The Performance of Characteristic-Sorted Portfolios: Evaluating the Past and Predicting the Future

Abstract

We study the fluctuating performance of characteristic-sorted portfolios through the lens of a statistical model that allows for persistent variation in expected returns. The model provides a simple formula for adjusting the standard errors of unconditional (or long-run) expected return estimates; with plausible persistence parameters, the standard errors double. Maximum likelihood tests of the model show that the magnitude of persistent variation is estimated very imprecisely: the historical data are consistent with both i.i.d. and highly persistent return processes. Finally, our Bayesian analysis of the model shows that with relatively agnostic prior beliefs about the persistence parameters, posterior estimates of expected returns exhibit large fluctuations over time.