Can CRRA preferences explain CAPM-anomalies in the cross-section of stock returns?

Abstract

A large number of empirical studies find evidence for systematic deviations from the CAPM. The CAPM tends to understate the returns on low-beta stocks and overstate the returns on high-beta stocks, which means that the security market line is too steep. Other well-documented anomalies are the size premium and the value premium. The CAPM is a special case of the consumption-based CAPM. This study addresses the question whether the consumption-based CAPM with constant relative risk aversion preferences can explain CAPM-anomalies. An example of an economy with power utility and lognormal returns is examined that can be solved in closed form. The model leads to a security market line that is flatter than in the CAPM and generates a size and a value premium. The comparative statics suggest that cross-sectional anomalies and the equity premium puzzle are of a very similar nature.