decay. With the currentprofit at about $9,000, a mental stop at about $6,000 seemsreasonable.
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OEX moved higher over the next month, but then it began to runinto some trouble. Moreover, there were some early assignments.The combination of these events “led” me out of the position. Thefollowing discussion concerns the handling of an early assignment.As June expiration approached, the short calls were rolled forward to avoidassignment:Bought 7 June 445 calls at 58 closingSold 7 July 445 calls at 60 openingCredit for this trade: 14 points ($1,400)However, within a week, and with nearly a month remaining until Julyexpiration, an early assignment notice was received on two of the July 445calls. This was highly unusual, coming so far in advance of expiration. Eventhough the option was very far in-the-money, I still considered it atypical tobe assigned a month before expiration. This assignment was received themorning after OEX had closed at 511.31. Thus, the price on the assignment was 511.31 – 445.00, or 66.31.There were actually quite a few OEX calls exercised that night. As hasoften been the case after early assignments, the market opened lower thenext morning but then began to recover. In fact, by noon it was well intopositive territory. As I said earlier, it has been my experience that this is acommon event— early sell-off, followed by rally, after an OEX call exercise.I had been feeling somewhat uneasy about not having taken a largerportion of the position off at the time of the last roll (to the July 505s).Therefore, I used this assignment as an opportunity to remove anotherpiece of the position. I sold out five of the long July 505 calls. This tradeoccurred around noon of the day of the assignment.Thus, the complete trade was:Bought 2 July 445 calls at 66.31 closingSold 5 July 505 calls at 15 closingNet debit for this trade: 57.62 points ($5,762)The remaining position, after the roll and assignment, was:Long 10 July 505 callsShort 5 July 445 callsNet credit to date: 333.38 points
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Handling an early assignment in the manner just described issomewhat risky. As I said, it has been my experience that the initialmarket sell-off caused by a fairly large OEX call exercise is quicklyreversed. But sometimes it isn’t. In those cases, you would fare worseby waiting to execute an offsetting trade against your early assignmentnotice. Therefore, if you decide to approach it in the manner that Idid, by not selling something immediately on the opening (wheneveryone else is), but by waiting to see if there is a reflex rally, thenyou need to have an absolute mental stop in your head. The mentalstop will keep you from “freezing” and holding on way too long.A good rule of thumb is to see where the S&P futures are tradingwhen the initial selling flurry, caused by the OEX call exercise, subsides. The S&Ps would normally be somewhat off their daily lows atthat point. I often use this as a mental stop: if the S&Ps then makeanother daily low, I will sell what I need to, in order to balance myposition. On the other hand, if a market rally develops, as was thecase in the previous example, then I would look for a place to sellinto the rally.I would not change my overall strategy, though. For example, ifthe market was going my way, I would not attempt to remain overly“long” the market over a longer period of time. After an early assignment, you should return to a balanced position at some point duringthe trading day on which you received the assignment. If you are ableto ride a rally and get a better price for your “resale,” so much thebetter, but don’t wait overnight to readjust the position.OEX continued to rally—confounding me, who was keeping my positiondelta neutral. When it reached 520 in late June, the implied volatility of theAugust 520 call was only 11.6 percent. So volatility had actually decreasedfrom the last time that a roll was made—into the 505s.Therefore, I decided to stay with the position, and executed the following trade:Sold 10 July 505 calls at 18 closingBought 10 Aug 520 calls at 101⁄2 openingCredit on this trade: 75 points ($7,500)The total position was then:
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545
Long 10 Aug 520 callsShort 5 July 445 callsNet credit to date: 408.38 pointsThe unrealized profit had grown to over $12,000. I moved my mentalstop up to $9,000; that is, if the position marked at $9,000 on anyday’s close, I would exit the next day.
This lengthy position was eventually terminated in August, butnot before a couple more early assignments.
I received early assignment notices on back-to-back days in July. On the firstone, I was assigned on all five of my short July 445 calls. I sold the Aug 445calls that day, taking in a net credit on the roll. On the very next day, I wasassigned on the Augusts! At that point, I decided that the only way to avoidthese early assignments was to roll to a higher strike, so I sold the August475 calls. I chose the 475 strike because the open interest was fairly largein that series. This last trade necessitated a debit because the strike wasmoved higher.The net debit from these two early assignments was 127.45 points($12,745). This left the position as:Long 10 Aug 520 callsShort 5 Aug 475 callsNet credit to date: 280.93
Eventually OEX rose to over 530 in late July, but then it began toslip in early August. Time decay was beginning to become a majorfactor, and a decision needed to be made as to whether to terminatethe position or to roll it once again, this time into September orOctober options.
With OEX at 525, the implied volatility of the at-the-money September callswas 12.7 percent and the Octobers were 13.0 percent. Since the range ofimplied volatility had been shrinking all year, these numbers were in the fifthand sixth percentiles. Given that fact, plus the fact that time decay had
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eroded the value of the long calls as OEX stabilized, I therefore decided toclose the position:Sold 10 Aug 520 calls at 8 closingBought 5 Aug 475 calls at 51 closingNet debit of this trade: 175 points ($17,500)The net realized credit of position to date was 105.93 points, or$10,593.A total of 304 contracts had been traded. At a commission rate of $4per contract, that is $1,216 in commissions. Thus, the net gain on theentire position was $9,377.
The first criticism that a hedged trader usually receives is alongthese lines: he had to manage a relatively complicated position forsix months, making numerous trades, and his net profit was $9,377.Meanwhile, OEX had risen 70 points. Wouldn’t he have been a lotbetter off just to hold the initial position or to have bought calls in thefirst place?Of course he would have, but that’s hindsight, and it is not whatthe goals were when the position was established. In reality, thisposition had an excellent rate of return and was hedged all the wayalong. Recall that the $9,377 profit was on an initial investment of$16,000, which represents about a 60 percent gain in six months.This is very attractive for a hedged position. Even more important,we were hedged at all times; if there had been a severe market correction, the short calls would have provided very good profit potential (just look at any of the profit graphs in this example).So, don’t confuse hedging with speculation. Yes, speculation hasmuch larger rewards, but hedging is supposed to provide steadierreturns. Moreover, when trading volatility with a hedged position, wehave the added advantage of having a statistical edge built in.This example was rather long, but it illustrated most of the decisions that the strategist needs to contemplate while such a position isin place: when and whether to roll the long calls up, when to roll theshort calls, how to handle early assignment, and collateral andprofit/ loss considerations. As I said in the preface, I am often askedwhat I use to make decisions regarding establishing a position and in
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547
follow-up action—how I decide which options to use, when to roll,how to handle early assignment, and so forth. Hopefully, the preceding example will answer some of those questions.This concludes the section on using backspreads to trade thevolatility skew. Obviously, not all backspreads work so well. However, the strategy is a very attractive one as long as you have a market where there is a volatility skew. I especially like the fact that youcan use simple spreads (rolling up the long calls, in the precedingexamples) in order to adjust the spread. This is a distinct advantageof a backspread as compared to a long straddle. With a straddle,when the underlying moves higher, your downside protection getsfarther and farther away. The only way to reneutralize a straddle is tosell the entire straddle and buy a new one at the higher strike. I havefound that, on average, I personally make better, more profitabledecisions with the backspread than with the straddle.
Put Ratio SpreadThe put ratio spread is also a viable strategy for trading the reversevolatility skew. You buy puts at one strike and sell puts at a lowerstrike. Since the puts purchased have a lower implied volatility thanthe puts sold (because of the reverse volatility skew), this position hasa nice statistical advantage, too. Many OEX traders use this strategyin one form or another because of the attractiveness of selling expensive out-of-the-money puts.If you buy and sell an equal number of puts, you have a bearspread with a theoretical advantage. That’s great; but if the marketcontinues to rise, as it has for over five years, you don’t make muchmoney from the bear spreads. Money managers sometimes takeadvantage of this volatility skew to buy bear spreads to act as insurance for their long stock positions. Admittedly, the bear spreadwouldn’t provide complete insurance—it’s only insurance down to thelower strike—but these money managers figure it’s better than nothing, and it isn’t so costly where there’s a reverse volatility skew present.The delta neutral version of the put spread is, of course, the putratio spread—buying perhaps one at-the-money put and selling twoout-of-the-money puts. Sometimes these put ratio spreads can even
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be established for credits, when the volatility skew is steep enough.This means that you would profit unless the market dropped throughthe lower break-even point of the ratio spread before expiration. Infact, a modest decline by the market to the striking price of the written puts could produce very good profits.Since the crash of 1987, it has not been at all uncommon to see prices suchas these in OEX options. This particular set of prices was recorded at theend of a very volatile day in the market, which saw the Dow up 35 in themorning, then down 90 points in the afternoon, before rallying 35 pointslate in the day to finish –20 for the day. The skew is usually quite pronounced after a day like that—which contains a big downdraft—and it isinvariably a good time to establish these put spreads.OEX: 587 on January 4Option
Price
Implied Volatility (%)
Feb 550 putFeb 555 putFeb 560 putFeb 565 putFeb 570 putFeb 575 putFeb 580 putFeb 585 put
1.812.192.693.194.135.006.387.88
16.616.015.414.614.313.713.212.6
You can see the nice, uniform pattern of implied volatilities increasingas the strikes get lower. This is a classic reverse skew.What is very interesting is that you can buy almost any one of these putsand sell two of the puts with a striking price 15 points lower, and still take ina credit. This makes a very attractive put ratio spread. For example, if youbought one Feb 585 put at 77⁄8 and sold two Feb 570 puts at 41⁄8, you wouldtake in a credit of 3⁄8 of a point. This might only be enough to cover commissions, but it is a very attractive spread, theoretically: the option you arebuying has an implied volatility of 12.6 percent, while the ones you are selling are trading with a 14.3 percent implied. That is a large discrepancy.The downside break-even point on this one-by-two ratio spread is about565, which is 22 points below the current OEX price. That’s plenty ofdownside cushion.
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A put ratio spread strategy can be operated much like the callratio spread strategy that was described earlier with an exampleusing corn options. In the put spread, usually no action is necessaryif the index rises. However, if the index declines, you would normallyhave a profit if the underlying gets down to the striking price of theputs that were sold (the exception would be a quick decline, and we’llget to that in a minute). At that point, you can decide if it is best totake some profits or to narrow your action points to protect the profits you have.The put ratio spread strategy consumes a lot in the way of collateral requirements, so it is best used by traders who have excess collateral in their accounts. Each naked index put requires collateral inthe amount of 15 percent of the index value, plus the put premium,less any out-of-the-money amount (if it’s out-of-the-money). This canbe expensive, although collateral can be equity in your account—itdoes not have to be cash. Thus, the excess value of your stocks andbonds can be used to finance this strategy.The problem with the put ratio spread strategy is that everyoneremembers the days on which this strategy was particularly poor, thecrash of 1987 and the 1989 crash caused by the United ArabLeague (UAL) leveraged buyout falling apart; then there was the1990 Iraq-inspired bear market. Admittedly, those were nasty times,but you could have hedged yourself so as to prevent disaster.In the UAL-induced crash of 1989, I had OEX put ratio spreads in place.However, I was able to hedge them with futures even as the market wasplunging. As long as the market is open and doesn’t gap through yourdownside, you can protect yourself.The downside breakeven was about 316, with the OEX index trading atlevels above 330. Then, on a quiet Friday afternoon—some self-employedtraders had already gotten bored with the market and had gone home—news came out that the UAL deal was going to collapse. UAL itself hadbeen trading at 249 and was halted at 243 due to an order imbalance.The stock market, though, knew what was coming and headed south—fast! OEX fell over 20 points that afternoon, to close just below 310 (theDow was off 190 points). OEX put premiums ballooned, and there wereseveral trading halts and rotations. No one can adjust a position in the midstof a trading halt, and to attempt to trade in a rotation is an exercise inmasochism.
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TRADING VOLATILITY
The S&P 500 futures were open for trading, though, and they wereavailable as a convenient hedge. When the market approached the downsidebreak-even point of the spread (316), enough S&P futures were sold to eliminate the downside risk—one future was sold for every five net naked puts inthe ratio spread position. This turns the naked puts into covered puts, ineffect, even though the S&P 500 and OEX aren’t exactly the same thing.Usually, though, the two indices perform in concert; and when you need ahedge of last resort, you can’t be picky about something like tracking error.
Thus, you can use the S&P futures as a hedge for OEX positions.If OEX is free trading, that wouldn’t be necessary. But if the ChicagoBoard Options Exchange (CBOE) declares fast market conditions inOEX, I would look to the futures as a hedge. You pretty much alwaysknow where the futures are trading; and while they do have limits,they are more flexible in fast markets than trying to get an optionorder executed. It should be noted that once you have sold thefutures as a hedge, if the market changes direction and heads backup again, you could have risk if it rallies above the striking price ofyour short puts. Of course, this is a problem with any adjustmentagainst short options in any strategy—you can be whipsawed. Thereis no easy remedy when it occurs. You just have to try to reduce yourrisk by executing closing trades to remove the short put /short futuresposition.
A Volatility Skew Biases a PositionIt is quite true, but not necessarily intuitively apparent, that when theoptions in a position have a volatility skew, that position is biased. Ifthe skew is a reverse one—à la OEX options—then the position hasa bullish bias: it will do better when OEX rises in price than would benormally expected, and it will do worse on the downside. On theother hand, if there is a positive skew, like grain options have, thenthe position has a bearish bias: it will do better on the downside thanyou would think.These biases will persist as long as the skew exists. If the skewdisappears, then the position will behave “normally.” The profit
TRADING THE VOLATILITY SKEW
551
graphs in the previous examples, designed to show how to trade thevolatility skew, had the volatility skew built into them. Any traderrelying on profit projections generated by a computer must be surethat the computer program doing the projections knows if there isvolatility skew or not and, if there is one, accounts for it in the profitforecasts.
To verify that a reverse skew puts a bullish bias in a position, consider theOEX backspread example that we have just examined. When the positionwas established, we had the following situation:OEX: 455 in FebruaryPositionLong 20 May 460 callsShort 10 May 445 calls
Implied Volatility (%)9.911.7
Later, in March, OEX had rallied, and we saw that the following impliedvolatilities were then evident:OEX: 475 in FebruaryPositionLong 20 May 460 callsShort 10 May 445 calls
Implied Volatility (%)13.016.0
Both options’ implied volatility had increased because they were nowboth in-the-money options. Remember that the deeper an option is in-themoney, when you have a reverse volatility skew, the higher is the impliedvolatility of that option.The increase of implied volatility from 9.9 percent to 13.0 percent onthe 20 calls that were long aids the position. Conversely, the increase inimplied volatility from 11.7 percent to 16.0 percent on the 10 short callshurts the position. Overall, though, the increase in implied volatility on 20long calls is more dominant than the increase in volatility on the 10 shortcalls. Thus, the position has been aided by the fact that OEX rose in pricewhile the volatility skew was still in place.If you would prefer to see actual prices to verify this bias, look at the following table:
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Position
Price
Implied (%)
OriginalLong 20 May 460 callsShort 10 May 445 calls
7161⁄2
9.911.7
1832
13.016.0
One month laterLong 20 May 460 callsShort 10 May 445 callsTotal Profit
Profit/Loss ($)
+22,000–15,500+6,500
However, suppose for a moment that there was no skew in evidenceand that the options retained their original volatility as OEX moved higher.Then the following situation would have existed one month later (accordingto our option model):
Long 20 May 460 callsShort 10 May 445 callsTotal Profit
Price
Implied (%)
Profit/Loss ($)
1731
9.911.7
+20,000–14,500+5,500
No increase implied; one month later position.
The presence of the volatility skew, which caused the implied volatilityof the in-the-money options to increase, resulted in the position making$6,500 instead of the $5,500 it would have made if implied volatilities hadremained as they were when the position was established. This $1,000increase in profit is the bias attributable to the volatility skew.
In a similar manner, we could show, but won’t bother goingthrough the details, that a forward skew biases a position in a bearishmanner. Thus, a seemingly neutral position in soybean options, forexample, will do worse than expected if soybeans rise in price.We point this out so that you will not be surprised when theseresults occur in your positions. As stated earlier, a computer programthat correctly incorporates the skewing into profit projections willgive you these accurate results. You may also want to anticipate thiseffect when you construct your initial position. For example, if youdetermine that an OEX backspread is neutral with 20 long calls and
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553
10 short calls, you know that the position will outperform on theupside and underperform on the downside. Thus, you might want tobuy only 18 calls while selling 10. This would compensate for thevolatility skew’s effect.
Finding Where Volatility Skewing ExistsHaving discussed how to trade the volatility skew, it is also importantto know where to find one. The easiest method seems to be to compute the statistical standard deviation of the individual striking priceswith the same expiration date. That is a simple computation, whichwe show by example momentarily.First, though, let’s define standard deviation for those who arenot familiar with the term. In order to determine the standard deviation of a group of numbers—implied volatilities of individual options,in this case—you first find the average of the group of numbers.Then, for each number, you (1) subtract that average from the individual number and (2) square the result of step 1. You add up allthese squares and, at the end, divide by how many were in thegroup, less one. Then you take the square root of that final result.What is left is called the standard deviation. For the purposes ofvolatility skewing, we compare that final result with the averageimplied volatility to see if it is significant.Mathematically, the formula, for the standard deviation of agroup of n numbers, is as follows. The symbol for percent standarddeviation is σ:
(
∑ Vi − µ
σ =
n−1µ
)
where Vi = implied volatility of an individual optionµ = average of all the Vin = number of items in the groupThe following example shows the actual calculations used todetermine the standard deviation of March soybean options on a par-
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TRADING VOLATILITY
ticular day. You will be able to see, with your naked eye, that there isa volatility skew here; but our intention is to prove, mathematically,that there is one. In this way, you can have a computer program lookfor these skews.The following example is concerned only with March soybean options. Theprices are closing prices.March Soybeans: 7583⁄4Strike
Call
Put
Implied
700725750775800825850875900
593⁄4381⁄224143⁄883⁄451⁄233⁄421⁄215⁄8
13⁄851⁄4151⁄43150n/an/an/an/a
15.3916.3318.9320.7422.7024.6526.9128.6730.00
Note that there are nine items in this group (i.e., nine different strikingprices in the same expiration month, for which we have computed theimplied volatility).First, we compute the average of these nine implied volatilities, whichcomes to 22.70. Now, we subtract that average from each of theseimplieds, and we square that result:
Strike
Implied
Difference fromAverage
Square of Differencefrom Average
700725750775800825850875900
15.3916.3318.9320.7422.7024.6526.9128.6730.00
–7.31–6.37–3.78–1.960.001.954.215.977.30
53.4540.6214.263.840.003.7917.7435.6453.26
THE AGGRESSIVE CALENDAR SPREAD
555
Now, we add up the “squares of difference,” the right-hand column inthis table, and get 222.61. The standard deviation is
σ = “Sum of squares of difference” / (n − 1)= 222.61 / 8= 5.275Finally, we express the standard deviation as a percentage of the average implied volatility:5.275/22.70 = 23.2%
The idea behind using the standard deviation is to see if there isa large distance between most of the implied volatilities of the individual options and the average volatility. A “large difference” is usually defined by the final percentage being over 15 percent. In thisexample, the final percentage is 23 percent; so we can definitelysay, mathematically, that there is a volatility skew in these Marchsoybean options.You will normally find volatility skews only in index and futuresoptions. It is rather rare to find them in equity options, althoughoccasionally you will see one in a takeover stock situation.
THE AGGRESSIVECALENDAR SPREADBefore concluding this chapter, we present one more strategy. It isrelated to volatility but isn’t technically a volatility trading strategy. Infact, in this strategy, which is a calendar spread strategy, we wantvolatility to remain the same (or go higher), as we would with any calendar spread. The difference here is that this position is establishedwhen implied volatility is already high—a dangerous move for a calendar spreader. However, offsetting that risk is the fact that this is avery short-term strategy, so a position is not in place for more than afew trading days. This often helps to mitigate the risk that impliedvolatility might collapse while the position is in place.
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TRADING VOLATILITY
When takeover rumors surface, implied volatilities tend to skyrocket. Strategists often look for ways to sell the extremely expensiveshort-term options while hedging themselves with either stock or alonger-term option. The following true-life example demonstratesthe situations that we often find in these cases.In the late spring of 1994, there were takeover rumors surrounding thestock of American Medical Holdings (symbol: AMI). The stock was tradingat 25, and the following prices prevailed, with about two weeks remaininguntil June expiration:AMI: 25Option
Price
Implied Volatility (%)
June 25 callJuly 25 call
11⁄227⁄8
10595
The near-term option is often much more expensive than any longerterm option when takeover rumors are “hot.” AMI was a typical situation inthat regard.
On the surface, the calendar spread is an attractive strategybecause it has limited risk no matter what happens. It is often a strategy that we are tempted to establish in high-volatility options becauseit seems that the risk is small compared to the possible expansionthat the spread would undergo if “nothing” happened.However, the calendar spread strategy in this situation isextremely dependent on implied volatility remaining inflated. If theimplied volatility collapses for one reason or another, the strategy willalmost surely lose. One way to increase your odds is to establish thecalendar spread when there is a very short time remaining until expiration, perhaps as little as a week or 10 days. In that case, there isless of a chance that the rumors will dissipate in so short a time, andtherefore there is more of a chance that the strategist will be able tocapture the decline in premium of the expensive short-term option,while the longer-term option retains its high implied volatility. If thatwere to happen, the spread would widen and produce a nice profitvery quickly.
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557
Any short-term option strategy is a risky one. When you areoperating any strategy with so short a time horizon as one week orless, you would have to consider that a speculative strategy. Speculation is not necessarily bad, but you must understand that even thoughyou are hedged, a big swing in returns can occur in the course of oneweek in this situation.If a takeover bid is made during the week in which you are holding the calendar spread, there is a significant chance that bothoptions will trade at or close to parity and that the maximum loss—equal to the initial debit paid for the spread—will be realized. A similarly poor result could occur if the stock collapsed during the ensuingweek, perhaps on an evaporation of the rumors.Figure 6.31 is a graph of a 10-lot calendar spread in the aforementioned AMI options. The spread was established with exactly aweek to go until expiration. It shows two scenarios. The first is ifimplied volatilities remain high: rumors still abound, but no actualnews is forthcoming. This ideal situation is represented by thehigher, profitable, curve on the graph. The second situation is ifimplied volatilities collapse to the 30 percent level, as represented byFigure 6.31AMI SHORT-TERM CALENDAR SPREAD
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the lower curve on the graph. The two curves are so far apart thatit appears they are depicting two totally unrelated strategies; butthey are not! Notice that, even at its best result, the spread wouldlose nearly $1,000 if volatilities collapse, whereas it could make asmuch as $1,000 if volatility remains high and AMI is near 25. Thispicture graphically depicts the risk/reward aspects of this strategy.Of course, the hope is that the shortness of time that the spreadmust be held will mitigate the chances of the profits falling on thatlower curve.This type of calendar spread should be removed on the Friday ofexpiration of the near-term option. It could conceivably be removedslightly earlier if the stock were very close to the strike and the spreadhad widened. You will probably find, however, that the near-termoptions will continue to have a large premium (implied volatility) rightup to the end, as speculators hope that a takeover bid will comebefore expiration Friday. This means that you will probably not havemuch of