  This paper investigates asset allocation problems 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 includes a joint estimation of
conditional expected returns and covariance matrix and considers estimation
risk for portfolio analysis. The hierarchical prior allows modeling different
assets separately while sharing information across assets. We demonstrate the
performance of the U.S. equity market. Though the Bayesian forecast is slightly
biased, our BH approach outperforms most alternative methods in point and
interval prediction. Our BH approach in sector investment for the recent twenty
years delivers a 0.92\% average monthly returns and a 0.32\% significant
Jensen`s alpha. We also find technology, energy, and manufacturing are
important sectors in the past decade, and size, investment, and short-term
reversal factors are heavily weighted. Finally, the stochastic discount factor
constructed by our BH approach explains most anomalies.
