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Sparse Portfolio Selection via Bayesian Multiple Testing

Author

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  • Sourish Das

    (Chennai Mathematical Institute)

  • Rituparna Sen

    (Indian Statistical Institute)

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 .

Suggested Citation

  • Sourish Das & Rituparna Sen, 2021. "Sparse Portfolio Selection via Bayesian Multiple Testing," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 585-617, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00240-z
    DOI: 10.1007/s13571-020-00240-z
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    References listed on IDEAS

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    1. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    2. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
    3. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
    4. Sourish Das & Aritra Halder & Dipak K. Dey, 2017. "Regularizing Portfolio Risk Analysis: A Bayesian Approach," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 865-889, September.
    5. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    6. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    7. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    8. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    9. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    10. Harvey, Campbell R. & Zhou, Guofu, 1990. "Bayesian inference in asset pricing tests," Journal of Financial Economics, Elsevier, vol. 26(2), pages 221-254, August.
    11. Jianqing Fan & Jingjin Zhang & Ke Yu, 2012. "Vast Portfolio Selection With Gross-Exposure Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 592-606, June.
    12. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    13. Kaushik Ghosh & Ram Tiwari, 2007. "Empirical process approach to some two-sample problems based on ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 757-787, December.
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