We present a Bayesian portfolio selection strategy, which uses the Capital Asset Pricing Model (CAPM). We propose a strategy which will mimic the market if the market is information efficient. However, the strategy will outperform the market if the market is not efficient. The strategy depends on the selection of a portfolio via Bayesian methodology for the parameters of the CAPM, which turns out to be multiple testing problems. We present the "discrete-mixture prior" model and "hierarchical Bayes model" for the intercept and slope parameters of CAPM. In hierarchical Bayes model, we use the half-Cauchy prior on the global shrinkage parameter of the model. We establish the Bayesian optimality properties of multiple testing rules from the Bayesian decision-theoretic point of view. The risk for the Bayesian decision rule up to $O(1)$ attains the risk of Bayes oracle. We present detailed empirical study, where 500 stocks from the New York Stock Exchange (NYSE) are considered, and S\&P 500 index is taken as the proxy for the market. The study of portfolio selection via four different strategies are examined over the period from the year 2006 to 2014. The out of the sample performance of the portfolio selected by the various methods is presented. Empirical results indicate that market is not efficient and it is possible to propose a strategy which can outperform the market.
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