S22 Part V: Index Options and Futures
Interpreting the Ratio. There are several philosophies as to how to inter
pret the ratio once it has been calculated. All philosophies are of the contrarian
variety, so the general comments made earlier that high ratios are bullish and
low ratios are bearish still hold true. However, quantifying just what is "high"
and what is "low" leaves room for interpretation.
One school believes that absolute ratios should be used. An example might be:
"if the 10-day moving average of the equity put-call ratio is over 0.60, that is abuy
signal." Unfortunately, applying absolute figures to any of the ratios can be counter
productive at times. If the market is in the grip of aprolonged bearish move, more
and more puts will continue to be purchased, sending the ratio quite high before it
can reverse and start coming back to normal levels. Therefore, it is better to look for
the ratios to make ahigh or alow before calling abuy or sell signal. This is amore
dynamic interpretation; it allows for buy and sell signals to come at different absolute
levels of the put-call ratio.
Figure 29-1 shows the 50-day equity put-call ratio going back several years (the
daily figures for the previous 50 trading days are averaged to produce the number
plotted on the chart each day). One can see that at certain times, the put-call ratio
reached extreme heights before finally generating abuy signal. Attempting to call abuy on the market at an absolute level would have been an error because the entry
point would have come too early. Notice that the readings in late 1990- as the mar
ket bottomed in advance of Operation Desert Storm - were actually higher on an
absolute basis than those made after the stock market crash in 1987. Similar obser
vations can be made for sell signals after the ratio has reached low levels: don'tantic
ipate - wait for the ratio to bottom out and tum up before declaring asell signal or
to roll over and turn down before declaring abuy signal.
The index put-call ratio is shown in Figure 29-2. It tells asimilar story to the
equity ratio, although there are certainly differences - beyond the obvious one that
the ratios have different absolute values. Note that this ratio averages about 1.00
while the equity ratio averaged about 0.50.
At times, index put buying becomes extensive even as the market climbs. This
does not generally happen with equity options. It seems that institutional money
managers, who are long stocks, are afraid that they will lose their profits after aquick
stock market advance. However, rather than sell their stocks, they buy puts (possibly
overpaying for them). Thus, they are really bullish (they own stocks), but they are
buying puts as ahedge.
This is adifficult situation for the contrarian. What is the institutional manag
er'strue bias? Is he bullish because he still owns stocks or is he bearish because he
is buying puts? This is the bane of contrary analysis - attempting to accurately inter
pret the data that is being received. Figure 29-2 shows that the index put-call ratio

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Chapter 29: Introduction to Index Option Products and Futures 523
is less reliable than the equity ratio, but is still helpful in determining market tops
and bottoms.
In summary, the put-call ratio is an easily calculated one. Daily fluctuations can
be smoothed out into 10-, 20-, or 50-day moving averages. The ratio should be inter
preted bullishly when there is too much put buying and bearishly when there is too
much call buying. The phrase "too much" is not easily interpreted, but looking for
local maxima or local minima in the chart pattern is areasonable way to approach the
problem. When the put-call ratio moving average is increasing, abuy signal would
not be given until the average rolls over and begins declining; asell signal would be
generated when the average which is declining bottoms out.
SUMMARY
There are several kinds of indices and several kinds of trading vehicles: cash-based
options, futures options, and futures. These various underlying securities have dif
fering terms in the way they trade and also in the way their options are designed. This
variety creates many opportunities for astute option strategists.

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532 Part V: Index Options and Futures
The key to determining whether it will be profitable to trade some derivative
security - options or futures - against aset of stocks is generally the level of premi
um in the futures contract itself. That is, if the S&P 500 Index is at 405.00 and the
futures are trading at 408.00, then there is apremium of 3.00 - the futures contract
is trading 3.00 points higher than the index itself. The absolute level of the premium
is not what is important, but rather the relationship between the premium and the
fair value of the future. We will look at how to determine fair value shortly.
The futures are the leaders among the derivative securities, especially the S&P
500 futures. Whenever these become overpriced, other derivative securities will gen
erally follow suit. There are also futures on the NYSE Index, the Value Line Index,
and the Japanese Nikkei 225 Index. Moreover, there are cash-based index options on
the S&P 500 Index (as opposed to the futures options on that index) and the NYSE
Index. These other securities would include the QEX (S&P 100) options and NYSE
futures and options. It follows as well that when the S&P 500 futures become under
priced, the other derivative securities quickly fall into line. If the other derivative
securities don'tfollow suit, then there is an opportunity for spreading one market
against another. That type of spreading can frequently be profitable, and is discussed
in the next chapter.
The normal scenario is for most of the derivative securities to follow the lead of
the S&P 500 futures. When this happens, the only thing that is fairly priced is the
index itself - that is, stocks. Consequently, the logical way to hedge the derivative
security is to do it with stocks. The small investor might hedge his own individual
portfolio, although that would not be aperfect hedge since his own portfolio is not
composed of the exact same stocks as any index. If the index is small enough, such as
the 30-stock DJX, then one might buy all 30 stocks and sell the futures when they are
overpriced. This is acomplete hedge and would, in fact, be an arbitrage. In the case
of alarger index such as the S&P 500, it would be possible only for the most profes
sional traders to buy all 500 stocks, so one might buy asmaller subset of the index in
hopes that this smaller set of stocks will mirror the performance of the index well
enough to simulate having bought the entire index. We take in-depth looks at both
types of hedging.
Even if the investor is not planning to use these hedging strategies, it is impor
tant for him to understand how they work These strategies have certain ramifications
for the way the entire stock market moves. In order to anticipate these movements,
aworking knowledge of these hedging strategies is necessary. The first thing that one
must know in order to implement any of these hedging strategies is how to determine
the fair value of afutures contract.

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Chapter 30: Stock Index Hedging Strategies
FUTURES FAIR VALUE
533
The formula for calculating the fair value of the futures contract is extremely simple,
although one of the factors is alittle difficult to obtain information on. First, let'slook
at the simple futures fair value formula:
Simple Formula:
Futures fair value= Index x [l +Timex (Rate - Yield)]
where index is the current value of the index itself, rate is the current carrying rate
(typically, the broker loan rate), yield is the combined annual yield of all the stocks in
the index, and time is the time, in years, remaining until expiration of the contract.
Example: Suppose the Zl'X Index is trading at 160.00, the broker loan rate is 10%,
the yield on the 500 stocks is 5%, and there are exactly 3 months remaining until
expiration of the futures contract. The time is .25, expressed in years, so the formu
la becomes
Future fair value= 160.00 x [l + .25 x (.10- .05)]
= 160.00 X (1 + .0125) = 162.00
Thus, the future should be trading at about 2 points above the value of the index
itself. This premium of the future over the index represents the savings in not having
to pay for and carry 500 stocks, less the loss of the dividends on the stocks ( the future
does not pay dividends). If the future should get very expensive - trading at 3.50 or
4 points over the index - then it would have to be considered very overvalued, and
an arbitrageur could move in to take advantage of that fact. Similarly, if the future
should trade cheaply, at less than apoint over fair value, there might be an arbitrage
available in that case as well.
The fair value is really only afunction of four things: the value of the index itself,
the time remaining until expiration, the current carrying rate, and the dividends
being paid by the stocks in the index until expiration. Notice that "the dividends paid
by the stock in the index until expiration" is not quite the same as the yield of the 500
stocks, which we used in the above simple formula. We will expand more on that dif
ference shortly.
Before doing that, however, let us look at how changes in the variables in the for
mula affect the fair value of the futures contract. More important, we are interested in
how changes in the variables affect the premium of the futures contract over the index
value. This is what one is primarily concentrating on when trading market baskets.
As the index value itself rises, the fair value premium rises. For example, if 2
points is the fair premium when the index is at 160, as in the above example, then 4

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S34 Part V: Index Options and Futures
points would be the fair premium if the index were at 320 and all the other variables
remained the same. Conversely, as the index falls, the fair value of the premium
shrinks.
The premium rises and falls in direct correlation with the carrying rate as well
as with time remaining until expiration. Note that this statement is true for stock
options also, and for the same reason: The savings in carrying costs are greater when
rates are higher, or when one must hold for alonger time, or both. In the above
example, if one were to assume there were 6 months to expiration instead of 3, the
fair value of the premium would increase to 4 points from 2 points. Similarly, if the
time were decreased, the fair value would be smaller.
Some investors, primarily institutional investors, use the short-term T-bill rate
rather than the carrying rate in order to determine the futures fair value. The reason
they do that is to determine whether the money they have in cash is better off in Tbills or in an arbitrage strategy such as this. More will be said about this use of the Thill rate later.
Dividends Have an Inverse Correlation to the Premium Value.
An increase in the overall yield of the index will shrink the fair value of the futures
contract. This is because the futures holder does not get the dividends and therefore
the future is not as valuable because of the loss of dividends. Conversely, if dividend
yields fall, then the fair value of the premium increases. This is not the whole story
on dividends, however.
Recall that afew paragraphs ago, it was pointed out that the yield and the
amount of dividends are not exactly the same thing. This is because stocks don'tpay
their dividends in auniform manner. Rather than paying acontinuous yield as bonds
do, stocks normally pay their dividends in four lump sums ayear. This means that the
yield variable in the simple formula shown above should be replaced by the actual
amount of dividends remaining until expiration. This fact makes the computation of
the fair value of the index alittle more difficult. In order to do it accurately, one must
know the dividend amounts and ex-dividend dates of each of the stocks in the index.
Knowing all of this information is afar more formidable task than knowing the yield
of the index, since the yield is published weekly in several places. In fact, the servic
es of acomputer are required in order to compute the actual dividend on the larger
indices, where 100 or more stocks are involved.
As aresult, the actual formula changes slightly from the simple formula shown
above:
Actual Formula:
Futures fair value = Index x ( 1 + Time x Rate) - Dividends

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Chapter 30: Stock Index Hedging Strategies 537
Example: Suppose that OEX is trading at 364.50 and a September OEX future - if
one existed would have afair value of 367.10. That is, the future would command
apremium of 2.60. Not only should afuture trade with that theoretical premium, but
so should the "synthetic OEX" composed of puts and calls at the same strike. Hence,
the synthetic OEX constructed with options should trade at about 367.10 also.
That is, if the OEX Sep 365 call were selling for 4.60 and the Sep 365 put were
selling for 2.50, then the synthetic OEX constructed by the use of these two options
would be priced at 367.10. Recall that one determines the synthetic cost by adding
the strike, 365, to the call price, 4.60, and then subtracting the put price: 365 + 4.60
2.50 = 367.0. This synthetic price of 367.10 is literally the same as the theoretical
futures price of 367.10.
The same calculations can be applied to any index with listed options trading.
Let us now return to the broader subject at hand - trading market baskets of stocks
against futures.
PROGRAM TRADING
Two terms that conjure up images of the stock market crash in 1987 and other severe
price drops are "program trading" and "index arbitrage." Neither one by itself should
affect the stock market, since they are two-sided strategies - involving buying stocks
and selling futures. This two-sided aspect should have little effect on the market, the
oretically. However, in practice, it is often the case that trades are not executed simul
taneously, and the stock market takes ajump or adive.
Program trading is nothing more than trading futures against ageneral stock
portfolio. Index arbitrage is trading futures against the exact stocks that comprise an
index.
Later discussions will assume that one is trying to create or simulate the index
itself in order to hedge it with futures. This is the arbitrage approach. However, there
are many other types of stock positions that may be hedged with the futures. These
might include aportfolio of one'sown construction containing various stocks, or
might include agroup of stocks from which one wants to remove "market risk."
Normally, one would not own the makeup of any index, but rather would have aunique combination of stocks in his portfolio. Such an investor may want to use
futures to hedge what he does own.
One reason why an investor who owned stocks would want to sell index prod
ucts against them might be that he has turned bearish and would prefer to sell futures
rather than incur the costs involved with selling out his stock portfolio (and repur
chasing it later). Commission charges are quite small on futures transactions as com-

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538 Part V: Index Options and Futures
pared to an equal dollar amount of stock. By selling the futures on an index - say, the
S&P 500- he removes the "market risk" from his portfolio (assuming the S&P 500
represents the "market"). What is left over after selling the futures is the "tracking
error." The discrepancy between the movement of the general stock market and any
individual portfolio is called "tracking error." This investor will still make money if his
portfolio outperforms the S&P 500, but he will find that he did not completely elim
inate his losses if his portfolio underperforms the index. Note that if the market goes
up, the investor will not make any money except for possible tracking error in his
favor.
REMOVING THE MARKET RISK FROM A PORTFOLIO
Stock portfolios are diverse in nature, not :p.ecessarily reflecting the composition of
the index underlying the futures contracts. The characteristics of the individual
stocks must be taken into account, for they may move more quickly or more slowly
than "the market." Let us spend amoment to define this characteristic of stocks that
is so important.
VOLATILITY VERSUS BETA
Recall that when we originally defined volatility for use in the Black-Scholes model,
we stated that Beta was not acceptable because it was strictly ameasure of the cor
relation of astock'sperformance to that of the stock market and was not ameasure
of how fast the stock changed in price. Now we are concerned with how the stock'smovement relates to the market'sas awhole. This is the Beta.
Unfortunately, Beta is not as readily available to the option strategist as is
volatility. Many option traders merely have to punch abutton on their quote
machines and they can receive estimates of volatility. However, Beta estimates are
more difficult to obtain, and the ones that are available are often for very long time
periods, such as several years. These long-term Betas cannot be used for the pur
poses of the index hedging discussed in this chapter. Therefore, if one does not have
access to shorter-term Beta calculations, then he can approximate Beta by compar
ing an individual stock'svolatility with the market'svolatility.
Example: XYZ is arelatively volatile stock, having both an implied and historical
volatility of 36%. The overall stock market has avolatility of 15%. Therefore, one
could approximate the Beta of XYZ as
Beta approximation = 36/15 = 2.40

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Chapter 30: Stock Index Hedging Strategies 541
or adjusted capitalization, in order to compensate for the higher volatility of the port
folio.
Asimilar process can be used for far larger portfolios. The estimate of volatili
ty is, of course, crucial in these calculations, but as long as one is consistent in the
source from which he is extracting his volatilities, he should have areasonable hedge.
There is no way to judge the future performance of aportfolio of stocks versus the
ZYX Index. Thus, one has to expect arather large tracking error. In this type of
hedge, one hopes to keep the tracking error down to afew percent, which could be
several points in the futures contracts over along enough period of time. Of course,
the tracking error can work in one'sfavor also. The main point to recognize here is
that the vast majority of the risk of owning the portfolios has been eliminated by sell
ing the futures contracts. The upside profit potential of the portfolios has been elim
inated as well, but the premise was that the investor was bearish on the market.
Note that if the futures are overpriced when one enacts his bearishly-oriented
portfolio hedge, he will gain an additional advantage. This will act to offset some neg
ative tracking error, should such tracking error occur. However, there is no guaran
tee that overpriced futures will be available at the time that the investor or portfolio
manager decides to tum bearish. It is better to sell the futures and establish the
hedge at the time one turns bearish, rather than to wait and hope that they will
acquire alarge premium before one sells them.
HEDGING PORTFOLIOS WITH INDEX OPTIONS
As mentioned earlier, one could substitute options for futures wherever appropriate.
If he were going to sell futures, he could sell calls and buy puts instead. In this sec
tion, we are also going to take amore sophisticated look at using index options against
stock portfolios.
First, let us examine how the investor from the previous example might use
index options to hedge his portfolio.
Example: Suppose that an investor owns the same portfolio as in the previous exam
ple: 3,000 COCO, 5,000 UTIL, and 2,000 OIL. He decides to hedge with index
UVX, which has options worth $100 per point. Assume that the volatility of the UVX
is 15%. This investor would then compute his total adjusted capitalization in the same
manner as in the previous example, again arriving at afigure of $720,000.
Suppose that the UVX Index is at 175.60. This investor would want to hedge his
$720,000 of adjusted capitalization with 4,100 "shares" of UVX ($720,000 + 175.60).
Since a 1-point move in UVX options is worth $100, this means that one would sell
41 UVX calls and buy 41 UVX puts. He would probably use the 175 strike or possi-

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542 Part V: Index Options and Futures
bly the 180 strike, since those strikes are the ones whereby the calls have the least
chance for early assignment.
Where short options are involved, as with the calls in the above example, one
must be aware of the possibility of early assignment exposing the portfolio.
Consequently, if the marketplace has an equal premium on the futures and the "syn
thetic" UVX, one should sell the futures in that case, because there is no possibility
of unwanted assignment. However, if the options represent asynthetic price that is
more expensive than the futures, then using the options may be more attractive.
Example: Suppose that our same investor has decided to hedge his portfolio with its
$720,000 of adjusted capitalization. He is indifferent as to whether to use the ZYX
futures or the UV:Xoptions. He will use whichever one affords him the better oppor
tunity. The following table depicts the prices of the securities that he is considering,
as well as their fair values.
Current Fair Index
Security Price Value Price
ZYX Jun Future 180.50 180.65 178.65
UVX Jun 175 Call 5 5 175.60
UVX Jun 175 Put 2 21/2 175.60
UVX Jun 180 Call 21/2 21/2 175.60
UVX Jun 1 80 Put 41/2 5 175.60
This investor essentially has three choices: (1) to use the ZYX futures, (2) to use
the UVX options with the 175 strike, or (3) to use the UV:Xoptions with the 180
strike. Notice that the ZYX future is trading 15 cents below its fair value (180.50 vs.
180.65). The UV:X Index fair value, as shown by the fair values of the options, is
177.50. This can be computed by adding the call price to the strike and subtracting
the put price. In the case of either strike, the fair values indicate a UV:X Index fair
value of 177.50.
However, the actual markets are slightly out of line. When using the actual
prices, one sees that he can sell the UV:X Index synthetically for 178.00 whether he
uses the l 75'sor the 180's. Thus, by using the UV:Xoptions he can sell the UVX
"future" synthetically for ½ point over fair value, while the ZYX futures would have
to be sold at 15 cents under fair value. Thus, the options appear to be abetter choice
since 65 cents ( the 50 cents that the UV:Xoptions are overvalued plus the 15 cents
that the futures are undervalued) is probably enough of an edge to offset the possi
bility of early assignment.

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Chapter 30: Stock Index Hedging Strategies 543
With the futures having been eliminated as apossibility, the investor must now
choose which strike to use. Since he will be selling calls and buying puts, and since
either strike allows him to synthetically sell the UVX "future" at 178, he should
choose the 180 strike. This should be his choice because the 180 calls are out-of-the
money and thus less likely to be the object of an early assignment.
HEDGING WITH INDEX PUTS
Let us now move on to discuss ways of hedging in which acomplete hedge is not
established, but rather some risk is taken. The main difference between options and
futures is that futures lock in aprice, while options lock in aworst-case price (at
greater cost) but leave room for further profit potential. To see this, consider along
stock portfolio hedged by short futures. In this case, one eliminates his upside profit
potential except for positive tracking error. However, if he buys put options instead,
he expends money - thereby incurring agreater cost to himself than if he had used
futures - but he still has profit potential if the market rallies.
One could hedge along stock portfolio with options by either buying index puts
or selling index calls. Buying the puts is generally the more attractive strategy, espe
cially if the puts are cheap. In order to properly establish the hedge, it is not only nec
essary to adjust the dollars of stock in accordance with the Beta, but the deltas of the
options must be taken into account as well. The following example will demonstrate
the use of puts to hedge aportfolio of diverse stocks.
Example: Assume that an investor has the same portfolio of three stocks that was
used in aprevious example: 3,000 GOGO, 5,000 UTIL, and 2,000 OIL. He has
become somewhat bearish on the market in general and would like to hedge some of
his downside risk. However, he decides to use puts for the hedge just in case there is
afurther rally in the market.
The table from the earlier example is reprinted below, showing the adjusted
volatilities and capitalizations for each stock in the portfolio. The total adjusted cap
italization of the portfolio is $720,000, as before.
Adjusted Adjusted
Volatility Quantity Capitalization
Stock Volatility (Step l) Price Owned (Step 2)
GOGO .60 4.00 25 3,000 $300,000
UTIL .12 0.80 60 5,000 240,000
OIL .30 2.00 45 2,000 180,000
Total adjusted capitalization: $720,000 (step 3)

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Chapter 30: Stock Index Hedging Strategies 545
In this case, the number of puts is determined by using the same formula as in
the above example and then also dividing by the absolute value of the delta:
Puts to buy = $720,000 / (100 X 180) / 0.60
= 67
Cost of protection: 67 x $450 = $30,150
In this case, the portfolio manager is spending much more for the puts, but for
his additional expense, he acquires immediate protection for his portfolio.
Furthermore, there is some intrinsic value to the puts he bought (2 points, or $13,400
on 67 of them). If the UVX Index drops at all, these puts will immediately begin to
hedge his entire portfolio against loss. Of course, if the market rises, he loses his
much more expensive insurance cost.
When one uses options instead of futures to hedge his position, he must make
adjustments when the deltas of the options change. This was not the case when futures
were used; perhaps with futures, one might recalculate the adjusted capitalization of
the portfolio occasionally, but that would not be expected to affect the quantity of
futures to any great degree. With put options, however, the changing delta can make
the position delta short when the market declines, or can make it delta long if the mar
ket rises. This situation is akin to being long astraddle the position becomes delta
short as the market declines and becomes delta long as the market rises.
Basically, the adjustments would be same as those that along straddle holder
would make. If the market rallied, the position would be delta long because the delta
of the puts would have shrunk and they would not be providing the portfolio with as
much adjusted dollar protection as it needs. The investor might roll the puts up to ahigher strike, amove that essentially locks in some of his stock profits. Alternatively,
he could buy more puts at the current (low) strike to increase his protection.
Conversely, if the market had declined immediately after the position was
established, the investor will find himself delta short. The delta of the long puts will
have increased and there will actually be too much protection in place. His adjust
ment alternatives are still the same as those of along straddle holder - he might sell
some of the puts and thereby take aprofit on them while still providing the required
protection for the stock portfolio. Also, he might roll the puts down to alower strike,
although that is aless desirable alternative.
HEDGING WITH INDEX CALLS
Another strategy to protect astock portfolio is to establish aratio write using short
calls against the long stock. This is the opposite of using puts for protection, in that
it is more equivalent to being short astraddle.

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546 Part V: Index Options and Futures
Example: In the last example, the March 180 put had adelta of -0.60. The March
180 call should then have adelta of 0.40. If the portfolio manager wanted to hedge
his portfolio by ratio writing calls against it, he could use the same formula as in the
previous example:
Calls to sell = $720,000 I (100 x 180) I 0.40 = 100
He would sell 100 calls to hedge his portfolio.
Adjustments would be made in much the same manner as those that astraddle
seller would make. If the market rises, the delta of the calls will increase and the posi
tion will be delta short. One would probably buy calls in that case. Follow-up action
for an actual short straddle might dictate buying in some of the underlying security
rather than buying the calls, but that is not arealistic alternative in this case, since the
sample portfolio is probably stable.
If, on the other hand, the market declined after the short calls were sold against
the portfolio, the position would become delta long as the delta of the calls shrinks.
The normal action in that case would be to roll the calls down and reestablish the
proper amount of protection for the portfolio.
Overall, hedging the portfolio with short index calls does not present as attrac
tive aposition as hedging with long index puts. This is due mostly to the nature of
what the portfolio manager is trying to accomplish, as opposed to the relative merits
of long and short straddles. As was pointed out in previous chapters, straddle selling,
while risky, is an excellent strategy on astatistical basis. However, in this section we
are not dealing with astrategist who is going to go out and buy stocks and then write
index calls against them. Rather, we have an existing portfolio and the portfolio man
ager is becoming bearish on the market. Thus, the stock portfolio is afixed entity and
the index options or futures are being built around it for protection.
Long puts serve the purpose of protection far better than short calls, for the fol
lowing reasons. First, the types of adjustments that need to be made by astraddle
seller often involve buying stock or at least buying relatively deep in-the-money calls.
Aportfolio manager or investor holding aportfolio stock may not need or want to get
involved in amulti-optioned position. Second, with calls there is large risk to the
upside in case of alarge market rally. Someone holding aportfolio of stocks might be
willing to forego upside profits ( as in the sale of futures), but generally would be quite
upset to sustain large losses on the upside. Using puts, of course, leaves room for
upside profit potential. Third, there is risk of early assignment with short index calls,
although that is of minor significance in this case since the portfolio of stocks would
have been long in any case. Other calls could be written immediately on the day after
the assignment. The only real drawback to using the puts is that premium dollars are

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Cbapter 30: Stock Index Hedging Strategies 547
paid out and, if the market stabilizes, the time value decay will cause aloss on the
puts. If one actually suspects that such astabilization might occur, he should use
futures against his position instead of puts or calls.
INDEX ARBITRAGE
As previously stated, index arbitrage consists of buying virtually all of the stocks in an
index and selling futures against them, or vice versa. Whenever the futures on an
index are mispriced, as determined by comparing their actual value with their fair
value, there may be opportunities for arbitrage if the mispricing is large enough.
When futures are extremely overpriced: buy stocks, sell futures; or when futures are
underpriced: sell stocks, buy futures. In either case, the arbitrageur is attempting to
capture the differential between the fair value price of the futures contract and the
price at which he actually buys or sells the index. First, we will examine fully hedged
situations - ones in which the entire index is bought or sold. After that, we will exam
ine smaller sets of stocks that are designed to simulate the performance of the entire
index.
Hedging indices which contain fewer stocks is easier than hedging larger
indices. Hedging aprice-weighted index is probably the simplest type of hedge. As
examples, the same sample indices that were constructed in the previous chapter will
be used.
Whenever futures or index options trade on an index, it is possible to set up
market baskets for arbitrage. The trader should determine, in advance, how many
shares of each stock he will buy or sell in order to duplicate the index. In aprice
weighted index, of course, he will buy the same number of shares of each stock. In acapitalization-weighted index, he will be buying different numbers of shares of each
stock. Let us first look at how the number of shares to buy is determined. Then we
will discuss some of the nuances, such as monitoring bids and offers of the indices,
order execution, and others.
HOW MANY SHARES TO BUY
In advance of actually trading the stocks and futures or options, one should deter
mine exactly how many shares of each stock he will be buying in each index he plans
to arbitrage. Normally, one would decide in advance how many futures contracts or
option contracts he will trade at one time. Then the number of shares of stock to be
bought as ahedge can be determined as well. Essentially, one is going to hedge equal
dollar amounts - that is, he will buy enough stocks to offset the total dollar amount
represented by the index.

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Chapter 30: Stock Index Hedging Strategies S49
Actually he would probably buy 15,100 shares of each stock against the index,
and on every fourth "round" (100 futures vs. stock) would buy 15,000 shares. This
would be avery close approximation without dealing in odd lots.
The trader might also use index options as his hedge instead of futures. The
striking price of the options does not come into play in this situation. Typically, one
would fully hedge his position with the index options - that is, if he bought stock, he
would then sell calls and buy puts against that stock. Both the puts and the calls
would have the same strike and expiration month. This creates ariskless position.
This position is aconversion.
Example: Suppose that cash-based options trade on this index, and that these
options are worth $100 per point as are normal stock options - that is, an option is
essentially an option on 100 shares of the index. The trader is going to synthetically
short the index by buying 100 June 105 puts and selling 100 June 105 calls. Assume
that the index data is the same as in the previous example, that 0.60298 shares of each
stock comprise the index. How many shares would one hedge these 100 option syn
thetics with?
Number of shares = .60298 x 100 contracts x 100 shares/contract
= 6029.8 shares
Note that in the case of aprice-weighted index, neither the current index value
nor the striking price of the options involved (if options are involved) affects the
number of shares of stock to buy. Both of the above examples demonstrate the fact
that the number of shares to buy is strictly afunction of the divisor of the price
weighted index and the unit of trading of the option or future.
Hedging acapitalization-weighted index is more complicated, although the
technique revolves around determining the makeup of the index in terms of shares
of stock, just as the price-weighted examples above did. Recall that we could deter
mine the number of shares of stock in acapitalization-weighted index by dividing the
float of each stock by the divisor of the index. The general formula for the number of
shares of each stock to buy is:
Shares of stock N Shares of N F . Futures unit
= . . xutures quantity x . to buy mmdex of trading
We will use the fictional capitalization-weighted index from the previous chap
ter to illustrate these points.
Example: The following table identifies the pertinent facts about the fictional index,
including the important data: number of shares of each stock in the index.

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554 Part V: Index Options and Futures
Commissions on futures are generally charged only when the position is closed
out. Generally, afutures commission on an S&P 500 contract might be reduced to
something like $10 per contract for this type of hedging. Since 185.00, the index
value, represents 11500th of the value of the futures contract, we can reduce the
futures commission to an index-related number by dividing the actual dollar com
mission by 500. Thus, the futures commission is, in index terms, 10/500, or .02. The
total commission for entering and exiting the position is thus 0.266 of index value,
0.123 each for the purchase and sale of the stocks and .02 for the futures.
Net profit = Futures
price
Futures fair Commission
value costs
= 188.50 - 187.00 - 0.27
= 1.23
This absolute net profit number can be converted into arate of return by annualiz
ing the profit and dividing by the current index price. Suppose that there are
two months exactly remaining until expiration. Then the rate of return is computed
as follows:
Incremental = Net profit x ( 1/Time remaining)
rate of return Index price
1.23 X ( 12/2)
185.00
= 3.99%
For the two-month time period, his return is about 2h of one percent.
At first glance, arate of return of almost 4% does not seem like much. But what
we have computed here is an incremental rate of return. That is, this return is over
and above whatever rate we used in determining the fair value of the futures. Thus,
if an institution were going to invest its cash at the prevailing short-term rate, and that
rate were used to determine the futures fair value in the above example, then the
institution could earn an additional 4%, annualized, if it arbitraged the futures rather
than put its money in the short-term money market.
TRADE EXECUTION
Most customers are not concerned with how the trades are executed, for they give
the order to their broker and let him work out the details. However, for those who
are interested in the actual trade execution, ashort section dealing with that topic is
in order.

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558 Part V: Index Options and Futures
That is, he would buy back the ones he is short and sell the next series of futures. For
S&P 500 futures, this would mean rolling out 3 months, since that index has futures
that expire every 3 months. For the XMI futures and OEX index options, there are
monthly expirations, so one would only have to roll out 1 month if so desired.
It is asimple matter to determine if the roll is feasible: Simply compare the fair
value of the spread between the two futures in question. If the current market is
greater than the theoretical value of the spread, then aroll makes sense if one is long
stocks and short futures. If an arbitrageur had initially established his arbitrage when
futures were underpriced, he would be short stocks and long futures. In that case he
would look to roll forward to another month if the current market were less than the
theoretical value of the spread.
Example: With the S&P 500 Index at 416.50, the hedger is short the March future
that is trading at 417.50. The June future is trading at 421.50. Thus, there is a 4-point
spread between the March and June futures contracts.
Assume that the fair value formula shows that the fair value premium for the
March series is 35 cents and for the June series is 3.25. Thus, the fair value of the
spread is 2.90, the difference in the fair values.
Consequently, with the current market making the spread available at 4.00, one
should consider buying back his March futures and selling the June futures. The
rolling forward action may be accomplished via aspread order in the futures, much
like aspread order in options. This roll would leave the hedge established for anoth
er 3 months at an overpriced level.
Another way to close the position is to hold it to expiration and then sell out the
stocks as the cash-based index products expire. If one were to sell his entire stock
holding at the time the futures expire, he would be getting out of his hedge at exact
ly parity. That is, he sells his stocks at exactly the last sale of the index, and the futures
expire, being marked also to the last sale of the index.
For settlement purposes of index futures and options, the S&P 500 Index and
many other indices calculate the "last sale" from the opening prices of each stock on
the last day of trading. For some other indices, the last sale uses the closing price of
each stock.
Example: In anormal situation, if the S&P 500 index is trading at 415, say, then that
represents the index based on last sales of the stocks in the index. If one were to
attempt to buy all the stocks at their current offering price, however, he would prob
ably be paying approximately another 50 cents, or 415.50, for his market basket.
Similarly, if he were to sell all the stocks at the current bid price, then he would sell
the market basket at the equivalent of approximately 414.50.

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Chapter 30: Stock Index Hedging Strategies 559
However, on the last day of trading, the cash-based index product will expire at
the opening price of the index. If one were to sell out his entire market basket of
stocks at the current bid prices at the exact opening of trading on that day, he would
sell his market basket at the calculated last sale of the index. That is, he would actu
ally be creating the last sale price of the index himself, and would thereby be remov
ing his position at parity.
The problem with this is that it is correct theory, but difficult to put into prac
tice. For example, if one has several million dollars of stocks to sell, he cannot expect
the marketplace to absorb them easily when they are all being sold at the last minute
on a Friday afternoon. We will discuss this more fully momentarily, when we look at
the impact of stock index arbitrage on the stock market in general.
There is another interesting facet of the arbitrage strategy that combines the
spread between the near-term future and the next longest one with the idea of exe
cuting the stock portion of the arbitrage at the close of trading on the day the index
products expire. Use of this strategy actually allows one to enter and exit the hedge
without having to lose the spread between last sale and bid or last sale and offer in
either case. Suppose that one feels that he would set up the arbitrage for 3 months if
he could establish it at anet price of 1.50 over fair value. Furthermore, if the fair
value of the 3-month spread is 2.10, but it is currently trading at 3.60, then that rep
resents 1.50 over fair value. One initiates the position by buying the near-term future
and selling the longer-term future for anet credit of 3.60 points. At expiration of the
near-term future, rather than close out the spread, one buys the stocks that comprise
the index at the last sale of the trading day, thereby establishing his long stock posi
tion at the last sale price of the index at the same moment that his long futures expire.
The resultant position is long stocks and short futures that expire in 3 months at apremium of 3.60. Since the fair value of such a 3-month future should be 2.10, the
hedge is established at 1.50 over fair value. The position can be removed at expira
tion in the same manner as described in the previous paragraph, again saving the dif
ferential between last sale and the bids of the stocks in the index. Note that this strat
egy creates buying pressure on the stock market at expiration of the near-term side
of the spread, and selling pressure at the latter expiration.
The final way to exit from one'sposition is to remove it before expiration.
Sometimes, there are opportunities during the last two or three weeks before the
futures expire. If one hedged with long stock and short futures, the opportunities
to remove the hedge arise when the futures trade below fair value - perhaps even
at an actual discount to parity. If the futures never trade below fair value, but
instead continue to remain expensive, then rolling to the next expiration series is
often warranted.

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Cbapter 30: Stock Index Hedging Strategies 561
Another risk that the arbitrageur faces is that of changes in the dividend payout
of the stocks in the index. Suppose that he is long stocks and short futures. If there
are enough cuts in dividend payout, or dividend payments are delayed past the expi
ration date of the futures, then he will lose some of his return. Arbitrageurs who are
short stocks and long futures would have similar problems if dividend payout were
increased especially if alarge special dividend were declared by acompany that ,is
amajor component of the index - or payment dates were accelerated.
If one holds the arbitrage until expiration, he will be able to unwind it at parity.
However, if he decides to remove the arbitrage before expiration, he might incur
increased costs that would harm his projected return. Instead of selling his stocks at
the last sale of the index, as he is able to do on expiration day, he would have to sell
them on their bids, afact that could cost him asignificant portion of his profit.
In alater section, where we discuss hedging the futures with amarket basket of
stocks that does not exactly represent the entire index, we will be concerned with the
greatest risk of all, "tracking error" - the difference between the performance of the
index and the performance of the market basket of stocks being purchased.
IMPACT ON THE STOCK MARKET
The act of establishing and removing these hedge positions affects the stock market
on ashort-term basis. It is affected both before expiration and also at expiration of
the index products. We will examine both cases and will also address how the strate
gist can attempt to benefit from his knowledge of this situation.
IMPACT BEFORE EXPIRATION
When bullish speculators drive the price of futures too high, arbitrageurs will attempt
to move in to establish positions by buying stock and selling futures. This action will
cause the stock market to jump higher, especially since positions are normally estab
lished with great speed and stocks are bought at offering prices. Such acceleration on
the upside can move the market up by agreat deal in terms of the Dow-Jones
Industrials in amatter of minutes.
Conversely, if futures become cheap there is also the possibility that arbi
trageurs can drive the market downward. If positions are already established from
the long side (long stock, short futures), then arbitrageurs might decide to unwind
their positions if futures become too cheap. They would do this if futures were so
cheap that it becomes more profitable to remove the position, even though stocks
must be sold on their bid, rather than hold it to expiration or roll it to another series.

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S64 Part V: Index Options and Futures
However, the concept is still avalid one, and it is now generally being practiced
with the purchase of put options. The futures strategy was, in theory, superior to buy
ing puts because the portfolio manager was supposed to be able to collect the pre
mium from selling the futures. However, its breakdown came during the crash in that
it was impossible to buy the insurance when it was most needed - similar to attempt
ing to buy fire insurance while your house is burning down.
Currently, the portfolio manager buys puts to protect his portfolio. Many of
these puts are bought directly over-the-counter from major banks or brokerage hous
es, for they can be tailored directly to the portfolio manager'sliking. This practice
concerns regulators somewhat, because the major banks and brokerage houses that
are selling the puts are taking some risk, of course. They hedge the sales (with futures
or other puts), but regulators are concerned that, if another crash occurred, it would
be the writers of these puts who would be in the market selling futures. in amad fren
zy to protect their short put positions. Hopefully, the put sellers will be able to hedge
their positions properly without disturbing the stock market to any great degree.
IMPACT AT EXPIRATION - THE RUSH TO EXIT
Some traders persist in attempting to get out of their positions on the last day, at the
last minute. These traders are not normally professional arbitrageurs, but institu
tional clients who are large enough to practice market basket hedging. Moreover,
they have positions in indices whose options expire at the close of trading (OEX, for
example). If these hedgers have stock to sell, what generally happens is that some
traders begin to sell before the close, figuring they will get better prices by beating
the crowd to the exit. Thus, about an hour before the close, the market may begin to
drift down and then accelerate as the closing bell draws nearer. Finally, right on the
bell that announces the end of trading for the day, whatever stock has not yet been
sold will be sold on blocks - normally significantly lower than the previous last sale.
These depressed sales will make the index decline in price dramatically at the last
minute, when there is no longer an opportunity to trade against it.
These blocks are often purchased by large trading houses that advance their
own capital to take the hedgers out of their positions. The hedgers are generally cus
tomers of the block trading houses. Normally, on Monday, the market will rebound
somewhat and these blocks of stock can be sold back into the market at aprofit.
Whatever happens on Monday, though, is of little solace to the trader trapped
in the aftermath of the Friday action. For example, if one happened to be short puts
and the index was near the strike as the close of trading was drawing near on Friday
afternoon, he might decide to do nothing and merely allow the puts to expire, figur
ing that he would buy them back for asmall cost when he was assigned at expiration.

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Cbapter 30: Stock Index Hedging Strategies 565
However, this flurry of block prints on the close might drive the index down by 2 or
3 points! This is an extremely large move for the index, and the option trader has no
recourse as the options cease trading. An index composed of only afew stocks, such
as the Dow-Jones 30 Industrials, will fall most dramatically when these events occur,
although the OEX will drop heavily as well.
We have also previously seen that the late market action on expiration day might
be bullish. If institutional arbitrageurs have established the futures spread by being
long the short-term futures and short the next series, then they will be buyers of
stocks at the close of trading on expiration day. Additionally, if the only remaining
arbitrage positions at expiration are short stocks versus long futures, then there might
also be buying pressure at expiration.
As might be expected, these events have not gone unnoticed and have caused
some consternation among both regulators and traders. There have been accusations
that some traders particularly those with foreknowledge of the block prints to come
buy very cheap index options on the last afternoon of trading and then force those
options to become profitable by selling their clients' portfolios in the manner
described above.
The strategist cannot be concerned with whether someone is acting irrationally
or worse. Rather, he must decide how he will handle the situation should it occur.
The key is to try to determine the direction that the market will move at the close of
expiration day, if that is discernible. If futures have had alarge premium for along
period of time, then one must assume that many hedgers have long stock versus short
futures. Furthermore, even if futures subsequently trade below fair value, there will
still be some hedgers who have stubbornly kept their positions, waiting to roll. The
strategist should recognize that fact and take appropriate action late on the last day
of trading: Don'testablish bullish positions at that time and don'tallow positions that
are expiring that day to become too bullish. That is, if one is short puts and the index
is trading near the striking price of the puts, then buy them back.
Thus, the strategist must be aware of how the futures have traded during the
last 3 months in order to determine how he will address his positions on the last day.
Even with this information, there is no guarantee that one can exactly predict what
will happen at expiration unless one is privy to the actual stock buy and sell orders.
This order flow information is closely guarded and known only to the firms that will
be executing the orders, generally on behalf of institutions. Consequently, it is avery
risky strategy to attempt to apply this information for establishing positions on expi
ration day itself. That is, if one expects stock buy orders at expiration, he might
decide to buy some cheap, expiring calls for himself on the last afternoon of trading.
Conversely, if he expects stock selling, he might buy puts. Given the fact that such
movements are hard to predict, such aggressive strategies are not warranted.

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566 Part V: Index Options and Futures
SIMULATING AN INDEX
The discussion in the previous section assumed that one bought enough stocks to
duplicate the entire index. This is unfeasible for many investors for avariety of rea
sons, the most prominent being that the execution capability and capital required
prevent one from being able to duplicate the indices. Still, these traders obviously
would like to take advantage of theoretical pricing discrepancies in the futures con
tracts. The way to do this, in ahedged manner, would be to set up amarket basket
of asmall number of stocks, in order to have some sort of hedge against the futures
position.
In this section, we will demonstrate approaches that can be taken to hedge the
futures position with asmall number of stocks. This is different from when we looked
at how to hedge individualized portfolios with index futures or options, because we
are now going to try to duplicate the performance of the entire index, but do it with
asubset of stocks in the index. In either of these cases, amathematical technique
called regression analysis can be used to measure the performance of these portfo
lios or small market baskets. However, we will take asimpler approach that does not
require such sophisticated calculations, but will produce the desired results.
USING THE HIGH-CAPITALIZATION STOCKS
Recall that in acapitalization-weighted index, the stocks with the largest capitaliza
tions (price times float) have the most weight. In many such indices, there are ahandful of stocks that carry much more weight than the other stocks. Therefore, it is
often possible to try to create amarket basket of just those stocks as ahedge against
afutures position. While this type of basket will certainly not track the index exactly,
it will have adefinite positive correlation to the index.
What one essentially tries to accomplish with the smaller market basket is to
hedge dollars represented by the index with the same dollar amount of stocks. No
hedge works in which the total dollars involved are not nearly equal. Listed below are
the steps necessary to compute how many shares of each stock to buy in order to cre
ate a "mini-index" to hedge futures or options on alarger index:
1. Determine the percent of the large index to be hedged (OEX, NYSE, S&P 500,
etc.) that each stock comprises. This information is readily available from the
exchange on which the futures or options trade or can be calculated by the meth
ods shown in Chapter 29.
2. Determine the percent of the mini-index to be constructed that each stock com
prises, by inflating their relative percentages to total 100%.

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568 Part V: Index Options and Futures
Recall how these items are calculated: The number of shares of astock in the
index is that stock'sfloat divided by the divisor of the index. Also, the percent of the
index is the stock'scapitalization (float times price) divided by the total capitalization
of the index (this is step 1 above). Finally, the index value is the index'stotal capital
ization divided by the index divisor.
With this information, we can now construct amini-index that could be used to
hedge the UVX itself. Notice that these four stocks alone comprise 28.4% of the
entire UVX index. We would want each of these four stocks to have the same relative
weight within our mini-index as they do within the UVX itself. The sum of the capi
talizations of the four stocks in the above table as well as their relative percentages
are given in the following table.
Pct of Pct of
Index Mini-Index
Stock Copitolizotion (Step 1) (Step 2)
IBM 78,000,000 13.1% 46.2%
XON 34,000,000 5.7% 20.1%
GE 31,500,000 5.3% 18.6%
GM 25,500,000 4.3% 15.1%
Total: 169,000,000 28.4% 100.0%
The percent of the mini-index is each of the four stocks' capitalizations as aper
cent of the sum of their capitalizations (step 2 from above). There are two ways to
compute step 2. First, for IBM one would divide 78 million (its capitalization) by 169
million (the total capitalization). Second, using the percentages from step 1, divide
IBM'spercent, 13.1, by 28.4, the total percent. Either method gives the answer of
46.2 percent. We have now constructed the relative percentages of the mini-index
that each stock comprises. Note that they are in the same relationship to each other
as they are in the UVX itself. Now it is asimple matter to convert that percent into
shares of stock, once we decide how many futures contracts to trade against our mini
index.
When we know the total dollar amount of futures to hedge and we know the
percent of the mini-index that each stock comprises, we can compute each stock'scapitalization within the mini-index. Finally, we divide by that stock'sprice to see how
many shares of each stock to buy. Assume that we are going to use UVX options,
which are worth $100 per point, in lots of 50 options. The total dollar amount of the
index with the UVX at 170.25 would then be $851,250 (170.25 x 100 x 50). This
accomplishes step 3. The following table shows the calculations necessary to deter
mine how many shares of stock to buy against these 50 option contracts.

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574 Part V: Index Options and Futures
tion. He would both sell calls and buy puts with the same striking price in order to
create the hedge. This is similar to aconversion arbitrage.
When attempting to hedge the S&P 500, one could use the S&P 500 futures
options or the S&P 500 cash options, but that would not necessarily present amore
attractive situation than using the futures. On the other hand, there is not aliquid
S&P 100 (OEX) futures contract, so that when hedging that contract, one generally
uses the OEX options. As mentioned earlier, inter-index option spreads between var
ious indices, including the S&P 100 and 500, will be discussed in the next chapter.
There is not normally much difference as to which of the two is better at any
one time. However, since afull option hedge requires two executions (both selling
the call and buying the put), the futures probably have aslight advantage in that they
involve only asingle execution.
In order to substitute options for futures in any of the examples in these chap
ters on indices, one merely has to use the appropriate number of options as com
pared to the futures. If one were going to sell OEX calls instead of S&P 500 futures,
he would multiply the futures quantity by 5. Five is the multiple because S&P 500
futures are worth $250 per point while OEX options are worth $100 per point, and
because the S&P 500 Index (SPX) trades at twice the price of OEX (OEX split 2-for
lin November 1997). Thus, if an example calls for the sale of 20 S&P 500 futures,
then an equivalent hedge with OEX options would require 100 short calls and 100
long puts.
One could attempt to create less fully hedged positions by using the options
instead of the futures. For example, he might buy stocks and just write in-the-money
calls instead of selling futures. This would create acovered call write. He would still
use the same techniques to decide how much of each stock to buy, but he would have
downside risk if he decided not to buy the puts. Such aposition would be most attrac
tive when the calls are very overpriced.
Similarly, one might try to buy the stocks and buy slightly in-the-money puts
without selling the calls. This position is asynthetic long call; it would have upside
profit potential and would lose if the index fell, but would have limited risk. Such aposition might be established when puts are cheap and calls are expensive.
TRADING THE TRACKING ERROR
Another reason that one might sell futures against aportfolio of stocks is to actually
attempt to capture the tracking error. If one were bullish on oil drilling stocks, for
example, and expected them to outperform the general market, he might buy sever-

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Chapter 30: Stock Index Hedging Strategies 577
that leads the investor to believe that the group no longer has the potential to out
perform the market.
If the futures are underpriced when one begins to investigate this strategy, he
should not establish the position. What is gained in tracking error could be lost in
theoretical value of the futures. Since one is establishing both sides of the hedge
(stocks and futures) at essentially the same time, he can afford to wait until the
futures are attractively priced. This is not to say that the futures must be overpriced
when the position is established, although that fact would be an enhancement to the
position.
If one thinks that aparticular group will underperform the market, he merely
needs to decide how many shares of each stock to sell short and then can determine
how many futures to buy against the short sales in order to try to capture the track
ing error. If one decides to capture the negative tracking error in this manner, he
must be careful not to buy overpriced futures. Rather, he should wait for the futures
to be near fair value in order to establish the position.
COLLATERAL REQUIREMENTS
In any of the portfolio hedging strategies that we have discussed in this section, there
is no reduction in margin requirements for either the futures or the options. That is,
the stocks must be paid for in full or margined as if they had no protection against
them, and the hedging security - the futures or options - must be margined fully as
well. Long puts would have to be paid for in full, short futures would require their
normal margin and would be marked to the market via variation margin, and short
calls would have to be margined as naked and would also be marked to the market.
Atrader who has not margined his stocks could use them as collateral for the naked
call requirements if he so desired.
SUMMARY
There have been two major impacts of index futures and options. One is that they
allow atrader to "buy the market" without having to select individual stocks. This is
important because many traders have some idea of the direction in which the mar
ket is heading, but may not be able to pick individual stocks well. The other, perhaps
more major, impact is that large holders of stocks can now hedge their portfolios
without nearly as much difficulty. The use of these futures and options against actu
al stock indices - real or simulated - has introduced astrategy into the marketplace
that did not previously exist. The versatility of these derivative securities is evidenced

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574 Part V: Index Options and Futures
tion. He would both sell calls and buy puts with the same striking price in order to
create the hedge. This is similar to aconversion arbitrage.
When attempting to hedge the S&P 500, one could use the S&P 500 futures
options or the S&P 500 cash options, but that would not necessarily present amore
attractive situation than using the futures. On the other hand, there is not aliquid
S&P 100 (OEX) futures contract, so that when hedging that contract, one generally
uses the OEX options. As mentioned earlier, inter-index option spreads between var
ious indices, including the S&P 100 and 500, will be discussed in the next chapter.
There is not normally much difference as to which of the two is better at any
one time. However, since afull option hedge requires two executions (both selling
the call and buying the put), the futures probably have aslight advantage in that they
involve only asingle execution.
In order to substitute options for futures in any of the examples in these chap
ters on indices, one merely has to use the appropriate number of options as com
pared to the futures. If one were going to sell OEX calls instead of S&P 500 futures,
he would multiply the futures quantity by 5. Five is the multiple because S&P 500
futures are worth $250 per point while OEX options are worth $100 per point, and
because the S&P 500 Index (SPX) trades at twice the price of OEX (OEX split 2-for
lin November 1997). Thus, if an example calls for the sale of 20 S&P 500 futures,
then an equivalent hedge with OEX options would require 100 short calls and 100
long puts.
One could attempt to create less fully hedged positions by using the options
instead of the futures. For example, he might buy stocks and just write in-the-money
calls instead of selling futures. This would create acovered call write. He would still
use the same techniques to decide how much of each stock to buy, but he would have
downside risk if he decided not to buy the puts. Such aposition would be most attrac
tive when the calls are very overpriced.
Similarly, one might ti:yto buy the stocks and buy slightly in-the-money puts
without selling the calls. This position is asynthetic long call; it would have upside
profit potential and would lose if the index fell, but would have limited risk. Such aposition might be established when puts are cheap and calls are expensive.
TRADING THE TRACKING ERROR
Another reason that one might sell futures against aportfolio of stocks is to actually
attempt to capture the tracking error. If one were bullish on oil drilling stocks, for
example, and expected them to outperform the general market, he might buy sever-

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Cbapter 30: Stock Index Hedging Strategies 577
that leads the investor to believe that the group no longer has the potential to out
perform the market.
If the futures are underpriced when one begins to investigate this strategy, he
should not establish the position. What is gained in tracking error could be lost in
theoretical value of the futures. Since one is establishing both sides of the hedge
(stocks and futures) at essentially the same time, he can afford to wait until the
futures are attractively priced. This is not to say that the futures must be overpriced
when the position is established, although that fact would be an enhancement to the
position.
If one thinks that aparticular group will underperform the market, he merely
needs to decide how many shares of each stock to sell short and then can determine
how many futures to buy against the short sales in order to try to capture the track
ing error. If one decides to capture the negative tracking error in this manner, he
must be careful not to buy overpriced futures. Rather, he should wait for the futures
to be near fair value in order to establish the position.
COLLATERAL REQUIREMENTS
In any of the portfolio hedging strategies that we have discussed in this section, there
is no reduction in margin requirements for either the futures or the options. That is,
the stocks must be paid for in full or margined as if they had no protection against
them, and the hedging security - the futures or options - must be margined fully as
well. Long puts would have to be paid for in full, short futures would require their
normal margin and would be marked to the market via variation margin, and short
calls would have to be margined as naked and would also be marked to the market.
Atrader who has not margined his stocks could use them as collateral for the naked
call requirements if he so desired.
SUMMARY
There have been two major impacts of index futures and options. One is that they
allow atrader to "buy the market" without having to select individual stocks. This is
important because many traders have some idea of the direction in which the mar
ket is heading, but may not be able to pick individual stocks well. The other, perhaps
more major, impact is that large holders of stocks can now hedge their portfolios
without nearly as much difficulty. The use of these futures and options against actu
al stock indices - real or simulated has introduced astrategy into the marketplace
that did not previously exist. The versatility of these derivative securities is evidenced

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CHAPTER 31
Index Spreading
In this chapter, we will look at strategies oriented toward spreading one index against
another. This may be done with either futures or options. In some cases, this is almost
an arbitrage because the indices track each other quite well. In others, it is ahigh
risk venture because the indices bear little relationship to each other. In any case, if
the futures relationship between the two indices is out of line, one may have an extra
advantage.
INTER-INDEX SPREADING
There are general relationships between many stock indices, both in the United
States and worldwide. The idea behind inter-index spreading is often to capitalize on
one'sview of the relationships between the two indices without having to actually
predict the direction of the stock market. Note that this is often the philosophy
behind many option spreads as well.
Sometimes an analyst will say that he expects small-cap stocks to outperform
large-cap stocks. This analyst should consider using an inter-index spread between
the S&P 500 Index and the Value Line Index (which contains many small stocks), or
perhaps between the S&Pand a NASDAQ-based index. If he buys the index that is
comprised of smaller stocks and sells the S&P 500 Index, he will make money if his
analysis is right, regardless of whether the stock market goes up or down. All he wants
is for the index he is long to outperform the index he is short.
Occasionally, the futures or options on these indices are mispriced in compar
ison to the way the indices are priced. When this happens, one may be able to cap
italize on the pricing discrepancy. At times, the spread between the index products
579

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580 Part V: Index Options and Futures
on two indices can trade at significantly different price levels from the spread
between the two indices themselves. When this happens, an inter-index spread
becomes feasible.
The margin requirements for these spreads are often reduced because margin
rules recognize that futures on one index can be hedged by futures on another index.
The general rule of thumb as far as selecting afutures spread to establish
between two indices is to compare the price difference in the respective futures to
the actual price difference in the indices themselves. If the difference in the futures
is substantially different from the difference in the cash prices of the indices, then
one would sell the more expensive future and buy the cheaper one. Several specific
spreads are discussed in this chapter.
Regardless of whether one is entering into the spread because he is trying to
predict the relationships between the cash indices, or because he knows the two
respective futures are out of line, he must decide in what ratio he wants to establish
the spread. There are two lines of thinking on this subject. The first is to merely buy
one future and sell one future (on two different indices, of course). Many chart books
and spread history charts are graphed in this manner - they compare one index to
another index on aone-for-one basis.
Example: Aspreader wants to buy the ZYX Index futures and sell ABX futures
against them. They are both trading in units of $500 per point, but ZYX is currently
at 175.00 while ABX is at 130.00. Thus, the current differential is 45.00 points. This
spreader would want the spread to widen to something larger in order to make
money. The following profit table shows how he could make a $2,500 profit if the
spread widens to 50.00 points, no matter which way the market goes.
Market ZYX ZYX ABX ABX Total
Direction Price Profit Price Profit Profit
up 185.00 +$5,000 135.00 -$2,500 +$2,500
neutral 177.00 + 1,000 127.00 + 1,500 + 2,500
down 160.00 - 7,500 110.00 + 10,000 + 2,500
Notice that in each case, the difference in the prices of the indices ZYX and ABX is
50.00 points. The profit is the same regardless of whether the general stock market
rose, was relatively unchanged, or fell.
The $2,500 profit is the five points of profit that the spreader makes by buying
the spread of 45.00 and selling it at 50.00 (5.00 points x $500 per point = $2,500).
The second approach to index spreading is to use aratio of the two indices. This
approach is often taken when the two indices trade at substantially different prices.

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Chpt,r 31: Index Spreading 581
J!"<>rexample, if one index sells for twice the price of the other, and if both indices
have similar volatilities, then aone-to-one spread gives too much weight to the
higher-priced index. Atwo-to-one ratio would be better, for that would give equal
weighting to the spread between the indices.
Example: UVX is an index of stock prices that is currently priced at 100.00. ZYX,
another index, is priced at 200.00. The two indices have some similarities and, there
fore, aspreader might want to trade one against the other. They also display similar
volatilities.
If one were to buy one UVX future and sell one ZYX future, his spread would
be too heavily oriented to ZYX price movement. The following table displays that,
showing that if both indices have similar percentage movements, the profit of the
one-by-one spread is dominated by the profit or loss in the ZYX future. Assume both
fi1tures are worth $500 per point.
Market ZYX ZYX uvx uvx Total
Direction Price Profit Price Profit Profit
up 20% 240 -$20,000 120 +$10,000 -$10,000
up 10% 220 - 10,000 110 + 5,000 - 5,000
down 10% 180 + 10,000 90 - 5,000 + 5,000
down 20% 160 + 20,000 80 - 10,000 + 10,000
This is not much of ahedge. If one wanted aposition that reflected the movement
of the ZYX index, he could merely trade the ZYX futures and not bother with aspread.
If, however, one had used the ratio of the indices to decide how many futures
to buy and sell, he would have amore neutral position. In this example, he would buy
two UVX futures and sell one ZYX future.
Proponents of using the ratio of indices are attempting strictly to capture any
performance difference between the two indices. They are not trying to predict the
overall direction of the stock market.
Technically, the proper ratio should also include the volatility of the two indices,
because that is also afactor in determining how fast they move in relationship to each
other.

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Chapter 31: Index Spreading 583
slightly more volatile than these two larger indices, and also has more technology and
less basic industry such as steel and chemicals. The OEX movement definitely has
good correlation to the S&P 500. The S&P 500 Index (SPX) currently trades at about
twice the "speed" of the OEX Index. This has been true since OEX split 2-for-lin
November 1997. Aone-point move in SPX is approximately equal to amove of 7.5
points in the Dow-Jones Industrial Average, while aone-point move in OEX is
approximately equal to 15 Dow points.
In general, it is easier to spread the indices by using futures rather than options,
although only the S&P 500 Index has liquid futures markets. (There is amini-Value
Line futures market, as well as Dow-Jones futures - both of which are fairly illiq
uid - but no futures trade on OEX.) One reason for this is liquidity - the index
futures markets have large open interest. Another reason is tightness of markets.
Futures markets are normally 5 or 10 cents wide, while option markets are 10 cents
wide or more. Moreover, an option position that is afull synthetic requires both aput
and acall. Thus, the spread in the option quotes comes into play twice.
The Japanese stock market can be spread against the U.S. markets by spread
ing a U.S. index against Nikkei futures or futures options, traded on the Chicago
Mere, or against JPN options, traded on the AMEX.
INTER-INDEX SPREADS USING OPTIONS
As mentioned before, it may not be as efficient to try to use options in lieu of the
actual futures spreads since the futures are more liquid. However, there are still
many applications of the inter-index strategy using options.
OEX versus S&P 500. The OEX cash-based index options are the most liquid
option contracts. Thus, any inter-index spread involving the OEX and other indices
must include the OEX options.
The S&P 100 was first introduced in 1982 by the CBOE. It was originally
intended to be an S&P 500 look-alike whose characteristics would allow investors
who did not want to trade futures ( S&P 500 futures) the opportunity to be able to
trade abroad index by offering options on the OEX. Initially, the index was known as
the CBOE 100, but later the CBOE and Standard and Poor's Corp. reached an
agreement whereby the index would be added to S&P'sarray of indices. It was then
renamed the S&P 100.
Initially, the two indices traded at about the same price. The OEX was the more
expensive of the two for awhile in the early 1980s. As the bull market of the 1980s
matured, the S&P 500 ground its way higher, eventually reaching aprice nearly 30
points higher than OEX. As one can see, there is ample room for movement in the
spread between the cash indices.

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584 Part V: Index Options and Futures
The S&P 500 has more stocks, and while both indices are capitalization-weight
ed, 500 stocks include many smaller stocks than the 100-stock index. Also, the OEX
is more heavily weighted by technology issues and is therefore slightly more volatile.
Finally, the OEX does not contain several stocks that are heavily weighted in the S&P
500 because those stocks do not have options listed on the CBOE: Procter and
Gamble, Philip Morris, and Royal Dutch, to name afew. There are two ways to
approach this spread - either from the perspective of the derivative products differ
ential or by attempting to predict the cash spread.
In actual practice, most market-makers in the OEX use the S&P 500 futures to
hedge with. Therefore, if the futures have alarger premium - are overpriced - then
the OEX calls will be expensive and the puts will be cheap. Thus, there is not as much
of an opportunity to establish an inter-index spread in which the derivative products
(futures and options in this case) spread differs significantly from the cash spread.
That is, the derivative products spread will generally follow the cash spread very
closely, because of the number of people trading the spread for hedging purposes.
Nevertheless, the application does arise, albeit infrequently, to spread the
premium of the derivative products in two indices on strictly ahedged basis with
out trying to predict the direction of movement of the cash indices. In order to
establish such aspread, one would take aposition in futures and an opposite posi
tion in both the puts and calls on OEX. Due to the way that options must be exe
cuted, one cannot expect the same speed of execution that he can with the futures,
unless he is trading from the OEX pit itself. Therefore, there is more of an execu
tion risk with this spread. Consequently, most of this type of inter-index spreading
is done by the market-makers themselves. It is much more difficult for upstairs
traders and customers.
USING OPTIONS IN INDEX SPREADS
Whenever both indices have options, as most do, the strategist may find that he can
use the options to his advantage. This does not mean merely that he can use asyn
thetic option position as asubstitute for the futures position (long call, short put at
the same strike instead of long futures, for example). There are at least two other
alternatives with options. First, he could use an in-the-money option as asubstitute
for the future. Second, he could use the options' delta to construct amore leveraged
spread. These alternatives are best used when one is interested in trading the spread
between the cash indices - they are not really amenable to the short-term strategy of
spreading the premiums between the futures.
Using in-the-money options as asubstitute for futures gives one an additional
advantage: If the cash indices move far enough in either direction, the spreader could

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O,apter 31: Index Spreading 585
still make money, even if he was wrong in his prediction of the relationship of the
cash indices.
Example: The following prices exist:
ZYX: 175.00
UVX: 150.00
ZYX Dec 185 put: 10½
UVX Dec 140 call: 11
Suppose that one wants to buy the UVX index and sell the ZYX index. He
expects the spread between the two - currently at 25 points - to narrow. He could
buy the UVX futures and sell the ZYX futures. However, suppose that instead he buys
the ZYX put and buys the UVX call.
The time value of the Dec 185 put is 1/2 point and that of the Dec 140 call is 1
point. This is arelatively small amount of time value premium. Therefore, the com
bination would have results very nearly the same as the futures spread, as long as
both options remain in-the-money; the only difference would be that the futures
spread would outperform by the amount of the time premium paid.
Even though he pays some time value premium for this long option combina
tion, the investor has the opportunity to make larger profits than he would with the
futures spread. In fact, he could even make aprofit if the cash spread widens, if the
indices are volatile. To see this, suppose that after alarge upward move by the over
all market, the following prices exist:
ZYX: 200.00
UVX: 170.00
ZYX Dec 185 put: 0 ( virtually worthless)
UVX Dec 140 call: 30
The combination that was originally purchased for 21 ½ points is now worth 30,
so the spread has made money. But observe what has happened to the cash spread:
It has widened to 30 points, from the original price of 25. This is amovement in the
opposite direction from what was desired, yet the option position still made money.
The reason that the option combination in the example was able to make
money, even though the cash spread moved unfavorably, is because both indices rose
so much in price. The puts that were owned eventually became worthless, but the
long call continued to make money as the market rose. This is asituation that is very
similar to owning along strangle (long put and call with different strikes), except that

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586 Part V: Index Options and Futures
the put and call are based on different underlying indices. This concept is discussed
in more detail in Chapter 35 on futures spreads.
The second way to use options in index spreading is to use options that are less
deeply in-the-money. In such acase, one must use the deltas of the options in order
to accurately compute the proper hedge. He would calculate the number of options
to buy and sell by using the formula given previously for the ratio of the indices,
which incorporates both price and volatility, and then multiplying by afactor to
include delta.
where
vi is the volatility of index i
Pi is the price of index iui is the unit of trading
and di is the delta of the selected option on index i
Example: The following data is known:
ZYX: 175.00, volatility= 20%
UVX: 150.00, volatility = 15%
ZYX Dec 175 put: 7, delta= - .45, worth $500/pt.
UVX Dec 150 call: 5, delta= .52, worth $100/pt
Suppose one decides that he wants to set up aposition that will profit if the
spread between the two cash indices shrinks. Rather than use the deeply in-the
money options, he now decides to use the at-the-money options. He would use the
option ratio formula to determine how many puts and calls to buy. (Ignore the put'snegative delta for the purposes of this formula.)
.20 175.00 500 .45 Option Ratio= -x ---x - x - = 6 731 .15 150.00 100 .52 .
He would buy nearly 7 UVX calls for every ZYX put purchased.
In the previous example, using in-the-money options, one had avery small
expense for time value premium and could profit if the indices were volatile, even if
the cash spread did not shrink. This position has agreat deal of time value premium
e:x--pense, but could make profits on smaller moves by the indices. Of course, either
one could profit if the cash indices moved favorably.

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Cl,apter 31: Index Spreading 587
Volatility Differential. Atheoretical "edge" that sometimes appears is that of
volatility differential. If two indices are supposed to have essentially the same volatil
ity, or at least arelationship in their volatilities, then one might be able to establish
an option spread if that relationship gets out ofline. In such acase, the options might
actually show up as fair-valued on both indices, so that the disparity is in the volatili
ty differential, and not in the pricing of the options.
OEX and SPX options trade with essentially the same implied volatility.
Thus, if one index'soptions are trading with ahigher implied volatility than the
other's, apotential spread might exist. Normally, one would want the differential
in implied volatilities to be at least 2% apart before establishing the spread for
volatility reasons.
In any case, whether establishing the spread because one thinks the cash index
relationship is going to change, or because the options on one index are expensive
with respect to the options on the other index, or because of the disparity in volatili
ties, the spreader must use the deltas of the options and the price ratio and volatili
ties of the indices in setting up the spread.
Striking Price Differential. The index relationships can also be used by the
option trader in another way. When an option spread is being established with
options whose strikes are not near the current index prices - that is, they are rela
tively deeply in- or out-of-the-money- one can use the ratio between the indices to
determine which strikes are equivalent.
Example: ZYX is trading at 250 and the ZYX July 270 call is overpriced. An option
strategist might want to sell that call and hedge it with acall on another index.
Suppose he notices that calls on the UVX Index are trading at approximately fair
value with the UVX Index at 175. What UVX strike should he buy to be equivalent
to the ZYX 270 strike?
One can multiply the ZYX strike, 270, by the ratio of the indices to arrive at the
UVX strike to use:
UVX strike= 270 x (175/250)
= 189.00
So he would buy the UVX July 190 calls to hedge. The exact number of calls to
buy would be determined by the formula given previously for option ratio.

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588
SUMMARY
Part V: Index Options and Futures
This concludes the discussion of index spreading. The above examples are intended
to be an overview of the most usable strategies in the complex universe of index
spreading. The multitude of strategies involving inter-index and intra-index spreads
cannot all be fully described. In fact, one'simagination can be put to good use in
designing and implementing new strategies as market conditions change and as the
emotion in the marketplace drives the premium on the futures contracts.
Often one can discern ausable strategy by observation. Watch how two popu
lar indices trade with respect to each other and observe how the options on the two
indices are related. If, at alater time, one notices that the relationship is changing,
perhaps aspread between the indices is warranted. One could use the NASDAQ
based indices, such as the NASDAQ-100 (NDX) or smaller indices based on it (QQQ
or MNX). Sector indices can be used as well. This brings into play afairly large num
ber of indices with listed options (few, if any, of which have futures), such as the
Semiconductor Index (SOX), the Oil & Gas Index (XOI), the Gold and Silver Index
(XAU), etc. The key point to remember is that the index option and futures world is
more diverse than that of stock options. Stock option strategies, once learned or
observed, apply equally well to all stocks. Such is not the case with index spreading
strategies. The diversification means that there are more profit opportunities that are
recognized by fewer people than is the case with stock options. The reader is thus
challenged to build upon the concepts described in this part of the book.

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590 Part V: Index Options and Futures
The discussion in this chapter concentrates on the structured products that are
listed and traded on the major stock exchanges. Abroader array of products -
typically called exotic options - is traded over-the-counter. These can be very com
plicated, especially with respect to currency and bond options. It is not our intent to
discuss exotic options, although the approaches to valuing the structured products
that are presented in this chapter can easily be applied to the overall valuation of
many types of exotic products. Also, the comments at the end of the chapter regard
ing where to find information about these products may prove useful for those seek
ing further information about either listed structured products or exotic options.
Part I: "Riskless" Ownership
of a Stock or Index
THE "STRUCTURE" OF A STRUCTURED PRODUCT
At many of the major institutional banks and brokerages, people are employed who
design structured products. They are often called financial engineers because they
take existing financial products and build something new with them. The result is
packaged as afund of sorts (or aunit trust, perhaps), and shares are sold to the pub
lic. Not only that, but the shares are then listed on the American or New York Stock
Exchanges and can be traded just like any other stock. These attributes make the
structured product avery desirable investment. An example will show how ageneric
index structured product might look.
Example: Let'slook at the structured index product to see how it might be designed
and then how it might be sold to the public. Suppose that the designers believe there
is demand for an index product that has these characteristics:
1. This "index product" will be issued at alow price - say, $10 per share.
2. The product will have amaturity date - say, seven years hence.
3. The owner of these shares can redeem them at their maturity date for the
greater of either a) $10 per share orb) the percentage appreciation of the
S&P 500 index over that seven-year time period. That is, if the S&Pdoubles
over the seven years, then the shares can be redeemed for double their issue
price, or $20.
Thus, this product has no price risk! The holder gets his $10 back in the worst
case (except for credit risk, which will be addressed in aminute).
Moreover, these shares will trade in the open market during the seven years, so
that if the holder wants to exit at any time, he can do so. Perhaps the S&Phas rallied

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