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