot afford to sell overpriced options or buy underpriced options ad infinitum. AtRisk Considerations 195
some point the size of the spread will simply become too large, and any additionaltheoretical edge will have to take a back seat to risk considerations. When that happensthere are only two choices: decrease the size of the spread or adjust in the underlyingmarket.
A disciplined trader knows that sometimes, because of risk considerations, the bestcourse is to reduce the size of the spread, even if it means giving up some theoreticaledge. This may be hard on the trader's ego, particularly if he must personally go backinto the market and either buy back options which he originally sold at a lower price,or Sell out options which he originally purchased at a higher price. However, if a traderis unwilling to swallow his pride from time to time, and admit that he made a mistake,his trading career is certain to be a short one.
If a trader finds that any delta adjustment in the option market that reduces his riskwill also reduce his theoretical edge, and he is unwilling to give up any theoretical edge,his only recourse is to make his adjustments in the underlying market. An underlyingcontract has no gamma, theta, or vega, so the risks of the position will remain essentiallythe same.
A QUESTION OF STYLE
Because most option pricing models assume that movement in the underlying contractis random, an option trader who trades purely from the theoretical values generated bya model should not have any prior opinion about the direction in which the underlyingmarket will move. In practice, however, many option traders begin their trading careersby taking positions in the underlying market, where direction is the primary consideration. Many traders therefore develop a style of trading based on presumed directionalmoves in the underlying market. A trader might, for example, be a trend follower,adhering to the philosophy that “the trend is your friend.” Or he might be a contrarian,preferring to “buy weakness, sell strength.”
Traders often try to incorporate their personal trading styles into their optionstrategies. One way to do this is to consider beforehand the adjustments which will berequired for a certain strategy if the underlying market begins to move. For example,suppose a trader sells straddles in such a way that he is initially delta neutral. Suchspreads have a negative gamma, so that as the market moves higher his delta positionis getting shorter, and as the market moves lower his delta position is getting longer. Ifthis trader likes to trade against the trend, he will avoid adjustments as much as possiblebecause his position is automatically trading against the trend. Whichever way themarket moves, the position always wants a retracement of this movement.
On the other hand, a trader who sells the same straddles but prefers to trade withthe trend will adjust at every opportunity. In order to remain delta neutral, he will beforced to buy underlying contracts as the market rises and sell underlying contracts asthe market falls.
The opposite is true for a trader who buys straddles. He has a positive gammaposition, so that as the market rises his delta is becoming longer, and as the market fallshis delta is becoming shorter. If this trader likes to trade with the trend, he will want to196 Chapter 9
adjust as little is possible in the belief that the market is likely to continue in the samedirection. However, if he prefers to trade against the trend, he will want to adjust asoften as possible. Every adjustment will represent a profit opportunity if the market doesin fact reverse direction.
A trader with a negative gamma is always adjusting with the trend of theunderlying market. A trader with a positive gamma is always adjusting against thetrend of the underlying market. If a trader prefers to trade with the trend or against thetrend, he should choose a strategy and an adjustment process that is appropriate to hispreference. A trader who prefers to trade with the trend can choose a strategy with apositive gamma together with less frequent adjustments, or a strategy with a negativegamma with more frequent adjustments. A trader who prefers to trade against the trendcan choose a strategy with a negative gamma together with less frequent adjustments,or a strategy with a positive gamma with more frequent adjustments. The purelytheoretical trader will not have to worry about this since for him there is no such thingas a trend. However, for most traders old habits, such as trading with or against thetrend, die hard.
LIQUIDITY
As long as a trader has an open option position it represents a risk. Even if the risk islimited to the current value of the options, by leaving the position open the trader isTisking the loss of that value. If he wants to eliminate the risk, he will have to take someaction which will in effect close out the position. Sometimes this can be done throughearly exercise, or by taking advantage of an opposing position to create an arbitrage.More often, however, in order to close out an open position a trader will be requiredgo into the marketplace and buy in any short options and sell out any long options.
An important consideration in deciding whether to enter into a trade is often theease with which the trader can reverse the trade. Liquid option markets, where thereare many buyers and sellers, are much less risky than illiquid markets, where there arefew buyers and sellers. In the same way, a spread which consists of very liquid optionsis much less risky than a spread which consists of one or more illiquid options. If a traderis considering entering into a spread where the options are illiquid, he ought to askhimself whether he is willing to live with that position until expiration. If the market isvery illiquid, that may be the only time he will be able to get out of the position atanything resembling a fair price. If the spread consists of long-term options, say ninemonths, the trader may find himself married to the position for better or worse, insickness and in health, for the next nine months. If he is unwilling to commit his capitalfor that period, perhaps he should avoid the position. Since there is greater riskassociated with a long-term investment than with a short-term investment, a trader whodoes decide to