Shrinkage Bayesian portfolio incorporating factor model in optimal portfolio selection: an empirical study.

Abstract

Parameter estimation based on shrinkage estimation under empirical Bayesian analysis has been proven by previous studies to outperform the maximum likelihood estimator (MLE). This study extends previous works by incorporating both the single index and the three-factor models in an empirical Bayesian approach to estimate grand mean. Six alternative strategies are employed to explore ex post portfolio performance when estimation risk is incorporated. These strategies are: naïve (equal weighted), passive (value weighted), mean-variance, Bayes-Stein, Bayes-CAPM, and Bayes-3-Factors portfolios. Among the six alternative strategies, the traditional, naïve, and passive portfolio strategies are outperformed by the shrinkage estimators because sample or historical averages seem to contain little useful information in the context of portfolio selection. However, shrinkage estimators incorporating the single index model have shown a noticeable improvement over optimized portfolios based on historical estimates. The result suggests that it is not necessary to include more explanatory factors in a shrinkage Bayesian incorporating factor model. Therefore, the shrinkage Bayesian portfolio, incorporating single index model or Bayes-CAPM seems to be an appropriate portfolio selection strategy.