Incomplete Information, Heterogeneous Beliefs and the Statistical Properties of Asset Prices

Abstract

I consider a pure exchange economy where the growth rate of aggregate consumption is mean reverting and unobservable. Agents have heterogenous beliefs which they continuously update. I study the properties of asset prices as they can be measured by an outside observer (objective probability). First, it is shown that under the objective probability, the market price of risk (Sharpe ratio) is larger than the complete information equivalent, if the agents with higher level of expectations about the growth rate also have higher level of conditional variances. I provide an analytical formula for the volatility of the stock price which identifies the respective contributions of information incompleteness and heterogeneity in beliefs. It is shown that the volatility can be higher or lower than the complete information case, depending on the parametrization. I found that a parametric specification which yields a high level of volatility necessarily implies a negative covariance of the stock return with the interest rate. Finally I discuss why asset returns appear predictable in the objective probability measure when agents rationally update their beliefs by taking into account the observable variations of the dividend.

Keywords: incomplete information, equity premium, volatility, heterogeneous beliefs

JEL Classification: G12