Aggregation of Information and Beliefs in Prediction Markets

We analyze a binary prediction market in which traders have heterogeneous prior beliefs and private information. Realistically, we assume that traders are allowed to invest a limited amount of money (or have decreasing absolute risk aversion). We show that the rational expectations equilibrium price underreacts to information. When favorable information to an event is available and is revealed by the market, the price increases and this forces optimists to reduce the number of assets they can (or want to) buy. For the market to equilibrate, the price must increase less than a posterior belief of an outside observer.