A Bayesian Methodology For Portfolio Optimization

Abstract

We developed a Bayesian method to optimize the portfolio in the stock market. We use the enhanced data set of stock historical return and Markov chain Monte Carlo method to obtain the posterior distribution of the stock average return. We show that if the extended data set size is infinite, the posterior distribution is consistent. We provide the credible interval for the out-of-sample return realized by the portfolio constructed from the posterior average return. In addition, we compared it with the out-of-sample return realized by the portfolio based on the maximum likelihood average return. In most cases, the Bayesian posterior average return outperforms the maximum likelihood average return.