hen stock index futures are treated as forward contracts, the equilibrium futures price is expected to be above the underlying spot index by an amount determined by the riskless rate of interest. The purpose of this article is to show that the discounts on stock index futures may occur when interest rates are stochastic and marking-to-market is considered. Applying an asset pricing model which takes account of inflation risk to the pricing of stock index futures, we show that: (1) the more volatile are stock returns and interest rates; (2) the greater the negative relationship between stock returns and interest rates; and (3) the higher the inflation risk premium, the greater and more likely the discounts.
'See K. French (1982). This relationship can be obtained by using a riskless bond and futures portfolio strategy demonstrated below. At time t , investors invest F, dollars in riskless bonds and purchase exp[R(t, & + l)] units of futures contract. At time L + 1, invest the net value of the portfolio, exp[R(t, L + l)]F,+, dollars, in riskless bonds and purchase exp[(R(t, t + 1) + R(t + 1, t + 2)] units of futures contracts. This strategy will be continued until contracts mature, at that time the value of the portfolio is exp[CT:: R(T. T + 111 zS,. Therefore, the current investment, F,, must be the present value of the portfolio value at time T, exp[ET:,' [R(T, T + I)]&.