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To: Robert Douglas who wrote (95356)1/7/2000 12:24:00 PM
From: GVTucker  Read Replies (1) | Respond to of 186894
 
Robert, RE: I don't know what you mean by fair value being subjective. I thought that the premium that the S&P futures had over the cash was strictly mathematical dealing with the relative return of the two. Since the dividend yield on the S&P 500 is below the risk-free rate of return, then the distant contracts sell at a premium. If the two get far enough out of line there is an arbitrage potential that is exploited and the relationship is restored. As an example of a futures contract where the payment is larger than the risk-free return you can look at the T-Bond contract. This future has distant contracts that sell at a discount to the nearby ones. Once again it is strictly a mathematical relationship with the relative return and the time until expiration of the contract.

Sorry, but the fair value is indeed a subjective number, and that subjective number is the risk premium.

Comparing the S&P to the T-Bonds is not a valid comparison. There is a positive expected return to the S&P 500 Index beyond the dividend yield. There is not a similar positive expected return to a Treasury Bond beyond the coupon.

Note, for example, that if the dividend yield were exactly what the risk free rate of return was, the future would NOT be equal to the cash index, because there is still an implicit risk premium in the equity market. Otherwise, everybody would own the future and not the cash, and the market would drive the premium of the future over the cash eventually to the risk premium.

The reason that you often see the S&P at a widely varying spread to the cash is that different people have different perceptions of the risk premium, even the arbs that only trade the cash and the future. This is markedly different form the Bond futures contract, which trades at a very tight spread to the cheapest to deliver cash bond; in this case, the only variable would be financing rate. For most arbs, this rate doesn't vary much.