990s than it was in the 1980s. You should also notethat the studies encompassing monthly expiration summaries priorto 1990 were hurt by the October 1987 expiration that lost 27 OEXpoints (that is, if you bought OEX on Friday night, October 16, youlost 27 points when it opened that much lower on Monday, October 19).These results are good enough to trade, so here is the system.Step 1. Using the OEX closes on Wednesday, Thursday, andFriday of expiration week, determine the largest change from theprevious Friday’s OEX close.Example 1: Suppose OEX closes at 530 on the second Friday of the expiration month. Then, during the ensuing week, the following closes are registered:
Day
OEX Close
Change fromSecond Friday
WednesdayThursdayFriday
528.35533.25529.50
–1.65+3.25–0.50
In this case, we would use +3.25 as the largest change, assuming buyprograms on Thursday pushed the OEX to that closing high for the threeday period.Example 2: Again, suppose OEX closed at 530 on the second Fridayof another expiration month. Then, during the ensuing week, the followingcloses are registered:
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Day
OEX Close
Change fromSecond Friday
WednesdayThursdayFriday
532.05529.00527.00
+2.05–1.00–3.00
In this case, we would use –3.00 as the largest change, indicating thatsell programs on Friday pushed the OEX to that closing low.
If the absolute value of the largest change is less than 1.50 OEXpoints, then don’t make a trade—there were apparently no buy orsell programs during expiration week, at least not enough to materially move the market.Step 2. If the largest change was at least 1.50 points in onedirection or the other, then do the following. If the largest changewas positive (Example 1), then buy programs took place during expiration week, and the system says to short the market. If the largestchange was negative (Example 2), then sell programs took placeduring expiration week, and the system says to buy the market.Given the statistics in the previous tables, you may want to take alarger position at quarterly expirations than you do at regularmonthly expirations.Step 3. Use an intraday stop of 3.10 OEX points if the marketmoves against you. Otherwise hold the trade until the following Friday (the Friday following expiration day) and close it down at thattime. If any of the Fridays in the system are holidays, then use Thursday’s close of that week instead of Friday for the appropriate calculation given earlier.It might be better to implement this strategy by buying OEX putsor calls, rather than by buying or shorting S&P 500 futures. Forexample, in the debacle of 1987, your loss would have been limitedhad you owned OEX calls rather than S&P futures.Finally, you should use some trading common sense. For example, if you have built up a very large profit in just a day or two of trading, it would probably be wise to realize at least a part of that profit.
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155
Even though the system says to hold on until Friday, you would beneglectful if you let the entire profit evaporate on a reverse moveby OEX.There does not seem to be any longer-term effect after expiration, as the market’s results are mixed when measured one monthafter expiration. In fact, the percentage of months that gainedground the month after expiration are about 60 percent—approximately what one would expect to find in an ongoing bull market ofsuch long duration.To summarize this entire section, it is important to understandthe effect of futures and options on the market at or near expiration.Moreover, this understanding can lead to profitable trades if youhave correctly assessed the arbitrageurs’ positions and intentions.Observing open interest can help determine the arbitrage position,as can receiving reliable reports from floor brokers. During expiration week, should you decide to trade along with the arbs, the safestway is to use the hedged strategy—buying OEX calls and selling S&P500 futures against them, for example—but outright call buying cansometimes be attempted successfully, as well. Also, it was shown thatexpiration activity is often reversed to a certain extent in the weekfollowing expiration. That postexpiration phenomenon can betraded as well, using the trading system presented.
Expiration’s Effect on Individual StocksOption expiration can also have an effect on the trading of an individual stock. In general, if a stock is near a particular strike in the lastday or two of its life and if there is a fairly large open interest in theputs and calls at that strike, then it’s possible that the stock will be“pulled” right to the striking price. As was the case with indexoptions affecting expiration, this phenomenon affecting stock is alsoarbitrage related. The arbitrage in this case is generally conductedby the market makers themselves, although in the distant past, it usedto be possible for upstairs traders to engage in this sort of arbitrageas well.
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Example: Suppose that on the Friday before February expiration (the lasttrading day), XYZ stock is trading with this market:Bid: 46.92
Asked: 46.94
Moreover, suppose there is a large open interest in the Feb 45 calls. Sincethis is the last day of trading, the market in the calls might be 1.90 bid,1.95 offered.The public owns these calls in large quantity, as evidenced by the largeopen interest. In general, a public customer will want to sell his calls ratherthan exercise them— due to commissions, margin, and so on. When a public customer looks at this market, he sees that he is not able to sell his callsat parity (which would be 1.92—the stock price, 46.92, minus the strikingprice, 45.00). However, he can sell them at 1.90, which is pretty close, sohe might well do so. The market maker buys the calls from the publiccustomer.From the market maker’s point of view, he does not want to be longcalls on this stock for even the balance of the day; so he executes an arbitrage to lock in small profit. These are the market maker’s trades:1. He buys the XYZ Feb 45 call at 1.90.2. He issues an exercise notice for the call: to buy 100 shares of XYZat 45.3. He sells 100 shares of the XYZ stock (short exempt) at 46.92.He is allowed to sell the stock on a downtick even though he doesn’ttechnically own it yet (this is what selling “short exempt” means) because hehas already issued an irrevocable exercise notice to exercise the calls.The market maker makes 2 cents on this transaction: he loses the 1.90he paid for the call; but the difference between the stock purchase price,45.00, and the stock sale price, 46.92, is a profit of 1.92, for an overallprofit of 2 cents.So the market maker, who has no costs except for minimal clearingcosts, will do this trade all day long. As long as the public wants to sell theircalls at even the tiniest discount to parity, he will execute this arbitrage.When open interest is in the thousands, this may result in tens of thousandsof shares of stock being traded.How does this affect the stock price? Notice that the market makerssells stock in the open market (100 shares at 46.92 in this example). As thepublic sells more and more calls and as the market maker buys them, he
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sells more and more stock. All of this selling begins to take its toll, and stockdrops. However, that may just spook more call owners, and they sell evenmore calls, in which case the market maker buys those calls and sells evenmore stock.Where does this spiral end? When the stock reaches the striking price.When that happens, the calls may be 0.05 bid and 0.10 offered, with thestock at 45.00. The market maker can no longer execute an arbitrage, andthe public may no longer want to sell calls at a mere nickel, so the processends—with the stock “pinned” to the striking price (if it were to rally again,the process would begin anew).
It should be noted that there is a companion arbitrage involvingputs. If the stock in the preceding example were to fall below thestrike, then the Feb 45 puts would be in-the-money, and a similararbitrage would take place: the public sells Feb 45 puts to the marketmaker. The market maker, in turn, after buying the puts at a slightdiscount, then buys the underlying stock and exercises the puts tosell the stock. Again, he makes a few cents on each trade. Meanwhile, he is now buying stock in this form of the arbitrage, and thatforces the stock back up to the striking price. When it reaches thestrike, this arbitrage will also cease.So, the stock is “pinned” to the strike by the call and the put arbitrage. That’s how stock can get pinned to the strike on expirationday. It has nothing to do with some nefarious X-Files–type conspiracy to make the poor options buyers lose their money, as some cynics have suggested. It is merely a function of the arbitrage that takesplace in the open market.It should be pointed out that if there is an extraneous news eventthat moves this stock, it can easily dominate the arbitrage effect. Thearbitrage scenario works only if there is little or no price influence inthe stock that day from external sources.
OPTIONS AS ANINSURANCE POLICYWe first entered the subject of how futures affect the market whenwe were discussing how derivatives can be used to hedge stocks.
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Examples of using futures as that hedge were 1980s–style portfolioinsurance and program trading. Options can, of course, be used asprotection for stocks as well, sometimes with greater efficiency.We saw earlier that insurance for individual stocks can be mostefficiently created by buying equity put options specifically againstthose stocks. This method—buying individual equity puts to protecteach individual equity in your portfolio—is often the most efficientand cost-effective way of creating insurance for a portfolio of stocks.You merely buy slightly out-of-the-money puts against the individualissues that you own. For example, if you own 2,000 shares ofMicrosoft, selling at 93, then you might want to buy 20 MicrosoftOct 80 puts as protection. Or if you desire greater protection, thenbuy 20 Oct 85 puts or even Oct 90s.You could buy puts individually for each stock in your portfolio(assuming that the stock has listed options trading). Then, when youwere done, you would have a “perfect” hedge—perfect in the sensethat the puts will increase in value at the same rate your stocks fall, ifthey fall far enough. Thus, no matter what happens to each stockindividually, your puts will provide protection below their respectivestriking prices.Money managers sometimes modify the insurance strategy so asto decrease the cost of the puts used as insurance: the stock ownernot only buys an out-of-the-money put as insurance, but also sells anout-of-the-money call in order to pay for most or all of the cost of hisput. The resultant position—long stock, long out-of-the-money put,and short out-of-the-money call—has a profit potential as shown inFigure 3.1. By using this strategy, which is called a collar, the stockowner is giving up some of his upside profit potential in order tolower the cost of his insurance. We’ll talk more about the collar strategy shortly.You can also protect an entire portfolio of stocks with index orsector options. This is an easier protection method, as you only needto place a single order and pay one commission in order to createthe protection. The problems with using index options are twofold:(1) there is almost certain to be tracking error (tracking error is aterm that describes the difference in performance between your portfolio and a broad-based index); (2) the index options often trade withan inflated implied volatility, meaning that you are “overpaying” for
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159
Figure 3.1THE COLLAR AS INSURANCE
your protection. Individual equity puts often trade with an impliedvolatility that is very much in line with the stock’s historical volatility.This means that you generally won’t be overpaying for individualequity puts. In addition, there is no tracking error when you buy individual equity puts. Despite these drawbacks, many portfolio managers prefer to use index options for protection, simply because theycan’t physically buy options on the 300, 400, or 500 stocks thatthey own in their large portfolios.Example: Suppose that a stockholder owns a rather diverse portfolio ofstocks— worth $1.4 million—and he wants a temporary hedge because hefeels the market is due for a sharp, short-term decline. He might decide tosell some S&P 500 futures against his portfolio. Recall that a one-pointmove in S&P futures is worth $500. Therefore, if the S&P 500 futureswere trading at 560, then each futures contract represents $280,000 worthof protection (560 times $500 per point). He would thus sell 5 futures tohedge his $1.4 million portfolio, since $1.4 million ÷ $280,000 = 5.
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Now suppose that the market does indeed drop and his portfolio losesalmost 15 percent of its value, falling to $1.2 million, a loss of $200,000.Furthermore, during the market decline, the S&P 500 futures drops by 30points. Thus, the five S&P futures that he is short netted a profit of only$75,000.Even though he sold an appropriate dollar amount of S&P 500futures, his portfolio and the S&P 500 performed in a different manner.This difference in performance may be due to tracking error. However, itcould be the Beta as well (we discuss Beta shortly). These two would accountfor the $125,000 net loss that he suffered in this example.
If you owned a portfolio of stocks that were the exact makeup ofthe S&P 500 or the OEX (S&P 100) indices, then you wouldn’t haveto worry about tracking error at all; you could easily compute thenumber of options or futures that would be required to hedge yourposition. However, no individual investors and few institutionalinvestors are in this position. Rather, you usually have a portfolio ofstocks that bear little resemblance to the indices themselves. In orderto hedge this portfolio, you have to use the options or futures thatare listed—ones that don’t exactly match the makeup of your portfolio. So you must try to select an index that will perform more or lesslike your portfolio of stocks if you want to use index puts as protection. If the portfolio is broad-based, then OEX or SPX will suffice. Ifthe portfolio is more specific, you may be better served by using putson a Sector index.It’s a simple matter to calculate your portfolio’s actual net worth;but when you are attempting to use index puts as protection—assuming you don’t own exactly the stocks that make up the index—then you must first calculate the adjusted net worth of your portfolio.In order to do this, it is necessary to use a factor that we call relativeBeta. We define relative Beta later, but for now suffice it to say thatit is a measure of how each stock in the portfolio in question relatesto the index that you are using as a hedge. Simply stated, if the relative Beta is 2.0, then the stock in question moves twice as fast as theindex in question.Example: To show how this calculation works, assume that a trader has asmall portfolio that consists of 1,000 IBM, 2,000 General Motors, 300
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161
Texas Instruments, and 500 AT&T. This is a rather diverse portfolio, so hemight consider using a broad-based index such as the OEX for his hedge. Inorder to do so, he multiplies the actual net worth by the relative Beta inorder to determine the adjusted net worth.
Stock
Quantity(a)
Price(b)
Net Worth(a × b = c)
RelativeBeta(d)
AdjustedNet Worth(c × d)
IBMGMTexas InstrumentsAT&T
1,0002,000300500
1105016050
110,000100,00048,00025,000_________
1.11.32.01.0
121,000130,00096,00025,000_________
Totals:
283,000
372,000
This portfolio’s adjusted net worth is higher than its actual net worth,indicating that it is more volatile than the OEX. If he were comparing theportfolio to a different index or sector, then the relative Betas wouldchange.Assume that OEX is trading at 525. Then he would divide 372,000 by525 to arrive at the number of “shares” of OEX he needs to hedge thisportfolio. That division tells him that 708.57 shares of OEX would berequired as a hedge. If he were going to buy OEX puts, which represent100 shares of OEX, then he would buy seven puts as a hedge.
The preceding example is a simple one, since you would expectthis portfolio to perform more or less like the stock market.Although, even that is a big assumption, since IBM was falling forquite some time, while the overall market was rising. The calculationsbecome more perplexing when you have a portfolio that performsless like the broad market and more like one of the sector indices.The following examples illustrate this problem.Example: Now suppose that we are discussing a more volatile, technologystock portfolio consisting of 2,000 Microsoft, 1,000 Intel, 500 TexasInstruments, and 500 IBM. This portfolio might perform extremely differently from the OEX. In fact, one of the technology sector indices
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might be a better hedge. First, let’s see how the calculations relate tothe OEX:Hedging with OEX
Stock
Quantity(a)
Price(b)
Net Worth(a × b = c)
RelativeBeta(d)
AdjustedNet Worth(c × d)
MicrosoftIntelTexas Inst.IBM
2,0001,000500500
10067160110
200,00067,00080,00055,000_________
3.14.02.01.1
620,000268,000160,00056,500__________
Totals:
402,000
1,104,500
This portfolio is almost three times as volatile as OEX (i.e., the adjustednet worth is almost three times the net worth). With OEX at 525, this wouldnecessitate hedging with 1,104,500/525, or 2,103.81, shares of OEX, or21 OEX puts.When the adjusted net worth is so disparate from actual net worth, youshould consider using a sector index as a hedge instead. The large discrepancy between actual and adjusted net worth indicates that tracking errorcould be a large problem. There is a Semiconductor Sector Index (Symbol:SOX) that might be a better hedge for this high-tech portfolio. Each stockhas a totally different relative Beta when the SOX is considered.Hedging with SOX
Stock
Quantity(a)
Price(b)
Net Worth(a × b = c)
RelativeBeta(d)
AdjustedNet Worth(c × d)
MicrosoftIntelTexas Inst.IBM
2,0001,000500500
10067160110
200,00067,00080,00055,000_________
1.21.51.00.7
240,000100,50080,00038,500________
Totals:
402,000
458,500
Using SOX gives us a much closer relationship between actual andadjusted net worth. Since SOX is trading at about 300, you would need
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458,400/300, or 1,528, shares of SOX to hedge this portfolio. Or youwould need to buy about 15 SOX puts.Note: the reason that the relative Betas are smaller for SOX is that theindex itself is quite volatile—as are these stocks—so on a relative basis, theindex’s volatility is much closer to the portfolio’s volatility.
This might be a good time to describe how to compute the relative Beta. Beta is a statistical measure that is used by portfolio managers to correlate how well a certain stock “tracks” the broad stockmarket. There are two problems with using Beta: (1) the Betas thatare published are generally for a long period of time, such as one ortwo years, and that is an awfully long time to be measuring how astock performs and (2) Beta is not really a measure of volatility, butof direction and volatility. Thus, a stock that goes up when the market goes down will have a small Beta, even though it might be a relatively volatile stock.IBM is a classic example of a relatively volatile stock that has a low Beta—atleast in the summer of 1995—because it has correlated poorly with thestock market in recent years. For example, IBM fell from 140 to 47 during1991 and 1992, while the broad stock market was rising about 20 percent.Then, from the summer of 1994 through the summer of 1995, IBM doubled in price, while the broad stock market rose 31 percent. The Beta hadfallen to 0.86 by the end of 1992, reflecting the negative correlationbetween IBM and the broad market. But, by the summer of 1995, it hadrisen to 1.52! So which one is correct? Both, but at different times. That’swhy it’s sometimes difficult to use Beta as the relative Beta.
Other measures of volatility that option traders are familiar withare the historical volatility and implied volatility of the stock’s options. Because you can also compute the historical and impliedvolatilities for an index or sector and its options, you can constructanother measure of relative Beta by dividing the stock’s volatilityby that of the index. For example, in the summer of 1995, IBM’shistorical volatility was approximately 24 percent, and OEX’s historical volatility was about 12 percent; so the relative Beta would be
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24/12, or 2.0. Incidentally, the same calculation done for IBM at theend of 1992 would have yielded a very similar result. So, this methodof computing relative Beta is more stable, as the volatility of a stocktends to remain fairly constant, even though its price may change.Using either historical or implied volatility for computing relativeBeta is acceptable, although my gut feeling is that the historicalvolatility method gives a better picture of how the stock is going toperform and, thus, reduces tracking error.The following fact, mentioned earlier, is worth repeating: if,when you compute the adjusted net worth with respect to a certain index, there is a large difference between the actual networth and the adjusted net worth, then you might be subjectingyourself to a rather large tracking-error exposure by using thatindex. Thus, you should be willing to use sector indices to hedgesmall portfolios and/or portfolios that do not correlate well with thebroad market.There are further nuances involved in hedging a portfolio ofstocks, and we will touch on some of them now. The precedingexamples involved calculating the number of “shares” of the indexthat were needed as a hedge. That number was then converted into“number of puts to buy” merely by dividing by 100. This assumesthat you are buying at-the-money puts as protection. In reality, thisprotection won’t be full protection until the index falls and the put’sdelta nears 1.0 (actually, minus 1.0).If you were to buy out-of-the-money puts, their protective qualitywouldn’t kick in until the index fell below the striking price of thoseputs. So, to be correct, you should convert the adjusted net worthdirectly into “number of puts” to buy by using the following formula,which is quite similar to what we did earlier:Adjusted net worthNumber of puts to buy = ______________________100 × strike price of putExample: Returning to the first OEX example, in which the portfolio consisted of IBM, GM, Texas Instruments, and AT&T, recall that the adjustednet worth was $372,000 vis-à-vis the OEX. OEX was trading at 525 at thetime. In order to determine how many puts to buy, according to the preceding formula, you would arrive at the following figures:
OPTIONS AS AN INSURANCE POLICY
Insurance PutStrike Price
FormulaResult
Number of Putsto Buy
525500475
7.08577.44007.8316
77 or 88
165
You can see that you would buy slightly more puts at lower strikesbecause you need them to provide “full” protection should the index fall tothat lower level. Of course, the protective capability of these out-of-themoney puts doesn’t take effect until the index drops in price. For example,with OEX at 525, if you buy the 475 puts, then you don’t have any realprotection until the index falls almost 10 percent (50/525 = 9.5%).
Buying out-of-the-money puts is a cheaper form of insurance—almost like disaster insurance. As with any type of insurance, whetherit be fire, personal injury, et cetera—it costs less if there is a smallerprobability of actually being used. Thus, the total dollars spent oninsurance will be far less if you buy out-of-the-money puts than if youbuy at-the-money puts. You need to make a decision on two things:(1) the length of the insurance, and (2) the deductible portion that youare willing to assume. As always, the bigger the deductible that youassume, the lower your insurance premiums will be. For example,many self-employed individuals have opted for high-deductible healthinsurance; they are willing to pay a couple of thousand dollars ofmedical expenses themselves, but they are insured for anything overthat amount, in case a real medical crisis arises. The cost of that formof insurance is much lower than a normal individual policy.The type of insurance you select for your stock portfolio can bestructured in a similar manner. The “deductible” portion of portfolioinsurance is the distance between the current index value and thestriking price of the out-of-the-money put that you are purchasing.With OEX at 585, you might buy Dec 575 puts and have very littledeductible—only 10 OEX points, or about 2 percent. This meansthat if your portfolio performs in line with OEX, your portfolio wouldbe protected if OEX fell below 575. Your portfolio would lose moneywhile OEX declined from 585 to 575, but below that level it wouldbe protected.
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This low-deductible policy would be fairly costly insurance—the putswould be rather expensive since they’re not very far out-of-the-money.On the other hand, you might decide to buy the 550 strike, which has amuch larger deductible of 35 OEX points, or 6 percent. That would beless costly because the puts are farther out-of-the-money.So, in the final analysis of purchasing insurance, you must knowwhat it costs and what kind of protection it provides. Thus, I would recommend making a table similar to the one shown in the next example.Example: Suppose that a money manager has a portfolio that has anadjusted net worth of $1.7 million. He wants to use OEX as a hedge but isuncertain about what strike price and expiration date to use. He might makea spreadsheet similar to the following one in order to help him decide.First, use the formula given earlier to decide how many puts to buy,depending on the striking price involved:Number of OEX Puts to BuyStriking Priceof Protective Put
Number of Puts Neededas Protection
450475500525
38363432
Second, assume that the following prices exist for puts of varying expirations at these striking prices. These prices conform closely with actualOEX put prices in effect during the late summer of 1995. The longer-termputs have higher implied volatilities than the short-term puts do; this is to beexpected and is a fact that buyers of insurance have to live with.Prices of Various OEX PutsExpirationStrike
Dec 1995
Dec 1996
Dec 1997
450475500525
13613
10142027
17212835
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167
Third, using the “number of puts to buy” from the first table in thisexample and the prices in this table, we can calculate the actual cost ofinsurance for these various striking prices and expiration dates. Obviously,longer-term insurance is going to cost more, and so is insurance with ahigher striking price because it provides more immediate protection (i.e., ithas a smaller deductible).Actual Dollar Cost of InsuranceExpirationStrike
Dec 1995($)
Dec 1996($)
Dec 1997($)
450475500525
3,80010,80020,40041,600
38,00050,40068,00086,400
64,60075,60095,200112,000
Finally, convert these actual dollar amounts into percentages of theactual net worth in order to see how the purchase of this insurance mightaffect performance figures.Cost of Insurance as a Percent of Net WorthExpirationStrike
Dec 1995(%)
Dec 1996(%)
Dec 1997(%)
450475500525
0.20.61.22.4
2.23.04.05.1
3.84.45.66.6
This portfolio manager can now see that if he buys the longest-term protection, using at-the-money options (Dec 1997 expiration, 525 strike), he willhave to pay 6.6 percent of the current value of his portfolio. If the market rallies over that time period, his performance will be 6.6 percent worse (about