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Sparse Portfolio Selection via Bayesian Multiple Testing

Sourish Das and Rituparna Sen ()
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Sourish Das: Chennai Mathematical Institute
Rituparna Sen: Indian Statistical Institute

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 15, 585-617

Abstract: Abstract We present Bayesian portfolio selection strategy, via the k factor asset pricing model. If the market is information efficient, the proposed strategy will mimic the market; otherwise, the strategy will outperform the market. The strategy depends on the selection of a portfolio via Bayesian multiple testing methodologies. We present the “discrete-mixture prior” model and the “hierarchical Bayes model with horseshoe prior.” We define the oracle set and prove that asymptotically the Bayes rule attains the risk of Bayes oracle up to O(1). Our proposed Bayes oracle test guarantees statistical power by providing the upper bound of the type-II error. Simulation study indicates that the proposed Bayes oracle test is suitable for the efficient market with few stocks inefficiently priced. The statistical power of the Bayes oracle portfolio is uniformly better for the k-factor model (k > 1) than the one factor CAPM. We present an empirical study, where we consider the 500 constituent stocks of S&P 500 from the New York Stock Exchange (NYSE), and S&P 500 index as the benchmark for thirteen years from the year 2006 to 2018. We show the out-sample risk and return performance of the four different portfolio selection strategies and compare with the S&P 500 index as the benchmark market index. Empirical results indicate that it is possible to propose a strategy which can outperform the market. All the R code and data are available in the following GitHub repository https://github.com/sourish-cmi/sparse_portfolio_Bayes_multiple_test .

Keywords: CAPM; Discrete mixture prior; Hierarchical Bayes; Oracle; Factor model; Primary 62F15; 62P05; Secondary 91G10; 62J15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00240-z

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