The paper addresses two major issues raised by information diversity in a speculative market. First, we analyze what property of an investor's information leads to an expected speculative profit and show that independence is more important than accuracy. Second, we consider whether the market price must become fully efficient, in the sense that every investor's information is accurately discounted, when traders use it rationally as an information source. We prove that for any information structure there is a unique equilibrium weighting of investor beliefs at which the price is fully efficient and also every trader's expected profit is zero. Except for special structures, however, this equilibrium need not be attained in finite time.