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