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