This paper analyzes a model of a futures market in which both pure speculators and producers participate. Traders form rational expectations about the return on holding futures (the spot price) on the basis of diverse private information and the futures price. Constant absolute risk aversion utility functions and normal distributions are assumed in the model. The theorems establish a set of necessary conditions, and a somewhat stronger set of sufficient conditions, for the strong informational efficiency of the futures market. Informational efficiency is taken to mean that the futures price is a sufficient statistic for all the information available about the spot price. In this model the futures price is not in general a sufficient statistic if information is available about both sides of the spot market.