Prediction Market Accuracy under Risk Aversion and Heterogeneous Beliefs ∗

In this paper, we characterize the equilibrium price of a prediction market in which risk averse traders have heterogeneous beliefs in probabilities. We show that the prediction market is accurate, in the sense that the equilibrium price equals the mean beliefs of traders, if and only if the utility function of traders is logarithmic. We also provide a necessary and sufficient condition for the equilibrium price to be systematically below the mean beliefs for all symmetric belief distributions. In particular, when traders’ risk preferences are such that twice absolute risk aversion is less than absolute prudence, this condition provides a rationale for the favorite-longshot bias.