Beauty Contests and Fat Tails in Financial Markets

Abstract

Using a simultaneous-move herding model of rational traders who infer other traders’ private information on the value of an asset by observing their aggregate actions, this study seeks to explain the emergence of fat-tailed distributions of transaction volumes and asset returns in financial markets. Without making any parametric assumptions on private information, we analytically show that traders’ aggregate actions follow a power law distribution. We also provide simulation results to show that our model successfully reproduces the empirical distributions of asset returns. We argue that our model is similar to Keynes’s beauty contest in the sense that traders, who are assumed to be homogeneous, have an incentive to mimic the average trader, leading to a situation similar to the indeterminacy of equilibrium. In this situation, a trader’s buying action causes a stochastic chain-reaction, resulting in power laws for financial fluctuations.