Factor Investing: A Bayesian Hierarchical Approach

Abstract

This paper investigates the asset allocation problem when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental characteristics. Our approach estimates the conditional expected returns and residual covariance matrix jointly, thus enabling us to consider the estimation risk in the portfolio analysis. The hierarchical prior allows the modeling of different assets separately while sharing information across assets. We demonstrate the performance of the U.S. equity market, our BH approach outperforms most alternative methods in terms of point prediction and interval coverage. In addition, the BH efficient portfolio achieves monthly returns of 0.92% and a significant Jensen's alpha of 0.32% in sector investment over the past 20 years. We also find technology, energy, and manufacturing are the most important sectors in the past decade, and size, investment, and short-term reversal factors are heavily weighted in our portfolio. Furthermore, the stochastic discount factor constructed by our BH approach can explain many risk anomalies.