normal distribution of prices. However, when askew is present, the skew is projecting a different sort of distributionfor prices. Figure 6.21 is a graph of the forward skew, such as you see
Figure 6.21FORWARD SKEW
524
TRADING VOLATILITY
in the grains and metals. Compare it to the graph of the lognormaldistribution in Figure 6.20. You can see that this one has a distinctlydifferent shape: the right-hand side of the graph is up in the air, indicating that this skewed distribution implies that there is a far greaterchance of the underlying rising by a huge amount. Also, on the leftside of the graph, the skewed distribution is squashed down, indicatingthat there is far less probability of the underlying falling in price thanthe lognormal distribution would indicate.The reverse volatility skew is shown is Figure 6.22. Note that itis also different from the regular lognormal distribution. In this case,however, the left-hand side of the graph is lifted higher, indicatingthat the probability of prices dropping is greater than the lognormaldistribution implies that it is. Similarly, the graph on the right flattens out on the right-hand side, which means that it is insinuatingthat prices won’t rise as much as the lognormal distribution saysthey will.Figure 6.22REVERSE SKEW
TRADING THE VOLATILITY SKEW
525
It is my opinion that skewed volatilities are not the correct pictureof the way markets move, and that the lognormal distribution is amuch truer picture. Therefore, when we find significant volatilityskewing in a particular group of options, we have a good tradingopportunity. A neutral option spread position can be established thathas a statistical advantage because the two options have differingimplied volatilities.The best place to look for this volatility skewing is in the optionswith the same expiration date, as shown in the previous tables ofOEX and corn options. The reason that I prefer using options withthe same expiration date as the basis of volatility skew trading is that,even if the skew doesn’t disappear by expiration, the very fact thatthe options must go to parity at expiration means that they will thenhave behaved in a manner similar to the underlying instrument—thatis, they will have adhered to the lognormal distribution, not to theskewed distribution.What we want to accomplish by trading the volatility skew is tocapture the implied volatility differential between the two options inquestion, without being overly exposed to price movements by theunderlying instrument. We could use the simple bull or bear spreads,but they are too price dependent. Accordingly, the best strategies arethe vertical spread strategies: ratio writes or backspreads.
Trading the Positive SkewWhen the volatility skew is positive, as it is with grain options, then itis the call ratio spread (Figure 6.23) or the put backspread (Figure6.24) that are the preferred strategies. The reason that these are thetwo chosen strategies is because, in each one, we are buying optionswith a lower striking price and selling options with a higher strikingprice. Since the higher strikes have the inflated volatility in a positivevolatility skew, these strategies offer a statistical advantage. Thisadvantage arises from the fact that we are buying the “cheap” option(s) and selling the relatively “expensive” option(s) simultaneously,on the same underlying.
526
TRADING VOLATILITYFigure 6.23CALL RATIO SPREAD
Figure 6.24PUT BACKSPREAD
TRADING THE VOLATILITY SKEW
527
The following data is excerpted from the earlier example of the forwardvolatility skew, using March corn options: 745:OptionMarch 750March 775
Implied Volatility (%)19.821.9
Either one of the two following strategies is delta neutral and takesadvantage of the forward skew. The following call ratio spread would be anattractive strategy for trading this volatility skew:Buy 10 Corn March 750 callSell 20 Corn March 775 callsBut if you felt that volatility could explode and therefore harm the position, you might want to use a put backspread:Buy 20 Corn March 750 putsSell 10 Corn March 775 putsOnce again, you would be buying options at the lower strike and sellingthe relatively more expensive options at the higher strike.
You could use the past history of implied volatility to help youdecide which strategy to use. If you see that the current implieds are inthe lower percentiles, then you might favor the backspread, becausethere is a better chance that implieds might increase while you havethe position in place. On the other hand, if implieds are already nearthe high end of their historic trading range, then you might favor thecall ratio spread, since it will profit if implied volatility declines.When you trade the volatility skew in this manner, there are several ways in which you can profit. First, you would profit almostimmediately if the volatility skew disappeared, because your optionswould then have the same implied volatility. That is a rather rareoccurrence, but it sometimes does happen. Second, you would profitif the underlying were within your profit range at expiration. Third,you could profit if implied volatilities move in your favor (i.e., higherif you own the backspread or lower if you have the call ratio spread
528
TRADING VOLATILITY
in place). You may want to refer back to Figure 6.3 for another picture of the profitability of this strategy.The summer of 1995 was a particularly good time for trading the volatilityskew in grain options, even though grain prices rose during that timeperiod. The skew was so steep that it presented traders with a good statistical edge. For Sep corn: 278, in early June 1995:Option
Price
Implied Volatility (%)
Sep 280 callSep 300 call
131⁄28
26.531.5
This is an unusually large difference in implied volatility for two optionsthat are only two striking prices apart. Moreover, implied volatility was inthe eighth percentile at the time, thus favoring the ratio spread strategy.Based upon the deltas of the options (not shown), we recommended thatcustomers establish the following basic position:Long 10 Sep 280 callsShort 16 Sep 300 callsThis position was established for a small debit of seven points ($350,since one point in grain options is worth $50). Thus, there was very littledownside risk. The upside risk was theoretically unlimited if corn were torise too far. The upside break-even point was approximately 332, so weplaced GTC buy stop orders to buy six Sep corn futures at 332 as a meansof limiting upside risk. However, since the profit potential was greatest ifcorn were at 300 at expiration, we were hopeful that the position could beremoved for a profit if corn were to rally to 300.Corn eventually rallied into the 295 area in mid-to-late July. The position acquired a nice unrealized profit at the time, and the volatility skew haddampened somewhat—27.5 percent for the Sep 280 call as compared to30.7 percent for the Sep 300 call. Thus, the profit resulted from a flattening of the volatility skew and a favorable movement by the underlying. Also,implied volatilities were about at the same absolute level—in the high 20s—so that was not much of a contributor to the profit.
When trading the volatility skew with ratio spreads, I generallyprefer to use an at-the-money option for the long side of the spread
TRADING THE VOLATILITY SKEW
529
and out-of-the-moneys for the short side of the spread. That isexactly the way the previous example is constructed. In this manner,we will normally have a profit if the underlying moves to the strikingprice of the spread. In fact, if the volatility skew has disappeared, orat least flattened somewhat, by the time that happens, we shouldhave a very good profit.It is always something of an art to decide when to take the profit,should it occur. If you are fortunate enough to have the underlyingmove to the striking price—as Sep corn did in the previous example—then you are tempted to leave the position as is, in order tocapture even more profits should the underlying remain near thathigher strike. What I recommend is to take one of these two actions:(1) take a profit on half of your position, or (2) set some mental stopsthat are close enough to the current price so that you will still lock ina good profit if they are hit.Continuing with the same Sep corn example, we can demonstrate the usefulness of tightening mental stops when a decent unrealized profit has builtup. By August 1, Sep corn had fallen all the way back to 280; and theoptions, which expired in mid-August, eventually all expired worthless, ascorn was at 275 by that time. If there had not been an attempt to lock insome profits with mental stops, the entire unrealized profit would have beenlost, and a loss equal to the initial debit would have resulted.So, when corn was in the high 290s, we set mental stops at 290 and310, intending to remove the position if either of those prices was hit. Onthe other hand, if corn were to remain between those two prices, greaterprofits would result. As we have already explained, corn fell in price, so weremoved the position when it reached 290 and took a profit. It wasn’t aslarge a profit as had been available when corn was near 300, but it was stilla profit.
Of course, one example doesn’t demonstrate an entire strategy.But to show that the volatility skew trading does give you a goodadvantage, I summarized our ratio writes from The Option Strategist newsletter over the past four years. All of these were based onvolatility skews. There were 39 of them, 24 of which were profitable,10 of which lost the small initial debit, and 5 of which suffered largerlosses. Larger losses can arise from (1) increasing implied volatility,
530
TRADING VOLATILITY
(2) a gap much higher by the futures, or (3) a reversal in trend afteran adjustment has been made (a “whipsaw”). None of the five losseswas caused by a gap; rather, the cause was either a quick moveresulting in exploding volatility or a whipsaw. The average positionwas held for 53 days, and the average profit on the 39 positions inthis strategy was over 50 percent on an annualized basis, assumingthat exchange minimum margin requirements were used. Thus, theratio spread strategy can be quite profitable when employed in ourstated manner: there is a forward volatility skew, and implied volatility is relatively high to begin with.The companion strategy for the forward volatility skew, usedwhen implied volatility is relatively low, is the put backspread. Thisstrategy is used less frequently than the call ratio spread, partiallybecause of the mechanics of the forward volatility skew itself. Theonly time that implied volatility drops in the grains is when prices havedropped. Since the put ratio backpsread makes its best profits whenprofits drop even further, it is not often a viable strategy to establish atalready-low price levels. However, it is a statistically viable strategy toadopt when the two predominant conditions exist simultaneously: (1)a forward volatility skew and (2) low implied volatility.
Trading the Negative SkewWhen implied volatilities are skewed in the negative direction, twostrategies that are the exact opposite of the previous ones are appropriate: either (1) the put ratio spread (Figure 6.25) or (2) the callbackspread (Figure 6.26). In these two strategies, we are buying theoption at the higher strike, which has the lower implied volatility, andselling the option with the lower strike, which has the higher impliedvolatility. Once again, there is a statistical advantage, since we areselling an option that is “expensive” on the same security on whichwe are buying an option. If implied volatility is low, the call backspread is the preferred strategy; but if implied volatility is near thehigh end of its range, then the put ratio spread would be the betterchoice of a strategy to trade the reverse skew.The reverse volatility skew is very prevalent in broad-based indexoptions, although it wasn’t always so (prior to 1987, there was a
TRADING THE VOLATILITY SKEWFigure 6.25PUT RATIO SPREAD
Figure 6.26CALL BACKSPREAD
531
532
TRADING VOLATILITY
slightly forward skew), and it may therefore disappear once againsomeday. Nevertheless, it appears with some frequency in futuresoptions markets that experience a sudden decline in price. In recentyears, it has appeared in cattle, T-bond, and crude oil options. Inthese cases, the reverse skew disappears as soon as the underlyingcommodity stabilizes in price. However, with the broad-based options, the skew has persisted for years, mostly due to the margin andsupply/demand factors that were discussed earlier.In Chapter 4, we pointed out that when OEX implied volatility islow, straddle buying is a good strategy. However, we can now refinethat statement because of the volatility skew: backspreads are thepreferred strategy in OEX options when implied volatility is low andthe reverse volatility skew is present. Since 1987, the call backspreadin OEX options has served very well as a strategy with which to takeadvantage of the reverse volatility skew. This is partly due to the factthat OEX options have, for the most part, traded near the lower endof their volatility range. If you wait for those opportunities to establish the backspread, the rewards are worthwhile.The subsequent story follows a backspread through severalmonths, pointing out how to make adjustments, how to take profits,and when to close the spread.
In February 1995, the implied volatility of OEX options was relatively low.This can sometimes be considered a market sell signal, but it is better interpreted as a precursor of a market explosion in one direction or the other. Atthat time, the following data was pertinent, and backspreads were established for ourselves and our customers:OEX: 455 on February 23, 1995With OEX at 455, we would buy calls with a strike of 455 or 460 andsell calls with strikes of 445 or below. These options should generally haveabout three months or more of life remaining, so time decay won’t be amajor factor right away. In addition, I sometimes like to purchase some outof-the-money puts in order to add some more downside potential to theposition, particularly if the striking price of the calls that are being sold is relatively near to the current price.
TRADING THE VOLATILITY SKEW
Option
Price
Implied Volatility (%)
May 460 callMay 445 callApril 445 put
7161⁄231⁄2
9.911.710.8
533
The basic backspread position that was established was:Buy 20 OEX May 460 callsSell 10 OEX May 445 callsBuy 10 OEX April 445 putsNet debit: 10 pointsThe May 445 calls being sold were trading with a higher implied volatility than that of the May 460s being bought, the natural by-product of establishing a call backspread when there is a reverse volatility skew. In this case,I used the April puts for the extra downside potential because they were acheaper price. In order to keep the calculations of credits and debits simple,we address commissions at the end of these examples.Figure 6.27 shows how the position would look at April expirationwith volatility still at the low end of the range (middle curved line), at Aprilexpiration with increased volatility (higher curved line), and if it dropped to6 percent (lowest line).The collateral required for a backspread is essentially the amount ofrisk; that is, if the underlying expired exactly at the higher strike at expiration, we would realize the maximum loss. That is the margin requirement.Stated in another manner, we must have collateral equal to the difference inthe strikes for each of the short calls, plus we must pay for any debitinvolved. If the position is established for a credit, as is often the case, thenthe credit may be used to reduce the spread requirement. In this case, thedifference in the strikes is 15 points ($1,500); and since we have 10 bearspreads, the collateral required is $15,000, plus the $1,000 debit of theposition.
Now, a position such as the one established in this example, isdelta neutral to begin with but it has volatility risk and gamma risk—it is not gamma neutral. This means that as soon as OEX begins torise, the position will become delta long; or if OEX should fall, theposition will become delta short.
534
TRADING VOLATILITYFigure 6.27OEX BACKSPREAD—STAGE 1
When OEX moves, we must decide how to adjust. This problemwas addressed earlier when we discussed the handling of long straddle positions. When a volatility skew is involved, we must look at boththe volatility skew and the level of implied volatility in order to determine what to do with the position.If OEX moves up, for example, and the position becomes quitedelta long, we will probably have a profit. If we don’t do somethingand OEX subsequently falls in price, we will lose this profit. So, wewould probably opt to take at least a partial profit if volatility hasincreased. However, if the volatility situation is about the same as itwas originally, we might decide to reneutralize the position. This isquite easily accomplished with backspreads: we merely have to rollthe long calls up to a higher strike. This action takes a realized profiton the calls we originally owned, while bringing a credit into ouraccount. Furthermore, we are then positioned to make money ifOEX subsequently falls or rises farther.
TRADING THE VOLATILITY SKEW
535
By the end of March, OEX had moved up to nearly 475, and the positionwas very delta long. Implied volatility had not really increased, nor had thevolatility skew disappeared. In fact, this was the situation:Option
Price
Implied Volatility (%)
May 475 callMay 460 callMay 445 call
71⁄21832
10.913.016.0
At first glance, it looks like implied volatility has increased substantiallyfor the options that we own—and it has. But that increase is due to thevolatility skew, not to any general increase in implied volatility. Notice thatthe now-at-the-money May 475 call has a volatility only slightly higher thanthe May 460s implied was when the position was established (10.9 percentas compared 9.9 percent). The volatility skew is what is causing the in-themoney calls (i.e., options with lower strikes) to have inflated implied volatility. We discuss this phenomenon in more detail later.The fact that the at-the-money call was still cheap was the overridingfactor in my decision to roll the calls up, rather than close the position,which at the time had an unrealized profit of about $3,500 (the April 445put was still selling for about one point). When rolling up, we should normally buy more than we sell in order to keep the position delta neutral.However, sometimes we’re swayed by technical factors, and the marketseemed overbought to us; so we only rolled an equal number:Bought 20 May 475 calls at 71⁄2 openingSold 20 May 460 calls at 18 closingNet credit of roll: 210 points ($21,000)After this adjustment, the position is:Long 20 May 475 callsShort 10 May 445 callsLong 10 April 445 putsNet credit to date: 200 points
Figure 6.28 shows the adjusted position at April expiration. The lowercurve on the graph shows the profits if implied volatility remains at the cur-
536
TRADING VOLATILITYFigure 6.28OEX BACKSPREAD—STAGE 2
rent low levels, while the higher curve depicts the situation if implied volatility increases.It should be pointed out that when we roll up, we increase our marginrequirement. In this particular case, the difference in the strikes between theshort calls and the long calls is now 30 points ($3,000). We still have 10 ofthe call bear spreads in the position, so the collateral requirement is now$30,000. Of course, the $21,000 credit that was obtained when we rolledup can be applied against this increased collateral requirement.
In a totally theoretical situation, I would always encourage returning the position to a delta neutral status when an adjustment is made.However, in these examples, we’re describing actual trading activity,and sometimes one modifies the theoretical approach in the heat ofbattle. A slight modification of this sort is a minor concession to mymarket opinion—it’s not like abandoning the backspread strategy fora totally one-sided position.
TRADING THE VOLATILITY SKEW
537
In the larger context, I was wrong, of course, about OEX beingoverbought at that point in 1995—it rallied for the rest of the year,with only a couple of pauses for breath. However, over the nextmonth, it did have some trouble advancing as it consolidated to workoff its overbought state. This meant that expiration was about amonth away. I don’t like to hold long or at- or out-of-the-moneyoptions with that little time remaining, so it was time to makeanother decision.OEX had crept up to about 479 by the third week of April, leaving only amonth of time remaining on the long May 475 calls. Once again, impliedvolatility was fairly low, so the decision was made to roll out to June optionsand stick with the position for another month in search of the elusiveincrease in implied volatility. The following trade was made:Bought 20 June 480 calls at 9 openingSold 20 May 475 calls at 91⁄2 closingNet credit of this roll: 10 points ($1,000)In addition, the April 445 puts had been sold for one point a couple ofweeks earlier. Since the short calls were now so deeply in-the-money, therewas no reason to buy another out-of-the-money put to add downside potential; the short calls were providing plenty of downside capability. Thesetrades brought in a total credit of 20 points, leaving the position in the following state:Long 20 June 480 callsShort 10 May 445 callsNet credit to date: 220 points
Even though the long options were rolled up to a higher strike, acredit was available because of the fact that OEX was just below the480 strike and implied volatility was low. With three weeks to go,there wasn’t much chance of an early assignment on the May 445calls, but the possibility increased as expiration approached. However, in any OEX spread, should a trader receive an early assignmentnotice, he should either quickly sell another, longer-term contract inits place, or he should remove the other side of the spread. He
538
TRADING VOLATILITY
should not decide to become a market predictor; that tack is usuallynot a wise one.It has been my general experience over the 13 years that OEXoptions have been trading that an early assignment is not necessarilyan unprofitable thing. True, it is an inconvenient occurrence, and itmakes a spread position assume a great deal of risk. That is why oneshould attempt to avoid early assignment. What I am saying, though,is that when I have received an early assignment notice, I have, onaverage, made money because the market moved favorably after theassignment. Perhaps those traders doing the exercising are doing sobecause of a short-term market opinion, and that opinion is wrong.In any case, it is not wise to tempt fate. So with about two weeksto go until May expiration, OEX took off to the upside, and the following adjustments were made.By the first week of May, OEX was in a fast-rising phase once again. It hadrallied to above 490. This was a major move that again made the entireposition delta long. Moreover, time was now getting quite short for the Mayoptions; the chances for early assignment were increasing with each passing day. In addition, implied volatilities had increased somewhat, althoughthey were by no means expensive:OptionJune 480 callJune 495 call
Implied Volatility (%)12.911.1
Finally, it should be noted that the unrealized profit of the position hadnow reached about $7,500, less commissions.Given the fact that the implied volatility of the at-the-money option wasstill as low as 11 percent, the decision was made to roll the position:Bought 20 June 495 calls at 9 openingSold 20 June 480 calls at 20 closingNet credit of this roll: 220 points ($22,000)Also, since expiration was approaching, the May calls were rolled toJune calls. When the long calls are so far in-the-money, it is sometimes necessary to roll to a higher strike. The decision as to which short strike to useis usually based on two factors: (1) the time value of the short option that
TRADING THE VOLATILITY SKEW
539
you are considering rolling into, and (2) the collateral requirement—rollingto a higher strike reduces the collateral requirement.Since there was a reasonable amount of time value premium in the June445 calls (almost two points), I decided to keep the short strike the same:Bought 10 May 445 calls at 531⁄2 closingSold 10 June 445 calls at 541⁄2 openingNet credit of this roll: 10 points ($1,000)These adjustments brought more credit into the position:Previous total position credit: 220 pointsRoll of long calls: 220 points creditRoll of short calls: 10 points creditNet position credit to date: 450 points creditThis is a credit of $45,000 dollars. But it is needed to reduce the collateral requirement, which grew again by rolling to the 495 strike. After this,the profit graph for the position at June expiration had improved, as shownin Figure 6.29 (straight lines). You can see that there is almost no area inwhich a loss can occur, although we would not want to give back the$7,500 that the position is currently ahead.The curved line shows the profit if implied volatility increases by the firstof June. It again demonstrates the powerful influence that implied volatilitycould have were it to increase to 15 percent or so.
When expiration approaches, the long side of a backspreadbecomes a concern in terms of time value decay (assuming that theunderlying is near the striking price of that long call). In addition, theshort side of the spread becomes a concern because of early assignment possibilities. You must remember that the intent of the positioncontinues to be to trade volatility. It is still low, so the decision ismade to remain in a backspread position, rather than just close it out.In the preceding case, the May options were rolled to Juneoptions. That one-month roll doesn’t add much time value premiumto the position. I have always felt that you need to investigate yourobjectives when rolling the long options. If you roll to the nearestavailable month, then you are playing it very tight to the vest. Youare exposed to time value decay, but your cost for rolling is smallest(i.e., June options cost less than July options). Since I was still having
540
TRADING VOLATILITYFigure 6.29OEX BACKSPREAD—STAGE 3
trouble believing that OEX could continue to advance at its thencurrent pace, I was keeping the rolls short-term, rolling merely frommonth to month.OEX wasted no time proving quite clearly that I was misjudging its power. Itrose to 505 by the first week of June. Grudgingly, implied volatility of theat-the-money options had increased as well—12.3 percent for the July calls.So, at this time, the position was 31⁄2 months old and the implied volatilityof the at-the-money calls had risen from 9.9 percent to 12.3 percent. Thisplaced the current implied volatility in the fourth percentile, no longercheap, but not expensive either.The prices and volatilities of the options being considered were:Option
Price
Implied Volatility (%)
June 495 callJune 445 callJuly 505 call
1361101⁄2
13.4n/a12.3
TRADING THE VOLATILITY SKEW
541
At this point, the entire position from inception had an unrealized gainof about $9,000, less commissions.Since the position had been working so well up until this time, I decidedon a halfway measure: I would remove some of the position in order to naildown some profits but would continue to hold the remainder of the positionto see if it could make even more money. The actual decision that I madewas to take off a quarter of the position and to roll the balance to the July505 calls.This was the removal of one quarter of the position:Sold 5 June 495 calls at 13 closingBought 3 June 445 calls at 61 closingDebit on this trade: 118 points ($11,800)And this was the roll of the remaining longs calls out to July:Sold 15 June 495 calls at 13 closingBought 15 July 505 calls at 10 openingCredit on this trade: 45 points ($4,500)The remaining position was now:Long 15 July 505 callsShort 7 June 445 callsNet credit to date: 377 pointsThis position had a collateral requirement of $42,000 (seven bearspreads with a 60-point, or $6,000, requirement for each one). The netcredit to date of the position was now 377 points less commissions (it hadbeen 450 points credit and was now reduced by the two trades just cited), sothat amount could be applied against the collateral requirement.After these trades, the position once again was approximately deltaneutral, but was somewhat smaller. Figure 6.30 shows the potential atJune expiration. It assumes that implied volatility remains unchanged at12.3 percent. Note that the position can no longer lose any money at all,although it could give back some of the nearly $9,000 in profits built up todate, if OEX were to stabilize near 505.
Perhaps in a more theoretical world, the entire position wouldhave been removed before this last roll was made, since impliedvolatility had risen to 12.3 percent for the at-the-money options.
542
TRADING VOLATILITYFigure 6.30OEX BACKSPREAD—STAGE 4
Perhaps it should have been. However, in the real world, we areconstantly fighting the battle between theory and reality. Any goodtrader wants to cut losses and let profits run, even in a hedged position such as this backspread. Since the position had been working sowell, I only removed a small part of it, electing to “let the profits run”if they could.I don’t think there’s always a “right” and a “wrong” thing to dowhen managing a hedged position. In a long volatility position likethis backspread, it’s important to let the position have some room tomove; but when the delta builds up too far, the position should bereneutralized. That had been done for this backspread position several times. As long as you are doing that and are mindful of a mentalstop, then you are proceeding correctly. The mental stop keeps youfrom becoming too complacent about time