Dynamic Portfolio Choice with Bayesian Learning

Abstract

This paper examines the importance of parameter uncertainty and learning in the context of dynamic portfolio choice. In a discrete time setting, we consider a Bayesian investor who faces parameter uncertainty and solves her portfolio choice problem while updating her beliefs about the parameters. For different return data generating processes, including i.i.d. returns, autoregressive returns, and exogenous predictability, we show how the investor makes dynamic portfolio choices, taking into account that she will learn from future data. We find that, in general, learning introduces negative horizon effects and that ignoring parameter uncertainty may lead to significant losses in certainty equivalent return on wealth. However, the significance of learning is reduced when the investor uses more past data in her estimation and/or when her risk aversion increases. Learning about unconditional expected returns appears to be the most important aspect of the learning process. Using the earnings-to-price ratio as a predictor and an empirical Bayes prior, we find that learning reduces, but does not necessarily eliminate, the positive hedging demands induced by predictability and correlation between the return and predictor innovations.