Persistent Expected Returns and the Cross-Section of Stock Returns

Abstract

Even though stock returns are not highly autocorrelated they may contain small but highly persistent expected returns. We develop a simulation framework that isolates the role of persistence and show that in the presence of even small persistent expected returns, biased estimates of their persistence level biases the estimation of the variance-covariance matrix of returns. The bias is more severe the greater the persistence and larger the cross-section of assets. The variance-covariance matrix of returns is a key input in asset pricing models and tests, hence standard tests are all affected by this bias. We define a test statistic that is immune to this bias and shows consistent results across the persistence levels and sample sizes. Our findings, further, suggest that estimating bounds and test statistics based on the conditional distribution of asset returns, leads to the tests that are dependent on the variance-covariance matrix of return residuals instead, which are unaffected by the biased estimates of the persistence level of expected returns. Hence, such tests provide more accurate results in the presence of persistent expected returns.

Keywords: persistent expected returns, stochastic discount factor bounds, asset pricing tests, conditioning information

JEL Classification: G11, G12