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