e 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 a profit.
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 a small cost when he was assigned at expiration.
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 a few 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 a large premium for a long
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't establish bullish positions at that time and don't allow 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 a very
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.
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 a variety 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 a hedged manner, would be to set up a market basket
of a small 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 a small 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
a subset of stocks in the index. In either of these cases, a mathematical technique
called regression analysis can be used to measure the performance of these portfo
lios or small market baskets. However, we will take a simpler approach that does not
require such sophisticated calculations, but will produce the desired results.
USING THE HIGH-CAPITALIZATION STOCKS
Recall that in a capitalization-weighted index, the stocks with the largest capitaliza
tions (price times float) have the most weight. In many such indices, there are a
handful of stocks that carry much more weight than the other stocks. Therefore, it is
often possible to try to create a market basket of just those stocks as a hedge against
a futures position. While this type of basket will certainly not track the index exactly,
it will have a definite 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 st


nly not track the index exactly,
it will have a definite 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 a larger 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%.
Cltapter 30: Stock Index Hedging Strategies 567
3. Decide the total dollar amount of the index to be traded at one time: index value
times futures or option quantity times unit of trading in the futures.
4. Multiply the total dollar amount from step 3 by each individual percentage from
step 2 to determine how many dollars of each stock to buy.
5. Divide the result from step 4 by the price of the stock in order to determine how
many shares to buy.
These steps will result in the construction of a mini-index consisting of a small
number of stocks that are grouped together in relative proportion to their weights in
the larger index, and have a total dollar amount sufficient to trade against the desired
futures or options trading lot. This approach ignores volatility. Even without account
ing for volatility, this approach is reasonable when using high-capitalization stocks to
hedge a broad-based index.
Among the largest-capitalization stocks are International Business Machines
(IBM), Exxon (XON), General Electric (GE), and General Motors (GM). As a result,
these four form the foundation of many small market baskets. All four are in the OEX
(S&P 100), the S&P 500, and other major capitalization-weighted indices. As a first
example, let us examine how one would hedge the futures using these four stocks
only, according to the five steps outlined above.
Example: Suppose we are attempting to create a hedge for a fictional index, the
UVX, by using IBM, XON, GM, and GE. The following table gives certain informa
tion that will be necessary in computing how many shares of each stock to use in the
small basket.
Stock Float
IBM 600,000
XON 850,000
CE 450,000
GM 300,000
UVX price: 170.25
Divisor: 3,500,000
Shores in
Price Index
130 0.171
40 0.243
70 0.129
85 0.086
Total capitalization: 595,875,000 (price times divisor)
Pct of
Index
Capitalization (Step 1)
78,000,000 13.1%
34,000,000 5.7%
31,500,000 5.3%
25,500,000 4.3%
28.4%
568 Part V: Index Options and Futures
Recall how these items are calculated: The number of shares of a stock in the
index is that stock's float divided by the divisor of the index. Also, the percent of the
index is the stock's capitalization (float times price) divided by the total capitalization
of the index (this is step 1 above). Finally, the index value is the index's total capital
ization divided by the index divisor.
With this information, we can now construct a mini-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 a per
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's percent, 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 a simple 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's
capitalization within the mini-index. Finally, we divide by that stock's price 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.
0.,ter 30: Stock Index Hedging Strategies 569
Capitalization Shares
Pct of in Mini-Index to Buy
Stock Mini-Index (Step 4) Price (Step 5)
IBM 46.2% 393,277 130 3,025
XON 20.1% 171,102 40 4,277
GE 18.6% 158,332 70 2,261
GM 15.1% 128,539 85 1,512
Total: 100.0% 851,250
Note that the capitalization of each stock in the mini-index is determined by multi
plying the desired trading lot ($851,250) by the percent of the mini-index that that
stock comprises. This completes step 4, and step 5 follows: The number of shares of
each stock to buy is then determined by dividing that numb

eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf


40 4,277
GE 18.6% 158,332 70 2,261
GM 15.1% 128,539 85 1,512
Total: 100.0% 851,250
Note that the capitalization of each stock in the mini-index is determined by multi
plying the desired trading lot ($851,250) by the percent of the mini-index that that
stock comprises. This completes step 4, and step 5 follows: The number of shares of
each stock to buy is then determined by dividing that number by the price of the
stock. For example, the calculation for IBM in the above table would be $851,250 x
.462 = $393,277; then $393,277/130 = 3,025.
Thus, one could attempt to hedge 50 UVX option contracts with the above
amounts of each of the four stocks. As a matter of practicality, one would not buy the
odd lots, but would probably round off each stock quantity to round lots: 3,000 IBM,
4,300 XON, 2,300 GE, and 1,500 GM.
As the prices of the stocks in the mini-basket change, the mini-basket needs to
be recalculated. This is because the current prices of the stocks in the index were
used to compute the mini-index. Thus, as the prices of the stocks change, the com
position of our mini-index will begin to deviate from the composition of the UVX.
Example: Suppose that oil stocks do poorly and XON falls to 35 (it was 40 when we
constructed the mini-index), while the other stocks are the same price as in the pre
vious example. Finally, suppose that the overall UV:X is unchanged at 170.25, even
though Exxon has changed substantially. We must recalculate step 1: Determine the
percent that each stock is of the UV:X. Assume the divisor is unchanged and each
stock's float is unchanged, so the percent is the price times the float divided by the
total capitalization (595,875,000).
Percent Percent of
Float Capitalization of Index Mini-Index
Stock Price (OOOs) (Millions) (Step l) (Step 2)
IBM 130 600 78.00 13.1% 47.3%
XON 35 850 29.75 5.0% 18.1%
GE 70 450 31.50 5.3% 19.1%
GM 85 300 25.50 4.3% 15.5%
Total: 164.75 27.7% 100.0%
570 Part V: Index Options and Futures
Note that the percent that Exxon comprises of the UVX as well as of the mini-index
has fallen. All three of the other stock's percentages have increased proportionately.
These percentage changes reflect the changes in the stock prices. Since we assumed
the UVX is unchanged, the capitalization of the desired mini-index is still $851,250
(170.25 x $100 per point x 50 options). Now, if we complete steps 4 and 5, we will
see how many shares of each stock make up the new version of the mini-index.
Capitalization Shores
in Mini-Index to Buy
Stock (Step 4) Price (Step 5)
IBM $402,641 130 3,097
XON 154,076 35 4,402
GE 162,589 70 2,323
GM 131,944 85 1,552
Total: $851,250
Compare the number of shares to be bought in this example with the number
of shares to be bought in the previous example. Actually, we are buying more shares
of each of the stocks. There are two reasons for this. In Exxon's case, we are buying
more shares since the price has dropped more as a percentage of its previous price
than its capitalization has dropped as a percentage. For the other stocks, we are buy
ing more shares because the capitalization of each has increased within the mini
index and the price is unchanged.
This example serves to show that as the prices of the stocks in the mini-index
change, the number of shares of each of the stocks might change. This means that
the hedger using this type of hedge should recalculate the makeup of the index rather
frequently - at least once a week. In actual practice, the hedger will know which
stocks are underperforming and which are outperforming. Hence, he will have some
idea of what needs to be done in advance of actually computing it.
There are many methods of approaching these "mini-indices." Some traders
who are extremely short-term oriented - possibly moving in and out of the futures
one or more times daily - might attempt to hedge the futures with only one stock
(generally the largest-capitalization stock, such as IBM, unless there is some reason
to believe that the general market is moving in a substantially different direction from
the largest of all stocks).
In other cases, hedgers with more capital and more resources but who are
unwilling to hedge the entire index might ti:y to use a larger mini-index to hedge with.
Gopter 30: Stock Index Hedging Strategies 571
In cases such as these, one is generally not interested in day-trading the futures and
stocks, but rather in attempting to simulate the full hedge against fair value, as
described earlier. For example, the top 30 capitalization stocks in the OEX make up
over 70% of the capitalization of the index. This provides very accurate tracking, but
still does not overly tax the execution capabilities of even a small trading desk. Such
a 30-stock mini-index can be calculated in exactly the same manner as in the previ
ous examples. Since it represents over 70% of the index, it will track the index quite
well, although not perfectly of course.
However, if one tried to simulate the S&P 500 Index by buying the top 50
stocks, he would still not own even 40% of the capitalization of the index. This does
not provide as accurate tracking as one would hope after having bought 50 stocks. As
a result, if one were trying to hedge the S&P 500 Index, he should use at least 200
stocks.
TRACKING ERROR RISK
In any such simulated index portfolio, there is the largest risk of all with regard to
index hedging, the tracking error. Tracking error is the difference in performance
between the actual index and the simulated index portfolio. There are statistical ways
to predict how closely a certain portfolio of stocks will simulate a given index. This is
something akin to pollsters predicting the margin of victory of an election before the
election is held. One may hear that a certain portfolio has a 98% correlation, say, to
an index it is intended to simulate.
What does this measure represent? First, it must be understood that


here are statistical ways
to predict how closely a certain portfolio of stocks will simulate a given index. This is
something akin to pollsters predicting the margin of victory of an election before the
election is held. One may hear that a certain portfolio has a 98% correlation, say, to
an index it is intended to simulate.
What does this measure represent? First, it must be understood that statistics
cannot predict the exact performance of any set of stocks with respect to any other
set, just as polls cannot exactly predict the outcome of an election. What the statis
tics do tell us is how probable it is that a certain portfolio will perform nearly the
same as another one. The concept of expected return, which was described earlier in
this book, is something like this. The statistical number does not guarantee that the
portfolio will perform like the index 98% of the time or that it will never deviate from
the index by more than 2%. It is merely a comparative measure that says that such a
portfolio has a good correlation to the index.
The actual risk that one is taking by using the simulated index instead of the
index itself is not completely measurable. If it were, then we could predict the exact
performance of the simulated index, which we just showed we could not. However,
assume an average performance - that the simulated index deviates from the real
index by 2% over the course of 1 year. If we are speaking of the S&P 500 at 415, then
2% would be 9.30 points over a 1-year period, or 2.33 points over a 3-month period.
572 Part V: Index Options and Futures
That is a substantial amount of movement when one considers that most of our arbi
trage examples were assuming profits of not much more than that. The compensat
ing factor to this risk is that the simulated index may outperform the actual index and
one could make more profits than would be available with arbitrage. If one had
enough capital and enough time to constantly be participating in such a simulated
index strategy, he would, over time, have a tracking error that is relatively small if his
simulated index has a high correlation to the index.
MONITORING THE HEDGE
Once the position has been established, the trader should have some way of moni
toring the position. Ideally, he would have a computer system that could compute his
mini-index in real time. This would allow accurate comparisons between the actual
index movement and the mini-index. Tracking error can, of course, work for or
against the trader.
It is not necessary to have a computer system built specifically for index hedg
ing. Many computerized systems provide for real-time profit and loss calculations on
a portfolio of the user's choosing. Any of these systems would be sufficient for com
putation of the relative value of the mini-index. In the course of computing the prof
it or loss on the portfolio, the program must compute the net value of the portfolio.
As long as this is available, one can convert it into a mini-index value, suitable for
comparison to the larger index. The "trick" is to use a mini-index multiplier that is a
power of 10. That is, the futures unit of trading times the futures quantity is a power
of 10. For example, if the futures unit of trading is $250 as with the S&P 500 futures,
then a quantity of 40 would result in a power of 10 ($250 X 40 = 10,000). This means
that the total capitalization of the mini-index portfolio should be able to be read as
the "index value" with the mere adjustment of a decimal point.
Example: If one is trading against futures that have a trading move of $500 per point,
then he might choose to use 20 futures against his mini-index. That is, the multipli
er is 20 x $500 or $10,000. If he were hedging against an index trading at 170.25, he
would then buy 10,000 x 170.25 or $1,702,500 worth of stock. The total value of the
stocks in his mini-index would total $1,702,500 initially and he could therefore deter
mine his mini-index value to be 170.2500 by moving the decimal point over four
places. The following table summarizes how this might be constructed using the four
stocks in the most recent example. Recall that in the previous example, the total cap
italization of the four-stock mini-index was $851,250. In this example we would have
had a total mini-index capitalization of twice that, or $1,702,500. Thus, the capital
ization and the number of shares to buy are doubled from the previous example.
Cl,apter 30: Stock Index Hedging Strategies
Capitalization
in Mini-Index
Stock (Step 4)
IBM $ 805,282
XON 308,152
GE 325,178
GM 263,888
Total: $1,702,500
Price
130
35
70
85
573
Shares
to Buy
6,194
8,804
4,646
3,104
Later, as the stocks change in value, one's computerized profit and loss system
could readily compute the total capitalization of the mini-index and, by moving the
decimal point over four places, have a "mini-index value" that could be compared
against the actual index (UVX in this case) in order to determine tracking error.
Example: Suppose that the stocks in the mini-index were to increase to have a total
value of $1,761,872 as shown in the following table.
Shares Current
Stock Owned Price Capitalization
IBM 6,194 135 $ 836,190
XON 8,804 37 325,748
GE 4,646 69 320,574
GM 3,104 90 279,360
Total: $1,761,872
The mini-index value is now 176.1872 (moving the decimal point over four places),
or 176.19. This means that our mini-index increased from a value of 170.25 to 176.19,
an increase of 5.94. This could be compared to the UVX movement during the same
period of time. For example, if the UVX had increased by 6.50 points over the time
period, then it is easy to see that the mini-index underperformed the UVX by 56
cents. If, at some other time, our mini-index had increased faster than the UVX, then
we would have tracking error in our favor.
USING OPTIONS INSTEAD OF FUTURES
As pointed out earlier, one could use options instead of futures wh


e
period of time. For example, if the UVX had increased by 6.50 points over the time
period, then it is easy to see that the mini-index underperformed the UVX by 56
cents. If, at some other time, our mini-index had increased faster than the UVX, then
we would have tracking error in our favor.
USING OPTIONS INSTEAD OF FUTURES
As pointed out earlier, one could use options instead of futures when hedging these
indices. Assuming one is creating a fully hedged situation, he would have positions
similar to conversions when he uses options to hedge a long stock market basket posi-
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 a conversion 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 a more
attractive situation than using the futures. On the other hand, there is not a liquid
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 a full option hedge requires two executions (both selling
the call and buying the put), the futures probably have a slight advantage in that they
involve only a single 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
l in 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 a covered 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 a position 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 a synthetic long call; it would have upside
profit potential and would lose if the index fell, but would have limited risk. Such a
position might be established when puts are cheap and calls are expensive.
TRADING THE TRACKING ERROR
Another reason that one might sell futures against a portfolio 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-
Cbapter 30: Stock Index Hedging Strategies 515
al drillers and sell S&P 500 futures against them. The sale of the futures essentially
removes "the market" from the package of drilling stocks. What would be left is a
position that will reflect how well the drillers perform against the general stock mar
ket. If they outperform, the investor will make money. In this section, we are going
to look at ways of implementing these hedging strategies. This investor is not partic
ularly concerned with predicting whether the market will go up or down; all he wants
to do is remove the "market" from his set of stocks. Then he hopes to profit if these
stocks do, indeed, outperform the broad market. Again, we will not use regression
analysis, but instead will concentrate on methods that are more simply implemented.
Often, investors or portfolio managers think in terms of industry groups. That
is, one may think that the oil drilling stocks will outperform the market, or that the
auto stocks will underperform, for example. In either case, one sells futures to
attempt to remove the market action and capitalize on the performance differential.
In some sense, one is creating a hedge in which he hopes to profit from tracking error.
In previous discussions, tracking error has not been considered a particularly desir
able thing. In this situation, however, one is going to attempt to profit by predicting
the direction of the tracking error and trading it.
The technique for establishing this hedge is exactly the same as in the examples
at the beginning of this chapter, when we looked at hedging a specific stock portfo
lio. The exception is that now one must decide which stocks to buy. Once that is
decided, he can use the four steps outlined previously to decide how many futures to
sell against them:
Step l: Compute each stock's adjusted volatility by dividing its volatility by that
of the market. Use Beta if the group's movement does not correlate well with the
general market.
Step 2: Multiply by the quantity and price of each stock to get an adjusted capi
talization.
Step 3: Add these to get the total capitalization for the portfolio.
Step 4: Determine how many futures to sell by dividing the index price into the
total adjusted capitalization.
Example: Suppose that an investor feels that oil drilling stocks will outperform the
market. He decides to invest $500,000 to buy equal dollar amounts of five drilling
stocks. Normally one would buy an equal dollar amount of each stock in this situa
tion. The stocks are Hughes Tool (HT), Fluor Corp (FLR), Schlumberger (SLB),
Kaneb (KAB), and Halliburton (HAL). The first table shows the price of ea


mple: Suppose that an investor feels that oil drilling stocks will outperform the
market. He decides to invest $500,000 to buy equal dollar amounts of five drilling
stocks. Normally one would buy an equal dollar amount of each stock in this situa
tion. The stocks are Hughes Tool (HT), Fluor Corp (FLR), Schlumberger (SLB),
Kaneb (KAB), and Halliburton (HAL). The first table shows the price of each stock
and how many shares of each will be purchased; $100,000 is invested in each stock.
576
Stock
FLR
HAL
HT
KAB
SLB
Price
20
50
25
10
40
Part V: Index Options and Futures
Quantify
Purchased
5,000
2,000
4,000
10,000
2,500
Now, if one obtains the volatilities of these stocks, he can perform the necessary
computations. These computations will tell him how many futures to sell against the
portfolio of drilling stocks. The volatilities and computations are given in the follow
ing table, assuming the market volatility is 15%. First, dividing the stock's volatility by
the market's volatility gives the adjusted volatility (step 1). That result multiplied by
the price and quantity of the stock gives the adjusted capitalization (step 2), and
adding these together gives the total adjusted capitalization (step 3).
Adjusted Adjusted
Volatility Quantity Capitalization
Stock Volatility (Step I) Price Owned (Step 2)
FLR .46 3.07 20 5,000 $ 306,667
HAL .30 2.00 50 2,000 200,000
HT .21 1.67 25 4,000 166,667
KAB .50 3.33 10 10,000 333,333
SLE .35 2.33 40 5,000 233,333
Total adjusted capitalization: $1,240,000 (step 3)
Assume that one wants to hedge with a fictional index, ZYX, and that ZYX futures are
worth $500 per point. If the ZYX Index is selling at 175, then one would sell 14
futures against this portfolio of drilling stocks: $1,240,000 + $500 per point+ 175 is
approximately equal to 14 (step 4).
In a situation such as this, one does not have to be bullish or bearish on the
market in order to establish the hedge. He is rather attempting to time the per
formance of the group in question. Similarly, the decision as to when to remove the
position is not a matter of market opinion. Perhaps one has an unrealized profit and
decides to take it, or perhaps something changes fundamentally within the group
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 a particular 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.
A trader 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 a trader 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 a strategy into the marketplace
that did not previously exist. The versatility of these derivative securities is evidenced
572 Part V: Index Options and Futures
That is a substantial amount of movement when one considers that most of our arbi
trage examples were assuming profits of not much more than that. The compensat
ing factor to this risk is that the simulated index may outperform the actual index and
one could make more profits than would be available with arbitrage. If one had
enough capital and enough time to constantly be participating in such a simulated
index strategy, he would, over time, have a tracking error that is relatively small if his
simulated index has a high correlation to the index.
MONITORING THE HEDGE
Once the position has been established, the trader should have some way of moni
toring the position. Ideally, he would have a computer system that could compute his
mini-index in real time. This would allow accurate comparisons between the actual
index movement and the mini-index. Tracking error can, of course, work for or
against the trader.
It is not necessary to have a computer system built specifically for index hedg
ing. Many computerized systems provide for real-time profit and loss calculations on
a portfo


a computer system that could compute his
mini-index in real time. This would allow accurate comparisons between the actual
index movement and the mini-index. Tracking error can, of course, work for or
against the trader.
It is not necessary to have a computer system built specifically for index hedg
ing. Many computerized systems provide for real-time profit and loss calculations on
a portfolio of the user's choosing. Any of these systems would be sufficient for com
putation of the relative value of the mini-index. In the course of computing the prof
it or loss on the portfolio, the program must compute the net value of the portfolio.
As long as this is available, one can convert it into a mini-index value, suitable for
comparison to the larger index. The "trick" is to use a mini-index multiplier that is a
power of 10. That is, the futures unit of trading times the futures quantity is a power
of 10. For example, if the futures unit of trading is $250 as with the S&P 500 futures,
then a quantity of 40 would result in a power of 10 ($250 x 40 = 10,000). This means
that the total capitalization of the mini-index portfolio should be able to be read as
the "index value" with the mere adjustment of a decimal point.
Example: If one is trading against futures that have a trading move of $500 per point,
then he might choose to use 20 futures against his mini-index. That is, the multipli
er is 20 x $500 or $10,000. If he were hedging against an index trading at 170.25, he
would then buy 10,000 x 170.25 or $1,702,500 worth of stock. The total value of the
stocks in his mini-index would total $1,702,500 initially and he could therefore deter
mine his mini-index value to be 170.2500 by moving the decimal point over four
places. The following table summarizes how this might be constructed using the four
stocks in the most recent example. Recall that in the previous example, the total cap
italization of the four-stock mini-index was $851,250. In this example we would have
had a total mini-index capitalization of twice that, or $1,702,500. Thus, the capital
ization and the number of shares to buy are doubled from the previous example.
Chapter 30: Stock Index Hedging Strategies
Capitalization
in Mini-Index
Stock (Step 4)
IBM $ 805,282
XON 308,152
GE 325,178
GM 263,888
Total: $1,702,500
Price
130
35
70
85
573
Shores
to Buy
6,194
8,804
4,646
3,104
Later, as the stocks change in value, one's computerized profit and loss system
could readily compute the total capitalization of the mini-index and, by moving the
decimal point over four places, have a "mini-index value" that could be compared
against the actual index (UVX in this case) in order to determine tracking error.
Example: Suppose that the stocks in the mini-index were to increase to have a total
value of $1,761,872 as shown in the following table.
Shares Current
Stock Owned Price Capitalization
IBM 6,194 135 $ 836,190
XON 8,804 37 325,748
GE 4,646 69 320,574
GM 3,104 90 279,360
Total: $1,761,872
The mini-index value is now 176.1872 (moving the decimal point over four places),
or 176.19. This means that our mini-index increased from a value of 170.25 to 176.19,
an increase of 5.94. This could be compared to the UVX movement during the same
period of time. For example, if the UVX had increased by 6.50 points over the time
period, then it is easy to see that the mini-index underperformed the UVX by 56
cents. If, at some other time, our mini-index had increased faster than the UVX, then
we would have tracking error in our favor.
USING OPTIONS INSTEAD OF FUTURES
As pointed out earlier, one could use options instead of futures when hedging these
indices. Assuming one is creating a fully hedged situation, he would have positions
similar to conversions when he uses options to hedge a long stock market basket posi-
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 a conversion 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 a more
attractive situation than using the futures. On the other hand, there is not a liquid
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 a full option hedge requires two executions (both selling
the call and buying the put), the futures probably have a slight advantage in that they
involve only a single 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
l in 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 a covered 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 a position would be most attrac
tive when the calls are very overpriced.
Similarly, one mi


ad of the futures. For example, he might buy stocks and just write in-the-money
calls instead of selling futures. This would create a covered 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 a position would be most attrac
tive when the calls are very overpriced.
Similarly, one might ti:y to buy the stocks and buy slightly in-the-money puts
without selling the calls. This position is a synthetic long call; it would have upside
profit potential and would lose if the index fell, but would have limited risk. Such a
position might be established when puts are cheap and calls are expensive.
TRADING THE TRACKING ERROR
Another reason that one might sell futures against a portfolio 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-
Chapter 30: Stock Index Hedging Strategies 575
al drillers and sell S&P 500 futures against them. The sale of the futures essentially
removes "the market" from the package of drilling stocks. What would be left is a
position that will reflect how well the drillers perform against the general stock mar
ket. If they outperform, the investor will make money. In this section, we are going
to look at ways of implementing these hedging strategies. This investor is not partic
ularly concerned with predicting whether the market will go up or down; all he wants
to do is remove the "market" from his set of stocks. Then he hopes to profit if these
stocks do, indeed, outperform the broad market. Again, we will not use regression
analysis, but instead will concentrate on methods that are more simply implemented.
Often, investors or portfolio managers think in terms of industry groups. That
is, one may think that the oil drilling stocks will outperform the market, or that the
auto stocks will underperform, for example. In either case, one sells futures to
attempt to remove the market action and capitalize on the performance differential.
In some sense, one is creating a hedge in which he hopes to profit from tracking error.
In previous discussions, tracking error has not been considered a particularly desir
able thing. In this situation, however, one is going to attempt to profit by predicting
the direction of the tracking error and trading it.
The technique for establishing this hedge is exactly the same as in the examples
at the beginning of this chapter, when we looked at hedging a specific stock portfo
lio. The exception is that now one must decide which stocks to buy. Once that is
decided, he can use the four steps outlined previously to decide how many futures to
sell against them:
Step 1: Compute each stock's adjusted volatility by dividing its volatility by that
of the market. Use Beta if the group's movement does not correlate well with the
general market.
Step 2: Multiply by the quantity and price of each stock to get an adjusted capi
talization.
Step 3: Add these to get the total capitalization for the portfolio.
Step 4: Determine how many futures to sell by dividing the index price into the
total adjusted capitalization.
Example: Suppose that an investor feels that oil drilling stocks will outperform the
market. He decides to invest $500,000 to buy equal dollar amounts of five drilling
stocks. Normally one would buy an equal dollar amount of each stock in this situa
tion. The stocks are Hughes Tool (HT), Fluor Corp (FLR), Schlumberger (SLB),
Kaneb (KAB), and Halliburton (HAL). The first table shows the price of each stock
and how many shares of each will be purchased; $100,000 is invested in each stock.
576
Stock
FLR
HAL
HT
KAB
SLB
Price
20
50
25
10
40
Part V: Index Options and Futures
Quantity
Purchased
5,000
2,000
4,000
10,000
2,500
Now, if one obtains the volatilities of these stocks, he can perform the necessary
computations. These computations will tell him how many futures to sell against the
portfolio of drilling stocks. The volatilities and computations are given in the follow
ing table, assuming the market volatility is 15%. First, dividing the stock's volatility by
the market's volatility gives the adjusted volatility (step 1). That result multiplied by
the price and quantity of the stock gives the adjusted capitalization (step 2), and
adding these together gives the total adjusted capitalization (step 3).
Adjusted Adjusted
Volatility Quantity Capitalization
Stock Volatility (Step 1) Price Owned (Step 2)
FLR .46 3.07 20 5,000 $ 306,667
HAL .30 2.00 50 2,000 200,000
HT .21 1.67 25 4,000 166,667
KAB .50 3.33 10 10,000 333,333
SLE .35 2.33 40 5,000 233,333
Total adjusted capitalization: $1,240,000 (step 3)
Assume that one wants to hedge with a fictional index, ZY.X, and that ZY.X futures are
worth $500 per point. If the ZY.X Index is selling at 175, then one would sell 14
futures against this portfolio of drilling stocks: $1,240,000 + $500 per point+ 175 is
approximately equal to 14 (step 4).
In a situation such as this, one does not have to be bullish or bearish on the
market in order to establish the hedge. He is rather attempting to time the per
formance of the group in question. Similarly, the decision as to when to remove the
position is not a matter of market opinion. Perhaps one has an unrealized profit and
decides to take it, or perhaps something changes fundamentally within the group
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


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 a particular 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.
A trader 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 a trader 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 a strategy into the marketplace
that did not previously exist. The versatility of these derivative securities is evidenced
578 Part V: Index Options and Futures
by the various strategies that were described in this chapter - hedging an actual index
or a simulated one, trading the tracking error, selling the futures instead of the entire
portfolio when one turns bearish, or buying the futures when they are cheap instead
of buying stocks. The owner of a stock portfolio, whether an individual or a large
institution, should understand these strategies because they are often preferable to
merely buying or selling stock.
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 a high
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's view 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&P and 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
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 a futures 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). Man


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 a one-for-one basis.
Example: A spreader 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 a ratio of the two indices. This
approach is often taken when the two indices trade at substantially different prices.
Chpt,r 31: Index Spreading 581
J!"<>r example, if one index sells for twice the price of the other, and if both indices
have similar volatilities, then a one-to-one spread gives too much weight to the
higher-priced index. A two-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, a spreader 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 a hedge. If one wanted a position that reflected the movement
of the ZYX index, he could merely trade the ZYX futures and not bother with a
spread.
If, however, one had used the ratio of the indices to decide how many futures
to buy and sell, he would have a more 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 a factor in determining how fast they move in relationship to each
other.
582 Part V: Index Options and Futures
where
p1 and p2 are the prices of the indices
v 1 and v 2 are the respective volatilities
and u1 and u2 are the units of trading ($500 per point, for example).
Including the volatility ensures that one is spreading essentially equal "volatili
ty dollars" of each index. Moreover, if the two futures don't have the same unit of
trading, that should be factored in as well.
Example: The ZYX Index is not very volatile, having a volatility of 15%. A trader is
interested in spreading it against the ABX Index, which is volatile, having a historical
volatility of 25%. The following data sum up the situation:
Unit of
Price Volatility Trading
ZYX Futures 175.00 15% $250/pt
ABX Futures 225.00 25% $500/pt
R . .25 225.00 500 abo=-X--X-
.15 175.00 250
= 4.286
In round numbers, one would probably trade four ZYX futures against one ABX
future.
INDEX CHARACTERISTICS
Before discussing specific spreads, it might be constructive to describe how the
makeup of the various indices that have listed options affects their price movements.
The Value Line Index is composed of 1,600 stocks, some of which are traded over the
counter. The Value Line Index movement is much more closely related to how small
stocks perform, while the S&P 500 Index reflects more heavily the performance of
the large-capitalization stocks. In fact, it has been said that a chart of the Value Line
Index looks almost like the advance-decline line ( the running daily total of advances
minus declines). The S&P 500, on the other hand, looks much more like the Dow
Jones 30 Industrials because of the heavy weighting given the large-capitalization
stocks.
The S&P 100 (OEX) contains 100 stocks, but is capitalization-weighted and the
stocks are generally the largest ones with listed options trading on the CBOE. Thus,
its performance is much more like the S&P 500 and NYSE indices. The OEX is
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 Ind


us,
its performance is much more like the S&P 500 and NYSE indices. The OEX is
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-l in
November 1997. A one-point move in SPX is approximately equal to a move of 7.5
points in the Dow-Jones Industrial Average, while a one-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 a mini-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 a full synthetic requires both a put
and a call. 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 a broad 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's array 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 a while in the early 1980s. As the bull market of the 1980s
matured, the S&P 500 ground its way higher, eventually reaching a price nearly 30
points higher than OEX. As one can see, there is ample room for movement in the
spread between the cash indices.
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 a few. 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 a larger 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 a hedged basis with
out trying to predict the direction of movement of the cash indices. In order to
establish such a spread, one would take a position 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 a syn
thetic option position as a substitute 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 a substitute
for the future. Second, he could use the options' delta to construct a more 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 a substitute for futures gives one an additional
advantage: If the cash indices move far enough in either direction, the spreader could
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: 15


ading the premiums between the futures.
Using in-the-money options as a substitute for futures gives one an additional
advantage: If the cash indices move far enough in either direction, the spreader could
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 a relatively 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 a profit if the cash spread widens, if the
indices are volatile. To see this, suppose that after a large 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 a movement 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 a situation that is very
similar to owning a long strangle (long put and call with different strikes), except that
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 a case, 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 a factor to
include delta.
where
vi is the volatility of index i
Pi is the price of index i
ui 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 a position 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's
negative 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 a very 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 a great 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.
Cl,apter 31: Index Spreading 587
Volatility Differential. A theoretical "edge" that sometimes appears is that of
volatility differential. If two indices are supposed to have essentially the same volatil
ity, or at least a relationship in their volatilities, then one might be able to establish
an option spread if that relationship gets out ofline. In such a case, 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's options are trading with a higher implied volatility than the
other's, a potential 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 a call on another index.
S


ng 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 a call 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.
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's imagination 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 a usable 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 a later time, one notices that the relationship is changing,
perhaps a spread 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 a fairly 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.
Structured Products
The popularity of derivative instruments and the kinds of risk-reducing, volatility
reducing effects that they can have on portfolios led to a new type of product in the
1990s. This new product, termed a structured product, has more appeal for investors
than for traders. In essence, enterprising designers at the major institutional broker
age firms have constructed a single security that behaves like a portfolio hedged by
options. These designers structure the combination of derivatives and stocks so that
the resulting product behaves in a manner that is attractive to many investors,
whether institutional or private. In this chapter, these structured products are exam
ined in detail, to give the reader the background so that in the future, he may ana
lyze similar products for himself.
Would you like to own an index fund that had no risk? Or, how about owning a
popular stock and getting a dividend payment that is much, much larger than the
stock itself pays? I think everyone would like to do those things. With structured
products, one can own similar investments, but they come with a cost. The two ques
tions asked previously might then be better restated as follows: Would you like to
own an index fund that had no risk, but that perhaps did not fully participate in all of
the upside movement of the market? It still has downside protection, and unlimited
profit potential on the upside. This is akin to owning the stock or the index and hav
ing protected it by buying a put option. Or, would you like to own that popular stock
and receive that huge dividend, but know that your profit potential is limited to a
fixed amount on the upside? This is akin to a covered call write.
These two questions describe the majority of the listed structured products in
existence today. They are attractive investments in their own right, but one must
carefully assess the products before buying them. This chapter is divided into two
main parts to discuss the two types of products: First, we'll discuss the "protected"
stock or index. Later, the discussion will tum to "covered write" products.
589
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. A broader 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 a fund of sorts (or a unit trust, perhaps), and shares are sold to the pub
lic. Not only that, but the shares are then lis


UCTURED 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 a fund of sorts (or a unit 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 a very desirable investment. An example will show how a generic
index structured product might look.
Example: Let's look 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 a low price - say, $10 per share.
2. The product will have a maturity 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&P doubles
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 a minute).
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&P has rallied
O,apter 32: Structured Products 591
dramatically, or perhaps he needs cash for something else - both might be reasons
that the holder of the shares would want to sell before maturity.
Such a product has appeal to many investors. In fact, if one thought that the
stock market was a "long-term" buy, this would be a much safer way to approach it
than buying a portfolio of stocks that might conceivably be much lower in value seven
years hence. The risk of the structured product is that the underwriter might not be
able to pay the $10 obligation at maturity. That is, if the major institutional bank or
brokerage firm who underwrote these products were to go out of business over the
course of the next seven years, one might not be able to redeem them. In essence,
then, structured products are really forms of debt (senior debt) of the brokerage firm
that underwrote them. Fortunately, most structured products are underwritten by
the largest and best-capitalized institutions, so the chances of a failure to pay at matu
rity would have to be considered relatively tiny.
How does the bank create these items? It might seem that the bank buys stock
and buys a put and sells units on the combined package. In reality, the product is not
normally structured that way. Actually, it is not a difficult concept to grasp. This
example shows how the structure looks from the viewpoint of the bank:
Example: Suppose that the bank wants to raise a pool of $1,000,000 from investors
to create a structured product based on the appreciation of the S&P 500 index over
the next seven years. The bank will use a part of that pool of money to buy U.S. zero
coupon bonds and will use the rest to buy call options on the S&P 500 index.
Suppose that the U.S. government zero-coupon bonds are trading at 60 cents
on the dollar. Such bonds would mature in seven years and pay the holder $1.00.
Thus, the bank could take $600,000 and buy these bonds, knowing that in seven
years, they would mature at a value of $1,000,000. The other $400,000 is spent to buy
call options on the S&P 500 index. Thus, the investors would be made whole at the
end of seven years even if the options that were bought expired worthless. This is why
the bank can "guarantee" that investors will get their initial money back.
Meanwhile, if the stock market advances, the $400,000 worth of call options will
gain value and that money will be returned to the holders of the structured product
as well.
In reality, the investment bank uses its own money ($1,000,000) to buy the secu
rities necessary to structure this product. Then they make the product into a legal
entity (often a unit trust) and sell the shares (units) to the public, marking them up
slightly as they would do with any new stock brought to market.
At the time of the initial offering, the calls are bought at-the-money, meaning
the striking price of the calls is equal to the closing price of the S&P 500 index on the
592 Part V: Index Options and Futures
day the products were sold to the public. Thus, the structured product itself has a
"strike price" equal to that of the calls. It is this price that is used at maturity to deter
mine whether the S&P has appreciated over the seven-year period - an event that
would result in the holders receiving back more than just their initial purchase price.
After the initial offering, the shares are then listed on the AMEX or the NYSE
and they will begin to rise and fall as the value of the S&P 500 index fluctuates.
So, the structured product is not an index fund protected by a put option, but
rather it is a combination of zero-coupon government bonds and a call option on an
index. These two structures are equivalent, just as the combination of owning stock
protected by a put option is equivalent to being long a call option.
Structured products of this type are not limited to indices. One could do the
same thing with an individual stock, or perhaps a group of stocks, or even create a
simulated bull spread. There are many possibilities, and the major ones will be dis
cussed in the following sections. In theory, one could construct products like this for
himself, but the mechanics would be too difficult. For example, where is one going
to buy a seven-year option in small quantity? Thus, it is often


thing with an individual stock, or perhaps a group of stocks, or even create a
simulated bull spread. There are many possibilities, and the major ones will be dis
cussed in the following sections. In theory, one could construct products like this for
himself, but the mechanics would be too difficult. For example, where is one going
to buy a seven-year option in small quantity? Thus, it is often worthwhile to avail one
self of the product that is packaged (structured) by the investment banker.
In actuality, many of the brokerage firms and investment banks that undetwrite
these products give them names - usually acronyms, such as MITTS, TARGETS,
BRIDGES, LINKS, DINKS, ELKS, and so on. If one looks at the listing, he may see
that they are called notes rather than stocks or index funds. Nevertheless, when the
terms are described, they will often match the examples given in this chapter.
INCOME TAX CONSEQUENCES
There is one point that should be made now: There is "phantom interest" on a struc
tured product. Phantom interest is what one owes the government when a bond is
bought at a discount to maturity. The IRS technically calls the initial purchase price
an Original Issue Discount (OID) and requires you to pay taxes annually on a pro
portionate amount of that OID. For example, if one buys a zero-coupon U.S. gov
ernment bond at 60 cents on the dollar, and later lets it mature for $1.00, the IRS
does not treat the 40-cent profit as capital gains. Rather, the 40 cents is interest
income. Moreover, says the IRS, you are collecting that income each year, since you
bought the bonds at a discount. (In reality, of course, you aren't collecting a thing;
your investment is simply worth a little more each year because the discount decreas
es as the bonds approach maturity.) However, you must pay income tax on the "phan-
Chapter 32: Structured Products 593
tom interest" you supposedly received each year. Those are the rules, and there isn't
anything you can do about them.
Since some structured products involve the purchase of zero-coupon bonds, the
IRS has ruled that owners of this type of structured product must pay phantom inter
est each year. Thus, structured products should be bought in a tax-free retirement
account (IRA, SEP, etc.) if at all possible, in order to avoid having to declare phan
tom interest on your tax return for each year you hold the product. The phantom
interest tax applies only to this type of structured product - one on which you are
guaranteed to get back a fixed amount at maturity - because this is the only type that
requires buying a zero-coupon bond in order to ensure that you'll get your money
back if the stock market goes down. The phantom interest concept does not apply to
the type of structured product to be discussed in the second part of this chapter. To
be certain, one should get the necessary information from his broker or should read
the prospectus of the structured product. Of course, any tax strategies should also be
discussed with a qualified tax professional.
CASH VALUE
The cash value of the structured product is what it will be worth at maturity. It is usu
ally stated in terms similar to those in the preceding example, and a formula is often
given. This example will clarify the typical nature of this formula:
Example: A structured product is issued at $10 per share. The terms stipulate that
the holder will receive back, at maturity, either $10 or 100% of the appreciation of
the S&P 500 index above a value of 1,245.27. (One would assume that the S&P 500
cash index closed at 1,245.27 on the day the structured product was issued.) The
prospectus will usually provide a formula for the cash surrender value, and it will be
stated something like this:
At maturity, the cash value will be equal to the greater of:
(a) $10
or (b) $10 + 10 x (Final Index Value - 1,245.27) / 1,245.27
where Final Index Value is, say, the closing value of the S&P 500
index on the maturity date.
The formula given is merely the arithmetic equivalent of the statement that one
will receive 100% of the appreciation of the S&P 500 Index above the strike price of
1,245.27. For those more adept at math, the formula can be reduced to common
terms, in which case it reads:
594 Part V: Index Options and Futures
Cash Surrender Value = $10 x Final Value/ 1,245.27
This shortened version of the formula only works, though, when the participa
tion rate is 100% of the increase in the Final Index Value above the striking price.
Otherwise, the longer formula should be used.
Not all structured products of this type offer the holder 100% of the appreci
ation of the index over the initial striking price. In some cases, the percentage is
smaller ( although in the early days of issuance, some products offered a percentage
appreciation that was actually greater than 100%). After 1996, options in general
became more expensive as the volatility of the stock market increased tremendous
ly. Thus, structured products issued after 1997 or 1998 tend to include an "annual
adjustment factor." Adjustment factors are discussed later in the chapter.
Therefore, a more general formula for Cash Surrender Value - one that applies
when the participation rate is a fixed percentage of the striking price - is:
Cash Surrender Value =
Guarantee + Guarantee x Participation Rate x (Final Index Value/ Striking Price - I)
THE COST OF THE IMBEDDED CALL OPTION
Few structured products pay dividends. 1 Thus, the "cost" of owning one of these
products is the interest lost by not having your money in the bank ( or money market
fund), but rather having it tied up in holding the structured product.
Continuing with the preceding example, suppose that you had put the $10 in
the bank instead of buying a structured product with it. Let's further assume that the
money in the bank earns 5% interest, compounded continuously. At the end of seven
years, compounded continuously, the $10 would be


in the bank ( or money market
fund), but rather having it tied up in holding the structured product.
Continuing with the preceding example, suppose that you had put the $10 in
the bank instead of buying a structured product with it. Let's further assume that the
money in the bank earns 5% interest, compounded continuously. At the end of seven
years, compounded continuously, the $10 would be worth:
Money in the bank = Guarantee Price x ert
= $10 x e 0-05 x 7 = 14.191, in this case
This calculation usually raises some eyebrows. Even compounded annually, the
amount is 14.07. You would make roughly 40% (without considering taxes) just by
1Some do pay dividends, though. A structured product existed on a contrived index, called the Dow-Jones
Top 10 Yield index (symbol: $XMT). This is a sort of "dogs of the Dow" index. Since part of the reason for owning a
"dogs of the Dow" product is that dividends are part of the performance, the creators of the structured product
(Merrill Lynch) stated that the minimum price one would receive at maturity would be 12.40, not the 10 that was
the initial offering price. Thus, this particular structured product had a "dividend" built into it in the form of an ele
vated minimum price at maturity.
Chapter 32: Structured Products 595
having your money in the bank. Forgetting structured products for a moment, this
means that stocks in general would have to increase in value by over 40% during the
seven-year period just for your performance to beat that of a bank account.
In this sense, the cost of the imbedded call option in the structured product is
this lost interest - 4.19 or so. That seems like a fairly expensive option, but if you con
sider that it's a seven-year option, it doesn't seem quite so expensive. In fact, one
could calculate the implied volatility of such a call and compare it to the current
options on the index in question.
In this case, with the stock at 10, the strike at 10, no dividends, a 5% interest
rate, and seven years until expiration, the implied volatility of a call that costs $4.19
is 28.1 %. Call options on the S&P 500 index are rarely that expensive. So you can see
that you are paying "something" for this call option, even if it is in the form of lost
interest rather than an up-front cost.
As an aside, it is also unlikely that the underwriter of the structured product
actually paid that high an implied volatility for the call that was purchased; but he is
asking you to pay that amount. This is where his underwriting profit comes from.
The above example assumed that the holder of the structured product is par
ticipating in 100% of the upside gain of the underlying index over its striking price.
If that is not the case, then an adjustment has to be made when computing the price
of the imbedded option. In fact, one must compute what value of the index, at matu
rity, would result in the cash value being equal to the "money in the bank" calcula
tion above. Then calculate the imbedded call price, using that value of the index. In
that way, the true value of the imbedded call can be found.
You might ask, "Why not just divide the 'money in the bank' formula by the par
ticipation rate?" That would be okay if the participation were always stated as a per
centage of the striking price, but sometimes it is not, as we will see when we look at
the more complicated examples. Further examples of structured products in this
chapter demonstrate this method of computing the cost of the imbedded call.
PRICE BEHAVIOR PRIOR TO MATURITY
The structured product cannot normally be "exercised" by the holder until it
matures. That is, the cash surrender value is only applicable at maturity. At any other
time during the life of the product, one can compute the cash surrender value, but
he cannot actually attain it. What you can attain, prior to maturity, is the market price,
since structured products trade freely on the exchange where they are listed. In actu
al fact, the products generally trade at a slight discount to their theoretical cash sur
render value. This is akin to a closed-end mutual fund selling at a discount to net
596 Part V: Index Options and Futures
asset value. Eventually, upon maturity, the actual price will be the cash surrender
value price; so if you bought the product at a discount, you would benefit, providing
you held all the way to maturity.
Example: Assume that two years ago, a structured product was issued with an initial
offering price of $10 and a strike price of 1,245.27, based upon the S&P 500 index.
Since issuance, the S&P 500 index has risen to 1,522.00. That is an increase of
22.22% for the S&P 500, so the structured product has a theoretical cash surrender
value of 12.22. I say "theoretical" because that value cannot actually be realized, since
the structured product is not exercisable at the current time - five years prior to
maturity.
In the real marketplace, this particular structured product might be trading at
a price of 11. 75 or so. That is, it is trading at a discount to its theoretical cash sur
render value. This is a fairly common occurrence, both for structured products and
for closed-end mutual funds. If the discount were large enough, it should serve to
attract buyers, for if they were to hold to maturity, they would make an extra 4 7 cents
(the amount of this discount) from their purchase. That's 4% (0.47 divided by 11.75
= 4%) over five years, which is nothing great, but it's something.
Why does the product trade at a discount? Because of supply and demand. It is
free to trade at any price - premium or discount - because there is nothing to keep
it fixed at the theoretical cash surrender value. If there is excess demand or supply in
the open market, then the price of the structured product will fluctuate to reflect that
excess. Eventually, of course, the discount will disappear, but five years prior to
maturity, one will often find that the product di