0, a relatively tight spread, then the following returns areobtained:530 call:540 call:550 call:560 call:570 call:
⫹2.7%⫹3.3%⫹3.9%⫹4.4%⫹3.9%
The out-of-the-money option now looks no better than the at-themoney. The returns that can be expected from the in-the-moneyoptions should probably be adjusted for a bid-ask spread wider than$0.10 as in-the-moneys have a tendency to be somewhat less liquid.So where does this leave us? With the at-the-money options.There are a couple of strong arguments to be made in favor ofselecting at-the-money options for short-term trades. The ﬁrst is liquidity. Traders congregate around at-the-money options, and thishas a tendency to narrow the bid-ask spread—not a negligible factor in short-term trading. The second is the fact that the at-themoney options’ delta will increase most rapidly if the index startsmoving in the anticipated direction. This is discussed in more detailin Chapter 9, in the section on gamma.If time decay is not really an issue for day traders, the same cannot be said about the options’ implied volatility. This can, and does,change from day to day and even during the course of a trading day.To gauge the importance of daily changes in the volatility level,we looked at the CBOE Volatility IndexSM (VIX®) from January 3,1995, to December 31, 2001. VIX calculates the implied volatility ofthe at-the-money options (our preferred choice) on the Standard &Poor’s 100 Index, and is discussed in more detail in Chapter 9. Wecalculated the point change in VIX for each trading day and presentour results in Table 7.5.Two observations: The ﬁrst is that more than 60% of the changesare within plus or minus one point, and more than 80% are withinplus or minus two points. Although these small changes will impactthe options’ values, they are not the ones about which we have to
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187
Table 7.5Number of DaysChange Observed
Percentage of DaysChange Observed
Decrease of more than 10
0
0%
Decrease of 9 to 10
1
0.06%
Decrease of 8 to 9
1
0.06%
Decrease of 7 to 8
2
0.1%
Decrease of 6 to 7
1
0.06%
Decrease of 5 to 6
7
0.4%
Decrease of 4 to 5
16
0.9%
Decrease of 3 to 4
21
1.2%
Decrease of 2 to 3
128
7.1%
Decrease of 1 to 2
208
11.5%
Decrease of 0 to 1
557
30.7%
Increase of 0 to 1
540
29.7%
Increase of 1 to 2
198
10.9%
Increase of 2 to 3
70
3.9%
Increase of 3 to 4
37
2.0%
Increase of 4 to 5
14
0.8%
Increase of 5 to 6
5
0.3%
Increase of 6 to 7
3
0.2%
Increase of 7 to 8
1
0.06%
Increase of 8 to 9
3
0.2%
Increase of 9 to 10
0
0%
Increase of more than 10
2
0.1%
Point Change in VIX
be greatly concerned. The second observation is that our study compares VIX from one day’s closing level to the next day’s closing levels. This could understate some intraday changes.But it is probably the other 20% of observations that are of mostconcern to traders: those instances where VIX moves by more than
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The Options Strategist
VIX Point Daily Change
20151050(5)(10)(15)(10)
(5)
0
5
10
OEX Percent Daily Change
Figure 7.1 OEX/VIX (1995–2001)
two points in either direction. In order to correlate changes in OEXto changes in VIX we graphed all of the 1,815 daily observations,comparing percent changes in OEX to point changes in VIX. Figure7.1 is what we obtained.Even though the number of data points turns the central part ofthe graph into one big blob, a clear picture emerges: VIX has a tendency to rise in falling markets, and vice-versa. Not only is there aninverse relationship, but the larger the market decline, the greaterthe increase in implied volatility, and the stronger the rally, the moreprecipitous the fall in implied volatility. (For those statisticallyinclined, the r2 of the data is ⫺0.806, a strong negative correlation.)This does have implications for short-term option traders.Put buyers are the obvious winners, assuming they buy theiroptions before the market declines. If their forecast of a lower market is correct, they’ll beneﬁt from both a falling index and higherimplied volatility. How should this fact impact strike price selection? Although we have never advocated purchasing far out-of-themoney put options, the observed changes in implied volatility leadone to select at- or slightly out-of-the-money puts. At-the-moneyputs are pure time premium and will obviously beneﬁt if impliedvolatility increases, and out-of-the-moneys usually gain the most,on a percentage basis, when volatility goes up. We favor staying relatively close to the at-the-moneys, remembering that 80% of ourobservations show little change in the volatility level.
Options on Exchange-Traded Funds and on Indices
189
The situation is more difﬁcult for call buyers. Knowing that yourforecast will be correct and that the market will rise means accepting the fact that implied volatility will decrease, thereby loweringthe value of your calls. Does this make it impossible to make moneybuying calls in rising markets? No, but it does mean that call buyers should favor options that are slightly in-the-money over thosethat are slightly out-of-the-money so that lower volatility will notbe as much of an issue. Remember also that most observationswhere volatility dropped dramatically corresponded to sharply rising markets. In most instances, call buyers were saved by the market even though volatility collapsed. Call buyers also may want totake a peek at the next section on spreading—a strategy that tries toreduce the impact of changes in volatility, although day traders willﬁnd no relief there.SpreadingBull and bear spreads, as described in Chapter 6, can be initiatedusing index options. A few caveats are in order before we look at anexample. First and foremost, we would not enter into any indexoption spreads that involve American-style options. There is noneed to deal with the headaches they can create, not to mention thepossible adverse ﬁnancial impact, when European-style options arereadily available. Second—and we will return to this later—oneshould remember that spreads trade at their maximum theoreticalvalue only under limited circumstances: very close to expiration orwhen both options are deep in-the-money.Bull and bear spreads were described as strategies that can beused to neutralize the high implied volatility associated with certain stocks. The same can be said relative to the more volatileindices. Take a trader who is short-term bullish on the Nasdaq-100Index (NDX). He ﬁnds the following call options listed for trading.NDX:April 1300 call:April 1325 call:April 1350 call:April 1375 call:April 1400 call:
1332.45$45.80–$53.80$31.80–$36.50$20.20–$23.20$11.90–$13.70$6.30–$7.70
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The Options Strategist
Table 7.6Buy 11350 Call
Buy 21375 Calls
Buy 1325–1375Call Spread
$23.20
$27.40
$24.60
NDX to Breakeven
1373.20 (⫹3.1%)
1388.70 (⫹4.2%)
1349.60 (⫹1.3%)
NDX to Double
1396.40 (⫹4.8%)
1402.40 (⫹5.2%)
1374.20 (⫹3.1%)
Risk
April options have four and a half trading days remaining—halfof the Friday preceding expiration week plus the four trading daysof expiration week (the last trading day for NDX options is theThursday preceding expiration Friday). Our trader looks at the following possible bullish strategies: buying the 1350 call at $23.20,buying two of the 1375 calls at $13.70 (total cost of $27.40), or buying the 1325–1375 bull call spread at $24.60 ($36.50 paid for the 1325call less $11.90 received from writing the 1375 call). All three strategies have approximately the same initial cost. How they will perform at expiration is summarized in Table 7.6.The spread’s attraction is obvious. On a 3.1% move to the upsidethe trader will double the capital allocated to the trade, while on asimilar move the 1350 call will barely be above breakeven and the1375 calls will still be underwater. The problem with spreads, thistrader knows, is that they react relatively slowly to quick moves inthe underlying index. This can be seen in Figure 7.2, which estimates the value of the spread on the Friday the trade is initiated,three days before expiration, and at expiration.Keep in mind that Figure 7.2 represents the spread’s value, notthe proﬁt or loss on the transaction. Also, any bid-ask spreads theremight be on the options were ignored in calculating the values. Notethat if NDX rises to 1375 (the spread’s upper strike price) on the daythe trade is established, the value of the spread barely rises above$30. And a similar move ﬁve days after the trade was initiated (withthree days left until expiration) sees the spread rise in value to a little under $35. No great guns.It should be obvious by now that the 1374.20 level given in Table7.6 as the point at which our trader will double his capital shouldbe qualiﬁed by saying that it assumes the spread is held to option
Options on Exchange-Traded Funds and on Indices
191
$60Value of Spread
$50$40Trade Day
$30
Exp. ⫺ 3
$20
Expiration
$10$0($10)1300
1325
1350
1375
1400
NDX Level
Figure 7.2 NDX 1325–1375 Bull Spread
expiration. And herein lies the trade-off in trading index optionspreads: even keeping in mind the limited proﬁt potential ofspreads, most traders would opt for the 1325–1375 bull spread basedon the data presented in Table 7.6. But the spread comes with a pairof handcuffs that tie the trader to his position until the expirationdate. Four and a half days may not seem like a long time to be married to one position, but to some traders it’s an eternity. And thisshould act as a warning that spreading is not for every trader, butfor those who have a slightly longer time horizon and are willing tostick with their position. And for those willing to enter into an eightday spread, there will remain the issue of what to do after optionexpiration when there are no longer any one-week options listed fortrading.The one area where spreading with index options is simpler thanspreading with equity options, is in cases where the spread is helduntil expiration. With equity options a trader will have to close outthe spread or, assuming both options are in-the-money, deal withone exercise and one assignment. With index options being cashsettled, there is no need to do anything. Using the above example,if NDX is below 1325 at expiration, both options will expire worthless; if it settles between 1325 and 1375, say at 1351.47, the short 1375call will expire worthless and the trader’s account will simply becredited $26.47, the in-the-money amount of the long 1325 call. Andﬁnally, if NDX is above 1375, say at 1386.55, the trader’s account
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The Options Strategist
would be credited the full value of the spread, $50, as he would becredited the in-the-money amount of the long 1325 call, $61.55, anddebited the in-the-money amount of the short 1375 call, $11.55.Butterﬂies and Other Inhabitants of the MenagerieWe have given numerous options seminars over the past twodecades, and one of the most often-asked questions before we beginis, “Are you going to talk about butterﬂies?” One of the most frequent comments after the presentations is, “You didn’t talk aboutbutterﬂies!” Obviously, inquiring minds want to know.To understand this strategy, start with a trader who expects theSemiconductor Sector (SOX) to be relatively stable over the next ﬁveweeks. The purest neutral strategy consists in writing an uncoveredstraddle. With the SOX at 567.69, the ﬁve-week 570 straddle is bidat $68. In dollar terms, this is a huge premium, representing 11.9%of the options’ strike price, and Figure 7.3 illustrates this short straddle’s proﬁt and loss potential at expiration. But this trader knowsthat the SOX can be extremely volatile and an uncovered straddleleaves him at risk to both a strong move up and a sharp correction.He probably couldn’t sleep at nightTo protect himself against a strong rally, he purchases a ﬁve-weekout-of-the-money call, paying $15.70 for the 620 strike. To insureagainst a meltdown in this sector he buys an out-of-the-money put,paying $17.90 for the 520 strike. Adding it all up, he pocketed $68$80
Profit/(Loss)
$60$40$20$0($20)($40)($60)($80)445
470
495
520
545
570
595
SOX Level at Expiration
Figure 7.3 Short SOX Straddle
620
645
670
695
193
Options on Exchange-Traded Funds and on Indices
for writing the straddle but paid out a total of $33.60 for his insurance, leaving him with a net credit of $34.40 on the total position.This $34.40 represents his maximum proﬁt potential, which he willrealize only if the SOX ﬁnal settlement level is 570.00 in ﬁve weeks.Figure 7.4 plots the butterﬂy’s proﬁt potential at option expiration.This is about half the proﬁt potential of the naked straddle, but itlets him dream sweet dreams.This trader has just purchased a 50-point butterﬂy. Yes, the position was established for a credit, but it is still considered a long butterﬂy (read on for an explanation). The 50-point refers to thedifference between the strike prices of the long and short options.It also helps in calculating the spread’s risk, which is equal to $50less the initial credit of $34.40, or $15.60.So why do we have a problem with this strategy? Count theoptions involved: two puts plus two calls equals four commissionsto initiate the position and another four if it is closed out before expiration. Add four bid-ask spreads getting in, up to four more exitingand the result is one very happy broker. The impact of all this slippage is magniﬁed the narrower the butterﬂy: look at a $5 butterﬂyon a $50 stock and there is virtually no way to make it work. Theexceptions are the more volatile indices where 40-, 50-, and 60-pointbutterﬂies can be easily created. If your options commissions do notchange with the premiums—i.e., your transaction costs for a $30option are the same as for a $3 one—buying one 50-point butterﬂyat $34.40 generates the same amount of net premium as buying ten
$40
Profit/(Loss)
$30$20$10$0($10)($20)445
470
495
520
545
570
595
SOX Level at Expiration
Figure 7.4 Long SOX Butterﬂy
620
645
670
695
194
The Options Strategist
5-point butterﬂies at $3.45 but the transaction costs on the 50-pointbutterﬂy will be roughly one-tenth those on the 5-point butterﬂy(roughly because we are ignoring minimum commissions).Another negative for the retail investor is the margin a lot of brokerage ﬁrms demand for butterﬂies. Some will treat the 50-pointbutterﬂy described above as a 50-point bull spread combined witha 50-point bear spread—which it is—but will ask traders to marginboth of these spreads even though only one can end being in-themoney at option expiration.The niche for this strategy is very small. Butterﬂies use three different strike prices and can be constructed using only three different options (as opposed to the four in the SOX example) if all callsor all puts are used. The 50-point butterﬂy in the preceding example could also have been initiated by buying one 520 call, writingtwo 570 calls, and buying one 620 call. Or it could have been doneby buying one 520 put, writing two 570 puts, and buying one 620put. When using either the three calls or the three puts a butterﬂywill be initiated for a debit; this is why this position is considered along butterﬂy. We will leave this for the more adventurous tradersto explore.Another endangered animal is the condor. The aim is the same aswith the butterﬂy, to beneﬁt from a stable market, but the tactic isslightly different. Instead of starting with a short straddle position,a trader will use a short combination. For example, someone whoexpects the Standard & Poor’s 100 Index (OEX) to be relatively stable over the next ﬁve weeks could write the 560 call and the 545 putfor a total premium of $19.50. The OEX is currently at 552.45, and ifit closes anywhere between 545 and 560 on expiration Friday, bothout-of-the-money options will expire worthless and our trader willpocket $19.50. This is illustrated in Figure 7.5.Although a short combination has breakeven points further fromthe current index level than does a straddle, it still incorporates twouncovered options with all their attendant risks. So our traderdecides to buy some protection and purchases the 575 call at $4.20and the 530 put at $6.00. Her net credit is therefore $9.30, the $19.50from writing the combo less the $10.20 paid for the long options. Herrisk is determined by the difference between the two calls’ (or the twoputs’) strike prices, 15 points, less the initial credit of $9.30, or $5.70.She would incur this loss if the OEX dropped below 530 or movedabove 575 at option expiration. This is illustrated in Figure 7.6.
195
Options on Exchange-Traded Funds and on Indices
$30
Profit/(Loss)
$20$10$0($10)($20)($30)500
515
530
545
560
575
590
605
OEX Level at Expiration
Figure 7.5 Short OEX Combo
Condors are similar to butterﬂies in that both beneﬁt from lowvolatility, have limited risk and limited proﬁt potential, and aremany-legged strategies. The condor is different in that for the samesecurity or index and the same expiration date it will have a lowerproﬁt potential, but this maximum proﬁt can be realized over arange of the underlying’s expiration date price, not at just one point.And all of the obstacles relating to butterﬂies are relevant tocondors.Butterﬂies and condors can also be sold. Take the case of aninvestor who expects an index to be very volatile over the short
$12
Profit/(Loss)
$8$4$0($4)($8)500
515
530
545
560
OEX Level at Expiration
Figure 7.6 Long OEX Condor
575
590
605
196
The Options Strategist
$6$4$2$0($2)($4)($6)70
80
90
100
110
120
130
100
110
120
130
Figure 7.7a Short Butterﬂy
$4$3$2$1$0($1)($2)($3)70
80
90
Figure 7.7b Short Condor
term. He could purchase a straddle or a combination, but he couldalso reduce the cost of these positions by writing one out-of-themoney call and one out-of-the-money put for each straddle orcombo purchased. In addition to reducing the cost, the short optionswill limit the proﬁt potential of these strategies. Generic proﬁt-andloss diagrams for a short butterﬂy and a short condor (both assuming a $100 stock and $10 intervals between the options’ strike prices)are given in Figures 7.7a and 7.7b.Variations on these two strategies include directional butterﬂiesand condors (achieved by setting the positions’ maximum proﬁt tar-
Options on Exchange-Traded Funds and on Indices
197
get above or below the current index level), and hybrids where anuneven number of puts and calls are used.Calendar SpreadsAs with butterﬂies, calendar spreads (which are also known as timespreads, or horizontal spreads) are designed to take advantage of a stable market. Unlike the former strategy, these do not require tradingup to four different option series to establish a position. Start withthe following quotes on the Standard & Poor’s 500 Index (SPX):SPX:April 1125 call:May 1125 call:June 1125 call:June (1 year plus) 1125 call:
1127.93$12.50–$13.90$25.20–$27.20$36.20–$38.20$103.00–$105.00
Note that the April option has 1 1⁄2 weeks until expiration, the May5 ⁄2 weeks, the June 10 1⁄2 weeks, and the June of the following year(the option identiﬁed as “one year plus” and trading at, yes, $100)just over 62 weeks.The strategy consists in purchasing a longer-dated option, andwriting a shorter-dated one. We will start by buying the May 1125call at $27.20 and writing the April 1125 call at $12.50, for an initialdebit of $14.70.Calendar spreads are usually initiated with at-the-money options.It is also possible to give the strategy a slight bias by selecting astrike price above or below the current index level. Simply keep inmind that the strategy’s proﬁtability reaches its maximum if theunderlying index closes at the options’ strike price when the shorterdated of the two options expires.As was seen in Chapter 4, time decay for at-the-money optionsaccelerates as the expiration nears; calendar spreads are designed tobeneﬁt from this phenomenon. Assuming the SPX remains at itscurrent level for the next week and a half, both the option we purchased and the option we have written will lose value, but the erosion of the April option’s time premium will be more rapid. Thismeans we will lose money on our long option but gain more on ourshort option. At the April expiration the value of the spread will be1
198
The Options Strategist
a function of both the level of the SPX index and the May option’simplied volatility (the April option will be worth its intrinsic valueand will not be impacted by any change in implied volatility).Looking at the time spread at the April expiration, there are twoworst-case scenarios. The ﬁrst is if the market collapses, leaving uswith two worthless calls. In this case, the loss would be equal to theinitial debit paid to enter into the position, $14.70, although the Maycall would still have four weeks of life left and it might be possibleto recoup part of our initial investment. The second worst case is ifthe market rallies strongly. Then both our long and our shortoptions would be deep in-the-money—the April trading at intrinsic value, the May not much above its intrinsic. The spread wouldhave to be unwound, the April option covered, and the May sold.And since both options would be trading close to intrinsic, exitingthe position would probably be done for a very small credit, or foreven money. Assuming the spread is liquidated for even money, theloss would then also be equal to the initial debit of $14.70.The best-case scenario is for SPX to close at 1125 at April expiration. The short April option would expire worthless and we wouldbe left holding the May option. Assuming no change in the options’volatility, the May 1125 call would be valued at $20.20 and if sold atthis price would generate a proﬁt of $5.50 ($20.20 less the initial debitof $14.70). Figure 7.8 illustrates the strategy’s proﬁt and loss at theApril expiration date, assuming no change in implied volatility.$10
Profit/(Loss)
$5$0($5)($10)($15)($20)1000
1050
1100
1150
SPX Level at April Expiration
Figure 7.8 SPX Time Spread
1200
1250
Options on Exchange-Traded Funds and on Indices
199
Compare the general shape of the graph in Figure 7.8 to that ofthe long butterﬂy spread in Figure 7.4. They are similar, with bothstrategies having limited risk and limited proﬁt potential that is realized when the underlying closes at a speciﬁc strike price. Since abutterﬂy spread can involve up to four different option series andthe time spread can be initiated with only two, traders may see anadvantage in the latter if only from a transaction’s costs point ofview.The major difference between butterﬂies and time spreads is thatthe value of the calendar spread at the short option’s expiration datewill be a function of the market’s implied volatility, whereas the butterﬂy’s value at expiration is purely a function of the underlyingindex’s level. This is where time spreads are somewhat counterintuitive. First, they are established for a debit, when for the most part,option strategies that look to take advantage of time decay are initiated for a credit. Second, the value of a time spread will be positively impacted by higher, not lower, implied volatility. Rememberthat in our example, at the April expiration, the short April call willeither be out-of-the-money and worthless, or in-the-money andtrading at or close to its intrinsic value. Neither of these outcomesis impacted by volatility. But we will still be long the May optionand the higher the implied volatility, the greater the value of theMay option and the higher the proﬁt on the transaction. Timespreads actually beneﬁt from higher implied volatility but are hurtby actual volatility.Why does the risk-reward ratio in our example look so unfavorable? We could lose $14.70 but only stand to make $5.50, and thatonly if the SPX closes at 1125. The answer is because of the expiration date of the option we wrote, just one and a half weeks away.Consider a calendar spread where we write the May 1125 call at$25.20 and purchase the June 1125 call at $38.20 for an initial debit,and ultimate risk, of $13.00. Given an index level of 1125 at the Mayexpiration, we can estimate the value of the June 1125 call (whichwill still have ﬁve weeks until it expires) to then be $22.45, for aproﬁt potential of $9.45. A longer time frame creates a more favorable risk-reward ratio because the further out the expiration date ofthe short option, the higher the probability that the market willmove away from its current level.
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The Options Strategist
It also should be noted that there is no need to trade optionsexpiring in two consecutive months when initiating a calendarspread. Going back to the quotes given above, a trader could havepurchased the June 1125 call at $38.20 and written the April 1125 callat $12.50, probably with the intention, at the April expiration, ofeither writing the May 1125 call if the April expires worthless orrolling the short April position into May if SPX ends up above 1125at expiration. And traders who are long-term neutral could purchase the far out June call at $105, write the April, and continue writing short-term options over the next 15 months.Calendar spreads also can comprise options with different strikeprices, in which case they are known as diagonal spreads. The mostpopular form of this strategy involves buying a longer-dated in-themoney option and writing a shorter-dated option that is either ator out-of-the-money. Purchasing the in-the-money option willincrease the initial cost of the position but will reduce the impact oftime decay on this long option. By writing an at-the-money (orslightly out-of-the-money) option, the trader can still take advantage of the accelerating time decay. Finally, puts can be substitutedfor calls because time decay does not differentiate between calls andputs.
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