Bayesian portfolio optimization with time-varying factor models

We develop a modeling framework to simultaneously evaluate various types of predictability in stock returns, including stocks' sensitivity ("betas") to systematic risk factors, stocks' abnormal returns unexplained by risk factors ("alphas"), and returns of risk factors in excess of the risk-free rate ("risk premia"). Both firm-level characteristics and macroeconomic variables are used to predict stocks' time-varying alphas and betas, and macroeconomic variables are used to predict the risk premia. All of the models are specified in a Bayesian framework to account for estimation risk, and informative prior distributions on both stock returns and model parameters are adopted to reduce estimation error. To gauge the economic significance of the predictability, we apply the models to the U.S. stock market and construct optimal portfolios based on model predictions. Out-of-sample performance of the portfolios is evaluated to compare the models. The empirical results confirm predictabiltiy from all of the sources considered in our model: (1) The equity risk premium is time-varying and predictable using macroeconomic variables; (2) Stocks' alphas and betas differ cross-sectionally and are predictable using firm-level characteristics; and (3) Stocks' alphas and betas are also time-varying and predictable using macroeconomic variables. Comparison of different sub-periods shows that the predictability of stocks' betas is persistent over time, but the predictability of stocks' alphas and the risk premium has diminished to some extent. The empirical results also suggest that Bayesian statistical techinques, especially the use of informative prior distributions, help reduce model estimation error and result in portfolios that out-perform the passive indexing strategy. The findings are robust in the presence of transaction costs.